B767-300 flight crew reported hydraulic system failure during climb. Diverted and landed uneventfully.

Narrative

On initial climb we received a C HYD PRESS EICAS message. We retracted flaps; engaged the C autopilot. I referenced the QRH as the PF continued our climb and assumed the radios. The second FO in the observer seat also opened a QRH and followed along. Before I shut down the center hydraulic pumps; I said to the PF 'the autopilot isn't going to like this; use the right autopilot'. Throughout the rest of the flight; we were incorrectly using the R autopilot from time to time; and disconnecting and hand flying when it could not keep up with the FD (Flight Director) pitch commands. By the time we had finished the checklist; recall review and after takeoff checklist; we were leveling at FL350. The A/P (Autopilot) was disconnected. While I was engaged with the company on SAT (Satellite) call; the PF said something about not liking the way the aircraft was handling at altitude. The mental model in my mind became unpleasant. I asked if there were objections to returning to ZZZZ; there were none. I told the observer pilot and the PF to work with ATC to return to ZZZZ; and to request priority handling if they had to. They did. I finished the call with Dispatch; who issued a reanalysis. I asked for a clearance direct to ZZZZZ; descend to 6;000 feet and hold for 20 minutes and it was granted. On our descent I called the company again and asked for an SME (Subject Matter Expert). The SME was helpful in reviewing the procedure; pointing out a few items and encouraged me to just stick to the procedure. Very helpful. We fully configured in the hold; including the deferred items descent; approach and landing checklist. We asked for and were issued vectors for ILS XXL. After landing and clearing right on taxiway 1; firemen approached the jet with chocks; I shutdown both engines. There was no bypass pin to be found so after consulting company again we partially pressurized (using reserve brakes and steering switch to power center c1) and taxied to parking. Cause: C HYD PRESS EICASThe bias I had for using the R autopilot was not helpful. I'm uncertain how I missed the information about the R autopilot elevator inop. I know I read everything; it just didn't make it past my eyes into my brain. Suggestions: I need to read intentionally; looking for things I'm wrong about. Carry bypass pins. Keep the SMEs at all costs.