---
tag: 0KABPMRHM2
kind: concept
name: Characteristic subgroup
msc: [20F28]
sources:
  - url: https://en.wikipedia.org/wiki/Characteristic_subgroup
    locator: Definition
same_as:
  wikidata: Q747027
  wikipedia: Characteristic subgroup
---

## Summary

A characteristic subgroup of a group is a subgroup that each automorphism of the group maps onto itself.
Each characteristic subgroup is normal.