So, beyond mathematicians' categorizing all the finite simple groups and enumerating all the ways you can get the rest of the finite groups out there by gluing smaller groups together, it turns out that that we have fairly good algorithms for enumerating all the groups of a given order, and of all the groups whose order is less than 2000, most of them have order 1024.
As this MathOverflow post and this blogpost point out, this sort of behavior may quite likely to be a general phenomenon.
Old news, but it's pretty damn neat.
