John Tynes, in his article on the subject in the roleplaying game Call of Cthulhu D20, laid out a structure of the Mythos which attempts to envision it from the point of view of a cultist. It centers on four of the gods:
Azathoth - god of entropy, change, chaos.
Shub-Niggurath - goddess of procreation and the creative urge, unrestrained growth.
Yog-Sothoth - god of time and probably space.
Nyarlathotep - Tynes seems unsure of the place of this god, whether he is the creation of the other Outer Gods or a parasite on their existence. The present author is of the opinion that, in this scheme, he represents the interaction of consciousness with the stochastic universe represented by the other Outer Gods.
In addition to these Outer Gods, Tynes sees the Great Old Ones in a role similar to that of angels in more traditional mythologies. Cthulhu is the angel of dreams and nightmares, Hastur the angel of decay and corruption, and so forth. He goes into some detail regarding Hastur in Delta Green: Countdown (a roleplaying supplement expanding on the Delta Green modern-day setting), tying him in with the King in Yellow and Carcosa of Robert Chambers.