C560 Captain reported a hydraulic system failure followed by a divert to a suitable airport.

Narrative

On takeoff out of ZZZ this morning we encountered the following problems. The landing gear would not retract. We had the following light indications: three green and one red unlocked indicator with the gear handle in the up position. We also had a STAB MIS COMP" annunciator illuminate. We executed the " the landing gear will not retract (red gear unlocked light remains on) QRH and " STAB MIS COMP" QRH checklists. neither checklist corrected the problems. After completing both checklist; I noticed the "hyd control" circuit breaker was popped. I tried resetting it once and it would not reset. While airborne I spoke with the Chief Pilot twice. On the second call; I told him the best thing to do was to [request priority handling] because we had several hydraulic issues going on. We agreed on diverting to ZZZ1. I advised the passenger of the situation and informed him that the company would be working on a recovery for them. The current status of the aircraft was geared down and locked; flaps seven and both hydraulic control and stab control circuit breakers popped. We executed the flap fail approach and flap fail landing QRC checklists. In the back of my mind; I was concerned that we would have a brake failure too because of all of the break issues with the XLS. I do know and understand that the hydraulic system and the brake system are too independent hydraulic systems. We brief the procedure for using the emergency pneumatic brake system. When we checked in with the tower; I told them we had no hydraulics or brakes. on the landing roll; I applied normal breaking; and it appeared to me that we were not decelerating; so I used the pneumatic emergency break system to stop the aircraft. At the time; it did not dawn on me how long it could take for the aircraft to slow down without all of our drag devices available to use. We were able to clear the active runway and stop just on the other side of the hold short line. We at that point coordinated to have the aircraft towed to the company facility.Suggestions: I thought as a crew we worked well together. We had a couple malfunctions with no way of correcting the problems. The only thing I second-guess myself on was the brake system. On the landing roll I applied normal and then more than normal break pressure without feeling the aircraft slowing that is when I made the decision to use the emergency pneumatic brake system."