Corollary 1

Tag 01CE, permanent. Cite it as [Bourbaki, Tag 01CE].

Lie Groups and Lie Algebras, chapter IX, § 4. Root system associated to a compact group

There are only finitely-many closed subgroups of G containing T.

Let H be such a subgroup; then $H_0\in \mathscr{H}$ , and $\mathscr{H}$ is finite. Moreover, H is a subgroup of $N_G(H_0)$ containing $H_0$ , and $N_G(H_0)/H_0$ is finite (§2, no. 4, Prop. 4 and Remark 2).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Corollary, § 4

Cites

Remark 2
§2, no. 4, Prop. 4