  Coexistence of antiferromagnetic order with superconductivity in many
families of newly discovered iron-based superconductors has renewed interest to
this old problem. Due to competition between the two types of order, one can
expect appearance of the antiferromagnetism inside the cores of the vortices
generated by the external magnetic field. The structure of a vortex in type II
superconductors holds significant importance from the theoretical and the
application points of view. Here we consider the internal vortex structure in a
two-band s$_\pm$ superconductor near a spin-density-wave instability. We treat
the problem in a completely self-consistent manner within the quasiclassical
Eilenberger formalism. We study the structure of the s$_\pm$ superconducting
order and magnetic field-induced spin-density-wave order near an isolated
vortex. We examine the effect of this spin-density-wave state inside the vortex
cores on the local density of states.
