AWS - MySQL server "Service CPU Usage" stuck at 50% / being throttled?
This is probably neither throttling nor a misconfiguration, nor anything related to AWS. Consider these points:


A c4.large instance has 2 cores.  
Any given query running in MySQL runs entirely within a single thread, and
a single thread within a process can only run on 1 core at any moment in time (though presumably the Windows process scheduler can move it between the cores at will), and
100% utilization of 1 core by 1 thread would show up as 50% CPU utilization.


What you appear to have here, rather than the server really being "under load," is a single CPU-bound query running.

Any user with the PROCESS privilege can run the SHOW FULL PROCESSLIST; query in MySQL and see what all the session (connection) threads in MySQL Server are doing at the moment.  Run this and you should find your CPU hog.  If you run another instance of the same query, you should find that the CPU utilization hits 100% with two CPU expensive queries running concurrently.  (Then you'll want to fix/optimize that query.) The TIME column tells you how long the connection has been in its current state.