  We investigate the possible regular magnetic order (RMO) for the spin models
with global O(3) spin rotation, based on a group theoretical approach for
triangular and kagome lattices. The main reason to study these RMOs is that
they are good variational candidates for the ground states of many specific
models. In this work, we followed the prescription introduced by Messio et al.
(L. Messio, C. Lhuillier, and G. Misguich, Phys. Rev. B, 2011, 83, 184401) for
the p6m group and extended their work for different subgroups of p6m, i.e., p6,
p3, p3m1, and p31m. We have listed all the possible regular magnetic orders for
kagome and triangular lattices, which fall into the category of these groups.
We calculate the energy and the spin structure factors for each of these
states.
