  We show that there is a one-to-one correspondence between compact quantum
subgroups of a co-amenable locally compact quantum group $\mathbb{G}$ and
certain left invariant C*-subalgebras of $C_0(\mathbb{G})$. We also prove that
every compact quantum subgroup of a co-amenable quantum group is co-amenable.
Moreover, there is a one-to-one correspondence between open subgroups of an
amenable locally compact group $G$ and non-zero, invariant C*-subalgebras of
the group C*-algebra $C^*(G)$.
