Abelian Non-isomorphic Classes Lister

Please enter a number between 2 and 239 [inclusive].
The isomorphism classes of your number will then be listed.
(You can also simply hit "Find Groups" to have a number chosen at random.)

80 = 2⁴ * 5
Thus there are five nonisomorphic abelian groups of order 80,
(1) Z₂ ⊕ Z₂ ⊕ Z₂ ⊕ Z₁₀
(2) Z₂ ⊕ Z₂ ⊕ Z₂₀
(3) Z₄ ⊕ Z₂₀
(4) Z₂ ⊕ Z₄₀
(5) Z₈₀

1. Determines factorization of number
2. Determines type of options to arrange factors
3. Determine all combinations
4. Check against numerical prediction of types for groups