TITLE: A question on terminology (Group Theory)
QUESTION [4 upvotes]: 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

REPLY [3 votes]: 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.

REPLY [3 votes]: You are referring to so-called CLT groups.  You might find this paper interesting.
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