  There is a growing family of rare-earth kagome materials with dominant
nearest-neighbor interactions and strong spin orbit coupling. The low symmetry
of these materials makes theoretical description complicated, with six distinct
nearest-neighbor coupling parameters allowed. In this Article, we ask what
kinds of classical, ordered, ground states can be expected to occur in these
materials, assuming generic (i.e. non-fine-tuned) sets of exchange parameters.
We use symmetry analysis to show that there are only five distinct classical
ground state phases occurring for generic parameters. The five phases are: (i)
a coplanar, 2-fold degenerate, state with vanishing magnetization (${\sf
A_1}$), (ii) a noncoplanar, 2-fold degenerate, state with magnetization
perpendicular to the kagome plane (${\sf A_2}$), (iii) a coplanar, 6-fold
degenerate, state with magnetization lying within the kagome plane (${\sf
E}$-coplanar), (iv) a noncoplanar, 6-fold degenerate, state with magnetization
lying within a mirror plane of the lattice (${\sf E}$-noncoplanar$_{6}$), (v) a
noncoplanar, 12-fold degenerate, state with magnetization in an arbitrary
direction (${\sf E}$-noncoplanar$_{12}$). All five are translation invariant
(${\bf q}=0$) states. Having found the set of possible ground states, the
ground state phase diagram is obtained by comparing numerically optimized
energies for each possibility as a function of the coupling parameters. The
state ${\sf E}$ noncoplanar$_{12}$ is extremely rare, occupying $<1\%$ of the
full phase diagram, so for practical purposes there are four main ordered
states likely to occur in anisotropic kagome magnets with dominant nearest
neighbor interactions. These results can aid in interpreting recent experiments
on ``tripod kagome'' systems R$_3$A$_2$Sb$_3$O$_{14}$, as well as materials
closer to the isotropic limit such as Cr- and Fe- jarosites.
