jats:titleAbstract</jats:title>jats:pThe electrochemical thermodynamic and kinetic characteristics of rechargeable batteries are critically influenced by the ordering of mobile ions in electrodes or solid electrolytes. However, because of the experimental difficulty of capturing the lighter migration ion coupled with the theoretical limitation of searching for ordered phases in a constrained cell, predicting stable ordered phases involving cell transformations or at extremely dilute concentrations remains challenging. Here, a group-subgroup transformation method based on lattice transformation and Wyckoff-position splitting is employed to predict the ordered ground states. We reproduce the previously reported Lijats:sub0.</jats:sub>jats:sub75</jats:sub>CoOjats:sub2</jats:sub>, Lijats:sub0.</jats:sub>jats:sub8333</jats:sub>CoOjats:sub2</jats:sub>, and Lijats:sub0.8571</jats:sub>CoOjats:sub2</jats:sub> phases and report a new Lijats:sub0.875</jats:sub>CoOjats:sub2</jats:sub> ground state. Taking the advantage of Wyckoff-position splitting in reducing the number of configurations, we identify the stablest Lijats:sub0.0625</jats:sub>Cjats:sub6</jats:sub> dilute phase in Li-ion intercalated graphite. We also resolve the Li/La/vacancy ordering in Lijats:sub3jats:italicx</jats:italic></jats:sub>Lajats:sub2/3−jats:italicx</jats:italic></jats:sub>TiOjats:sub3</jats:sub> (0 < jats:italicx</jats:italic> < 0.167), which explains the observed Li-ion diffusion anisotropy. These findings provide important insight towards understanding the rechargeable battery chemistry.</jats:p>