Just throwing it out there. I think it would be beneficial if there could be a forum contributed guide with descriptions to atonal subcategories.
Music without a tonal center has been around for over a century and much of what is called atonal is far more than just that but I have yet to locate an intelligent guide that presents the myriad of subcategories / schools of thought.
Potential contenders for subcategories might include:
12 tone serialism
Methodical Music that adheres to unique rules
Music with consonant harmonies but without a tonal center
Fundamentally rhythmically complex music (random pitched)
*Some category names above might be incorrect.
Please Note: This thread is not intended to be a format for opinions about such music but rather a resource that could shed light on a very vague tradition.