# Direct factor of normal subgroup

From Groupprops

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

View other such compositions|View all subgroup properties

## Contents

## Definition

A subgroup of a group is termed a **direct factor of normal subgroup** if it satisfies the following equivalent conditions:

- It can be expressed as a direct factor of a normal subgroup of the whole group.
- It is a direct factor inside its normal closure.