The USDA plant site shows six species (in the U.S.) for the Genus Arctium. Three species are shown in Iowa.
BONAP (The Biota of North America Program) also shows six species in the U.S. with three species in Iowa, none of which are native. One species (A. minus) is common in Iowa; the other two species (A. lappa and A. tomentosum) are infrequent.
The Arctium species you are most likely to encounter in Iowa are:
Arctium lappa (great burdock) - [infrequent]
Arctium minus (common burdock) - [frequent]
Arctium tomentosum (woolly burdock) - [infrequent]