  We propose a classification of group properties according to whether they can
be deduced from the assumption that a group's subgroup lattice contains an
interval isomorphic to some lattice. We are able to classify a few group
properties as being "interval enforceable" in this sense, and we establish that
other properties satisfy a weaker notion of "core-free interval enforceable."
We also show that if there exists a group property and its negation that are
both core-free interval enforceable, this would settle an important open
question in universal algebra.
