1. The problem statement, all variables and given/known data Count and describe the different isomorphism classes of abelian groups of order 1800. I don't need to list the group individually, but I need to give some sort of justification. 2. Relevant equations 3. The attempt at a solution I'm using the theorem to classify finitely generated abelian groups, As always we will have Z_1800 to begin with. Also we know 1800=23(32)(52). But how do I count all of the possibilities?