A classification (up to conjugacy) of all closed subgroups of the (identity component of the) Lorentz group $\mathrm{SO}(1,3)_0$ in terms of the subalgebras of its Lie algebra was given in

• R. Shaw. The subgroup structure of the homogeneous Lorentz group. The Quaterly Journal of Mathematics, Oxford 21 (1970) 101-124

(see also the book of Hall: Symmetry and Curvature Structure in General Relativity).

My question is whether there exists a similar classification for $\mathrm{SO}(1,n)_0$, $n\ge 4$.