R. sativus raphanistroides is accepted as a synonym of Raphanus sativus/Raphanus sativus var. sativus according to Tropicos (http://www.tropicos.org/Name/4104873?tab=acceptednames). The same is true of R. s. longipinnatus (http://www.tropicos.org/Name/4105774?tab=acceptednames). R. s. caudatus is an obligate synonym of Raphanus caudatus (http://www.tropicos.org/Name/100358953), accepted by POWO as a synonym of R. raphanistrum sativus. Raphanus bipinnatus is not accepted as a published name in POWO, The Plant List, IPNI, or Tropicos; it is clearly being used to refer to Daikon radishes, though, which are a type of cultivated radish (and referrable to R. s. longipinnatus mentioned above). Raphanus sativus is accepted on POWO and The Plant List as a synonym of R. raphanistrum sativus, which it is an obligate synonym of. Tropicos accepts R. sativus as the current name, but since they are obligate synonyms, it shouldn't much matter which is in use, the subspecies, or the species.
Also, "Raphanus raphanistrum subsp. sativum" is misspelled, though understandably.