A description of solvable Lie groups with a given uniform subgroup

The article contains a method of describing all connected simply connected solvable Lie groups with a given uniform subgroup (not necessarily discrete). It is proved that such groups always form, up to isomorphism, no more than a countable set, and that this set decomposes into a finite number of classes of groups with isomorpbic commutator subgroups.
Bibliography: 9 titles.