Abstract: $N_\infty$-operads over a group $G$ encode homotopy commutative operations together with a class of equivariant transfer (or norm) maps. Their homotopy theory is given by transfer systems, which are certain discrete objects that have a rich combinatorial structure defined in terms of the subgroup lattice of $G$. In this talk, we will show that when $G$ is finite Abelian, transfer systems are in bijection with weak factorization systems on the poset category of subgroups of $G$. This leads to an involution on the lattice of transfer systems, generalizing the work of Balchin-Bearup-Pech-Roitzheim for cyclic groups of squarefree order. We will conclude with an enumeration of saturated transfer systems and comments on the Rubin and Blumberg-Hill saturation conjecture. This is joint work with Evan Franchere, Usman Hafeez, Peter Marcus, Kyle Ormsby, Weihang Qin, and Riley Waugh.