...Gw XXXIX. Chords Wizard...	Welcome to Guitarweek! A flower will die if you don't water it!... ----------------
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   An Inverted Chord is just a chord that doesnt start from its root tone, The tones C E G make a 'C major' and inverting it would be just shuffling around the 'order' of the tones. A common notation for these chords is the simplified chord name with a forward slash(/) and the tone it starts with:
(Simplified Chord Name / Starting-Tone )

root inversion - C E G (starts with 1st)    "C/C" (not used)
first inversion -  E G C (starts with 3rd)    "C/E"
second inversion - G C E (starts with 5th)  "C/G"
third inversion - A G E C - (starts with xtension)  "C/A"

   The 'root' inversion is not really inverted at all, And the third inversion is when extended chords is used. The order of the remaining tones after the 'starting tone' does not really matter, The core of the chord still exist no matter how you shuffle the tones around. If a chord does not start with its 'naming tone' then it is inverted. The 'type' of inversion should be ignored and more focus should be on the formula (chord name / starting tone) that it uses, This is so it won't be confusing when you use extended or modified chords like "C11" (CEGF) (C/F) or "C9" (CEGD) (C/D)...

A "C major second inversion" would be 'C/G' because the 'G' is the 5th of the C major chord...
A "C minor second inversion" would be 'Cm/G' because the 'G' is the also the 5th of the C minor chord...
A "C augmented second inversion" would be 'Caug/G#' because the 'G#' is '5th' of the C augmented chord

"C major" root Inversion (C/C)

"C major" first Inversion (C/E)

"C major" second Inversion (C/G)

   Inversions seem to be ignored when the shuffled tone create another chord like 'A C E G' inverted would be 'C E G A', You could also say that you started with 'C E G A' and inverted it to 'A C E G'.  We have a big beef about these chords, The chord should be named as an 'A minor 7th' or "A C E G' because a 'seventh (ACEG)' is stronger than a 'thirteenth (CEGA)'...

(Am7) root Inversion (Am/A) - OR - (C13th) third Inversion (C/A)

   Chords should always be resolved to its simplest form, It would not really matter when looking at someone else's song but does matter more if you are composing your own song. A chord is a set of tones 'played together' so the order of the tones shouldn't be what determines the actual chord is, ACEG and CEGA are the same set of tones so the 'set of tones' should be the determining factor...