There appears to be an increasing number of articles that deal with strengthening the glutes. In each of them there is little to no distinction made between the three “gluteus” muscles: gluteus maximus, gluteus medius and gluteus minimus. It is assumed that all glute exercises involve these three muscles and develop them equally.
For example, in one article the best exercise to develop the glutes was the side lying leg raise. However, this exercise is effective only for developing the gluteus medius and partially, the gluteus minimus. Surprisingly, the source given for this information was from a reportedly reputable source.
In regard to the gluteus muscles it should be noted that the gluteus maximus is the largest and most powerful of the three muscles. It is primarily involved in hip joint extension, the act of bringing the thigh from a hip flexed position to the anatomical position.
The hip flexors and the ligaments that cross the front of the hip joint do not allow the leg to go behind the pelvis from the anatomical position. In order to get the leg to go behind the body the pelvic girdle must rotate forward. This is visible by and arching of the lower back.
The gluteus maximus is also involved in hip joint outward rotation which is usually seen in rotation of the leg to the outside. The lowermost fibers of this muscle assist in hip joint abduction while the uppermost fibers assist in hip joint adduction. For the most part they are weak in these actions and the main load falls on the other gluteus muscles.
Because of the diverse actions of these three muscles there is no one exercise that will strengthen all of these muscles in one movement. Understand that because a muscle is activated as a stabilizer to maintain joint integrity, it does not mean that this muscle is undergoing the same type of contraction.
To strengthen any one of the gluteus muscles the muscle must be used in a movement in which it is actively involved. When a muscle only acts as a stabilizer, it undergoes an isometric contraction, not a concentric contraction which will bring about the most gains in dynamic strength. Isometric strength only develops strength at a specific point in the range of motion in which you hold the movement.
For more information on the role and function of the gluteus and other muscles see Biomechanics and Kinesiology of Exercise.