  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 non-supersymmetric 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 $\mathbb{C}_{s}$ and the split quaternions
$\mathbb{H}_{s}$. 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
non-supersymmetric Maxwell-Einstein theories there is no splitting of orbits,
namely there is only one orbit for each non-maximal rank element of the
relevant Jordan algebra (in $D=5$ and $6$) or of the relevant Freudenthal
triple system (in $D=4$).
