We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $\ensuremath{\gamma}$ and ${\ensuremath{\gamma}}_{0}$ and a single parameter ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for
N=2 atoms, numerically for up to 30 atoms, and obtain the large-
N limit by a mean-field approach. We find that there is a critical difference ${\ensuremath{\gamma}}_{0}\ensuremath{-}\ensuremath{\gamma}$ that depends on
N beyond which superradiance is lost. We show that exact nontrivial dark states (i.e., states other than the ground state with vanishing spontaneous emission) only exist for $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$ and that those states (dark when $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$) are subradiant when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{0}$.
We derive a Markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states, and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion.