Function restriction formalism chart

Note:


 * Endo-invariance implies join-closed.
 * Balanced implies transitive. Conversely, any function-restriction-expressible subgroup property that is transitive, must be balanced.
 * Invariance implies intersection-closed.
 * Left-inner implies left-extensibility-stable, that in turn implies intermediate subgroup condition.
 * Quotient-hereditary invariance implies quotient-transitive