The gluteus maximus is an underactive muscle if you have Kyphotic Lordotic Posture (rounding in the front of the shoulders and an anterior tilt in your pelvic position). The reason for this anterior tilt (which causes a noticeable arch in the low back), is the overactivity of the psoas and quads and under-activity of the abdominal muscles.
How to train the glut max with Lordosis?
The most important thing for a Lordotic client to remember to do when executing glut max exercises is to work in either a neutral or posteriorly tilted pelvis (tucked under). This will allow the psoas and quads to release so the gluts can fire. I preferred a posterior tilt when I first began training my gluts with Lordosis. But, after years and more awareness of the internal lift in my pelvic floor muscles (TVA), I have found that training them with a neutral pelvis, which I strive to maintain in my day to day life, is preferable.
In regards to strength work for your glut max, my suggestion would be 3-4x a week. Select three different exercises for this muscle group. Spend one minute doing unilateral (single leg work) on your non-dominant leg, and then one minute using both legs for each exercise. Repeat this unilateral and double leg glut max work for 2 to 3 sets. A set is one minute or 8-12 slow reps.
Take your time.
Inhale to prepare and exhale on the effort, pulling your belly button in towards your spine and lifting in and up on your pelvic floor muscles (the muscles that stop your stream of pee) to contract your transverse abdominis (the deepest layer of your core) to protect your lower back.