Lagrange-like subloop

Definition
A subloop of a finite loop is termed a Lagrange-like subloop if the order (i.e., the number of elements) of the subloop divides the order of the loop.

Relation with other properties

 * Algebra loop satisfying the weak Lagrange property is a finite algebra loop in which every subloop is Lagrange-like.
 * Algebra loop satisfying the strong Lagrange property is a finite algebra loop in which every subloop satisfies the weak Lagrange property.

Stronger properties
All the properties below are stronger conditional to the ambient loop being finite.