The writer used a real character, a revolutionary extremist Sergei G. Nechaev, to create Verkhovensky. You can find a lot of material about Nechaev, and about his relations with the leaders of Russian revolutionary movements abroad, like M. Bakunin (Paul Avrich's book). The connection to the 1st International could be drawn to Dostoevsky's character through relations of Nechaev and Bakunin (the latter is also known for his involvement in its creation and participation in its activity). I do not think that it was a direct mentioning by the author, at least, I could find only indirect pointing to that organization: 1) Part 3, Chapter 1. I; 2) Part 2, Chapter 1. III, conversation of Stavrogin with Shatov about Verkhovensky; 3) Part 2, Chapter 8, "Ivan Tsarevich"; 4) Part 2, Chapter 6, VII. Conversation of Stavrogin and Verkhovensky.
