The Harmonic min scale is a natural min scale with the 7th raise a half step
e.g. A harm min: A B C D E F G# [A]
D----------------6-7-
A--------5-7-8-------
E-5-7-8--------------
I'm sure you can complete the scale on the rest of the strings and all over the fretboard , here are the names of the modes for this scale.
1- Aeolian maj7 (harmonic minor)
2- Locrian maj6
3- Ionian #5
4- Dorian #4
5- Phrygian maj3
6- Lydian #2
7- Mixolydian #1