As with the Roman alphabet, which you may be familiar with it (since you are using it to read this answer), different letters have different symmetries.
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In caps there is 1. lower case none.
zero, all the keys have different letters, numbers, or symbols
Not many. Depending on how you write, the letters L, O, Q, and X can have diagonal lines of symmetry.
the answer is U O S H K Z X N A D=2 0R MORE LINES OF SYMMETRY
4 Lines of symmetry