The Hayward fault in California's San Francisco Bay area produces large earthquakes, with the last occurring in 1868. We examine how physics-based dynamic rupture modeling can be used to numerically simulate large earthquakes on not only the Hayward fault, but also its connected companions to the north and south, the Rodgers Creek and Calaveras faults. Equipped with a wealth of images of this fault system, including those of its 3D geology and 3D geometry, in addition to inferences about its interseismic creep-rate pattern and rock-friction behavior, we use a finite-element computer code to perform 3D dynamic earthquake rupture simulations. We find that the rock properties affect the locations and amount of slip produced in our simulated large earthquakes. Crucial factors that control rupture behavior in our modeling are the earthquake nucleation locations, the fault geometry, and the data that reveal where the fault system is creeping or locked. Our findings suggest that large Rodgers Creek-Hayward-Calaveras-Northern Calaveras (RC-H-C-NC) fault-system earthquakes may result from dynamic rupture that starts in a locked part of the fault system, but is then stopped by the creeping parts, leading to high-magnitude-6 earthquakes; or, from dynamic rupture that starts in a locked part of the fault system, then cascades through some of the creeping parts, leading to magnitude-7 earthquakes.