G is a group, H is a subgroup of G, and N a normal group of G. Prove that N is a normal subgroup of NH. So I have already proved that NH is a subgroup of G. To prove that N is a normal subgroup of NH I said the we need to show $xNx^{-1}$ is a subgroup of NH for all $x\in NH$
Or am i defining it wrong? 

For any subgroup $K$ of $G$ with $N \subset K \subset G$, you can show that $N$ is a normal subgroup of $K$. Also, you can easily show $N \subset NH$.
