Of the fifteen-hundred or so men enrolled, a faction is loyal to Logain. Taim also has his own faction. The one hundred men who attend his private classes are certainly his and, of these, very many (if not all) are likely Darkfriends. Some Soldiers and Dedicated would also feel loyal to the M’Hael—although Taim’s harsh behavior is unlikely to make him very popular. A large portion of the Soldiers and Dedicated do not have any specific loyalty, and we could assume that they would obey Rand over Taim.
It is also hinted in a Fortelling made by Nicola (a novice for the "rebel" Aes Sedai in Salidar at the time, though she later leaves to become a novice in the tower) that the Asha'man would bring balance to the Aes Sedai. "the Guardians will balance the Servants."
Beyond this system instituted by Rand al'Thor for the training program, however, the field organization of the Asha'man (instituted by Mazrim Taim) is akin to battle units. Modern female Aes Sedai have a very gradual hierarchy based on an individual's strength in the One Power; the Asha'man use a more explicitly militaristic system. However, it should be noted that Soldier, Dedicated, and Asha'man bear similarity to the Aes Sedai ranks of Novice, Accepted, and Aes Sedai, which is in keeping with the commonly repeated theme of the series in which men and women, while having equal-yet-different strengths and weaknesses, differing in their abilities but having a parity with each other. (see Yin and Yang, a common theme of the Wheel of Time.) One other important difference is that Soldiers and Dedicated are expected to serve in the field, being Soldiers ready to fight almost from the moment they can touch the Source. Aes Sedai do not allow Novices and Accepted (except in very rare cases) to go on field assignments, thinking they need to be protected until they are fully trained. Ranks have been created like Tsorovan'm'hael, "storm leader", and the rank below it, Baijan'm'hael, "attack leader"; these ranks have thus far only been confirmed to belong to Asha'man who follow Taim, and have ended up trying to kill Rand. Mazrim Taim himself holds the rank of M'hael, or simply "Leader" in the Old Tongue, and his position seems to combine the roles of Aes Sedai Mistress of Novices and Amyrlin Seat. This seems to be approximately equal to the Amyrlin Seat, but M'hael strongly implies leader of everything, not just the Asha'man. Though it seems more likely that Rand ought to hold that position in truth, since he is the Dragon Reborn, Rand does not have the time to train, and leaves it over to Taim, who is abusing his position to build his own power-base against Rand.
Taim's jealousy over Rand's destiny has led him to subvert commands given by Rand (such as who are to be placed on the Traitor's Tree list for desertion), so it is unclear exactly how much power Rand actually holds with the rank-and-file Asha'man. Those who have served directly under Rand seem to be loyal to him in his position as the Dragon Reborn.
Males who can channel saidin often describe it as a torrential storm of fire and of ice which they must continually fight to maintain control, whereas women are taught to surrender to saidar, and in surrendering to it they gain control over it. In addition, the taint placed on saidin by the Dark One makes their training particularly hazardous, and several Asha'man have already had to be "put to sleep" with poisoned wine due to growing insanity. Rand's instructions to Mazrim Taim were explicit: he needs an army of male channelers to help fight the Last Battle with him. However, he does not have time to train them himself. This seems to be the reason that he continues to allow Taim to train his Asha'man despite growing evidence that Taim has priorities that conflict with Rand's eventual purpose.
From the start Asha'man do all their chores with saidin, even if it takes them much longer than the normal time it would take to do a chore by hand. Although their primary purpose is to learn how to inflict damage with the One Power, all Ashaman learn Healing and, at Rand's instruction, how to use a sword as well as unarmed Aiel martial arts. Should an Asha'man defect, they are hunted down and have their head hung on the Traitor's Tree.
Recently an offer from Rand himself has been accepted by the Salidar Aes Sedai to bond Soldiers and Dedicated to a total of forty seven of their number. However the Red Ajah have also made a truce with the Asha'man, allowing the bonding of Asha'man to members of their Ajah, done by Mazrim Taim without the knowledge of Rand or his most powerful Asha'man ally, Logain Ablar. How these two separate agreements will converge in the future is uncertain.
The last time official rolls were given, the counts were 29 Asha'man, 97 Dedicated, and 322 Soldiers. These numbers are almost certainly low, as there has been a substantial time lapse between this roll call and current events. According to Logain, there are 41 Asha'man by Knife of Dreams, but this may not include those Asha'man outside of the Black Tower. Also in the last chapter the Aes Sedai see some one hundred men with dragon and sword pins when they meet Taim. It is also stated that the Black Tower almost matches the White Tower in numbers, something which has also been hinted at by prophecies spoken during the series.