[WCSTombs]

This "classification" is pretty much a tautology and provides no information. The enumeration of all subgroups of a cyclic group and their orders is one of the most basic facts in all of group theory and known by pretty much everyone who has studied the subject at all. Thus, I'm completely failing to see the point in any of this.

[richard_chase]

It was more to provide a hopefully new perspective on some existing problems in number theory.

[WCSTombs]

Then nice try I guess, but there is nothing remotely new about any of this. You're not going to find a new perspective on something in math using a completely routine application of a well-known theorem. You'll need to either work really hard or come up with a genuinely new idea, and probably both.