In mathematics, in the field of group theory, a subgroup of a group is said to have the Congruence Extension Property or to be a CEP subgroup if every congruence on the subgroup lifts to a congruence of the whole group. Equivalently, every normal subgroup of the subgroup arises as the intersection with the subgroup of a normal subgroup of the whole group. In symbols, a subgroup is a CEP subgroup in a group if every normal subgroup of can be realized as where is normal in . The following facts are known about CEP subgroups: Every retract has the CEP. Every transitively normal subgroup has the CEP. References . . Subgroup properties