  The Hermitian part of the dipole-dipole interaction in infinite periodic
arrays of two-level atoms yields an energy band of singly excited states. In
this Letter, we show that a dispersion relation, $\omega_k-\omega_{k_\ex}
\propto (k-k_{\ex})^s$, near the band edge of the infinite system leads to the
existence of subradiant states of finite one-dimensional arrays of $N$ atoms
with decay rates scaling as $N^{-(s+1)}$. This explains the recently discovered
$N^{-3}$ scaling and it leads to the prediction of power law scaling with
higher power for special values of the lattice period. For the quantum optical
implementation of the Su-Schrieffer-Heeger (SSH) topological model in a
dimerized emitter array, the band-gap-closing inherent to topological
transitions changes the value of $s$ in the dispersion relation and alters the
decay rates of the subradiant states by many orders of magnitude.
