In [this paper][1] (1998) by M. Izumi, R. Longo, S. Popa, there is the following result (page 49) on compact groups:     
    
![enter image description here][2]  

By applying this result to finite groups, we get a Galois correspondence between subgroups and subsystems (of unitary representations).   
 
Such a result seems "fundamental" in the finite group theory but I didn't know an "old" reference for it.     

*Question*: What's the first reference for this result in finite group theory? 


  [1]: http://www.sciencedirect.com/science/article/pii/S0022123697932286#
  [2]: https://i.sstatic.net/S5YgO.png