They sat between the Girondists on the Right and, The Mountain or Jacobin party on the left. (Our modern usage of Right/Conservative and Left/Liberal stems from this seating arrangement). None of these three groups was an organized party as is known today. The Mountain and the Girondists did consist of individuals with similar views and agendas who socialized together and often coordinated political plans. The Plain, however, consisted of delegates that did not belong to either of these two groups and as such was even more amorphous.
The Plain constituted the majority of delegates to the Convention and would vote with either the Girondists or Mountain depending on the issue at hand, the current circumstances and mood of the Convention. Initially they sided with the Girondists, but latter backed the Mountain in executing Louis XVI and inaugurating the Terror. Later they abandoned the Mountain inaugurating the Thermidorian Reaction.