# Isomorph-normal coprime automorphism-invariant subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: isomorph-normal subgroup and coprime automorphism-invariant subgroup

View other subgroup property conjunctions | view all subgroup properties

## Contents

## Definition

A subgroup of a finite group is termed **isomorph-normal coprime automorphism-invariant** if it satisfies the following two conditions:

- is isomorph-normal in : Every subgroup of isomorphic to is a normal subgroup of .
- is a coprime automorphism-invariant subgroup of : Any automorphism of whose order is relatively prime to the order of satisfies .