Distance runners need to have strong glutes and a strong core. Your sport requires you to be moving for hours and the repetition with each time your foot contacts the ground requires strengthening to be able to sustain the volume to continue to push on.
Common injuries in running tend to be ankle, knee, hip or low back pain.
To be able to prevent the onset of these injuries, you need to make sure you have strong muscles that are able to stabilize the joints as well.

Core exercises are important for everything you do, especially for runners. As you are out and moving for long periods of time, you need to have a strong core to be able to stabilize your pelvis when you run so you don't compensate and move your low back instead. All the motion should be the femur, or thigh bone, moving on the hip bone.
There is a theory called lower cross syndrome. We spend a lot of time at our jobs or in school hitting, so our hip flexors, the muscles in front of the hip, are shorter and weaker because we don't use it as much. This muscle tends to pull our pelvis forward putting stress on the back. Focusing on strengthening the core and lengthening the hip flexors can help reduce strain on the back. Planks and dead bugs are my 2 favorite exercises to engage the core. Not just a crunch, working the rectus abdominis, or the 6 pack muscle, but the whole core that includes the transverse abdominis, wrapping around the whole trunk, the diaphragm and the pelvic floor.
Balance is another great concept for runners. Balancing on one foot helps the muscles work to stabilize at the foot, ankle, knee, hip and back. When running you're always on one foot and all the muscles in your leg need to support you. Balance training can help prevent injuries and engage and strengthen all the right muscles. Single leg balance and banded runners are 2 great options for this.

Banded runners is also a great exercise to strengthen your hip flexors. When running long distances i tend to feel the front of my hips are weak. especially since they're inactive all day when I sit at work. This is a great sport specific exercise that helps me strengthen the hip flexor, like im running, and also focus on stability.

The final 4 exercises, band walks, monster walks, side lying leg raises and clam shells all help work on the gluteus medius, the stabilizing muscle on the side of your hip. These muscles help make sure that when you're balanced on one foot, the opposite hip does not drop due to weakness. If this muscle is weak and your hip were to drop when running, you would lose efficiency and further injuries could continue to develop. This muscle also helps with tracking at the knee. As it works to stabilizes the hip, it keeps the femur straight during all its activities so that the knees are straight too. If the glute is weak, the knee tends to collapse in leading to injuries like knee pain and patella femoral syndrome. This causes a lot of pain for runners and these 4 exercises help strengthen and control the gluteus Medius to prevent that.
Take a look at the image demos below.