Let $H$ ={$e, (1, 2) (3, 4)$} and $K$ ={$e, (1, 2) (3, 4), (1, 3) (2, 4), (1, 4) (2, 3)$} be subgroups of $S_4$, where $e$ denotes the identity element of $S_4$. Then
- $H$ and $K$ are normal subgroups of $S_4 $.
- $H$ is normal in $K$ and $K$ is normal in $A_4$.
- $H$ is normal in $A_4$ but not normal in $S_4$.
- $K$ is normal in $S_4$, but $H$ is not.
How should I able to solve this problem. Can anyone help me please.