HS-125 includes

Hawker 125–1A
Hawker 125–3A
Hawker 125-400

Hawker 125-600
Hawker 125-700
Hawker 125-800/800XP

I found this on http://www.proavi8or.com/pages/ratings.html

Although I think it would be added since it really is just a larger 800 but I would also think it would have been on the list. I havent found too many people who offer the 125 type. Pan Am academy even seperates the training between the -700 and -800