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.