Hawk Moths (order lepidoptera, family sphingidae) are a large subset of all moths. They are generally large moths, with streamlined bodies, long narrow fore wings, and smaller hind wings. They are able to hover, and to fly at extremely high speeds (one of the fastest insects in the world - they have been clocked at 53 km/h). They are also sometimes called Sphinx Moths or Hummingbird Moths.
Hawk Moths are class Insecta (insects), order Lepidoptera (moths and butterflies), family Sphingidae. It seems to be a fairly large family.