Neutrinos in SM

The SM gauge group is based on the following symmetry: $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y\overrightarrow{\text{spontaneously broken}}SU(3{)}_C\times U(1{)}_{EM}$

Here, $U(1{)}_{EM}$ couples to the electromagnetic charge $Q_{EM}=T_{L3}+Y$ where $T_{L3}$ is the weak component of isospin (third generator of $SU(2{)}_L$)

We have 3 generations of fermions: identical gauge quantum number but different masses.