# Composition series

This article defines a property that can be evaluated for a subgroup seriesView a complete list of properties of subgroup series

## Contents

## Definition

A **composition series** for a group is a subnormal series where all the quotient groups (of successive terms) are simple groups.

## Relation with other properties

## Facts

- If a group has two composition series, then they both have the same length, and each simple group occurs with the same multiplicity as a quotient in both. This is the content of the Jordan-Holder theorem.