2007+ Fiat 500 Transmission
Quick note: much of this information is based off of North American (Mexico Manufacture) vehicles. The North American fiats are much more straightforward in configuration- with fewer options, models, and variations in powertrains. If you are looking for information for a euro-market 500, please be aware that there may be differences. Creating a subheading detailing these differences is also a good idea.
C510
The C510 is a heavy duty 5 speed manual transaxle found in all turbocharged 500 applications, including all model years of the Abarth and 500t, and all 500s from 2018 onwards. For stock power levels, these are very robust and durable units and generally provide a long service life, especially when maintained properly. Like the X1/9 transmissions, reverse gear is non synchronized. Shifting into a forward gear (or just waiting a long time) after depressing the clutch, and before shifting to reverse is crucial to ensure the longevity of the transmission. Failure to do so can damage not only the reverse gear hardware, but all components in the case due to metal fragments.
Power Handling:
Despite arguably being the weakest link in the powertrain of the modern 500, these transmissions can and will handle a fair amount of torque. Pre 2015 transmissions are happy until ~250 crank TQ, but any more may be pushing the limits. I am searching for more information on the common cause of failure, so that information will be added in the future. Starting in 2015, the C510 got a refresh which includes a more convenient drain plug, and stronger internals.