  We classify all connected subgroups of SO(2,n) that act irreducibly on
$\R^{2,n}$. Apart from $SO_0(2,n)$ itself these are $U(1,n/2)$, $SU(1,n/2)$, if
$n$ even, $S^1\cdot SO(1,n/2)$ if $n$ even and $n\ge 2$, and $SO_0(1,2)$ for
$n=3$. Our proof is based on the Karpelevich Theorem and uses the
classification of totally geodesic submanifolds of complex hyperbolic space and
of the Lie ball. As an application we obtain a list of possible irreducible
holonomy groups of Lorentzian conformal structures, namely $SO_0(2,n)$,
SU(1,n), and $SO_0(1,2)$.
