  We study the superradiant evolution of a set of $N$ two-level systems
spontaneously radiating under the effect of phase-breaking mechanisms. We
investigate the dynamics generated by non-radiative losses and pure dephasing,
and their interplay with spontaneous emission. Our results show that in the
parameter region relevant to many solid-state cavity quantum electrodynamics
experiments, even with a dephasing rate much faster than the radiative lifetime
of a single two-level system, a sub-optimal collective superfluorescent burst
is still observable. We also apply our theory to the dilute excitation regime,
often used to describe optical excitations in solid-state systems. In this
regime, excitations can be described in terms of bright and dark bosonic
quasiparticles. We show how the effect of dephasing and losses in this regime
translates into inter-mode scattering rates and quasiparticle lifetimes.
