  We investigate how the different types of supernovae are relatively affected
by the metallicity of their host galaxy. We match the SAI Supernova Catalog to
the SDSS-DR4 catalog of star-forming galaxies with measured metallicities.
These supernova host galaxies span a range of oxygen abundance from 12 +
log(O/H) = 7.9 to 9.3 (~ 0.1 to 2.7 solar) and a range in absolute magnitude
from MB = -15.2 to -22.2. To reduce the various observational biases, we select
a subsample of well-characterized supernovae in the redshift range from 0.01 to
0.04, which leaves us with 58 SN II, 19 Ib/c, and 38 Ia. We find strong
evidence that SN Ib/c are occurring in higher-metallicity host galaxies than SN
II, while we see no effect for SN Ia relative to SN II. We note some extreme
and interesting supernova-host pairs, including the metal-poor (~ 1/4 solar)
host of the recent SN Ia 2007bk, where the supernova was found well outside of
this dwarf galaxy. To extend the luminosity range of supernova hosts to even
fainter galaxies, we also match all the historical supernovae with z < 0.3 to
the SDSS-DR6 sky images, resulting in 1225 matches. This allows us to identify
some even more extreme cases, such as the recent SN Ic 2007bg, where the likely
host of this hypernova-like event has an absolute magnitude MB ~ -12, making it
one of the least-luminous supernova hosts ever observed. This low-luminosity
host is certain to be very metal poor (~ 1/20 solar), and therefore this
supernova is an excellent candidate for association with an off-axis GRB. The
two catalogs that we have constructed are available online and will be updated
regularly. Finally, we discuss various implications of our findings for
understanding supernova progenitors and their host galaxies.
