The full names for these are German 6th, Italian 6th (that 5 is wrong), Neapolitan 6th, French 6th and I don`t know the other one. The first three are built on chord IV- in C major, this would be F. You turn the chord into its 1st inversion (ie A C F) and flatten the bottom note and sharpen the top note, thus gving you the Italian 6th chord. For the German 6th, you add flat 3, ie Eb.l For the French 6th, you add scale degree 2, ie D. These are called augmented 6ths and move outward to chord V. (Ab-c-F#- G-B-D-G. The Neapolitan 6th is built on the flat 2 of the scale. Usually seen in 1st inversion. (ie in C major, Ab, Db, F). Called a 6th because of the interval between its top and bottom notes.