superior gluteal artery
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].