LAUSR

In this note, we describe first the structure of minimal non-Iwasawa finite groups. Then we determine the minimal non-Iwasawa finite groups which are modular. Also, we find connections between minimal non-Iwasawa finite groups and the subgroup commutativity degree, and we give an example of a family of non-nilpotent modular finite groups $$G_n$$Gn, $$n\in \mathbb {N}$$n∈N, whose subgroup commutativity degree tends to 1 as n tends to infinity.