Actually there were quite a few variants that were designated, but either were produced in low numbers or weren't widely used due to the specific tasks the variant was made for. I have shamelessly ripped the following list of variants from the following site:
http://www.vectorsite.net/avhuey.html The list is not really fully complete since it is not totally up to date, and does not include the UH-1Y and the AH-1Z. Note that the UH and the AH designations never crossed, e.g, no UH-1Q or W, but there was AH-1Q and W. I guess the AH-1 is counted as family. (there were also AH-1Q,R,S,T, i think) However, there was a UH-1U, if I am not mistaken...
Please note that 204 and 205 were both the original single-engine 'hueys', with the 205 being the stretched version. the UH-1H was from the 205 series. 212, 214 and 412 are twin-engined.
Model 204 variants include: XH-40: Three initial prototypes, with Lycoming T53-L-1 engine (522 kW / 700 SHP) and teetering-bar rotor.
YH-40: Six evaluation rotorcraft, with T53-L-1A engine (574 kW / 770 SHP) and 30 centimeter (1 foot) fuselage stretch.
HU-1: Nine preproduction rotorcraft, similar to YH-40.
UH-1A (HU-1A): Initial full-production rotorcraft, similar to YH-40. 183 built.
UH-1B (HU-1B): Stretched variant with wider-span rotor. Early production fitted with T53-L-5 engine (642 kW / 860 SHP), later production with T53-L-11 engine (821 kW / 1,100 SHP). At least 1,033 built.
Model 204B: Commercial version of UH-1B.
UH-1C: Gunship-optimized UH-1B with T53-L-11 engine, Model 540 rotor, and greater fuel capacity. About 750 built.
UH-1E: USMC version of UH-1B, with rescue hoist, rotor brake, and USMC avionics. 250 built.
TH-1E: Same as UH-1E but with dual controls for training. 20 built.
UH-1F: USAF version of UH-1B, with General Electric T58-GE-3 engine (962 kW / 1,290 SHP) and wider rotor. 146 built.
TH-1F: Trainer version of UH-1F, build in small numbers.
HH-1K: US Navy SAR variant of UH-1B, with T53-L-13 engine (1,044 kW / 1,400 SHP) and USN avionics. 27 built.
TH-1L Seawolf: Trainer version of HH-1K, 90 built.
UH-1L: Utility version of HH-1K, 8 built.
UH-1M: Night combat derivative of UH-1C with sensor systems and T53-L-13 engine. Built in small numbers, some converted from UH-1Cs.
UH-1P: Psychological warfare conversion of UH-1F, with loudspeaker system.
AB-204: Italian Agusta-Bell license-built Model 204. Agusta-Bell offered many custom fits, including a Rolls-Royce / Bristol Gnome H.1200 engine (895 kW / 1,200 SHP) or a General Electric T58-GE-2 engine (988 kW / 1,325 SHP).
AB-204AS: Agusta-Bell maritime warfare version of Model 204, with search radar, dunking sonar, and accommodations for torpedoes and antiship missiles.
Model 205 variants include: YUH-1D: Prototype / evaluation version of Model 205, with stretched fuselage, T53-L-11 engine, wider rotor.
UH-1D: Production Model 205, similar to YUH-1D. 2,008 built.
UH-1H: Definitive Model 205 version, with T53-L-13 engine and improved avionics. 3,573 built for US Army and 1,372 built for export sales.
EH-1H: Three experimental UH-1H conversions to the SIGINT role.
UH-1H: UH-1H conversion for DustOff / medevac role, with rescue hoist and other small changes. 220 conversions.
HH-1H: USAF version of UH-1H for SAR role, with rescue hoist. 30 built.
CH-118 (CUH-1H): Canadian Armed Forces version of UH-1H.
UH-1J: Japanese derivative of UH-1H, built by Fuji, with T53-L-703 engine (1,343 kW / 1,800 SHP), countermeasures, and cockpit improvements. At least 78 built.
AB-205: Italian Agusta-Bell license-built Model 205, with many optional custom fits.
Model 212 Twin Huey variants include:UH-1N: UH-1H with PWC T400-CP-400 Twin Pac engine system (1,141 kW / 1,530 SHP). 300 built for USAF, USMC, USN.
VH-1N: USMC VIP transport version of UH-1N, with two conversions and six new-build rotorcraft.
CH-135 (CUH-1N): Canadian Armed Forces version of UH-1N, 50 built.
AB-212AS: Italian Agusta-Bell maritime warfare variant, with search radar, dunking sonar, autopilot system, and capability to carry torpedoes and antiship missiles.
Model 412 variants include: Model 412: Model 212 with four-blade composite folding rotor and PWC PT6T-3B-1 engine (977 kW / 1,310 SHP).
CH-146 Griffon: Canadian Armed Forces version of Model 412, 100 built.
Model 412SP: Greater fuel capacity and take-off weight.
Model 412HP: Improved transmission system..
Model 412EP: New PT6T-3D engine and redundant digital automatic flight control system.
Model 412EP Sentinel: Heli-Dyne maritime warfare variant produced by Heli-Dyne with radar, sonar, and other gear.
Model 412AH: Attack helicopter variant with Lucas 12.7 millimeter gun turret. Not produced.
AB-412 Grifone: Italian Agusta-Bell variant, modified for multirole military operation.
Model 214 variants include: Model 214 Huey Plus prototype: Heavy-lift UH-1H derivative with fully-rated T53-L-13 engine, Nodomatic rotor, structural improvements.
Model 214A Isfahan: Improved Model 214 with Lycoming LTC4B-8D engine (2,186 kW / 2,930 SHP). 293 built for Iranian Army.
Model 214B BigLifter: Commercial version of Model 214A, built in small numbers.
Model 214C: SAR version of Model 214A for Iranian Air Force, 39 built.
Model 214ST (Stretched Twin): Biggest member of Huey family, with larger and modernized fuselage, twin GE T700 engines (2,424 kW / 3,250 SHP total). Sold on the commercial and international markets. [/url]