Question

find sub groups of (A5 *Cp) with p=2,3.5.7,11 and p≠2,3,5,7,11 and find any sub group is solvable group

Answer 1

Answer:

It follows that quotient groups (which are the same as homomorphic images) of soluble groups are themselves soluble. There is a rather strong converse to the above lemma: Proposition 6.11 Let G be a group and N be a normal subgroup of G such that both G/N and N are soluble. Then G is soluble