  Let $m \geqslant 6$ be an even integer. In this short note we prove that the
Jacobian variety of a quasiplatonic Riemann surface with associated group of
automorphisms isomorphic to $C_2^2 \rtimes_2 C_m$ admits complex
multiplication. We then extend this result to provide a criterion under which
the Jacobian variety of a quasiplatonic Riemann surface admits complex
multiplication.
