Games You Don't Think About #5: Pondering symmetrical numbers on a digital clock

Toys
- Knowledge of a digital clock face with a seven segment display (an actual clockface of this sort can be used as a reference, but is not required)
- pictures in your imagination.
Winning Condition:
- decide how many possible time configurations exist on a 24-hour digital clock (with a 7-segment display) that possess symmetry.
Restrictions/Rules:
- none
Time to play:
- 1-5 minutes
Tips/clarifications:
- consider both reflection symmetry and rotational symmetry
- 1
Good points
- requires visualisation to complete - a moderately unusual thing
- multiple routes to completion. With multiple numbers possessing symmetry but various rules (governing time) dictating what numerals may appear where, it's up to players to consider and apply these rules as they see fit to their mental model.
- no confirmation of success. Means answers must be double-checked and requires some confidence in the answer.
Negatives
- like all genuine puzzles, it can only be played once
- no confirmation of success. Can result in uncertainty and a general uneasiness.