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The query <q> <q>[[Satisfies property::Normal subgroup]]</q> OR [[Satisfies property.Stronger than::Normal subgroup]] [[Category:Particular subgroups]]</q> was answered by the SMWSQLStore3 in 0.0222 seconds.

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 Group partSubgroup part
A3 in S3Symmetric group:S3Cyclic group:Z3
A4 in S4Symmetric group:S4Alternating group:A4
Baer norm
Center
Center of M16M16Cyclic group:Z4
Center of central product of D8 and Z4Central product of D8 and Z4Cyclic group:Z4
Center of dihedral group:D16Dihedral group:D16Cyclic group:Z2
Center of dihedral group:D8Dihedral group:D8Cyclic group:Z2
Center of direct product of D8 and Z2Direct product of D8 and Z2Klein four-group
Center of nontrivial semidirect product of Z4 and Z4Nontrivial semidirect product of Z4 and Z4Klein four-group
Center of quaternion groupQuaternion groupCyclic group:Z2
Center of semidihedral group:SD16Semidihedral group:SD16Cyclic group:Z2
Center of special linear group:SL(2,3)Special linear group:SL(2,3)Cyclic group:Z2
Center of special linear group:SL(2,5)Special linear group:SL(2,5)Cyclic group:Z2
Center of unitriangular matrix group:UT(3,p)Unitriangular matrix group:UT(3,p)Group of prime order
Central subgroup generated by a non-square in nontrivial semidirect product of Z4 and Z4Nontrivial semidirect product of Z4 and Z4Cyclic group:Z2
Cyclic maximal subgroup of dihedral group:D16Dihedral group:D16Cyclic group:Z8
Cyclic maximal subgroup of dihedral group:D8Dihedral group:D8Cyclic group:Z4
Cyclic maximal subgroup of semidihedral group:SD16Semidihedral group:SD16Cyclic group:Z8
Cyclic maximal subgroups of quaternion groupQuaternion groupCyclic group:Z4
D8 in D16Dihedral group:D16Dihedral group:D8
D8 in SD16Semidihedral group:SD16Dihedral group:D8
Derived subgroup
Derived subgroup of M16M16Cyclic group:Z2
Derived subgroup of dihedral group:D16Dihedral group:D16Cyclic group:Z4
Derived subgroup of nontrivial semidirect product of Z4 and Z4Nontrivial semidirect product of Z4 and Z4Cyclic group:Z2
Diagonally embedded Z4 in direct product of Z8 and Z2Direct product of Z8 and Z2Cyclic group:Z4
Direct product of Z4 and Z2 in M16M16Direct product of Z4 and Z2
Epicenter
First agemo subgroup of direct product of Z4 and Z2Direct product of Z4 and Z2Cyclic group:Z2
First omega subgroup of direct product of Z4 and Z2Direct product of Z4 and Z2Klein four-group
Group of integers in group of rational numbersGroup of rational numbersGroup of integers
Klein four-subgroup of M16M16Klein four-group
Klein four-subgroup of alternating group:A4Alternating group:A4Klein four-group
Klein four-subgroups of dihedral group:D8Dihedral group:D8Klein four-group
Non-central Z4 in M16M16Cyclic group:Z4
Non-characteristic order two subgroups of direct product of Z4 and Z2Direct product of Z4 and Z2Cyclic group:Z2
Normal Klein four-subgroup of symmetric group:S4Symmetric group:S4Klein four-group
Q8 in SD16Semidihedral group:SD16Quaternion group
Q8 in central product of D8 and Z4Central product of D8 and Z4Quaternion group
SL(2,3) in GL(2,3)General linear group:GL(2,3)Special linear group:SL(2,3)
Socle
Subgroup generated by a non-commutator square in nontrivial semidirect product of Z4 and Z4Nontrivial semidirect product of Z4 and Z4Cyclic group:Z2
Z2 in V4Klein four-groupCyclic group:Z2
Z4 in direct product of Z4 and Z2Direct product of Z4 and Z2Cyclic group:Z4
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