  We classify a supersymmetric extension of the Standard Model by discrete
symmetries originating from finite modular symmetries $\Gamma_N$. Since all the
couplings in supersymmetric theories of finite modular symmetries $\Gamma_N$
are described by holomorphic modular forms with even modular weights,
renormalizable and non-renormalizable operators such as baryon- and/or
lepton-number violating operators are severely constrained. From the modular
transformation of matter multiplets with modular weight $1/M$, we find
$\mathbb{Z}_{2M}$ symmetries, including the generalized baryon and lepton
parities, $R$-parity, $\mathbb{Z}_3$ baryon triality and $\mathbb{Z}_6$ proton
hexality. Such $\mathbb{Z}_{2M}$ symmetries are enlarged to $\mathbb{Z}_{2M}
\rtimes \mathbb{Z}_2^{\text{CP}}$ symmetries together with the CP
transformation.
