Strong magnetic fluctuations can provide a coupling mechanism for electrons that leads to unconventional superconductivity. Magnetic order and superconductivity have been found to coexist in a number of magnetically mediated superconductors, but these order parameters generally compete. We report that close to the upper critical field, CeCoIn5 adopts a multicomponent ground state that simultaneously carries cooperating magnetic and superconducting orders. Suppressing superconductivity in a first-order transition at the upper critical field leads to the simultaneous collapse of the magnetic order, showing that superconductivity is necessary for the magnetic order. A symmetry analysis of the coupling between the magnetic order and the superconducting gap function suggests a form of superconductivity that is associated with a nonvanishing momentum.