Anyone familiar with Luftwaffe (WW2) Aircraft ID codes?

[Von Due]

Here's the thing:

There is one particular aircraft that flew during WW2 before being shot down. It was a Heinkel 111 with the ID code 5J + CN. I am attempting to place that aircraft in the squadron it flew, if possible down to its number within the squadron, so to know that plane's individual place in the squadron.

Here's what I got so far:
The bombers were organized in Combat Wings (KG) and Combat Wing 4 (KG4) had the code 5J, so this aircraft was part of KG4, which I already knew but this verified that 5J was indeed referring to KG4.

Then things get a bit cloudier but a couple of things from Wikipedia:
Each KG was organized in groups (Gruppe). At the time this aircraft was shot down in late April 1940, KG4 consisted of 3 groups + HQ (Gruppe I, Gr. II and Gr. III + HQ).
Each Gruppe would consist of 3 squadrons (Staffel) where the Sqdr. 1-3 were in Gr I, Sqdr 4-6 in Gr.2 and so on and so forth.

This aircraft flew in sqdr. 5, in Gr. II. in KG4. This I know for a fact. It adds up to what Wiki says about number of squadrons per group.

From https://de.wikipedia.org/wiki/Geschwaderkennung and http://www.luftfahrt-erfurt.de/seite14.htm it seems obvious that the N in CN refers to Sqrd. 5, therefor also Gr. II. However, those 2 pages appear to disagree in the C.

From the German Wiki (I don't read German really but I think I could make out the few bits I needed above) it appears that the C would refer to Gr. II which would make sense. Then CN would spell out Gr. II/Sqdr. 5 but that other page has another bomber in the same KG named BN and if I would follow the same system as on Wiki, that B would refer to Gr. I and not (as it seems to me) the 2nd individual plane in squadron 5 (N, Gr. II).

Could any of you who do read German tell me if I read that thing totally wrong or if there is a discrepancy between the 2 pages?

Would any of you happen to know how to read the ID codes down to the smallest details it offers?

I am thinking: Would it make sense to ID individual aircrafts down to squadron size only and not down to individual aircrafts? I would think not but that the CN part does indeed tell which individual craft we have here. I am going for

5J = KG4
C = 3rd plane in
N = squadron 5 (therefor Gr.II)

but would appreciate any Germanspeaking person or someone familiar with these codes to verify or tell me I'm wrong. The older system they used as explained in the 2nd link seems to say F was plane 7 but I can't seem to work out how F could mean plane 7 and not 6.