  Until now, how the magnetic fields in M/X-class flaring active regions (ARs)
differ from C-class flaring ARs remains unclear. Here, we calculate the key
magnetic field parameters within the area of high photospheric free energy
density (HED region) for 323 ARs (217 C- and 106 M$/$X-flaring ARs), including
total photospheric free magnetic energy density E$_{free}$, total unsigned
magnetic flux $\Phi$$_{HED}$, mean unsigned current helicity h$_{c}$, length of
the polarity inversion lines $L$$_{PIL}$ with a steep horizontal magnetic
gradient, etc., and compare these with flare/coronal mass ejection (CME)
properties. We first show the quantitative relations among the flare intensity,
the eruptive character and $\Phi$$_{HED}$. We reveal that $\Phi$$_{HED}$ is a
measure for the GOES flux upper limit of the flares in a given region. For a
given $\Phi$$_{HED}$, there exists the lower limit of F$_\mathrm{SXR}$ for
eruptive flares. This means that only the relatively strong flares with the
large fraction of energy release compared to the total free energy are likely
to generate a CME. We also find that the combinations of E$_{free}$-$L$$_{PIL}$
and E$_{free}$-h$_{c}$ present a good ability to distinguish between C-class
and M$/$X-class flaring ARs. Using determined critical values of E$_{free}$ and
$L$$_{PIL}$, one predicts correctly 93 out of 106 M/X-class flaring ARs and
159/217 C-class flaring ARs. The large $L$$_{PIL}$ or h$_{c}$ for M$/$X-class
flaring ARs probably implies the presence of a compact current with twisted
magnetic fields winding about it.
