Every fingering that fits a hand
x32010
open
x35050
easy
x32050
easy
x32013
moderate
x3201x
open
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 x32010: 3 fingers, held at the 1st fret.
2 of them use open strings, which is what makes a shape quiet to change to.
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
032010
C/G
332010
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.