the U(1) spin-rotational invariance of the Cooper pairs that arises in a magnetic field. This generically leads to two different species of fractional vortices whose fractional fluxes sum to $\Phi_0$. When stable, these fractional vortices form interlacing lattices analogous to vortex.antivortex lattice configurations proposed by Refs. @PhysRevLett.71.2138 [@PhysRevLett.71.2142] in the context of a two-dimensional (2D) superfluid and the configuration in two-component Bose condensates proposed by Ref. @PhysRevLett.88.180403.

The rest of the paper consists of the following. In section \[sec:OP\], we give a pedagogical introduction to the symmetry properties of triplet OP. In particular, we will show how U(1)$\times$U(1) symmetry can arise in the OP of such systems. In section \[sec:GibbsFree\] we discuss the form of Gibbs free energy that is allowed by various symmetries in the problem when spin-orbit coupling is not included. In section \[sec:G\] we provide the general theoretical framework for the vortex lattice phases. In section \[sec:LLL\] we show that the lowest Landau level solution often provides an adequate description and we discuss this solution for the lattice of HQV’s. In section \[sec:SO\] we consider the effect of U(1)$\times$U(1) symmetry breaking driven by spin-orbit coupling. In section \[sec:observation\] we lay out predictions for how to detect the 