For $n$ at least 5, the index of a subgroup of $Alt(n)$ is at least $n$.

For $n$ at least 5, the index of a subgroup of $Alt(n)$ is at least $n$.

Can someone can help me get started with this problems?
Prove that $A_n$ does not have a proper subgroup of index less than $n$
for all $n \geq 5$.