Representations by quadratic forms have long been studied through the geometric language of quadratic lattices. In this talk, we approach a quadratic lattice through two of its substructures: lattice cosets and full-rank sublattices. In the first part, we briefly introduce theta series of lattice cosets and then look at a graph structure on ternary cosets that reflects their algebraic relationships. In the second part, we turn to counting sublattices of a binary lattice up to isometry, and see how this leads to a Dirichlet series closely related to the arithmetic of imaginary quadratic fields.