For $n\le4$ is the alternating group $A_n$ simple?

Question

We know that $\forall n\geq 5,$ the alternating group $A_n$ is simple.

But for $n\leq 4$ is the alternating group $A_n$ simple? I can't find examples of them. Please help me! Thank you.

Answer 1

We have $A_1 \cong C_1$, $A_2 \cong C_1$, so they are not simple since definition of simple groups exclude trivial group. $A_3 \cong C_3$, which is a cyclic group of prime order, therefore simple. For $A_4$, since $V_4 \triangleleft A_4$, $A_4$ is not simple.