---
tag: 0CB0DX5BVV
kind: concept
name: Normal subgroup
aliases: [invariant-subgroup]
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Normal_subgroup
    locator: Definitions
same_as:
  wikidata: Q743179
  wikipedia: Normal subgroup
---

## Summary

A normal subgroup of a group is a subgroup that is equal to each of its conjugates.
The normal subgroups are exactly the subgroups that give quotient groups, and exactly the kernels of homomorphisms.