Flight crew flying CE680 aircraft reported hydraulic failure during departure climb. Flight diverted and landed uneventfully.

Narrative

After takeoff with a positive rate of climb; the Pilot Not Flying (PNF) called positive rate. The Pilot Flying (PF) called for gear up. The PNF place the gear handle in the UP position. PNF noticed that the landing gear did not retract. Simultaneously; the PF stated we have an EICAS message for HYDRAULIC PRESSURE LOW L and R; and HYDRUALIC VOLUME LOW. At this time the Tower switched us to Departure. PNF informed Departure that we were having an issue and we were allowed to hold over the airport. The PNF ran the Emergency/Abnormal checklist for HYDRAULIC PRESSURE LOW L and R; and HYDRUALIC VOLUME LOW. The PNF also placed the landing gear handle back in the Down position. The gear position indicator indicated 3 green and no red lights. The PNF then informed the passengers of the problem and advised them that we were going land at ZZZ1. The PNF then [requested priority handling] to Departure Control and advised them that we wanted to proceed to ZZZ1. Enroute the PNF called company at ZZZ1 and requested that a tug with the appropriate tow bar be ready to dispatch to our position. At ZZZ1 we did a low approach for the Control Tower to visually verify the landing gear position. On the second approach we landed on Runway XXL and taxied off on Taxiway 1. After clearing the runway; we stopped; shut-down the engines; and held our position until the tug arrived. We were towed to company's ramp with no further incident.