Summary: We create a method which allows an arbitrary group \(G\) with an infra-invariant system \(\mathcal L(G)\) of subgroups to be embedded in a group \(G^*\) with an infra-invariant system \(\mathcal L(G^*)\) of subgroups so that \(G_\alpha^*\cap G\in\mathcal L(G)\) for every subgroup \(G_\alpha^*\in\mathcal L(G^*)\) and each factor \(B/A\) of a jump of subgroups in \(\mathcal L(G^*)\) is isomorphic to a factor of a jump in \(\mathcal L(G)\) or to any specified group \(H\). Using this method, we state new results on right-ordered groups. In particular, it is proved that every Conrad right-ordered group is embedded with preservation of order in a Conrad right-ordered group of Hahn type (i.e., a right-ordered group whose factors of jumps of convex subgroups are order-isomorphic to the additive group \(\mathbb R\)); every right-ordered Smirnov group is embedded in a right-ordered Smirnov group of Hahn type; a new proof is given for the Holland-McCleary theorem on embedding every linearly ordered group in a linearly ordered group of Hahn type.