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Abelian Non-isomorphic Classes Lister

List all non-isomorphic abelian classes for natural numbers from 2 to 239

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.)

64 = 2 * 2 * 2 * 2 * 2 * 2
Thus there are eleven nonisomorphic abelian groups of order 64,
(1) Z2 ⊕ Z2 ⊕ Z2 ⊕ Z2 ⊕ Z2 ⊕ Z2
(2) Z2 ⊕ Z2 ⊕ Z2 ⊕ Z2 ⊕ Z4
(3) Z2 ⊕ Z2 ⊕ Z4 ⊕ Z4
(4) Z4 ⊕ Z4 ⊕ Z4
(5) Z2 ⊕ Z2 ⊕ Z2 ⊕ Z8
(6) Z2 ⊕ Z4 ⊕ Z8
(7) Z8 ⊕ Z8
(8) Z2 ⊕ Z2 ⊕ Z16
(9) Z4 ⊕ Z16
(10) Z2 ⊕ Z32
(11) Z64


  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