Abelian groups of order $2^7 3^4 5^2$

Question

How many non-isomorphic Abelian groups of order $2^7 3^4 5^2$ are? How to find?

Answer 1

Total Partitions of $7, 4$ and $ 2$ are $14, 5$ and $2$ respectively - for example, partitions of $7$ are: $7$; $6,1$; $5,2$; $5,1,1$; $4,3$; $4,2,1$; $4,1,1,1$; $3,2,2$; $3,2,1,1$; $3,1,1,1,1$; $2,2,2,1$; $2,2,1,1,1$; $2,1,1,1,1,1$; $1,1,1,1,1,1,1$. So there are $14×5×2=140$ non isomorphic Abelian groups of the given order.