Fallacy of Division
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.
Fallacy Files:
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