# Isomorph-free maximal subgroup of finite group

From Groupprops

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: finite group

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

## Contents

## Definition

An **isomorph-free maximal subgroup of finite group** is a subgroup of a finite group satisfying the following equivalent conditions:

- It is both an isomorph-free subgroup (in particular, isomorph-free subgroup of finite group)and a maximal subgroup (in particular, a maximal subgroup of finite group) of the whole group.
- It is both an isomorph-containing subgroup and a maximal subgroup of the whole group.
- It is both a prehomomorph-contained subgroup and a maximal subgroup of the whole group.