# Normal subgroup of complemented normal subgroup

From Groupprops

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: normal subgroup and complemented normal subgroup

View other such compositions|View all subgroup properties

## Contents

## Definition

### Definition with symbols

A subgroup of a group is termed a **normal subgroup of complemented normal subgroup** if there exists a subgroup of containing such that is a normal subgroup of and is a complemented normal subgroup of .

## Relation with other properties

### Stronger properties

- Base of a wreath product
- Base of a wreath product with diagonal action
- Direct factor of complemented normal subgroup
- Complemented normal subgroup of complemented normal subgroup