Several hundred Aes Sedai fled the city of Tar Valon during the Schism.
The White Tower Schism is the name of the separation of the White Tower that would eventually lead to war between two opposing factions of Aes Sedai and later on to their eventual reunion, timely after the Battle of Tar Valon.
See also: Hall of the Tower during the White Tower Schism
Elaida's White Tower
Elaida's White Tower was one of the two main factions among the Aes Sedai. It consisted of those that chose to remain in the White Tower after the coup led by Elaida do Avriny a'Roihan.
Loyalist Hall
Under Elaida, Alviarin Freidhen was chosen as Keeper of the Chronicles but was deposed due to her disappearance during the Siege of Tar Valon. She was replaced by Tarna Feir. Of the Sitters newly raised, only the Reds and Shevan were not unusually young.
There was no Blue Ajah in the Loyalist Tower, and Elaida had it removed from her stole and seat.
Rebel Aes Sedai
The rebel Aes Sedai made up the other of the two main factions. It consisted of those that rejected Elaida's coup and decided to support an organized resistance against her as Amyrlin Seat.
The rebel Hall
The rebel Aes Sedai raised Egwene al'Vere as Amyrlin and Sheriam Bayanar to Keeper of the Chronicles. The rebel Hall of the Tower, called the Little Hall by the rebel Aes Sedai, was an inn before Salidar was abandoned years before. Each of the Sitters who had fled the Tower gained a place in this Hall, except one Blue who presumably died escaping. Except for Romanda Cassin and Moria Karentanis, the others were unusual choices for Sitters. See voting history for a full analysis of the rebel Hall's votes.
There is no Red Ajah among the rebel Aes Sedai, however their color remains in the stole of the Amyrlin Seat.
Unaligned sisters
Unaligned sisters are the third faction created in the conflict, consisting of those that did not pick a side in this conflict. Among these are several of the sisters that weren't residing in the White Tower at the time of the instigating conflict. This faction is fairly large, accounting for a little more than a third of all Aes Sedai.
There are also some sisters who are of unknown affiliation in that they have usually only been mentioned before the events of the White Tower schism.
Activity
Deposition
Elaida do Avriny a'Roihan led a faction of eleven Sitters that deposed the current Amyrlin Seat Siuan Sanche for her dealings with the Dragon Reborn. The other ten Sitters were not informed of the meeting at which they voted to depose her. The Blues were not informed pursuant to the rules for deposing an Amyrlin, but the other seven were likely excluded because they couldn't be counted on to vote as the former desired.
Of the ten, all but one, Seaine Herimon, left the Tower (although one of the Blues may have died during the struggle after Siuan's deposition was announced). The Blues and, it seems, Janya Frende genuinely fled the Tower. The other five were a different story.
The split
Gawyn Trakand helped Siuan escape the tower. Several hundred sisters fled the Tower as well, including the entire Blue Ajah and all of the ten sisters who had not been informed of the deposition save Seaine Herimon, who remained a loyalist.
Five of those sitters had originally been sent by their Ajahs. The Heads of the five "unaligned" (i.e., not Blue or Red) Ajahs met and decided to send one Sitter per Ajah to help guide the rebels toward reconciliation:
In their places, the Heads directly appointed themselves or women younger than what was usual for a woman to hold a chair in the Hall. These replacements were only meant to serve for a short period—presumably until the five Sitters returned.
In Salidar
In Salidar, the five Sitters found a rebellion led by Sheriam and five other women that was better organized than the Ajah Heads had anticipated. Although it has never been stated explicitly, it seems probable they divided into factions meant to keep the Hall paralyzed by playing Romanda Cassin and Lelaine Akashi against one another. By the time the schism healed, Ajah Head Jesse Bilal believed some of the five Sitters had come to side with the rebels more often than the Tower.
Aside from the five Sitters sent by the Ajah Heads, the Blues, and Janya, the rebel Sitters were too young or otherwise unusual. Romanda Cassin likely obtained her seat because of her previous experience, but it is not clear who was responsible for choosing the young Sitters. The five Sitters could have been responsible, but so too could Sheriam's group have been. Whoever chose them, the young Sitters generally voted as a bloc in favor of decisive action such as declaring war against Elaida. In fact, the five Sitters sent from Tar Valon generally found themselves virtually alone on the losing end of votes, bringing with them, at most, Romanda.
Reunification
The White Tower was eventually healed when Seanchan forces attacked in the Battle of Tar Valon. Elaida was captured and the White Tower reunified under rebel Amyrlin Egwene al'Vere.