Classical
Steenrod Algebra A (p=2)
The mod-2 Steenrod algebra, generated by Sqi operations with Adem relations
Steenrod Algebra A (p=3)
The mod-3 Steenrod algebra, generated by β and Pi operations
Steenrod Algebra A (p=5)
The mod-5 Steenrod algebra, generated by β and Pi operations
Dual / P*
P* (p=2)
The quotient Hopf algebra A*/E* used in the Cartan-Eilenberg spectral sequence
Motivic
Motivic Steenrod Algebra (p=2)
The motivic Steenrod algebra over Spec ℤ at the prime 2