There are two companies under the 501st Legion. They are the Shell Unit and the Torrent Company.
The Shell Unit specializes in emplacements and vehicles. They use a wide variety of turrets and assault vehicles.
The Torrent Company is a special forces unit that has existed ever since the 501st Legion was founded.
The 501st Legion has existed for decades and has been a popular staple of both the Republic, Empire and New Imperium armies. In it's early years, the 501st Legion worked for the Jedi Order and fought against the Confederacy of Independent Systems. Their two Companies are Shell and Torrent. They heavily valued a "Brotherhood Code" in both the Clone Wars, and the New Imperium.
The idea of a company centered around artillery and assault vehicles wasn't conceived for the 501st until the fall of the Empire. This led to the forming of Shell Company. The Shell Company was founded by CC-5343 "Jackal" after the death of Darth Vader.
After Order 66 and Operation: Knightfall, the 501st became "Vader's Fist" and was mainly composed of Jango-Fett clones from the Clone Wars. Their Brotherhood Code was disbanded due to the rough nature of the Empire. After Darth Vader's death however, CC-5343 "Jackal" made it imperative that the 501st adopt their own code, known as the "501st Honor Code" or as commonly referred to as "The Brotherhood Code".
The new 501st Brotherhood Code states that all 501st troopers will consider eachother as brothers. No matter race, religion, or creation, all troopers will consider each other as members of a large family. There are still existing clones within the 501st, but acceptance of other races and species is a characteristic Commander Jackal has become known for.