The superior gluteal artery (gluteal artery) is the largest branch of the internal iliac artery, and appears to be the continuation of the posterior division of that vessel. It is a short artery which runs backward between the lumbosacral trunk and the first sacral nerve, and, passing out of the pelvis above the upper border of the Piriformis, immediately divides into a superficial and a deep branch. Within the pelvis it gives off a few branches to the Iliacus, Piriformis, and Obturator internus, and just previous to quitting that cavity, a nutrient artery which enters the ilium. [WP,unvetted]. [ http://en.wikipedia.org/wiki/Superior_gluteal_artery ]