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 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!