Different internet resources suggest Hastur (see also: The Yellow Site Wikia, Cthulhu Wiki)is an enemy, @Hypnosifl notes, I believe correctly that Lovecraft established no such relationship in his own work.
Rather, that rivalry was suggested by August Derleth, in his "Cthulhu Mythos" stories, published after Lovecraft's death. And many take issue with Derleth's interpretations, from what I've read, as he portrays the Cthulhu as predominately evil, where as Lovecraft's own text seemingly suggests the Cthulu and other Old Ones are in fact chaotic neutrals and not explicitly "evil" in a human sense, even if deathly destructive...
See Castro's speech (from Lovecraft's "The Call of Cthulhu":
Then the liberated Old Ones would teach them new ways to shout and kill and revel and enjoy themselves, and all the earth would flame with a holocaust of ecstasy and freedom.
Given the potentially problematic nature of the expanded canon, I want to examine just the original Lovecraft-authored mythos.
Lovecraft clearly depicts the Cthulhu as a supremely destructive and powerful entity. And that in turn suggests it likely has some known enemies. Were any discussed?