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Yep exactly. And when the fifth is in the bass, it's a second inversion. Then with 7th (and 9th etc.) chords you can have more than just 2 inversions.
A quite common bass movement will lead to you using a couple of inversions in direct succession.
E.g.: In C major, the bass moves thus, C D E.
There are several ways of harmonizing this bass line. The common one involving some inversions would be: C (root), G (2nd inversion), C (1st inversion).
Second inversion chords aren't as common as first inversion chords. This is because the 4th between the bass note and the root note of the chord is a dissonance. In the example above, it is permissible, because it is a passing six-four (2nd inversion) chord. Fourths between the bass and an upper part are always dissonances, but not between any two upper parts.
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