Well ... yeah. "Immoral and amoral god"* sounds a lot like the definition I was using for "Cthulhu", in fact.
*(as opposed to capital-G-God)
That seems to cheapen Cthulhu, to be honest. The emotional impact of Lovecraft's stories, and of their descendants such as the Azathoth metaphor, relies not on an immoral or amoral Power (that's well-trod territory in many religions and not a few fantasies) but rather on Powers with motivations fundamentally incompatible with human minds: entities of godlike potency that can neither be mollified nor bargained with nor easily apprehended in native reasoning modes.
That doesn't describe the occupants of any historical mythology I can think of, at least not i...
Happy New Year! Here's the latest and greatest installment of rationality quotes. Remember: