Recent stringent experiment data of neutrino oscillations induces partial symmetries such as Z 2 and Z 2 × CP to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could express a residual CP symmetry. Lepton mixing matrices from S 3 group algebras are of the trimaximal form with the μ − τ reflection symmetry. Accordingly, elements of S 3 group algebras are equivalent to Z 2 × CP . Comments on S 4 group algebras are given. The predictions of Z 2 × CP broken from the group S 4 with the generalized CP symmetry are also obtained from elements of S 4 group algebras.