Populations of cortical neurons flexibly perform different functions; for the primary motor cortex (M1) this means a rich repertoire of motor behaviors. We investigate the flexibility of M1 movement control by analyzing neural population activity during a variety of skilled wrist and reach-to-grasp tasks. We compare across tasks the neural modes that capture dominant neural covariance patterns during each task. While each task requires different patterns of muscle and single unit activity, we find unexpected similarities at the neural population level: the structure and activity of the neural modes is largely preserved across tasks. Furthermore, we find two sets of neural modes with task-independent activity that capture, respectively, generic temporal features of the set of tasks and a task-independent mapping onto muscle activity. This system of flexibly combined, well-preserved neural modes may underlie the ability of M1 to learn and generate a wide-ranging behavioral repertoire.