relation of classification of finite group and finite simple group. I know that classification of finite simple group is completed.
From the fact, can we say that classification of finite group is completed?
I know a few relations of finite group and finite simple group, but can't think that the relation is so powerful. 
For example, can we enumerate the group of order $n$ for any natural number $n$?

The classification of all finite groups depends on solving the group extension problem, which has been heavily studied but not yet fully solved. 
