## Showing Subgroups of a Permutation Group are Isomorphic

Define two subgroups of S6:
G=[e, (123), (123)(456)]
H=[e, (14), (123)(456)]

Determine whether G and H are isomorphic.

It seems as if they should be since they have the same cardinality and you can certainly map the elements to one another, but I don't know what other factors need to be considered when deciding whether they are isomorphic.
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 H is not a subgroup since (14)(123)(456) = (123456) which is not in H. Are you sure you've written down the correct group?
 Oops. I meant G=<(123), (123)(456)> and H=<(14), (123)(456)>.

 Tags group theory, isomorphic, isomorphism, permutations
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