There is no illithid subtype.
MINOR RITUALS
Some characters may wish to gain the benefits of a particular
type or subtype of monster, without actually becoming a
specific kind of monster.
Ritual of Association
This minor ritual gives the character a racial subtype or
type modifier ...
I'm unaware of any minor ritual that states explicitly that it changes type and type alone that would fullfill the stated purpose of minor rituals in the first sentence that disribes what a minor ritual is intended to do. I would think that type modifier as stated in the Ritual of Association is changing/modifying the type since I can't find any mention of type modifier in any monster manual.
Also as Illithids have variants (Ulithards, Elder Brains, Urophins, Neothelids, along with the entire Thoon entries in MMV)) this could be seen as subtypes.