Symmetric group-3AS4
type: Ontology
creation date: 2026-06-07T03:19:44+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Symmetric group:S4
type: Subject
type: Category:Particular groups
type: Category:Symmetric groups
page: https://groupprops.subwiki.org/wiki/Symmetric_group-3AS4
wiki namespace: 0
wiki page content language: en
dissatisfies property: Abelian group
dissatisfies property: Metacyclic group
dissatisfies property: Nilpotent group
dissatisfies property: Supersolvable group
dissatisfies property: T-group
dissatisfies property: HN-group
importance rank: 2
member of family: Coxeter group
member of family: Symmetric group
member of family: Symmetric group on finite set
member of family: Symmetric group of prime power degree
member of family: Projective special linear group
member of family: Projective special linear group of degree two
member of family: Projective general linear group
member of family: Projective general linear group of degree two
member of family: General affine group
member of family: Von Dyck group
member of family: Triangle group
member of family: General affine group of degree two
member of family: General semiaffine group
member of family: General semiaffine group of degree one
order: 24
page class: Term
satisfies property: Solvable group
satisfies property: Rational-representation group
satisfies property: Rational group
satisfies property: Ambivalent group
satisfies property: Finite group
satisfies property: Monolithic group
satisfies property: One-headed group
satisfies property: Complete group
satisfies property: Group having subgroups of all orders dividing the group order
wiki page modification date: 2026-01-10T01:43:20Z
modification date#aux: 2461050.5717593
wiki page sort key: Symmetric group:S4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_81a9d4a46a209e0d0e37e7580eb8e4a6
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Order of a group;24
number: 24
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Order_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_bee3e09ed34e26351b5c52a1512d97a0
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Exponent of a group;12
number: 12
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Exponent_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_e2e30fd08e157af0b81c36e2bfd99520
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Derived length;3
number: 3
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Derived_length

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_39772cad9c2b5e494b34989a9ae06e3b
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Frattini length;1
number: 1
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Frattini_length

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_5e221dcc4544cb5197d6f466b985fadc
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Minimum size of generating set;2
number: 2
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Minimum_size_of_generating_set

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_c673d5b507e529840d1fbac07d4f28a2
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Subgroup rank of a group;2
number: 2
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Subgroup_rank_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_b80f3911c824347edc609042a873cac0
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Max-length of a group;4
number: 4
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Max-2Dlength_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_cdb6306290fb8572656d5fc428cdf7a4
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Composition length;4
number: 4
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Composition_length

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_090c866c8a25d10f57f85208f9b242f2
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Chief length;3
number: 3
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Chief_length

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_6df57152dfb297d0fccdd6df615a95bb
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Number of subgroups;30
number: 30
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_subgroups

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_301c5f4cb34dcd8806c60c06caeba69d
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Number of conjugacy classes;5
number: 5
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_conjugacy_classes

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_3f5c21eb9c0b738051bf9c55b660bcfb
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#Number of conjugacy classes of subgroups;11
number: 11
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_conjugacy_classes_of_subgroups

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_eb80cfa545496d2ce247227fac27e806
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
wiki page sort key: Symmetric group:S4#24;12
number: 24
text: 12

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY107e1afaf27abd2b54010adc00f1bdb1
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 2
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY107e1afaf27abd2b54010adc00f1bdb1

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYa354b8a4817e439b7316dbacfc4099c0
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: plainlist
query size: 3
query string: Fact about.Page::Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERYa354b8a4817e439b7316dbacfc4099c0

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY66ad828ae7d67d129c7dbb978a6eb752
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: plainlist
query size: 4
query string: Fact about.Page::Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY66ad828ae7d67d129c7dbb978a6eb752

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYd9b1e0821c9ef6263b49db942a32d3bd
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: plainlist
query size: 4
query string: Fact about.Page::Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERYd9b1e0821c9ef6263b49db942a32d3bd

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYfc608116e6b1ec5a9bce9dc9e8ae7e2e
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: plainlist
query size: 4
query string: Fact about.Page::Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERYfc608116e6b1ec5a9bce9dc9e8ae7e2e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY1657698b1760927187a08bb967ff8809
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 4
query string: Term Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY1657698b1760927187a08bb967ff8809

