Illuminati is not associated with Satanism at all. They are 2 whole different things. Their beliefs match nowhere. The Illuminati now is just an atheist organization (if still exists).
So let us start by, what is illuminati?
Illuminati is an ORGANIZATION of powerful people.
How did it start?
It started by philosophers by them thinking they are illuminated by God. Therefore the name.
So? Do you see the similarity? Yes me too..nowhere. Illuminati believed they are sent by "God" and Satanists believe in Satan himself as an entity or his beliefs.