The Fallacy of Division (Wizard, Web) occurs when applying a general rule about a whole object to its component parts. For instance, supposing that because the US exports corn and soybeans, all States in the US export corn and soybeans.
Some properties are such that, if a whole object has the property, then all of its parts will, too—for example, invisibility. However, not all properties are like this—for instance, visibility. Let's call a property which distributes from a whole object to each of its parts a "dissective" property, using Nelson Goodman's term. If P is a dissective property, then the argument form above is validating, by definition of what such a property is. However, if P is not dissective, then the argument form is non-validating, and any argument of that form commits the fallacy of Division.
Sibling Fallacy: Composition