# Category:Conjunctions of group property with subgroup property

From Groupprops

This category lists subgroup properties expressed as a conjunction of a group property (that the subgroup must satisfy as an abstract group) and a subgroup property (that depends on its embedding in the whole group).

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

The following 63 pages are in this category, out of 63 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 pronormal subgroup
- Abelian subnormal subgroup
- Abelian Sylow subgroup
- Abelian verbal subgroup

### C

### F

### H

### N

- Nilpotent characteristic subgroup
- Nilpotent Hall subgroup
- Nilpotent normal subgroup
- Nilpotent pronormal subgroup
- Nilpotent subnormal subgroup
- Normal subgroup of prime order
- Normal subgroup whose automorphism group is abelian
- Normal subgroup whose inner automorphism group is central in automorphism group