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I think most of the 3 notes played at the beginning of Ocarina of Time's Lost Woods theme for reference.
In C, these 4 are considered triads:
Major: C E G Minor: C Eb G Diminished: C Eb Gb Augmented: C E G#
The other ways in which you can alter the 3rd and 5th are to lower the 3rd and raise the 5th, which is the same as a major triad in 1st inversion. However, I can't figure out what lowering just the 5th does. It seems to create a major second interval (enharmonically diminished 3rd) and doesn't fit into any inversion of another chord.
Is there a special name for this chord, when would it be appropriate to use it?