Strong coupling between light and matter is possible with a variety of organic materials. In contrast to the simpler inorganic case, organic materials often have a complicated spectrum, with vibrationally dressed electronic transitions. Strong coupling to light competes with this vibrational dressing and, if strong enough, can suppress the entanglement between electronic and vibrational degrees of freedom. By exploiting symmetries, we can perform exact numerical diagonalization to find the polaritonic states for intermediate numbers of molecules and use these to define and validate accurate expressions for the lower polariton states and strong-coupling spectrum in the thermodynamic limit. Using this approach, we find that vibrational decoupling occurs as a sharp transition above a critical matter–light coupling strength. We also demonstrate how the polariton spectrum evolves with the number of molecules, recovering classical linear optics results only at large N.