# Category:Conjunctions of group property on ambient group with subgroup property

From Groupprops

## Pages in category "Conjunctions of group property on ambient group with subgroup property"

The following 62 pages are in this category, out of 62 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### C

- Central subgroup of finite group
- Characteristic direct factor of abelian group
- Characteristic direct factor of nilpotent group
- Characteristic subgroup of abelian group
- Characteristic subgroup of finite group
- Characteristic subgroup of group of prime power order
- Characteristic subgroup of nilpotent group
- Characteristic subgroup of solvable group
- Coprime automorphism-invariant normal subgroup of group of prime power order
- Coprime automorphism-invariant subgroup of group of prime power order

### F

### I

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

### N

### P

- P-automorphism-invariant subgroup of finite p-group
- P-core-automorphism-invariant subgroup of finite p-group
- Powering-invariant characteristic subgroup of nilpotent group
- 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
- Pure subgroup of torsion-free abelian group

### S

- 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
- Subnormal subgroup of finite group