---
tag: 0053CQE9Y2
kind: concept
name: Sylow p-subgroup
msc: [20D20]
sources:
  - url: https://en.wikipedia.org/wiki/Sylow_theorems
    locator: lead section
---

## Summary

Let $G$ be a finite group, let $p$ be a prime number, and let $p^n$ be the largest power of $p$ that divides $|G|$.
A Sylow $p$-subgroup of $G$ is a subgroup of order $p^n$.