# Isomorph-normal characteristic subgroup of group of prime power order

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: isomorph-normal characteristic 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

## Contents

## Definition

A subgroup of a group is termed an **isomorph-normal characteristic subgroup of group of prime power order** if is a group of prime power order and is an isomorph-normal characteristic subgroup: is an isomorph-normal subgroup of (every subgroup isomorphic to it is normal) and is a characteristic subgroup of .

## Relation with other properties

### Stronger properties

- Isomorph-free subgroup of group of prime power order
- Subisomorph-containing subgroup of group of prime power order
- Characteristic maximal subgroup of group of prime power order

### Weaker properties

- Characteristic subgroup of group of prime power order, characteristic subgroup
- Isomorph-normal subgroup of group of prime power order, isomorph-normal subgroup
- Normal subgroup of group of prime power order, normal subgroup
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order, isomorph-normal coprime automorphism-invariant subgroup