Geodesic
A~description of solvable Lie groups with a~given uniform subgroup
Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 83-99

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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. 
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     author = {M. V. Milovanov},
     title = {A~description of solvable {Lie} groups with a~given uniform subgroup},
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M. V. Milovanov. A~description of solvable Lie groups with a~given uniform subgroup. Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 83-99. http://geodesic.mathdoc.fr/item/SM_1982_41_1_a4/