A computer program outputs the following Cayley tables for groups of order 4.
Wikipedia tells me that there are only two groups of order 4, the cylic group ($Z_4$) and the Klein four-group ($Dih_2 = Z_2 \times Z_2$), so some of these groups must be isomorphic.
* [e][a][b][c]
[e] e a b c
[a] a e c b
[b] b c e a
[c] c b a e
* [e][a][b][c]
[e] e a b c
[a] a e c b
[b] b c a e
[c] c b e a
* [e][a][b][c]
[e] e a b c
[a] a c e b
[b] b e c a
[c] c b a e
* [e][a][b][c]
[e] e a b c
[a] a b c e
[b] b c e a
[c] c e a b
Which of these groups are isomorphic and why?