  Solar flares and coronal mass ejections (CMEs), especially the larger ones,
emanate from active regions (ARs). With the aim to understand the magnetic
properties that govern such flares and eruptions, we systematically survey all
flare events with GOES levels of >=M5.0 within 45 deg from disk center between
May 2010 and April 2016. These criteria lead to a total of 51 flares from 29
ARs, for which we analyze the observational data obtained by the Solar Dynamics
Observatory. More than 80% of the 29 ARs are found to exhibit delta-sunspots
and at least three ARs violate Hale's polarity rule. The flare durations are
approximately proportional to the distance between the two flare ribbons, to
the total magnetic flux inside the ribbons, and to the ribbon area. From our
study, one of the parameters that clearly determine whether a given flare event
is CME-eruptive or not is the ribbon area normalized by the sunspot area, which
may indicate that the structural relationship between the flaring region and
the entire AR controls CME productivity. AR characterization show that even
X-class events do not require delta-sunspots or strong-field, high-gradient
polarity inversion lines. An investigation of historical observational data
suggests the possibility that the largest solar ARs, with magnetic flux of
2x10^23 Mx, might be able to produce "superflares" with energies of order of
10^34 erg. The proportionality between the flare durations and magnetic
energies is consistent with stellar flare observations, suggesting a common
physical background for solar and stellar flares.
