  Galaxies are generally found to follow a relation between their size and
luminosity, such that luminous galaxies typically have large sizes. The recent
identification of a significant population of galaxies with large sizes but low
luminosities ("ultra diffuse galaxies", or UDGs) raises the question whether
the inverse is also true, that is, whether large galaxies typically have high
luminosities. Here we address this question by studying a size-limited sample
of galaxies in the Coma cluster. We select red cluster galaxies with sizes
$r_{\mathrm{eff}} > 2 \ \mathrm{kpc}$ down to $M_{g} \sim -13 \ \mathrm{mag}$
in an area of $9 \ \mathrm{deg}^2$, using carefully-filtered CFHT images. The
sample is complete to a central surface brightness of $\mu_{g,0}\approx 25.0 \
\mathrm{mag\,arcsec}^{-2}$ and includes 90% of Dragonfly-discovered UDGs
brighter than this limit. Unexpectedly, we find that red, large galaxies have a
fairly uniform distribution in the size-luminosity plane: there is no peak at
the absolute magnitude implied by the canonical size-luminosity relation. The
number of galaxies within $\pm 0.5$ magnitudes of the canonical peak ($M_g =
-19.69$ for $2<r_{\mathrm{eff}}<3$ kpc) is a factor of $\sim 9$ smaller than
the number of fainter galaxies with $-19<M_g<-13$. Large, faint galaxies such
as UDGs are far more common than large galaxies that are on the size-luminosity
relation. An implication is that, for large galaxies, size is not an indicator
of halo mass. Finally, we show that the structure of faint large galaxies is
different from that of bright large galaxies: at fixed large size, the S\'ersic
index decreases with magnitude following the relation $\log_{10} n \approx
-0.067M_g-0.989$.
