What are all invariant random subgroup on Sub ($R^n$) and Sub($G$)?

Question

Let $G$ be a locally compact group. The space Sub($G$) be the closed subgroup of $G$ and $\mu$ be a borel probability measure of Sub($G$) which is invariant under all inner automorphism.

What are all such measure other than point mass measure? Is there any classification for $R^n$ ?