Check the order of a subgroup of the alternating group $A_n$

Question

Question :

For a positive integer $n \geq 4$ and a prime $ p \leq n$. Let $U_{p,n}$ denote the union of all p- syllow subgroups of the alternating Group $A_n$ on n letters . Also let $K_{p,n}$ denote the subgroup of $A_n$ genrated by $U_{p,n}$ and let $|K_{p,n}|$ denote the order of $K_{p,n}$. Then Which of the following are true

1. $|K_{2,4}| = 12$

2. $|K_{2,4}| = 4$

3. $|K_{2,5}| = 60$

4. $|K_{3,5}| = 30$

I have tried

(1) If $|K_{2,4}| = 12$, then $K_{2,4} = A_4$, but order of every element of $K_{2,4}$ is power of 2, which is a contradiction. I think this is not true. Similarly (3) is not true.

(2) Let $H_1 = < (1 2 3 4) > = \{I , (1 2 3 4) , (1 3 ) (2 4) , (1 4 3 2) \}$ be a syllow 2-subgroup. Similarly $H_2 = < (1 3 2 4) > = \{ I , ( 1 3 2 4) , (1 2 ) (3 4) , ( 1 4 2 3) \}$ be another syllow subgroup. Thus (2) is not true.

(4) if $|K_{3,5}| = 30$, then $K_{3,5}$ is a normal subgroup of $A_5$, but $A_5$ is simple , which is a contradiction

Please check my solution and if you you want to any change please correct me.

Thank you.