Every fingering that fits a hand
5047
easy
x047
easy
544x
easy
5443
moderate
5447
hard
What is true of it
Caug is C, E and G♯ — 1, 3 and #5 counted from C.
The easiest of the 5 fingerings below is 5047: 3 fingers, held at the 4th fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
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
Caug/E
x443
Caug/G♯
100x
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.