I proved the following statement:
The composition factors of every finite solvable group are isomorphic to cylic groups of prime order.
I want to use this result to prove that every two finite solvable groups of the same order have the same composition factors.
If I knew that for every prime number in the decomposition of the order of the groups there is a composition factor that is cyclic of that order I would obviously be finished. However, I'm not even sure if this statement is true and I don't have a good idea on how to proceed in case the statement isn't true.
Help will be appreciated! :)