Encyclopedia of Groups

Solution 1:

EDIT: Lance Pollard notes that the links below are broken. Groups of order up to 30 are (currently) available at https://en.wikipedia.org/wiki/List_of_small_groups and at http://www.math.ucsd.edu/~atparris/small_groups.html

Groups of order less than 30 are at http://opensourcemath.org/gap/small_groups.html

Also, http://world.std.com/~jmccarro/math/SmallGroups/SmallGroups.html goes up to order 32.

Solution 2:

You may also want to read a nice article of Conway, Dietrich and O'Brien http://www.math.auckland.ac.nz/~obrien/research/gnu.pdf

And also the paper of Besche, Eick and O'Brien http://www.math.auckland.ac.nz/~obrien/research/2000.pdf which contains a table of the number of groups of order $n < 2001$.

Solution 3:

Depending on your needs, Wolphram|Alpha or Mathematica itself might be helpful. See here for the computational overview, and here for the data function (open up the "More Information" for the sorts of things you can search.)