This is the full list of vendor- and product IDs from the gamecontrollerdb.txt file in the TheC64 firmware version 1.3.2. It is unclear whether this is used for both (Mini and Maxi) variants of the emulator by Retro Games Ltd.
The list is sorted on the vendor ID and product ID.
0001:0001 Nintendo Wiimote
0010:0082 Akishop Customs PS360+ v1.66
0078:0006 Microntek USB Joystick
0079:0006 DragonRise Inc. Generic USB Joystick
0079:0006 USB gamepad
0079:0011 Retrolink SNES Controller
0079:0011 USB Gamepad1
0079:181c SPEEDLINK COMPETITION PRO Game Controller for Android
0079:1843 Mayflash GameCube Controller Adapter
0079:1844 Mayflash GameCube Controller
0079:18d2 MAGIC-NS
0079:18d4 GPD Win 2 Controller
040b:6533 Speed-Link Competition Pro
0428:4001 Gravis GamePad Pro USB
044f:b300 Thrustmaster Firestorm Dual Power
044f:b312 Thrustmaster vibrating gamepad
044f:b315 Thrustmaster Dual Analog 4
044f:b320 Thrustmaster 2 in 1 DT
044f:b323 Thrustmaster Dual Trigger 3-in-1
044f:b326 Thrustmaster Gamepad GP XID
044f:d008 Thrustmaster Run N Drive Wireless
044f:d009 Thrustmaster Run N Drive Wireless PS3
045e:000e Microsoft SideWinder
045e:0202 Old Xbox pad
045e:0285 Microsoft X-Box pad (Japan)
045e:0289 Microsoft X-Box pad v2 (US)
045e:028e Microsoft X-Box 360 pad
045e:028e Speedlink TORID Wireless Gamepad
045e:028e SpeedLink XEOX Pro Analog Gamepad pad
045e:028e X360 Controller
045e:0291 X360 Wireless Controller
045e:02a1 X360 Wireless Controller
045e:02a1 Xbox 360 Wireless Receiver (XBOX)
045e:02d1 Microsoft X-Box One pad
045e:02d1 Microsoft X-Box One pad v2
045e:02dd Microsoft X-Box One pad (Firmware 2015)
045e:02e0 Xbox One Wireless Controller
045e:02e3 Microsoft X-Box One Elite pad
045e:02ea Xbox One Wireless Controller
045e:02fd Xbox One Wireless Controller
045e:0719 X360 Wireless Controller
046d:c20a Logitech Inc. WingMan RumblePad
046d:c211 Logitech WingMan Cordless RumblePad
046d:c215 Logitech Logitech Extreme 3D
046d:c216 Logitech Dual Action
046d:c218 Logitech RumblePad 2
046d:c219 Logitech Cordless RumblePad 2
046d:c219 Logitech F710 Gamepad (DInput)
046d:c21d Logitech F310 Gamepad (XInput)
046d:c21e Logitech F510 Gamepad (XInput)
046d:c21f Logitech F710 Gamepad (XInput)
047d:4005 Gravis Eliminator GamePad Pro
04b4:010a CYPRESS USB Gamepad
050d:0803 Nostromo n45 Dual Analog Gamepad
054c:0268 PS3 Controller
054c:05c4 PS4 Controller
054c:09cc PS4 Controller
054c:0ba0 PS4 Controller
056e:2003 JC-U3613M - DirectInput Mode
057e:0330 Nintendo Wii Remote Pro Controller
057e:2006 Joy-Con (L)
057e:2007 Joy-Con (R)
057e:2009 Nintendo Switch Pro Controller
0583:2060 iBuffalo SNES Controller
05a0:3232 8Bitdo Zero GamePad
05ac:3232 VR-BOX
05fd:3000 InterAct GoPad I-73000 (Fighting Game Layout)
06a3:0109 Saitek P880
06a3:040b Saitek P990 Dual Analog Pad
06a3:040c Saitek P2900 Wireless Pad
06a3:f518 Saitek PLC Saitek P3200 Rumble Pad
06a3:f622 Cyborg V.3 Rumble Pad
06a3:f623 Saitek Cyborg V.1 Game Pad
06a3:ff0c Saitek P2500 Force Rumble Pad
0738:3250 Mad Catz FightPad PRO (PS3)
0738:3384 Mad Catz FightStick TE S+ (PS3)
0738:3480 Mad Catz fightstick (PS3)
0738:4716 Mad Catz Wired Xbox 360 Controller
0738:4738 Mad Catz Wired Xbox 360 Controller (SFIV)
0738:5266 Mad Catz C.T.R.L.R
0738:8250 Mad Catz FightPad PRO (PS4)
0738:8384 Mad Catz FightStick TE S+ (PS4)
0738:8480 Mad Catz fightstick (PS4)
0738:8818 MadCatz PC USB Wired Stick 8818
0738:8838 MadCatz PC USB Wired Stick 8838
07b5:0315 impact
0810:0001 Twin USB PS2 Adapter
0810:0003 USB Gamepad
0810:e501 NEXT SNES Controller
0925:0005 Sony PS2 pad with SmartJoy adapter
0925:03e8 Mayflash Wii Classic Controller
0925:8866 MP-8866 Super Dual Box
0926:8888 Cyber Gadget GameCube Controller
0955:7210 NVIDIA Controller
0955:7214 NVIDIA Controller v01.04
0b05:4500 ASUS Gamepad
