The M-23 Doorgun Mount was used on long-bodied UH-1D/H Huey "Slick" (troop Carrier) helicopters. They started showing up in late '64 to early '65.

They were the standard US Army weapons mount on UH-1H Slicks up through the late '90s when Blackhawks replaced Hueys.

They are still used on modern UH-1H+ Huey II models today, like this Iraqi Air Force example.

UH-1Cs were strictly gunships and mounted a variety of gun/missile combinations that were fixed in a forward-firing orientation. They did have "free" M60s (handheld with a bungee cord or surgical tubing securing them to the ceiling of the helo) manned by the crewchiefs though.
A few examples.



Free M-60 on UH-1C


Later, a swing-out mount was used for the M60.

More info on helicopter armament systems
here.