Energy conservation is ubiquitous in the understanding of the process of high harmonic generation. Yet, a complete quantum optical description of the photon-number resolved structure implied by exact energy conservation remained elusive. Here, we solve this problem by introducing a new information-theoretic perspective that separates the microscopic dynamics from the constraints imposed by energy conservation and only considers the imposed symmetry structure of the underlying state space. This leads to a decomposition into invariant eigenspace sectors of fixed energy, which we refer to as the energy-conserving subspaces of high harmonic generation. The resulting weighted-photon-number sector structure is the Fock-space counterpart of the familiar harmonic energy conservation condition and makes the photon number correlations required by exact energy exchange between the participating field modes explicit. Energy conservation fixes the allowed support of the optical state, whereas the microscopic electron dynamics determine the amplitudes within this support. Coherent population of several allowed photon partitions can consequently generate intermode entanglement and nonclassical reduced states. More generally, the construction provides an information-theoretic description of symmetry constraints in strong-field processes without requiring a complete solution of the microscopic dynamics.