Here's a grammatical construction that has been bothering me all day.

Consider the sentence, "I saw him do ten push-ups."

Is "him" the subject of "saw," or is it the direct object of "do"? Or both?
If "him" is the subject of "do" then why is it not "he"?
What is the tense/mood of "do"? It's not conjugated, and it's not quite an infinitive (since it's not "to do"), which suggests that it's not indicative.
I'm utterly confused.

kniv"English is so convoluted..."etsil