Not sure on the 510.specifically but many of the stocks for the 500A12g will fit the 500C 20g with only a minor overhang on the 20g's slightly narrower receiver. The exceptions are some of the PG stocks that have cutouts for the bolt release. Some of these can still be used if you are comfortable using a dremmel.
The forends are not compatable across gauges due to the smaller diameter of the magazine tube.
With the 20g your options are limited compared to the 12g models.