Is there any simple way of telling if two groups are isomorphic? For example, given a list like this and asked to partition into isomorphism classes

1.

2.

3.

4.

5.

6. under symmetric set difference

7. Solutions of in

8.

9.

10.

Can I work out if they are isomorphic without listing out the elements of each, trying to find a map to from each one to another etc?