# Homomorph-containing subgroup

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Contents

## Definition

## Relation with other properties

### Weaker properties

- Intermediately fully characteristic subgroup
- Fully characteristic subgroup
- Strictly characteristic subgroup
- Intermediately characteristic subgroup
- Characteristic subgroup
- Isomorph-free subgroup in case the subgroup is co-Hopfian as a group: it is not isomorphic to any proper subgroup of itself.

## Facts

- The omega subgroups of a group of prime power order are homomorph-containing.
`Further information: Omega subgroups are homomorph-containing`