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.
The paper was translated into English in American Mathematical Society Translations: Series 2, Volume 6, 1957 DOI:10.1090/trans2/006 You should check your local libraries for journal holdings. Most math departments would have collected this journal. Here is a very partial find in a library mostly reporting libraries which have only a few volumes of this journal (including the desired volume).
Since 2000, it is also available in Dynkin's Selected Papers MR1757976 Find in a library. The paper begins on page 175.