The primary conflict in the novel Chrysalids is brought about by the government's choice to control and oppress people with genetic mutations, including telepathy. This central conflict manifests in all three categories of conflict: person versus society, person versus person, and person versus self.
The person versus society conflict exists by simple fact that the government policy requiring genetic purity even exists. This policy shapes the way the characters pass through the spaces they live in and means that institutional power has the power to end their lives.
The person versus person conflict emerges any time an individual—for instance Anne's husband, Alan—chooses to act to give more power to those social institutions, like Alan did by ratting them out. By choosing to participate in the social oppression, these individuals bring themselves directly into the conflict at hand.
The person versus self conflict is reflected in the struggles of the oppressed characters to figure out how to navigate their lives. For instance, Aunt Harriet's suicide can be interpreted as an expression of her turning the conflict her society had with her in on herself.