# Group of prime power order in which all maximal subgroups are automorphic

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

A **group of prime power order in which all maximal subgroups are automorphic** is a group of prime power order in which all maximal subgroups are automorphic subgroups. In other words, given any two maximal subgroups, there is an automorphism of the whole group sending one to the other.

## Relation with other properties

### Stronger properties

- Cyclic group of prime power order
- Finite elementary abelian group
- Homocyclic group of prime power order