Leaders
Tier Harribel
and her Faccion
Cyan Sung-Sun, Emilou Apache & Franceska Mila Rose
Numeros
The Números are the combat specialists in Harribel's army of Arrancar. The Números are assigned a two digit number at birth from 11 to 99 to indicate their age (Número 11 is the oldest, Número 99 is the youngest). The basic Número uniform consists of a white-collared jacket and robes held with a black sash. However, the uniform is customizable, giving each Número a sense of individuality. The fighting ability of the Números is thought to be superior to all other arrancar, except for the Espada (current and former). The strongest Números are chosen by the Espada to become their Fracción.
Exequais
The Exequias are Arrancar that form an execution division in Sōsuke Aizen's army of Arrancar. They are responsible for dealing with rebels and intruders in Las Noches, usually terminating both hence their name. They appear to be the Arrancar equivalent of Soul Society's Onmitsukidō. Since Aizen's defeat they report to Tier.
The Espada, much like with the Números, seem to have a level of control over the Exequias: Szayel Aporro Granz ordered them to kill the intruders and retrieve the bodies of their defeated opponents, though how much control they have is uncertain. After being summoned by Szayel, the Exequias proceeded to act under Rudobōn's command.
Rudobōn reveals to Rukia that the special ability of his Zanpakutō, Arbol, allows him to create the underlings who are seen following him. This explains why they all have identical masks and Zanpakutō. Technically, Rudobōn is the sole member of the Exequias, with the other members merely being his creations with no individuality seen thus far.
The uniform of the Exequias is the custom white jacket and hakama worn by all Arrancar in Harribel's army. All Exequias however have the same skull-like mask. Rudobōn's seniority is reflected in the different mask he wears compared to the human like skulls of his subordinates.
List Of Exequais
N/A
Privarion
The Privaron Espada are former Espada who have officially lost their rank and are assigned a three-digit number. Being former Espada, they are far stronger than the normal Números. They reside in Tres Cifras, which translates literally from Spanish as "Three Digits". As mentioned by Dordonii, these former "naturally created" Espada were rendered obsolete after Aizen began artificially creating Arrancar to meet his own standards.
List Of Privarions
107th: Gantenbainne Mosqueda
Espada
The Espada are the top-ranked Arrancar in Harribel's army of Hollow-Shinigami hybrids, are the most powerful Hollows under Harribel's command, and are the main rivals of the Gotei 13. Despite their late appearance into the plot, the Espada are often considered to be the primary antagonists of Bleach, particularly during the second 1/3rd of the series, being responsible for much of the conflict that has transpired within the series' continuity.
The Espada are regarded as the most powerful Arrancar in existence. At any given time, the Espada has a nominal composition of ten members, all hand-picked and ranked by Harribel herself now. Along with Tier and her Faccion, the Espada as a group possess comparable strength to Soul Society's Gotei 13 Shinigami captains.
Each Espada member is chosen for their superior combat ability and then assigned a number from 1 to 10 (1 presumably being the strongest) that indicates their rank and relative power level, which is tattooed somewhere on their body. For instance, Grimmjow Jaegerjaquez's is located on the mid-back area and Coyote Starrk's is on the back of his left hand.
The Espada are given free control over the Números and may choose as many of them as they like to become their Fracción. Similar to the power gap between captains and lieutenants in the Gotei 13, the strength of the Espada far surpasses that of the average Número. Aizen himself is confident enough of his Espada's abilities to send them out on potentially hazardous missions, such as gathering information in the real world, fighting Shinigami captains inside Las Noches and Karakura Town by themselves, and gathering the Vasto Lorde for the cause.
Being Harribel's most direct subordinates (not counting Sung-Sun, Apache and Mila Rose), the Espada are privy to Harribel's plans and most intimate secrets. Harribel's respect for the Espada's abilities is reflected on her manner of addressing them, often referring to them as "my dear" and "Espada" and sits at the head of the same table with them, while discussing the events around Hueco Mundo. Harribel treats them as equals.
Their immense amount of power and leadership status among the Arrancar also grants each Espada the authority to exert command over Harribel's other forces within Las Noches: the Números, the Exequias, and their own Fracción. There seems to be a sort of hierarchy among the Espada; a higher-ranked member apparently can give orders to lower-ranked members. This is demonstrated when Aizen orders Ulquiorra Cifer to kidnap Orihime Inoue; the Arrancar led by Ulquiorra included Luppi (the then-sixth Espada), Yammy Rialgo (the tenth/zero), Grimmjow Jaegerjaquez, and Wonderweiss Margera (unassigned). Various missions usually involve one or more Espada operating together, with the most senior member exercising command over the others; typicaly, non-combat missions, such as searching for the Vasto Lorde and gathering pre-invasion data in the Human world, include a senior Espada and a lower-ranked one being sent out in pairs. While the lower-ranked members usually have little restraint in taking their own initiative (thus exceeding their orders), higher-ranked members usually stick to Harribel's commands, and are often the first to bail the others out of trouble, because in Nelliel Tu Oderschvank's own words, they wish to, "prevent the Espada from losing one of their own." However, Harribel's attitude toward the offending Espada members seem to be one of leniency, officially forgiving them (though not without severe sanctions).
Aside from regularly appearing in Harribel's throne and debriefing room, the Espada are known to have their own quarters within Las Noches; those that have been seen appear to have been modified to suit the specific Espada's taste. Szayel Aporro Granz, for instance, possesses a large building that he refers to as his "palace," complete with a hidden, indestructible laboratory and a changing room; Zommari Leroux has been shown on one occasion to await orders inside a meditation room; Coyote Starrk's room is designed along the lines of a lounging chamber and Aaroniero Arruruerie's tower, accessed via a hanging bridge, effectively keeps out sunlight and contains nooks and crannies for hiding cushions and other implements whose purpose is to make his shape-shifting abilities more convincing.
As Aaroniero Arruruerie notes, all of the Espada, except for himself, were AT LEAST Adjuchas-class Menos before becoming Arrancar.
According to Ulquiorra, any Espada ranked 4th or higher are not allowed to release their Zanpakutō within Harribel's palace, as their Resurrección's released powers are enough to destroy the majority of Las Noches.
Most recently, Yammy Rialgo stated that the Espada are not assigned numbers from 1 to 10, but rather, 0 to 9.
List Of Espada
Cero Espada (Zero Espada, Sacrifice) - Tier Harribel
Fracción - Sun-Sun, Apache, Mila Rose
Primeria Espada (First Espada, Loneliness) - Vacant
Fracción - N/A
Segunda Espada (Second Espada, Despair) - Vacant
Fracción - N/A
Espada Tres (Third Espada, Rage) - Vacant
Fracción - N/A
Espada Cuatro (Forth Espada, ???) - Vacant
Fracción - N/A
Quinto Espada (Fifth Espada, ???) - Vacant
Fracción - N/A
Sexta Espada (Sixth Espada, ???) - Grimmjow Jaegerjaquez
Fracción - N/A
Septima Espada (Seventh Espada, ???) - Vacant
Fracción - N/A
Octava Espada (Eighth Espada, ???) - Vacant
Fracción - N/A
Noveno Espada (Ninth Espada, ???) - Vacant
Fracción - N/A