# Isomorph-free maximal subgroup of group of prime power order

From Groupprops

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: isomorph-free subgroup and maximal subgroup of group of prime power order

View other subgroup property conjunctions | view all subgroup properties

This article describes a property that arises as the conjunction of a subgroup property: isomorph-free maximal subgroup with a group property imposed on theambient group: group of prime power order

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Definition

A subgroup of a group of prime power order is termed an **isomorph-free maximal subgroup** if it is both an isomorph-free subgroup and a maximal subgroup (in particular, a maximal subgroup of group of prime power order).

## Relation with other properties

### Weaker properties

- Prehomomorph-contained subgroup of group of prime power order
- Isomorph-free subgroup of group of prime power order
- Characteristic subgroup of group of prime power order
- Characteristic maximal subgroup of group of prime power order
- Coprime automorphism-invariant maximal subgroup of group of prime power order
- Isomorph-normal characteristic subgroup