  Given $n \in \mathbf{N},$ consider the imprimitive wreath product $C_2 \wr
S_n.$ We study the structure of modules whose ordinary characters form an
involution model of $FC_2 \wr S_n,$ where $F$ is a field of odd prime
characteristic. We classify the vertices of these modules in this case. We then
use this classification of the vertices to describe certain columns of the
decomposition matrix of $C_2 \wr S_n.$
