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We construct two flavor models based on $S_4$ family symmetry and generalisedCP symmetry. In both models, the $S_4$ family symmetry is broken down to the$Z^{SU}_2$ subgroup in the neutrino sector, as a consequence, the trimaximal$\text{TM}_1$ lepton mixing is produced. Depending on the free parameters inthe flavon potential, the Dirac CP is predicted to be either conserved ormaximally broken, and the Majorana CP phases are trivial. The two models differin the neutrino sector. The flavon fields are involved in the Dirac mass termsat leading order in the first model, and the neutrino mass matrix containsthree real parameters such that the absolute neutrino masses are fixed.Nevertheless, the flavon fields enter into the Majorana mass terms at leadingorder in the second model. The leading order lepton mixing is of thetri-bimaximal form which is broken down to $\text{TM}_1$ by the next to leadingorder contributions.

Generalised CP and Trimaximal TM$_1$ Lepton Mixing in $S_4$ Family Symmetry