The URL ought to designate the resource, and the parameters ought to modify to the representation.

/groups/list?sort=field&order=desc&number=10
/groups/list?sort=field&order=desc&number=20

In each case you are asking for the same resource (a list of groups), but you are asking for a different representation of that resource (10 at a time or 20 at a time).

To me, this is the split between what belongs in the URL and what belongs in the parameters.