Let G be a locally compact group and let L(G) be the set of all closed subgroups of G. The family \(\{\) \(F\in L(G) :\) \(H\subseteq F\subseteq HU\}\) forms the base of a topology \(\tau\) on L(G) (H\(\in L(G)\), U runs over a neighbourhood base of unit of G). It is proved that the space \(L_{\tau}(G)\) is discrete iff G is a Lie group.