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 $\mathrm{SO}(1,n)\_0$, $n\ge 4$. 



Subgroup structure of $\mathrm{SO}(1,n)_0$
I would expect this to become impractical (although in practice there is an algorithm) as $n$ increases. There are results for $n=4$ in this paper:


*Quantum numbers for particles in de Sitter space* by J Patera, P Winternitz, H Zassenhaus.
Published in the [Journal of Mathematical Physics (1976) vol. 17 (5) pp. 717-728](http://jmp.aip.org/resource/1/jmapaq/v17/i5/p717_s1). ([MathSciNet](http://www.ams.org/mathscinet/search/publications.html?pg1=MR&s1=MR0406126))


