  We classify the large $N$ limits of four-dimensional supersymmetric gauge
theories with simple gauge groups that flow to superconformal fixed points. We
restrict ourselves to the ones without a superpotential and with a fixed flavor
symmetry. We find 35 classes in total, with 8 having a dense spectrum of chiral
gauge-invariant operators. The central charges $a$ and $c$ for the dense
theories grow linearly in $N$ in contrast to the $N^2$ growth for the theories
with a sparse spectrum. The difference between the central charges $a-c$ can
have both signs, and it does not vanish in the large $N$ limit for the dense
theories. We find that there can be multiple bands separated by a gap, or a
discrete spectrum above the band. We also find a criterion on the matter
content for the fixed point theory to possess either a dense or sparse
spectrum. We discover a few curious aspects regarding supersymmetric RG flows
and $a$-maximization along the way. For all the theories with the dense
spectrum, the AdS version of the Weak Gravity Conjecture (including the convex
hull condition for the cases with multiple $U(1)$'s) holds for large enough $N$
even though they do not have weakly-coupled gravity duals.
