Z(2) topology in two-dimensional group IVA materials has been explained by the band orders due to the crystal field splitting at the point in the Brillouin zone, while spin-orbit coupling (SOC) was considered just to open a band gap. By using a multi-orbital tight-binding model, we show that the SOC induces band inversion between the conduction and valence bands at the point in plumbene, which also is the case in stanene when the SOC strength increases. As a result of the band inversion, plumbene becomes a spin Chern insulator with a spin Chern number C-S = 2 and, as the SOC strength increases, stanene undergoes a topological phase transition from a Z(2) topological insulator to a spin Chern insulator with C-S = 2. Under a staggered AB-sublattice potential, plumbene undergoes a phase transition from the spin Chern insulator with C-S = 2 to a Z(2) topological insulator with C-S = 1.