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYa9a75f5fa17ed845d420af1850d8954e
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERYa9a75f5fa17ed845d420af1850d8954e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY38dac736c00235f85ee98b46761fdbc4
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY38dac736c00235f85ee98b46761fdbc4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYf26ee598267970fbdff626070ceb47da
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 4
query string: Symmetric group:S4 Fact
wiki page sort key: Symmetric group:S4# QUERYf26ee598267970fbdff626070ceb47da

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYc6b7a9fe1add102116ea8dea77c21906
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERYc6b7a9fe1add102116ea8dea77c21906

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY99041a86afce8366df6833a01220baa6
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY99041a86afce8366df6833a01220baa6

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY4841116140193fcb9ae17b8ff4c11ca2
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY4841116140193fcb9ae17b8ff4c11ca2

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY3cf5f36108b7575753fa5dee54ce6b9a
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: Symmetric group:S4
wiki page sort key: Symmetric group:S4# QUERY3cf5f36108b7575753fa5dee54ce6b9a

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYd8a215079cc37ae0e8dc5b4dee03fcb5
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 2
query string: Symmetric group on finite set
wiki page sort key: Symmetric group:S4# QUERYd8a215079cc37ae0e8dc5b4dee03fcb5

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYe84534dc854595f3aa145417b6a3e6d1
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 2
query string: Coxeter group
wiki page sort key: Symmetric group:S4# QUERYe84534dc854595f3aa145417b6a3e6d1

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYe5d265551c981541962e6573e68ca290
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 2
query string: Von Dyck group
wiki page sort key: Symmetric group:S4# QUERYe5d265551c981541962e6573e68ca290

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY0f2fbde8a7d5ba3d57210e6273e166e2
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 2
query string: Triangle group
wiki page sort key: Symmetric group:S4# QUERY0f2fbde8a7d5ba3d57210e6273e166e2

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY2c46463cfb77735ea25aca71bff94574
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY2c46463cfb77735ea25aca71bff94574

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYacd6782405b5c4ed7822d117a82e59e4
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Exponent of a group 12 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERYacd6782405b5c4ed7822d117a82e59e4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY8af81a31ec7a65623ad7b2ed21f8eafb
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Exponent of a group 12
wiki page sort key: Symmetric group:S4# QUERY8af81a31ec7a65623ad7b2ed21f8eafb

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY75e177f93cdca86380c19c4851b29bac
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Derived length 3 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY75e177f93cdca86380c19c4851b29bac

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY86f0a963559c347bfb62bb5639b2c4bc
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Derived length 3
wiki page sort key: Symmetric group:S4# QUERY86f0a963559c347bfb62bb5639b2c4bc

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY719861a83d4e97bddaaddb3e7b76e3e5
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Frattini length 1 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY719861a83d4e97bddaaddb3e7b76e3e5

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY3c6b993c49d03cfb6e2d4956d672a7a4
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Frattini length 1
wiki page sort key: Symmetric group:S4# QUERY3c6b993c49d03cfb6e2d4956d672a7a4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYc2b6b71218cc42f91e99e0ff6c1db56b
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Minimum size of generating set 2 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERYc2b6b71218cc42f91e99e0ff6c1db56b

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYe750a6e6983602278a40c54230968a76
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Minimum size of generating set 2
wiki page sort key: Symmetric group:S4# QUERYe750a6e6983602278a40c54230968a76

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY54da2ed4bf95f60bb3294ddabd59fb43
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Subgroup rank of a group 2 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY54da2ed4bf95f60bb3294ddabd59fb43

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY2efb9d62dc2164771a85458ee7bafc0e
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Subgroup rank of a group 2
wiki page sort key: Symmetric group:S4# QUERY2efb9d62dc2164771a85458ee7bafc0e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY74c6e8d9c72e1a5942e96a45abb41c1d
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Max-length of a group 4 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY74c6e8d9c72e1a5942e96a45abb41c1d

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY5026c0f2f993b37cc26bc1289364b5c4
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Max-length of a group 4
wiki page sort key: Symmetric group:S4# QUERY5026c0f2f993b37cc26bc1289364b5c4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYc27fbb6ed25854c668fe0499b04aff49
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Composition length 4 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERYc27fbb6ed25854c668fe0499b04aff49

