They are sets not necessarily groups. A set is just a collection of elements a group is a set which has to strike some criteria which I can't fully remember but as you said identity, inverse and things of that nature. One of the things it requires is an operation though which none of the sets we are talking about have unless you are being specific i.e. r,+ (reals and addition).
N/Q isn't a thing I don't think as that would be the naturals without the rationals which rather than being empty I think just doesn't make sense.
It's been 5 years since I've done anything involving groups though so it's all a bit patchy.
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