Let L {\mathbf {L}} be the set of all Fitting classes F \mathfrak {F} with the following two properties: (i) F ⊇ N \mathfrak {F} \supseteq \mathfrak {N} , the class of all finite nilpotent groups, and (ii) every F \mathfrak {F} -avoided, complemented chief factor of any finite soluble group G G is partially F \mathfrak {F} -complemented in G G . It is shown that L {\mathbf {L}} is a complete sublattice of the complete lattice N {\mathbf {N}} of all nontrivial normal Fitting classes, and, moreover, it is lattice isomorphic to the subgroup lattice of the Frattini factor group of a certain abelian torsion group due to H. Lausch.