  We present the complete scheme of the application of the one-and two
dimensional 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 space
formalisms. From this method one obtains the Kramer, Belinsky-Ruffini,
Dobiasch-Maison, Cl\'{e}ment, Gross-Perry-Sorkin solutions etc. as special
cases.
