# normal subgroup

> English word · Noun

## Definitions
1. A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg⁻¹ is in H.

## Etymology
The term was coined by Évariste Galois.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/normal-subgroup