The matching conditions for a breaking $G \rightarrow \prod_i G_i$ are
$$\omega_G-\frac{C_2(G)(\mu)}{12 \pi}=\omega_{G_i}-\frac{C_2(G_i)(\mu)}{12 \pi} ,$$
where $C_2(g)$ denotes the quadratic Casimir invariant for the adjoint representation of the group $g$. (See, for example, Eq. 7 in Implications of the CERN LEP results for SO(10) grand unification )
However, for example, for the braking chain $SU(4) \times SU(2)_L \times SU(2)_R \rightarrow SU(3_C) \times SU(2)_L \times U(1)_Y$ we have the matching condition
$$ \omega_{U(1)_Y} = \frac{3}{5}\left( \omega_{SU(2)_R} - \frac{2}{12\pi} \right) + \frac{2}{5}\left( \omega_{SU(4)_C} - \frac{4}{12\pi} \right)$$
(See, for example, Eq. 8 in Implications of the CERN LEP results for SO(10) grand unification )
Where does this matching condition for $U(1)$ subgroups come from?