Profile sets without any profiles or target groups allocated to them are possible, but they are meaningful only as "markers" in the allocation to a campaign.
Subsets as an additional grouping of profiles/target groups within a set or alone are possible; a special target group can be generated from a subset, which will represent the duplicate-free "OR" association of the business partners of all the assigned profiles / target groups.
A target group can exist without reference to a profile. If so, it must however reference a profile set ("lies in profile set..") or as a subset, if present ("is attached to profile set ...").
If a target group is created with the profile set reference "is attached to" (that is, to a subset), it will have the status "active"; and any available target groups of the profile of the subset will be set to "inactive".
A target group with profile reference always has a set reference ("lies in profile set ..").
A target group with profile reference cannot be attached directly to a profile set.
Within a profile set, a target group without profile reference is represented by an icon indicating a single target group.
You cannot move target groups from one profile set to another, however you can copy existing target groups.