The G- orbits for G=S(1), G=S(2) and their Subgroups

Let (G, * ) is a group and X is a nonempty set and let group action are given. For any point the set is called G- orbits of the element x. Let (G, * ) is a group then, the smallest G- invariant subset containing is G- orbit of x. In this paper G-orbits of the similarity group S(n) and all subgroups of it in case n=1 and n=2, which are G- invariant subspaces therewithal, are obtained