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We determine and classify the electric-magnetic duality orbits of fluxes supporting asymptotically flat, extremal black branes in D = 4 , 5 , 6 space–time dimensions in the so-called nonsupersymmetric magic Maxwell–Einstein theories, which are consistent truncations of maximal supergravity and which can be related to Jordan algebras (and related Freudenthal triple systems) over the split complex numbers ℂ s and the split quaternions ℍ s . By studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the electric-magnetic duality symmetry group, we obtain that, as for the case of maximal supergravity, in magic nonsupersymmetric Maxwell–Einstein theories there is no splitting of orbits, namely there is only one orbit for each nonmaximal rank element of the relevant Jordan algebra (in D = 5 and 6) or of the relevant Freudenthal triple system (in D = 4). [ABSTRACT FROM AUTHOR]