Geass Order

The Geass Order (ギアス嚮団), also translated as the Geass Cult or Geass Directorate, is a secretive group that studies and produces Geass users. Its last known location is a large underground city, also called the Geass Order, which is within the Chinese Federation territory. Before the assault instigated by the Black Knights, it was under the control of V.V., and so was presumably under Britannian influence.

Description
Origins of The Geass Directorate are unknown but since its former leader was C.C. in Code Geass Akito the Exiled, it is implied that its former headquarters was in E.U. The Geass Directorate plays a major role in Code Geass: Oz The Reflection due to its known members.

Though its location usually changes with each leader, it is currently located in an enormous underground cavern beneath Taklamakan Desert in the Chinese Federation. The Geass Order seems to be, for the most part, a fairly modern medium-sized city, complete with streetlights, roadways, ornate buildings, and even an underground train system. The location of the directorate may be the Taklamakan Desert in our Xinjiang, which resembles the desert as seen in Code Geass (a huge erg). Moreover, when Lelouch talks in video communication to V.V, the   terminal communication line briefly appears to be located to the south of a geographical entity that has the same administrative borders as Xinjiang, where is the Taklamakan desert. Another location of the Geass Directorate was said to be in E.U. territory despite C.C.'s departure during the member's escape from the Black Knight's assault.

Most of the city is lit with an eerie purple glow that emanates from a Thought Elevator at the head of the city.

Code Geass Akito The Exiled
In Leila's past, it was revealed that C.C. was the head of the Order that time with other members implying that their headquarters was in E.U before moving to the Chinese Federation. Their style of clothing differs from the ones in Lelouch of The Rebellion. The Dimensional Supervisor has a connection with the order.

After the battle between Europia United and Euro Britannia is over, they were able to rescue Lelouch and Suzaku with Rolo. However, Rolo informed Lelouch and Suzaku that the Emperor wants to see Lelouch

Code Geass Oz: The Reflection
to be added

Assault on the Geass Order
After the death of Shirley Fenette, an embittered Zero decides to launch an attack on the order as to destroy the existence of Geass as a whole. Crashing through the shallow roof of the cavern, the Black Knights, on Zero's orders, indiscriminately slaughter the city's unarmed inhabitants. While V.V. attempts to stave off the attack with the Siegfried, a group of hooded order members attempt to escape the city with essential Geass research in a bullet train. C.C., however, intervenes and destroys the train before it can exit the compound.

Lelouch, pursuing the wounded (though immortal) V.V. to the Thought Elevator, in which the Emperor can be seen standing. After the Emperor and V.V. exchange a few words, Lelouch finds himself suddenly transported out of the city and onto the Sword of Akasha. Some of the order agents can be seen reporting to Charles zi Britannia after V.V's death implying he's their new leader.

Ragnarok Connection
After declaring war against Britannia, Charles made his appearance on television mocking Zero's foolish action up until now. Charles and the survivors of the Geass Order went to Kamine Island to perform their activities. The members were later slain by Suzaku before confronting Charles to gain revenge of what he did especially to Euphemia. Lelouch later attacked the emperor's forces and confronted him in order to stop his plan.

Unnamed Children
When Zero led the Black Knights to destroy the Geass Order, some unnamed children were present who referred to Rolo as "Big Brother Rolo". One of them displayed a Geass power, able to control another person's body. All of the children were killed by Rolo.

Nightmare of Nunnally
The Geass Order in Nightmare of Nunnally is similar but slightly different. They go by the name Eden Vital Religious Order whose goal is dedicated to unleashing the Heaven's Door (which is in fact Ragnarok Connection) to bring humanity into one being. The organization is highly structured, with different divisions such as the Heretical Trial Division run by Cardinals, Rolo Vi Britannia among them. Like in the anime, it is implied that they research Code R, duplicating C.C.'s powers furthering Geass abilities. They also deal with the use of witchcraft as they once tried to burn Nunnally for her crimes by Rolo's orders, only to be stopped by Lelouch, Suzaku, and Euphemia. This implies they deal with religious-like techniques to demonstrate their organization's philosophy. When Charles Zi Britannia declares the Holy Nation of Eden Vital to replace Britannia, the Order seizes control of the Britannian government. All Cardinals were to replace Viceroys and have them under arrest to ensure Heaven's Door's fruition. They later battled against the Britannians loyal to Euphiemia and the Black Knights at Kaminejima Island only to be defeated when Charles and Marianne were rejected by Nunnally's choice to follow the future (similar to Lelouch in the anime) instead of living in Heaven's Door which was the past. Presumably, the organization was disbanded thereafter.