---
tag: VAF6B01Q8W
kind: statement
role: theorem
name: Extension of Lagrange's theorem
msc: [20D60]
sources:
  - wikipedia: en:31150@r1321322691
    locator: Lagrange's theorem (group theory), section Extension
    note: adopted
    mention: wikipedia://en/31150#DCKK
    sections: [Statement]
inventory: [ZEB8CBSA85]
---

## Statement

If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then

$$[G:K] = [G:H]\,[H:K].$$