In season 3 episode 3 of Hannibal, there is a part where Hannibal says "In Roman times... each carcass was divided: prime cuts went to nobility, second to the clergy, third to the bourgeoisie and fourth to the army. The quinto quarto, the offal, went to the poor."
I'm not aware of this hierarchy ever being applied specifically. The actual division of meat depends on the particular circumstances of the sacrifice and varies widely.