While many were outraged by the coup, they were also equally appalled by the very idea of joining a rebel faction of Aes Sedai, never mind forming an army and beseiging Tar Valon. For this reason, they did not join the rebels, but neither did they want to return to the Tower while Elaida was Amyrlin. This faction is fairly large, accounting for a little more than a third of all Aes Sedai.
In Crossroads of Twilight, Elayne starts to ponder about the implications of the unaligned third of Aes Sedai becoming organized. She imagines a steady stream of Aes Sedai passing information to one another from Caemlyn to the Blight.
Cadsuane and the Dragon Reborn
First and foremost among these sisters is Cadsuane Melaidhrin. Cadsuane has, after a rocky start, accepted Rand's offer to be his advisor. Not only was this a wise move to have such an experienced sister on his side, but she leads several other sisters that were unaligned who have important skills and, indeed, some of the unaligned sisters that were seen in Caemlyn were overheard whispering her name and trying to keep that fact hidden.
Sisters who are unaligned
A short (and incomplete) list of those sisters who remain unaligned is as follows. All Red Ajah sisters remained loyal to the White Tower, and all Blue Ajah sisters supported the Rebels (though not all actually joined the Rebels due to the distance) :