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Hello, I need to know (connected closed) Lie subgroups of SO(2)×So(n), indeed these are compact Lie subgroups of SO(2,n) which I am looking for. But I don't know what we can say about the Lie subgroups of product Lie groups. I'll be thankful if some someone help me in this subject. Thanks in advanced.

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Lie Subgroups of SO(2)×So(n)

Hello, I need to know (connected closed) Lie subgroups of SO(2)×So(n), indeed these are compact Lie subgroups of SO(2,n) which I looking for. But I don't know what we can say about the Lie subgroups of product Lie groups. I'll be thankful if some help me in this subject. Thanks in advanced.