  We study the indivisible intervals and the monotonicity of the growth of the
exponential type in the chains of de Branges subspaces in terms of the spectral
measure. We prove that for spectral measures supported on $\mathbb Z$, there
exist at most two subspaces of the same type, which then bound an indivisible
interval. Furthermore, in this case, we study possible locations of the
indivisible intervals.
