  We elucidate the pivotal role of the bandstructure's orbital content in
deciding the type of commensurate magnetic order stabilized within the
itinerant scenario of iron-pnictides. Recent experimental findings in the
tetragonal magnetic phase attest to the existence of the so-called charge and
spin ordered density wave over the spin-vortex crystal phase, the latter of
which tends to be favored in simplified band models of itinerant magnetism.
Here we show that employing a multiorbital itinerant Landau approach based on
realistic bandstructures can account for the experimentally observed magnetic
phase, and thus shed light on the importance of the orbital content in deciding
the magnetic order. In addition, we remark that the presence of a hole pocket
centered at the Brillouin zone's ${\rm M}$-point favors a magnetic stripe
rather than a tetragonal magnetic phase. For inferring the symmetry properties
of the different magnetic phases, we formulate our theory in terms of magnetic
order parameters transforming according to irreducible representations of the
ensuing D$_{\rm 4h}$ point group. The latter method not only provides
transparent understanding of the symmetry breaking schemes but also reveals
that the leading instabilities always belong to the $\{A_{1g},B_{1g}\}$ subset
of irreducible representations, independent of their C$_2$ or C$_4$ nature.
