We measured the long-lived cosmogenic radionuclides 10Be, 26Al, and 36Cl in 47 H chondrite falls: 13 Cluster 1 members, 9 Cluster 5 members, and 25 random falls. From the date and time of fall, Clusters 1 and 5 were previously identified as possible coorbital meteoroid streams with distinctive thermal histories being confirmed by contents of volatile trace elements. Here, we use model data, including a three-radionuclide plot (10Bebulk/26Albulk versus 36Clmetal/26Albulk) and the multivariate statistical techniques of logistic regression and linear discriminant analysis to compare radionuclide levels and their utility to differentiate specific suites from other H chondrites. From our radionuclide results and from noble gas data from other workers, we identified 35 falls with simple irradiation histories and cosmic ray exposure ages >4 Ma. Eight others exhibit evidence for shorter (≤4 Ma) exposure, three of which had complex exposure histories (two having been reported by others previously); three others may have had such a history. In any event, the small proportion of H chondrite falls with complex exposure histories supports recent suggestions that they are not commonly encountered, as earlier workers suggested. Although cosmogenic radionuclides do not differentiate between Cluster 1 and a random set of H chondrites, H chondrites that lost 3He from solar heating are distinguishable from those with normal 3He levels.