In finite group theory, $p$-groups or simple groups can be considered as building blocks of all the groups. What is known about these families of groups is that
The classification of simple groups is done.
The classification of $p$-groups is much difficult problem.
Due to classification of simple groups, many problems from different areas of mathematics have been solved; there is a book Atlas of Finite Simple Groups: Ten years on, which perhaps contains some work with this thought.
On the other hand, although classification of $p$-groups is difficult, many researchers are focused on classifying $p$-groups having a specific property. For example, such work is collected in five big volumes (each $\geq$ 600 page, multiple of thousands of problems in total), only devoted to finite $p$-groups by Berkovich and Janko, in which, the authors state in preface that their aim is classification w.r.t. some properties.
I wondered many times, but didn't get any definite answer to following question while discussing with some people working on $p$-groups. I thought it may not be good to post this question on group-pub-forum to de-motivate some group-theoriests. The question is
As long as classification of some types of $p$-groups is concerned, has its application appeared in some other branch of mathematics (or at least, in algebra, or at least in group theory itself!)?