In frontal zones, water masses that are tens of kilometers in extent with origins in the mixed layer can be identified in the pycnocline for days to months. Here, we explore the pathways and mechanisms of subduction, the process by which water from the surface mixed layer makes its way into the pycnocline, using a submesoscale-resolving numerical model of a mesoscale front. By identifying Lagrangian trajectories of water parcels that exit the mixed layer, we study the evolution of dynamical properties from a statistical standpoint. Velocity and buoyancy gradients increase as water parcels experience both mesoscale (geostrophic) and submesoscale (ageostrophic) frontogenesis and subduct beneath the mixed layer into the stratified pycnocline along isopycnals that outcrop in the mixed layer. Subduction is transient and occurs in coherent regions along the front, the spatial and temporal scales of which set the scales of the subducted water masses in the pycnocline. As a result, the tracer-derived vertical transport rate spectrum is flatter than the vertical velocity spectrum. An examination of specific subduction events reveals a range of submesoscale features that support subduction. Contrary to the forced submesoscale processes that sequester low potential vorticity (PV) anomalies in the interior, we find that PV can be elevated in subducting water masses. The rate of subduction is of similar magnitude to previous studies (~100 m/year), but the pathways that are unraveled in this study along with the Lagrangian evolution of properties on water parcels, emphasize the role of submesoscale dynamics coupled with mesoscale frontogenesis.