We study gauge symmetry breaking patterns of the five-dimensional SU(5) grand gauge-Higgs unification compactified on an orbifold S1/Z2 with the Hosotani mechanism in the framework of the diagonal embedding method. We find matter contents that lead to the SU(3)×SU(2)×U(1) gauge symmetry on the global minimum of the effective potential and also present examples of matter content for which each regular subgroup of SU(5) is realized as vacuum configuration. The finite-temperature phase transitions for the models with the gauge symmetry of the standard model at zero temperature and also for supersymmetric models are studied. We show in a certain model with supersymmetry that the vacuum of the standard model selected dynamically before the inflation continues to stay there up to the present.
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