It = empty subject
will be = CopV
great to live here = AP (form) ('great' is the head); C (function), predicate adjective
[Pro] to live here = infinitive adverb clause modifying the predicate adjective 'great'. This is the extraposed subject with which an attribute named by the word 'great' is associated. Syntactically, the association is realized by postmodification.
Pro = null subject (you can't see it but it is there)
to live = V
here = optional predicate adjunct of location (pro-adverb)
To recap, 'to live here' is a modifier (modifying 'great') and is part of the complement.
thing belonging to this group = C (function); NP (form) ('thing' is the head)
belonging to this group = describes 'thing' (adjective)