Seated on side-ribs
The current refereeing rules give two examples of invalid pins. One where tori is controlling uke by sitting on their side with legs under their body:
This kind of osaekomi-waza is not valid and the referee must call mate if there is no progression in the action.
Kesa-like holds without arm
They provide a further three examples where tori has their arm wrapped solely around uke's neck, which in addition to being non-standard will incur mate immediately (to prevent situations where uke may endanger their neck):
This kind of osaekomi-waza is not valid and the referee must call mate immediately.
It is never allowed to hold an osaekomi just around the head/neck without control of at least one arm.
There is also the crucifix hold, which as far as I'm aware does not come under any of the official Kodokan pin groupings:
Note: the Kodokan used to designate the collar choke executed from this position as jigoku-jime, but I believe it is now officially considered a variant of okuri-eri-jime.
Visually distinct but classified pins
Note that the Kodokan classifies the pin sankaku-gatame as a variant of kuzure-kami-shihi-gatame.
Higher quality images taken from: Explanatory guide of the judo refereeing rules 9 March 2018 (Referee Commission) (p.25).