Is there a word for 'groups' that implies mutual exclusivity?
If the main feature of the 'groups' that you want to highlight is that each is a disjoint set (an item can't be in more than one group at a time), then I'd consider using an analogous real world object's name. At the most generic level, your group is a container, but you might also consider, box, bin or bucket.
Bucket is a good choice, because nobody imagines an object being inside more than one bucket at a time, or (full) buckets within buckets, whereas containers in general can be nested. The word in already used in software design patterns like the leaky bucket precisely because of those connotations.
You could highlight that each 'group' is a particular category of thing by calling them named buckets.