Type Ia supernovae are bright stellar explosions thought to occur when a thermonuclear runaway consumes roughly a solar mass of degenerate stellar material. These events produce and disseminate iron-peak elements, and properties of their light curves allow for standardization and subsequent use as cosmological distance indicators. The explosion mechanism of these events remains, however, only partially understood. Many models posit the explosion beginning with a deflagration born near the center of a white dwarf that has gained mass from a stellar companion. In order to match observations, models of this single-degenerate scenario typically invoke a subsequent transition of the (subsonic) deflagration to a (supersonic) detonation that rapidly consumes the star. We present an investigation into the systematics of thermonuclear supernovae assuming this paradigm. We utilize a statistical framework for a controlled study of two-dimensional simulations of these events from randomized initial conditions. We investigate the effect of the composition and thermal history of the progenitor on the radioactive yield, and thus brightness, of an event. Our results offer an explanation for some observed trends of mean brightness with properties of the host galaxy.