Trails.com explains that the main muscles used in cycling are the gluteal muscles (gluteus maximus and gluteus minimus), quadriceps, hamstrings, and calf muscles. Other muscles are also used for stability.
Quadriceps, the large muscles on the front of the thigh, are responsible for straightening the leg and pushing the pedal downward during the stroke. The gluteus maximus and gluteus minimus are located in the buttocks and are responsible for the top of the stroke: pushing the pedal forward. The hamstrings are located on the back of the thighs and work with the calf muscles, which are on the back of the lower legs, to lift the pedal up. Trails.com states that muscles in the upper body, such as core and arm muscles, can also be used, depending on the type of bike ride and handlebars.