Exercise 1, § 3

Let $\Gamma$ be a subgroup of Q(R) of finite index, and $P =\Gamma \cap R$. The algebra $\mathfrak{h}+\mathfrak{g}^P$ is reductive, and any reductive subalgebra of $\mathfrak{g}$ containing $\mathfrak{h}$ can be obtained in this way (use Chap. VI, §1, Exerc. 6 b)).