The possibility of a subharmonic-resonance triad in the transition process for a flat-plate boundary layer at Mach three was demonstrated using Direct Numerical Simulations (DNS). The parameters controlling such a resonance triad were investigated in detail. Finally, the interaction of this triad with the so-called 'oblique breakdown' scenario was studied. To this end, the mechanisms were invoked separately and in combination. By itself the oblique breakdown leads to a faster growth of instability waves than the subharmonic resonance. However, in a combination with a subharmonic-resonance triad, the dominant modes of the oblique breakdown experience a slower growth, whereas those of the subharmonic resonance are more amplified. Overall, the interaction promotes transition and the rise in skin friction and the drop in shape factor are moved upstream when compared to the oblique breakdown.