Proving H is Normal in Finite Group with One Subgroup

[joecoz88]

Homework Statement

If G is a finite group that has exactly one subgroup H of a given order, then H is normal.

Homework Equations

N/A

The Attempt at a Solution

I cannot figure out what makes a subgroup H special if it is the only one of a given order...

 

[e(ho0n3]

Pick a g in G. What is the order of g^-1Hg?