A question on terminology (Group Theory)

Question

Is there a standard adjective to describe a finite group $G$ of composite order which possesses, for each (positive) divisor $d$ of $|G|$, a subgroup of order $d$?

I would guess "Lagrangian" but I can only seem to get one hit in the literature.

Many thanks!

JTE

Answer 1

Such is called a CLT group (it stands for Converse of Lagrange's Theorem).

We do know supersolvable groups $\subset$ CLT groups $\subset$ solvable groups, both strictly.

Answer 2

You are referring to so-called CLT groups. You might find this paper interesting.