Transfer systems are relatively simple combinatorial objects which classify the homotopy types of N-infty operads, an equivariant analogue of E-infty operads. In this talk, we informally present this homotopy-theoretic story so as to motivate the combinatorial study of saturated transfer systems, which in good cases classify linear isometries operads. We then give a novel method for enumerating saturated transfer systems on cylindrical modular lattices, for instance the subgroup lattices of finite cyclic groups, and tightly characterize the asymptotic behavior in the height of the cylinder. This talk presents joint work with several Reed College students along with Angélica Osorno and Kyle Ormsby.