# Why is every subgroup of order $p^{n-1}$ normal? [duplicate]

If $|G|=p^{n}$

Then

Why is it that every subgroup of order $p^{n-1}$ is normal?

## marked as duplicate by Ben West, Alex M., Vlad, Shailesh, choco_addictedApr 18 '16 at 8:12

A subgroup of index $p$ where $p$ is the smallest prime dividing the order of the group is a normal subgroup.