---
tag: 0XV2A49X6Q
kind: concept
name: Composition series
msc: ["20E15", 20D30]
specializes: [0ZZR8D7Y1Z]
sources:
  - url: https://en.wikipedia.org/wiki/Composition_series
    locator: For groups
same_as:
  wikidata: Q2525646
  wikipedia: Composition series
inventory: [FDZAFM4G3W]
---

## Summary

A composition series of a group is a subnormal series in which each factor group is simple.
It cannot be refined further, and its factors are unique up to order by the Jordan–Hölder theorem.