10.56 (1986)

No. The lattice $L$ of all varieties of nilpotent 2-groups of class $\leqslant 4$ is non-distributive (Yu. A. Belov, Algebra and Logic, 9, no. 6 (1970), 371-374; R. A. Bryce, Philos. Trans. Roy. Soc. London (A), 266 (1970), 281–355, footnote on p. 335). The mapping $\mathcal{V} \to \mathcal{V} \cap \mathcal{F}$, where $\mathcal{F}$ is the class of all finite groups, is an embedding of $L$ into the lattice of formations. (L. Kovács, Letter of May, 12, 1988.) See also (L. A. Shemetkov, A. N. Skiba, Formations of algebraic systems, Nauka, Moscow, 1989 (Russian)).