What you have is correct in some degree.
Class A 0.0.0.0 - 127.255.255.255
Class B 128.0.0.0 - 191.255.255.255
Class C 192.0.0.0 - 223.255.255.255
Class D 224.0.0.0 - 239.255.255.255
Class E 240.0.0.0 - 255.255.225.255
With that said Classful networks are no longer used and have not been for a very long time.
What you want to be using is the private address range which is.
10.0.0.0 - 10.255.255.255
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255
Using Classful addresses in your private LAN that are outside the Private subnet scope will cause your grief.
Forget the term network class. Forget class A, B, C networks as this does not exist any longer.
People only still make reference to this because they are misinformed.
No matter how hard we push that terminology just won't die for some reason.
