This question is bit long but please help me:

1.Let , where is finite group and be Sylow subgroup of . Show is Sylow p-subgroup of .

Let , , . And I think have something to do with this question, but I have no idea.

2.Consider Sylow 2-subgroups . Show if is Sylow p-subgroup of then is not Sylow p-subgroup of if .

Don't know how to do it at all, please help

Thank you.