  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.
