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We present the complete scheme of the application of the one-and twodimensional subspace and subgroups method to five-dimensional gravity with a$G_{3}$ group of motion. We do so in the space time and in the potential spaceformalisms. From this method one obtains the Kramer, Belinsky-Ruffini,Dobiasch-Maison, Cl\'{e}ment, Gross-Perry-Sorkin solutions etc. as specialcases.Comment: 18 pages, 7 tables, to appear in J. Math. Phy

Five-dimensional axisymmetric stationary solutions as harmonic maps