Every fingering that fits a hand
x003
open · no 5
5003
easy · no 5
540x
easy · no 5
5403
easy · no 5
5433
moderate
What is true of it
C is C, E and G — 1, 3 and 5 counted from C.
On an instrument that cannot reach all 3, the 5 goes first, in that order.
The easiest of the 5 fingerings below is x003: one finger, held at the 3rd fret.
1 of them use open strings, which is what makes a shape quiet to change to.
It leaves out the 5. 4 strings cannot carry 3 notes, and the 5 is the one this chord can lose without changing what it is.
1 string stays silent.
Where its notes are on the neck
The brass dots are C, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
C/E
x403
C/G
000x
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.