0c12:0005 AxisPad
0c12:0005 Manta Dualshock 2
0c12:0e10 ZEROPLUS P4 Gamepad
0c45:4320 XEOX Gamepad SL-6556-BK
0e6f:011e Rock Candy PS3 Controller
0e6f:011f Rock Candy
0e6f:0130 EA Sports PS3 Controller
0e6f:0139 Afterglow Controller for Xbox One
0e6f:0139 Afterglow Prismatic Controller
0e6f:0139 Afterglow Prismatic Wired Controller 048-007-NA
0e6f:0146 Rock Candy Xbox One Controller
0e6f:0164 PDP Battlefield One
0e6f:0213 Afterglow
0e6f:0214 PS3 Controller
0e6f:02a8 PDP Wired Controller for Xbox One
0e6f:0301 Logic3 Controller
0e6f:0401 Gamestop Logic3 Controller
0e6f:0413 Generic X-Box pad
0e8f:0003 PS3 Controller
0e8f:0008 Gasia Co. Ltd PS(R) Gamepad
0e8f:0012 GreenAsia Inc. USB Joystick
0e8f:1006 GreenAsia Electronics 4Axes 12Keys GamePad
0e8f:3013 HuiJia SNES Controller
0f0d:0009 Natec Genesis P44
0f0d:000d hori
0f0d:0010 HORI CO. LTD. FIGHTING STICK 3
0f0d:0022 HORI CO. LTD. REAL ARCADE Pro.V3
0f0d:005e Hori Fighting Commander 4 (PS4)
0f0d:005f Hori Fighting Commander 4 (PS3)
0f0d:0066 HORIPAD 4 (PS4)
0f0d:0067 HORIPAD ONE
0f0d:006a HORI CO. LTD. Real Arcade Pro.4
0f0d:006b HORI CO. LTD. Real Arcade Pro.4
0f0d:006e HORIPAD 4 (PS3)
0f0d:0092 Hori Pokken Tournament DX Pro Pad
0f0d:00ee HORIPAD mini4
0f30:010b Jess Tech GGE909 PC Recoil Pad
0f30:0110 Jess Tech Dual Analog Rumble Pad
0f30:1112 QanBa Arcade JoyStick
11c9:55f0 HJC Game GAMEPAD
11ff:3331 PC Game Controller
11ff:3341 PS2 Controller
12bd:d015 Tomee SNES USB Controller
1345:3008 NYKO CORE
146b:0d01 Revolution Pro Controller
14d8:6208 HitBox (PS3/PC) Analog Mode
14d8:cd07 Toodles 2008 Chimp PC/PS3
1532:0401 Razer Panthera (PS4)
1532:0402 Razer Panthera (PS3)
1532:0900 Razer Serval
1532:0a03 Razer Wildcat
1532:1000 Razer RAIJU
1689:fd00 Razer Onza Tournament Edition
1689:fd01 Razer Onza Classic Edition
1689:fe00 Razer Sabertooth
16c0:0487 Serial/Keyboard/Mouse/Joystick
16c0:05e1 Xin-Mo Xin-Mo Dual Arcade
1949:0402 Amazon Fire Game Controller
1949:0402 Ipega PG-9069 - Bluetooth Gamepad
1a34:0809 SL-6566
1a34:0836 PS3 Controller
1a34:f705 GameCube {HuiJia USB box}
1bad:f016 Mad Catz Xbox 360 Controller
1bad:f02e Mad Catz Fightpad SFxT
1bad:f038 Street Fighter IV FightStick TE
1bad:f501 Hori Pad EX Turbo 2
1c59:0023 Retro Games LTD THEC64 Joystick
1c59:0024 Retro Games LTD THEC64 MS Joystick
1d57:0021 Retro Games The64 Joystick Prototype
1d59:0022 Retro Games The64 Joystick Prototype
2002:9000 8Bitdo NES30 Pro
20bc:5500 GameSir G3w
20bc:5500 ShanWan PS3/PC Wired GamePad
20d6:0dad Moga Pro
20d6:6271 Moga Pro 2 HID
20d6:89e5 Moga 2 HID
20d6:ca6d PowerA Pro Ex
20e8:5860 Cideko AK08b
22ba:1020 Jess Technology USB Game Controller
24c6:5300 PowerA
24c6:543a PowerA 1428124-01
24c6:5b02 Thrustmaster GPX Gamepad
24c6:5d04 Razer Sabertooth
2563:0523 ShanWan USB Gamepad
2563:0575 SHANWAN PS3/PC Gamepad
25f0:83c1 Goodbetterbest Ltd USB Controller
25f0:c121 ShanWan Gioteck PS3 Wired Controller
2717:3144 XiaoMi Game Controller
2810:0009 8Bitdo SFC30 GamePad
2836:0001 OUYA Game Controller
289b:0003 raphnet.net 4nes4snes v1.5
28de:1102 Steam Controller
28de:1105 Steam Controller
28de:1106 Steam Controller
28de:1142 Steam Controller
28de:11fc Steam Controller
28de:11ff Steam Virtual Gamepad
28de:1201 Steam Controller
28de:1202 Steam Controller
2dc8:2830 8Bitdo SFC30 GamePad
2dc8:3810 8Bitdo FC30 Pro
2dc8:3820 8Bitdo NES30 Pro
2dc8:6100 8Bitdo SF30 Pro
2dc8:9001 8Bitdo NES30 Pro 8Bitdo NES30 Pro
3820:0009 8Bitdo NES30 Pro
4c50:5453 PS3 Controller
5347:6d61 GameStop Gamepad
5347:6d61 GS gamepad
6258:3320 Xbox 360 Wireless Controller
6258:4720 Xbox Gamepad (userspace driver)
6469:6469 idroid:con
6666:0667 boom PSX to PC Converter
6666:8804 Super Joy Box 5 Pro
dead:beef Hidromancer Game Controller
f000:0003 RetroPad
f000:00f1 Super RetroPort