The anaphase-promoting complex or cyclosome (APC) is an unusually complicated ubiquitin ligase, composed of 13 core subunits and either of two loosely associated regulatory subunits, Cdc20 and Cdh1. We analyzed the architecture of the APC using a recently constructed budding yeast strain that is viable in the absence of normally essential APC subunits. We found that the largest subunit, Apc1, serves as a scaffold that associates independently with two separable subcomplexes, one that contains Apc2 (Cullin), Apc11 (RING), and Doc1/Apc10, and another that contains the three TPR subunits (Cdc27, Cdc16, and Cdc23). We found that the three TPR subunits display a sequential binding dependency, with Cdc27 the most peripheral, Cdc23 the most internal, and Cdc16 between. Apc4, Apc5, Cdc23, and Apc1 associate interdependently, such that loss of any one subunit greatly reduces binding between the remaining three. Intriguingly, the cullin and TPR subunits both contribute to the binding of Cdh1 to the APC. Enzymatic assays performed with APC purified from strains lacking each of the essential subunits revealed that only cdc27Δ complexes retain detectable activity in the presence of Cdh1. This residual activity depends on the C-box domain of Cdh1, but not on the C-terminal IR domain, suggesting that the C-box mediates a productive interaction with an APC subunit other than Cdc27. We have also found that the IR domain of Cdc20 is dispensable for viability, suggesting that Cdc20 can activate the APC through another domain. We have provided an updated model for the subunit architecture of the APC.