If $G=(A×B)\rtimes(C×D);$ $|A|=5,|B|=7,|C|=2,|D|=3,$ $C$ induces inversion on $A×B$, & $D$ acts nontriv on $B$, then ${\rm cs}^*(G)=\{2,6,7,14,35\}$

Question

I'm trying to understand how the author calculates the conjugacy sizes here:

Consider $G= (A \times B) \rtimes (C \times D)$, where $A$, $B$, $C$, $D$ are cyclic groups of order 5, 7, 2, 3, respectively, $C$ induces the inversion map on $A \times B$, and $D$ acts nontrivially on $B$. Then $\operatorname{cs}^*(G)=\{2, 6, 7, 14, 35\}$.

Here the $\operatorname{cs}^*(G)$ is the set of all sizes of conjugacy classes of $G$ except $1$.

I am somehow new to semidirect products but I think I understand the semidirect product here. I tried to check when an element commutes with another. But it gets so complicated and confusing and I can't get anywhere. I appreciate any tip on how to approach this.