The 5E Monster Manual says the following about mind flayers (p. 221):
Solitary mind flayers are likely rogues and outcasts.
Also specific to 5E, Volo's Guide to Monsters has a lengthy section on Mind Flayers on p. 71-81.
Here's a little snippet:
It is convenient for humanoids to understand a mind flayer colony by thinking of it as a single individual — the elder brain — directing a number of subservient, remote minds, which are the individual mind flayers.
And here's another one:
Rarely, the process of ceremorphosis yields an ulitharid, a more powerful mind flayer that isn’t beholden to the elder brain’s whims. . . . Eventually, if the colony grows to sufficient size, the ulitharid strikes out on its own. Half the mind flayers and thralls in the colony undertake a great migration, seeking a new lair at least 100 miles away from the old one. Once the ulitharid finds a suitable spot, its followers construct a new lair while it transforms into an elder brain.
There is some varying information on solitary mind flayers. Volo's also says:
An illithid can be part of its colony’s network of minds only while it is within five miles of the elder brain. Beyond that distance, it is on its own. Mind flayers that venture away from the colony do so only under strict orders from the elder brain.
So, to answer your question, illithids are usually found in groups, and a single one is a rarity. A single one might be a rogue or outcast, or might be on a mission directed by its elder brain.