Does it make sense to say that "there are more non-Abelian groups than Abelian groups"? Firstly, does the family of all non-isomorphic non-Abelian groups have a well defined cardinality? How about the family of all non-isomorphic Abelian groups? If they are both defined, how do they compare?
Does the statement "there are more non-Abelian groups than Abelian groups" make any mathematical sense at all?
I am aware of a related question but my question should be different.


Firstly, does the family of all non-isomorphic non-Abelian groups has a well defined cardinality? 

No, being a proper class, it does not have a cardinality.

How about the family of all non-isomorphic Abelian groups? 

No: same reason.

If they are both defined, how do they compare?

N/A

Does the statement "there are more non-Abelian groups than Abelian groups" make any mathematical sense at all?

Maybe, but not in the sense of cardinality. You would have to be more specific about the context you are working in.
