I was recommended to consult a mathematical text:
E. B. Dynkin, “Semisimple subalgebras of semisimple Lie algebras”, Mat. Sb. (N.S.), 30(72):2 (1952), 349–462.
But I find that the paper is written in Russian русский: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=5435&option_lang=eng http://www.mathnet.ru/links/83b544bbde2b8abefdb3d6ede25dcb92/sm5435.pdf
Do we know any English translation of the original paper? Thank you - please provide the English version link.