This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
The Glutaeal Artery is the largest branch of the internal iliac. It arises far back in the pelvis, opposite the lower part of the sacro-iliac symphysis, and immediately passes backwards between the lumbo-sacral nerve which afterwards lies in front of it, and first sacral nerve which lies behind it; and above the pyriform muscle, in order to escape from the pelvis, by- passing through the upper part of the great sacro-sciatic notch. While within the pelvis, it gives off some small branches to the pyriform muscle, to the rectum, and to the areolar tissue. After this very short course, in which it is accompanied by the superior glutaeal nerve, it divides opposite the posterior margin of the glutaeus minimus muscle, between it and the pyriformis, and under cover of the glutaeus maximus, into a superficial and a deep branch.
The superficial branch ascends between the glutaeus maximus and medius, and divides into numerous lesser branches, some of which supply these muscles and the great sacro-sciatic ligament; while others are distributed to the sacro-lumbalis muscle and the integuments: some of these branches communicate with the sciatic artery.
The deep branch takes a direction obliquely upwards and forwards between the glutaeus medius and minimus muscles. After giving a small nutritious artery to the ilium, it divides into two lesser branches; the superior of which follows accurately the middle curved line upon the bone, which marks the upper margin of the glutaeus minimus. This branch supplies, in its course, the last-mentioned muscle and the glutaeus medius, and having arrived at the anterior superior spine of the ilium, it anastomoses with the ilio-lumbar, circumflexa ilii, and external circumflexa femoris arteries. The inferior branch runs downwards and forwards between the two lesser glutaei muscles, which receive many branches from it, and having arrived at the great trochanter, supplies the pyriformis muscle and capsule of the hip-joint, and communicates with branches of the sciatic and internal circumflexa femoris arteries.