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY98e023fac27cc6e8077e60ab8e628369
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Composition length 4
wiki page sort key: Symmetric group:S4# QUERY98e023fac27cc6e8077e60ab8e628369

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY2136616b8ca5977c350203a2f7c6d2a5
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Chief length 3 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY2136616b8ca5977c350203a2f7c6d2a5

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYc50491b3f22ac65dd61e60c095661ec6
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Chief length 3
wiki page sort key: Symmetric group:S4# QUERYc50491b3f22ac65dd61e60c095661ec6

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY6054319080231f9350113634ee52237c
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of subgroups 30 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY6054319080231f9350113634ee52237c

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY8a239fa0592b9f9deb52905da4d31790
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of subgroups 30
wiki page sort key: Symmetric group:S4# QUERY8a239fa0592b9f9deb52905da4d31790

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYe71ed69a665f2a303364684726dad64e
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes 5 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERYe71ed69a665f2a303364684726dad64e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY73f27a0f765d5240815037f97dd48bde
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes 5
wiki page sort key: Symmetric group:S4# QUERY73f27a0f765d5240815037f97dd48bde

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERY2683b5391a92aada019db08987316c11
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes of subgroups 11 Order of a group 24
wiki page sort key: Symmetric group:S4# QUERY2683b5391a92aada019db08987316c11

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYc8cc0777a476d5dc0c766e76a693ac1f
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes of subgroups 11
wiki page sort key: Symmetric group:S4# QUERYc8cc0777a476d5dc0c766e76a693ac1f

http://groupprops.subwiki.org/wiki/Special:URIResolver/Symmetric_group-3AS4-23_QUERYaabc9b9e4c6f4aae05741ca3ac60abb2
type: Subject
master page: Symmetric group:S4
wiki namespace: 0
query depth: 0
query format: plainlist
query size: 1
query string: Groups of order 24
wiki page sort key: Symmetric group:S4# QUERYaabc9b9e4c6f4aae05741ca3ac60abb2

Pronormal not implies NE
type: Subject
page: https://groupprops.subwiki.org/wiki/Pronormal_not_implies_NE
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Pronormal not implies NE

2-subnormal not implies hypernormalized
type: Subject
page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_not_implies_hypernormalized
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: 2-subnormal not implies hypernormalized

Subgroups of all orders dividing the group order not implies supersolvable
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroups_of_all_orders_dividing_the_group_order_not_implies_supersolvable
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Subgroups of all orders dividing the group order not implies supersolvable

Finite solvable not implies p-normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_solvable_not_implies_p-2Dnormal
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Finite solvable not implies p-normal

Sylow not implies local divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Sylow_not_implies_local_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Sylow not implies local divisibility-closed

Sylow not implies CDIN
type: Subject
page: https://groupprops.subwiki.org/wiki/Sylow_not_implies_CDIN
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Sylow not implies CDIN

P-solvable not implies Glauberman type for p
type: Subject
page: https://groupprops.subwiki.org/wiki/P-2Dsolvable_not_implies_Glauberman_type_for_p
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: P-solvable not implies Glauberman type for p

Subgroups of all orders dividing the group order not implies Sylow tower
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroups_of_all_orders_dividing_the_group_order_not_implies_Sylow_tower
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Subgroups of all orders dividing the group order not implies Sylow tower

Pronormal not implies join with any distinct conjugate is the whole group
type: Subject
page: https://groupprops.subwiki.org/wiki/Pronormal_not_implies_join_with_any_distinct_conjugate_is_the_whole_group
wiki namespace: 0
wiki page content language: en
particular example: Symmetric group:S4
wiki page sort key: Pronormal not implies join with any distinct conjugate is the whole group

S4 in S5
type: Subject
page: https://groupprops.subwiki.org/wiki/S4_in_S5
wiki namespace: 0
wiki page content language: en
subgroup part: Symmetric group:S4
wiki page sort key: S4 in S5

Particular example
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AParticular_example
wiki namespace: 132
wiki page content language: en
wiki page sort key: Particular example

Subgroup part
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ASubgroup_part
wiki namespace: 132
wiki page content language: en
wiki page sort key: Subgroup part
type: wpg