of its formation (halving of the vortex lattice unit cell). Experiments have already determined the vortex lattice structure successfully at low fields in Sr$_2$RuO$_4$ [@Nature.396.242; @PhysRevLett.84.6094] and the observed square lattice geometry was consistent with the theoretical prediction by one of the present authors based on a chiral triplet order parameter in Ref. . However, Ref.  considered the limit of strong spin-orbit coupling, which leads to vortex lattices of full quantum Abrikosov vortices. Recently, measurements of the Knight shift for the field along the $c$-axis [@PRL.93.167004] as well as ARPES data [@haverkort:026406; @liu:026408] indicate that that spin-orbit coupling is perhaps not so strong. Therefore, in this paper, we extend the studies of Ref.  to allow for weak spin-orbit coupling, leading to the possibility of HQV lattices for fields along the $c$-axis. Additionally, the organic superconductor (TMTSF)$_2$ClO$_4$ naturally has weak spin-orbit coupling and Knight shift measurements provide evidence for a spin-triplet state at high magnetic fields [@organic], which is precisely the situation we consider here. We also provide an analysis of this case and the closely related case for cobaltate spin-triplet superconductors [@Nature.Physics.1.91].

In this paper, we study the energetics of different vortex lattice configurations. The key additional physical ingredient is 