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The query [[Particular example::Alternating group:A4]] [[Page class::Fact]] was answered by the SMWSQLStore3 in 0.0095 seconds.

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Finite solvable not implies supersolvable, Lattice-complemented not implies permutably complemented, No proper nontrivial transitively normal subgroup not implies simple, Normal-extensible not implies extensible, Normal-extensible not implies inner, Order-conjugate and Hall not implies order-dominating, Sylow tower not implies subgroups of all orders dividing the group order