Prime knots and their symmetries have been studied and tabulated for more than a hundred years, but very little attention has been given to the tabulation of composite knots. We will develop a combinatorial strategy for tabulating composite knots and computing their symmetries knowing the symmetries of the prime factors. Along the way we will discuss the properties of an interesting combinatorial description of knot and link diagrams called the planar diagram code (PD-code). The PD-code exists in the literature~cite{KnotAt}, but there does not exist a formal discussion of their properties.
