Cthylla is an offspring of Cthulhu and Idy-haa. She is the daughter of Cthulhu, and is critical to his plans, as should Cthulhu somehow die, Cthylla will give birth to him once again. As such, she is guarded by Deep Ones and Yuggya, in what can be assumed to be R'lyeh, as she was at first from the star Xoth, but came to Earth.
