The categories of chords besides major and minor in the other main sections are listed here:
Besides the categories listed above plus major and minor that are listed elsewhere you may turn into some additional chords. To help you figure out rare chords the following examples with explanations will hopefully guide you.
CMin7 - alternative chord symbol for C minor seventh.
E△ - alternative chord symbol for E major.
A° - alternative chord symbol for A diminished.
F(#5) - alternative chord symbol for F augmented.
Fno3 - F major with no third.
E/G# - inverted E chord with G sharp as the bass note.
E7/B - inverted E seventh chord with a B as the bass note.
C/D - C major with D as bass note.
F/E - F major with E as bass note.
C6/9 - C six-nine chord, which more correctly is written with the 6 and 9 in small letters over and under each other.
Abmaj7(#11) - A flat major seventh sharp eleventh chord.
B#9b5 - B sharp ninth flat fifth.
A#9#5 - A sharp ninth sharp fifth.