• Blattodea (cockroaches)
  
• Mantodea (mantids)
  
• Isoptera (termites)
  
• Zoraptera
  
• Grylloblattodea
  
• Dermaptera (earwigs)
  
• Plecoptera (stoneflies)
  
• Orthoptera (grasshoppers, crickets, katydids)
  
• Phasmatodea (walking sticks, timemas)
  
• Embioptera (webspinners)
  
• Mantophasmatodea (gladiators)
  
• Superorder Hemipterodea
  
  • Psocoptera (booklice, barklice)
    
  • Phthiraptera (lice)
    
  • Hemiptera (true bugs)
    
  • Thysanoptera (thrips)
    
• Superorder Endopterygota
  
  • Miomoptera - extinct
    
  • Megaloptera (alderflies, etc.)
    
  • Raphidioptera (snakeflies)
    
  • Neuroptera (net-veined insects)
    
  • Coleoptera (beetles)
    
  • Strepsiptera (twisted-winged parasites)
    
  • Mecoptera (scorpionflies, etc.)
    
  • Siphonaptera (fleas)
    
  • Protodiptera extinct
    
  • Diptera (true flies)
    
  • Trichoptera (caddisflies)
    
  • Lepidoptera (butterflies, moths)
    
  • Hymenoptera (ants, bees, wasps, etc.)

Neoptera is a classification group that includes almost all the winged insects, specifically those that can flex their wings over their abdomens (in contrast to Paleoptera). This was in contrast with the more ancient orders of winged insects, which are unable to flex their wings in this way.

ITIS treats Neoptera as a superorder; other authorities treat it, as here, as in infraclass, and recognise several superorders within it.

The insect orders (non-extinct) currently recognised within the neopteran group include the following:

Grylloblattaria -- rock crawlers.

Phasmida -- walking sticks.

Orthoptera -- grasshoppers and crickets.

Mantodea -- mantids.

Blattaria -- cockroaches.

Isoptera -- termites.

Dermaptera -- earwigs.

Embioptera -- webspinners.

Plecoptera -- stoneflies.

Zoraptera -- zorapterans.

Psocoptera -- psocids, book lice.

Phthiraptera -- lice.

Hemiptera -- bugs.

Homoptera -- cicadas, hoppers, aphids, scale insects.

Thysanoptera -- thrips.

Neuroptera -- lace wings, ant lions, dobsonflies.

Coleoptera -- beetles.

Strepsiptera -- twisted wing parasites.

Mecoptera -- scorpionflies.

Siphonaptera -- fleas.

Diptera -- flies and mosquitoes.

Tricoptera -- caddisflies.

Lepidoptera -- butterflies, moths, skippers.

Hymenoptera -- bees, wasps, ants.