Homotopical combinatorics uses tools from combinatorics to explore and understand structures in equivariant homotopy theory. One object of study in this field is a G-transfer system. We will define transfer systems and present the differences between abelian and non-abelian transfer systems. We then explore structural characteristics of the lattice of transfer systems for some non-abelian groups, such as D₉ and F₅. For these groups, we classify the (co)saturation of the transfer systems. We also present a proof that width, the number of arrows needed to generate a complete transfer system, can be determined by the prime factorization of the order for a dihedral group.
