Like chords, it is also possible to identify modes by certain notes contained in them. The 3rd identifies whether a mode belongs to a major or minor group, but other notes narrow the possibilities even further.
E.g. The only difference between the Ionian and Mixolydian modes is that the Ionian contains a natural 7th, while the Mixolydian contains a flattened 7th. Shown below are the notes which identify each mode. This becomes easy to understand if you play through all the modes starting from the same note.