Swords of Sanghelios

The Covenant Separatists are a breakaway faction of the Covenant, led by the Elites and formed after they were replaced within the Covenant by the Brutes at the end of Halo 2.

Background
The Covenant separatists are made up of the Sangheili, Unggoy, and Lekgolo castes within the Covenant's hierarchical society. This faction was created at the beginning of the Civil War of the Covenant and since then has been fighting the Covenant Loyalists, led by the Prophets and their Jiralhanae, Yanme'e, Kig-Yar and some Unggoy supporters.

It is speculated that this disgruntled faction is lead by Rtas 'Vadumee and/or the Arbiter. Fronts of this war include High Charity, the Covenant's slipspace-capable capital, Delta Halo, and areas of space where Covenant ships operate.

This is not necessarily the first internal dispute in the Covenant's society; when the current Arbiter was assigned to his office, he was reminded by the High Prophet of Mercy that an Arbiter was necessary during the Grunt Rebellion, which was a conflict between the Covenant and its lowest caste, the Unggoy.

How the faction comes to life
The High Prophet of Regret led a botched mission to Earth and was forced into The First Battle of Earth upon discovering what turns out to be the Human homeworld. He escapes to Delta Halo, but is killed by the Master Chief, which is considered a significant failure in the Sangheili's oath to protect the Prophets.

The remaining Prophets, led by the High Prophet of Truth, used this opportunity to replace the Sangheili with the Jiralhanae as their guards. However, this move effectively shames and angers the Sangheili, who have grown accustomed to their comfortable position in the caste system, and they threaten to resign from the High Council.

Later, the Councilors are assassinated by the Jiralhanae at the behest of the Prophets; This purge, along with the understanding of what the Halos actually are meant to do, help divide the Covenant along the lines seen in the war. Instead of a Great Journey, the Gravemind's revelation regarding the superweapon contradicts the Covenant's belief system and is motivating at least the Arbiter in his eventual opposition to the Covenant as they try to activate Delta Halo later in the game.

Military Forces
The Separatists are speculated to be commanded by Rtas 'Vadumee and/or the current Arbiter. Their military includes Sangheili, Unggoy and Lekgolo castes, along with ships of various classes loyal to their cause.

Also involved in this faction is the UNSC's most effective Spartan, the Master Chief; through an alliance of convenience, he is meant to stop the Prophet of Truth and his guards at the behest of the Gravemind, the apparent leader of the Flood. The Arbiter, meanwhile, is meant to recover the Index and prevent its activation by the Prophets and their proxies.

It is currently unknown how this alliance will progress in the future, but it is expected by many to become official as the Sangheili have long respected a number of human traits which would otherwise draw a race into the covenant.