Some monodromy groups of finite index in $Sp_4(\mathbb{Z})$

We determine the index of five of the $7$ hypergeometric Calabi-Yau operators that have finite index in $Sp_4(\mathbb{Z})$ and in two cases give a complete description of the monodromy group. Furthermore we found six non-hypergeometric Calabi-Yau operators with finite index in $Sp_4(\mathbb{Z})$, most notably a case where the index is one.