Possible candidates for a supersymmetric SO(10) model with an intermediate scale

We study the possibility of an intermediate scale existing in supersymmetric SO(10) grand unified theories. The intermediate scale is required to be around ${10}^{12}$ GeV so that neutrinos can obtain masses suitable for explaining the experimental data on the deficit of solar neutrinos with the Mikheyev-Smirnov-Wolfenstein solution and the existence of hot dark matter. We show that any Pati-Salam-type intermediate symmetries are excluded by requiring reasonable conditions and only SU(2${)}_{\mathit{L}}$×SU(2${)}_{\mathit{R}}$×SU(3${)}_{\mathit{C}}$×U(1${)}_{\mathit{B}\mathrm{-}\mathit{L}}$ is likely to be realized as an intermediate symmetry.