There are two more open chord shapes that sound very good although they're not as 'flexible' as the other three: we can use them only for major chords (as fully open chords, that is) but they are very important to know: the C and G shapes.
We can play a C major chord on 5 or 6 strings, if we add a low G on the six string: it's the first time we see a chord that doesn't begin with the root (in this case G is the fifth) but it's not at all uncommon to do that, most of the A and D chords we saw in the previous lessons can be played with their fifths as the lowest note (open E or A respectively).
When the lowest note in a chord is not the root we have an inversion. As we said before, it's important that we have all the notes that make up a single chord but the order is not fixed; inversions lend a different character to chords and are a very useful tool for arranging.
In the first C major chord we could play also the open E on the sixth string and we would get another inversion of C, this time with a low major third: as always, play the different inversions of the chord and listen closely to the changes in the chord's texture as you change the lowest note.
Sometimes we say that we play a C major over G (or E) when we want exactly that kind of inversion and the chord symbol will be C/G (C/E).
We'll expand on the concept of inversions in the Theory and Chords sections of the site.