I have a huge test tommorow on this subject, and I'm pretty bad at it...Hope you'll be able to help me...

1. Prove that $\displaystyle [S_{n}$ doesn't have any subgroup of index t where 2<t<n and n>=5.

2. Let G be an abelian finite group which isn't cyclic. Prove that there is a prime number p such as G contains a subgroup that is isomorphic to CpxCp.

3. Prove that every group G of order 30 contains a subgroup of order 15.

Thanks a lot!