Gauge symmetry breaking from extra space $S^1/Z_2$

We study a mechanism of symmetry transition upon compactification of 5-dimensional field theory on $S^1/Z_2$. The transition happens unless all components in a multiplet of a symmetry group have a common $Z_2$ parity on $S^1/Z_2$. This mechanism is applied to a breakdown of SU(5) gauge symmetry in grand unified theory and phenomenological implications are discussed.