A clear transition feature of galaxy quenching is identified in the multi-parameter space of stellar mass ($M_*$), bulge to total mass ratio ($B/T_{rm m}$), halo mass ($M_{rm h}$) and halo-centric distance ($r/r_{180}$). For given halo mass, the characteristic stellar mass ($M_{*, rm ch}$) for the transition is about one-fifth of that of the corresponding central galaxy, and almost independent of $B/T_{rm m}$. Once $B/T_{rm m}$ is fixed, the quenched fraction of galaxies with $M_{*} < M_{*, rm ch}$ increases with $M_{rm h}$, but decreases with $M_*$ in the inner part of halos ($r/r_{180} < 0.5$). In the outer part ($r/r_{180} > 0.5$), the trend with $M_{rm h}$ remains but the correlation with $M_*$ is absent or becomes positive. For galaxies above $M_{rm *, ch}$ and with $B/T_{rm m}$ fixed, the quenched fraction increases with $M_{rm *}$, but depends only weakly on $M_{rm h}$ in both the inner and outer regions. At fixed $B/T_{rm m}$ and $M_*$, the quenched fraction increases with decreasing $r/r_{180}$ for galaxies with $M_{*} < M_{*, rm ch}$, and depends only weakly on $r/r_{180}$ for galaxies with $M_{*} > M_{*, rm ch}$. Our finding provides a physically-motivated way to classify galaxies in halos into two classes based on their quenching properties: an `upper class with $M_{*} > M_{rm *,ch}$ and a `lower class with $M_{*} < M_{rm *,ch}$. Environmental quenching is important for `lower class galaxies, while internal quenching plays the dominating role for the `upper class.
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