There's also this to consider;
Unbeknownst to many surface-dwellers, the dreaded mind flayers are devoutly religious beings. Unlike the atheistic aboleths, illithids give constant thought to their gods and both fear and honor their race’s clerics. These are the three known deities worshiped by mind flayers.

ILSENSINE
The God-Brain
Deity of illithids, mental domination, and psychic magic
Alignment: Lawful evil
Domains: Evil, Law, Knowledge, Magic, Trickery
Subdomains: Deception, Discipline, Divine, Slavery, Thought
Favored Weapon: Unarmed strike or tentacle

The mind flayers themselves do not know if Ilsensine is their creator or if he merely “adopted” them, but regardless the God-Brain epitomizes everything the illithids strive to be: pure thought, unfettered from physical constraints and bent on the domination of all minds in creation. Almost all illithids venerate Ilsensine, though outright worship is uncommon: to most illithids, Ilsensine is an ideal to strive for, not a cause to dedicate onesself to. Most mind flayer cities, cells, or ships contain a shrine to Ilsensine. The rare temples of the God-Brain are complex networks of curving halls patterned after the tangled gray matter of a humanoid brain. Its unholy symbol is an illithid’s head grasping the world in its tentacles.

Ilsensine’s priesthood is small and secretive, and many cults contain more psychics than clerics. Priests of Ilsensine are respected but not envied, because they forgo the honor of joining with their community’s elder brain upon death, instead allowing their spirits to join Ilsensine in his otherworldly realm, the Caverns of Thought on the Astral Plane. Ilsensine’s priesthood is devoted to archiving the history and knowledge of the illithids, as well as honing their mental powers to their utmost potential. Their ability to control the undead (which are immune to most telepathic attacks) makes them feared by other illithids.

On rare occasions, cults of Ilsensine crop up among human psychics. These deviant cults seek to emulate mind flayers, sometimes even cannibalizing other humans’ brains, and are often led by an illithid cleric.

Ilsensine is a being of pure mental energy with no real form, but when it deigns to communicate with its followers, it projects the form of a massive green brain with thousands of ganglia trailing off into the distance.

MAANZECORIAN
The Keeper
Deity of knowledge and secrets
Alignment: Lawful evil
Domains: Darkness, Evil, Knowledge, Law, Rune
Subdomains: Devil, Language, Loss, Memory, Thought
Favored Weapon: Quarterstaff

Unlike Ilsensine, Maanzecorian’s origin is known to all mind flayers. Once the greatest psychic ever to rise in the primordial Illithid Empire, Maanzecorian ascended to godhood with Ilsensine’s sponsorship and has served as the God-Brain’s loyal advisor ever since. Maanzecorian is deferential to Ilsensine, and his priesthood, though smaller, is given equal respect in illithid culture. His unholy symbol is a silver crown set with a red gem.

Maanzecorian is a god of philosophy and secrets, concerned with the pursuit and exploitation of knowledge. His priesthood, consisting almost equally of clerics, psychics, and occultists, believes that other races may possess knowledge of use to mind flayers, and may even diplomatically approach non-illithids for exchanges of information; however, they still see other beings as potential slaves or food, and quickly betray their allies when they are no longer of use. As a god of secrets, a rare few illithid wizards and sorcerers, heretics among the rest of their kind, pray to Maanzecorian to conceal their activities and grant them deeper arcane knowledge.

Maanzecorian appears as a towering ulitharid with greenish skin and yellowed tusks on either side of his eight tentacles, a silver crown with a blinding red gem levitating above his head.

THOON
All
Deity of constructs and quintessence
Alignment: Neutral evil
Domains: Artifice, Evil, Madness, Void, War
Subdomains: Blood, Construct, Dark Tapestry, Insanity, Toil
Favored Weapon: Heavy flail

Mind flayers are known to cross the vast gulfs of the Dark Tapestry in their nautiloid ships, and it was on one such excursion through interstellar space that a fleet of illithids on a mission of exploration came in contact with the unspeakable force they named Thoon. These illithids returned (or were sent back) warped in mind and body, fanatically devoted to the worship of Thoon, which they described alternately as either a god or philosophy. When questioned, they answer only that “Thoon is Thoon, and Thoon is all.” Thoon’s priests claim to receive mental instructions from this mysterious force, but whether Thoon truly speaks to them or they are simply mad, few can say. The fact that Thoon’s clerics receive power from this alien source, however, is not in doubt.

Using their strange visions and mental instructions, the mind flayers of Thoon animate horrific constructs and travel the planets and planes in search of a substance they call quintessence, a life-giving energy radiated by a rare few living beings. Not all creatures of the same race contain quintessence, but the illithids’ constructs are designed to sense it within them. Once detected and secured, the quintessence is extracted, killing the victim and preventing it from returning from the dead with any spell less than true resurrection. The quintessence, distilled into a glowing green fluid, is then used to power more Thoon constructs.

The mind flayers of Thoon terrify other illithids, who see the Thoon flayers as heretics against Ilsensine and fear the spread of their alien philosophy. The illithids of Thoon seek to spread their faith by the sword, destroying the elder brains of other illithid communities and subverting its tadpoles, and the sight of heavily-armored clerics of Thoon sends an illithid community into an uproar as they scramble to destroy the interlopers.

The true nature of Thoon is unknown. The few human scholars who know of it guess that it may be a heretofore unknown Outer God, akin to Azathoth and Nyarlathotep, but this is only crude supposition. Its unholy symbol is a simple green metallic disc.