Systems of ordinary differential equations modelling coupled cells with `wreath product' coupling have been the subject of recent research. For identical cells, such systems can have interesting symmetries. The basic existence theorem for Hopf bifurcation in the symmetric case is the equivariant Hopf theorem, which involves isotropy subgroups with a two-dimensional fixed-point subspace (called -axial). A classification theorem for -axial subgroups in wreath products has been presented by Dionne et al. However, their classification is incomplete: it omits some -axial subgroups in some cases. We provide a complete classification of the -axial subgroups in wreath products. We also classify the maximal isotropy subgroups for these groups.