That is actually a very close assessment … It is to do with phonetics …
Group 1 letters when their names are spelt - the beginning sound is made with their own letter sounds. For example:
aey, bee, dee … etc … As you can see the names of the letters all start with their own letters themselves.
Group 2 letters are all named with beginning letter sounds that are made from other letters in the alphabet. For example:
c = see, f = eff, h = aitch … etc
Group 3 letters have names that the beginning sound cannot be made from any single letter in the alphabet.
e - contains a beginning sound in its name that is neither phonetically “e” nor phonetically “i” … rather double e is used to make the “ee” sound.
for o - it is not possible to use any one letter to make the sound for the beginning of this letter. It is neither “a” nor “e” nor “o” phonetically. The name of this letter starts strangely between the sounds “ur” and “a” … but is not exactly either sound and it transforms in to an “o” sound and then finishes off in a “ou” sound …