# Lagrange theorem for finite groups

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Lagrange theorem for finite groups](https://ocme.evemisslab.com/en/atlas/atlas-lagrange-theorem-finite-groups/)

Equal-size left cosets of a subgroup H partition the finite group G, so |G|=[G:H]*|H| and |H| divides |G|.

atlas-lagrange-theorem-finite-groups · canonical_mko

[Lagrange theorem for finite groups](https://ocme.evemisslab.com/en/mko/mko-lagrange-theorem-finite-groups/)

## Prerequisite nodes


- [Finite group](https://ocme.evemisslab.com/en/atlas/atlas-finite-group/)
- [Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/atlas/atlas-subgroup-homomorphism/)
- [Natural-number divisibility](https://ocme.evemisslab.com/en/atlas/atlas-natural-divisibility/)
- [Cardinality comparison of sets](https://ocme.evemisslab.com/en/atlas/atlas-cardinality-comparison/)
- [Quotient set](https://ocme.evemisslab.com/en/atlas/atlas-quotient-set/)