# Normal subgroup having no common composition factor with its quotient group

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Contents

## Definition

A subgroup of a group of finite composition length is termed a **normal subgroup having no common composition factor with its quotient group** if is a normal subgroup of and no composition factor of is isomorphic to any composition factor of the quotient group .

## Relation with other properties

### Stronger properties

### Weaker properties

### Incomparable properties

- Complemented normal subgroup:
`For full proof, refer: No common composition factor with quotient group not implies complemented` - Normal subgroup having no nontrivial homomorphism to its quotient group:
`For full proof, refer: No common composition factor with quotient group not implies no proper nontrivial homomorphism to quotient group, No proper nontrivial homomorphism to quotient group not implies no common composition factor with quotient group` - Fully invariant subgroup