In GAP 3 there was a strict distinction between parent groups and subgroups. The use of the name ``parent'' (instead of ``supergroup'') was chosen to indicate that the parent of an object was more than just useful information. In fact the main reason for the introduction of parents was to provide a common roof for example for all groups of polycyclic words that belonged to the same PC-presentation, or for all subgroups of a finitely presented group (see Elements of Finitely Presented Groups). A subgroup was never a parent group, and it was possible to create subgroups only of parent groups.
In GAP 4 this common roof is provided already by the concept of families, see Families in the Reference Manual. Thus it is no longer compulsory to use parent groups at all. On the other hand, parents may be used in GAP 4 to provide information about an object, for example the normalizer of a group in its parent group may be stored as an attribute value. Note that there is no restriction on the supergroup that is set to be the parent, it is possible to create a subgroup of any group, this group then being the parent of the new subgroup. This permits for example chains of subgroups with respective parents, of arbitrary length.
As a consequence, the Parent command cannot be used in GAP 4 to
test whether the two arguments of CommutatorSubgroup fit together,
this is now a question that concerns the relation between the families
of the groups. So the 2-argument version of Parent and the now
meaningless function IsParent have been abolished.
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GAP 4 manual