6 D Lie algebra studied by Ovsiannikov.
L . V . Ovsiannikov . The group analysis algorithms . In “Modern Group Analysis : advanced analytical and computational methods in mathematical physics”, Proceedings of the International Workshop, Acireale, October 27-- 31, 1992, Edited by N . H . Ibragimov, M . Torrisi and A . Valenti, Kluwer Academic Publishers, 277-- 289, 1993.

SetDirectory[NotebookDirectory[]];

<<"SymboLie.wl"

gens={{1,0,0},{0,1,0},{t,0,0},{0,t,0},{y,-x,0},{0,0,1}};vars={x,y,t};pars={{},{}};

cs=StructureConstants[gens,vars];

ct = CommutatorTable[cs];ct//MatrixForm

FastRun=1;

Timing[alg1=SubAlgebra[cs,pars,1];]

PrintOptimal[alg1]

PrintGraph[alg1,1]

Timing[alg2=SubAlgebra[cs,pars,2];]

PrintOptimal[alg2]

PrintGraph[alg2,1]

Timing[alg3=SubAlgebra[cs,pars,3];]

PrintOptimal[alg3]

PrintGraph[alg3,1]

Timing[alg4=SubAlgebra[cs,pars,4];]

PrintOptimal[alg4]

PrintGraph[alg4,1]

Timing[alg5=SubAlgebra[cs,pars,5];]

PrintOptimal[alg5]

PrintGraph[alg5,1]

alg={alg1,alg2,alg3,alg4,alg5}

SessionTime[]