  We present a general method to unfold energy bands of supercell calculations
to primitive Brillouin zone using group theoretical techniques, where an
isomorphic factor group is introduced to connect the primitive translation
group with the supercell translation group via a direct product. Originating
from the translation group symmetry, our method gives an uniform description of
unfolding approaches based on various basis sets, and therefore, should be easy
to implement in both tight-binding model and existing ab initio code packages
using different basis sets. This makes the method applicable to a variety of
problems involving the use of supercells, such as defects, disorder, and
interfacial reconstructions. As a realistic example, we calculate electronic
properties of an monolayer FeSe on SrTiO$_3$ in checkerboard and collinear
antiferromagnetic spin configurations, illustrating the potential of our
method.
