# Category:Subgroup property conjunctions

From Groupprops

This category lists subgroup properties obtaind as the conjunction (AND) of two or more subgroup properties, that are considered more fundamental or important

## Pages in category "Subgroup property conjunctions"

The following 200 pages are in this category, out of 210 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### A

- Abelian characteristic subgroup
- Abelian conjugacy-closed subgroup
- Abelian critical subgroup
- Abelian direct factor
- Abelian fully invariant subgroup
- Abelian hereditarily normal subgroup
- Abelian marginal subgroup
- Abelian normal subgroup
- Abelian normal subgroup of group of prime power order
- Abelian pronormal subgroup
- Abelian subgroup of maximum order which is normal
- Abelian subnormal subgroup
- Abelian Sylow subgroup
- Abelian verbal subgroup
- Automorphism-faithful AEP-subgroup
- Automorphism-faithful normal subgroup

### C

- C-closed normal subgroup
- C-closed self-centralizing subgroup
- Center-fixing automorphism-balanced subgroup
- Central subgroup
- Central subgroup of finite group
- Central subgroup of normalizer
- Centralizer-free normal subgroup
- Centralizer-free subgroup
- Characteristic AEP-subgroup
- Characteristic central factor
- Characteristic central subgroup
- Characteristic direct factor
- Characteristic direct factor of abelian group
- Characteristic direct factor of nilpotent group
- Characteristic maximal subgroup of group of prime power order
- Characteristic subgroup of abelian group
- Characteristic subgroup of finite group
- Characteristic subgroup of finite index
- Characteristic subgroup of group of prime power order
- Characteristic subgroup of nilpotent group
- Characteristic subgroup of solvable group
- Characteristic transitively normal subgroup
- Characteristically complemented characteristic subgroup
- Class two characteristic subgroup
- Class two normal subgroup
- Commutator-in-center subgroup
- Complemented central factor
- Complemented characteristic subgroup
- Complemented fully invariant subgroup
- Complemented homomorph-containing subgroup
- Complemented isomorph-containing subgroup
- Complemented transitively normal subgroup
- Complete characteristic subgroup
- Complete direct factor
- Completely divisibility-closed normal subgroup
- Component
- Conjugacy-closed characteristic subgroup
- Conjugacy-closed Hall subgroup
- Conjugacy-closed normal subgroup
- Coprime automorphism-faithful characteristic subgroup
- Coprime automorphism-faithful normal subgroup
- Coprime automorphism-invariant normal subgroup
- Coprime automorphism-invariant normal subgroup of group of prime power order
- Coprime automorphism-invariant subgroup of group of prime power order
- Core-free 2-subnormal subgroup
- Core-free permutable subgroup
- Core-free subnormal subgroup
- Cyclic characteristic subgroup
- Cyclic isomorph-containing subgroup
- Cyclic normal subgroup

### D

### F

- Finite characteristic subgroup
- Finite elliptic subgroup
- Finite fully invariant subgroup
- Finite injective endomorphism-invariant subgroup
- Finite isomorph-free subgroup
- Finite normal subgroup
- Finite subgroup
- Finite subnormal subgroup
- Finite verbal subgroup
- Finitely generated normal subgroup
- Free factor of free group
- Fully invariant direct factor
- Fully invariant subgroup of abelian group
- Fully invariant subgroup of finite group
- Fully invariant subgroup of nilpotent group
- Fully normalized potentially fully invariant subgroup

### H

### I

- Isomorph-automorphic normal subgroup
- Isomorph-free maximal subgroup of finite group
- Isomorph-free maximal subgroup of group of prime power order
- Isomorph-free subgroup
- Isomorph-free subgroup of finite group
- Isomorph-free subgroup of group of prime power order
- Isomorph-normal characteristic subgroup
- Isomorph-normal characteristic subgroup of group of prime power order
- Isomorph-normal coprime automorphism-invariant subgroup
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order
- Isomorph-normal subgroup of group of prime power order

### L

### M

### N

- Nilpotent characteristic subgroup
- Nilpotent Hall subgroup
- Nilpotent normal subgroup
- Nilpotent pronormal subgroup
- Nilpotent subnormal subgroup
- Normal AEP-subgroup
- Normal fully normalized subgroup
- Normal Hall subgroup
- Normal intermediately AEP-subgroup
- Normal subgroup contained in centralizer of derived subgroup
- Normal subgroup having a 1-closed transversal
- Normal subgroup in which every subgroup characteristic in the whole group is characteristic
- Normal subgroup of finite group
- Normal subgroup of finite index
- Normal subgroup of finitely generated group
- Normal subgroup of group of prime power order
- Normal subgroup of nilpotent group
- Normal subgroup of periodic group
- Normal subgroup of prime index
- Normal subgroup of prime order
- Normal subgroup whose automorphism group is abelian
- Normal subgroup whose center is contained in the center of the whole group
- Normal subgroup whose derived subgroup equals its intersection with whole derived subgroup
- Normal subgroup whose focal subgroup equals its derived subgroup
- Normal subgroup whose inner automorphism group is central in automorphism group
- Normal Sylow subgroup
- Normality-large normal subgroup

### O

### P

- P-automorphism-invariant subgroup of finite p-group
- P-core-automorphism-invariant subgroup of finite p-group
- Perfect 2-subnormal subgroup
- Perfect characteristic subgroup
- Perfect direct factor
- Perfect normal subgroup
- Perfect subnormal subgroup
- Periodic normal subgroup
- Periodic subgroup
- Permutable 2-subnormal subgroup
- Permutable subnormal subgroup
- Permutably complemented Hall subgroup
- Powering-invariant central subgroup
- Powering-invariant characteristic subgroup
- Powering-invariant characteristic subgroup of nilpotent group
- Powering-invariant normal subgroup
- Powering-invariant normal subgroup of nilpotent group
- Powering-invariant subgroup of abelian group
- Powering-invariant subgroup of nilpotent group
- Prehomomorph-contained subgroup of finite group
- Pronormal Hall subgroup
- Proper characteristic subgroup
- Proper normal subgroup
- Pure subgroup of torsion-free abelian group

### R

### S

- Self-centralizing direct factor
- Self-centralizing normal subgroup
- Self-normalizing Sylow subgroup
- Simple normal subgroup
- Simple subnormal subgroup
- Solvable characteristic subgroup
- Solvable normal subgroup
- Subgroup of abelian group
- Subgroup of finite abelian group
- Subgroup of finite cyclic group
- Subgroup of finite group
- Subgroup of finite index in finitely generated group
- Subgroup of finite nilpotent group
- Subgroup of finite solvable group
- Subgroup of free group
- Subgroup of nilpotent group
- Subgroup of solvable group
- Subgroup whose normalizer equals its normal closure
- Subnormal subgroup of finite group
- Subnormal subgroup of finite index
- Subnormal-permutable subnormal subgroup
- Sylow direct factor
- Sylow retract