The solar flare is a sudden eruptive solar phenomenon with significant enhancements in solar X-ray and Extreme Ultraviolet radiations, resulting in large amounts of energy being injected into the planetary atmosphere. Case studies have been extensively presented to analyze the effect of extremely large flares on the Martian upper atmosphere, but the general features of the Martian thermospheric response to flares are still poorly understood. In this work, we select 12 intense solar flares that occurred between 2015 and 2017 and investigate the densities and compositional variations of the dayside Martian thermosphere to these flares with the aid of the measurements made by the Mars Atmosphere and Volatile EvolutioN. The statistical studies indicate that the responses of the Martian thermosphere to flares are complicated that both the class of the flare and the wavelength of the enhanced radiation may have prominent influences on the thermal expansion of the atmosphere and the atmospheric photochemical reactions.