What are the importance of the factionless and the Gd's in the novel

The group from Chicago struggles constantly with a crisis of identity outside the city. They have each come to identify with the faction from which they came. Cara and Caleb are Erudite, leaning on their intelligence and rationality more than anything, Christina and Peter are Dauntless, knowing that they are brave and can face their fears better than anyone, and Tobias and Tris have come to identify as Divergent, not quite fitting into one of the factions, but thriving still. The factions and their implications are all that mattered to these characters for the majority of their lives. When they get to the Bureau, they are told that the factions were meaningless, only part of an experiment.

Suddenly, their identities mean nothing. Then, making things only worse, many of the characters are told that their genes are damaged. They're told that they have limitations, making them less than people with pure genes. Tobias, no longer able to identify as Divergent, has no idea what to think of himself. Cara and Caleb are even more at a loss in this new world, as the revelations that the outside world brought are almost too much to think about rationally.

Learning that the world in which you live is a lie brings about an overwhelming shock to the characters. They have to cope with these facts, changing their worldviews and altering what they come to identify by in the process. Many of the characters have nothing to lean on but each other.