Quantum theory pillars include entanglement and operator commute failure. Page curves quantify the bipartite entanglement of many-body systems in a random pure state. This entanglement is known to decrease if we restrict the wide range of observables (abelian “charges”) to exchange with each other. Non-abelian charges, which cannot be exchanged with each other, are currently of interest in quantum thermodynamics. For example, non-commuting charges have been shown to reduce the rate of entropy production and may increase finite-size deviations from eigenstate thermalization. We bridge quantum thermodynamics to many-body physics to quantify the effect of charge non-exchange (the non-abelian nature of symmetry) on the Page curve. First, he builds two models that are very similar but differ in whether they commute or not. We show analytically and numerically that the non-commuting fare case has greater entanglement. Therefore, non-exchange of charges may promote entanglement.