The ground-state behavior of two-dimensional symmetrical mixtures subjected to the external potential of square symmetry is discusses. It is demonstrated that different commensurate, high order commensurate as well as incommensurate phases may appear depending on the properties of the mixture as well as on the corrugation of external potential. In particular, it is shown that a finite corrugation of external potential considerably influences the stability of-different ordered states. The ground-state calculations are confirmed by finite temperature grand canonical Monte Carlo simulations.