[SOLVED] group theory problem 1. The problem statement, all variables and given/known data Classify the factor group (Z_4 cross Z_4 cross Z_8)/<(1,2,4)> according to the fundamental theorem of finitely generated abelian groups. 2. Relevant equations 3. The attempt at a solution <(1,2,4)> has order 4 so the factor group has order 32, so there are seven possibilities: (Z_2)^5 Z_32 (Z_2)^3 cross Z_4 Z_16 cross Z_2 Z_8 cross Z_2 cross Z_2 Z_2 cross Z_4 cross Z_4 Z_8 cross Z_4 Anyone have any ideas about how to do this without doing a lot of tedious calculations?