Okay, let me shoot for guessing the rule (and if that fails, back to finishing the individual single letters
):
AKHTBN iff each letter written in uppercase exhibits either flip or rotational symmetry. More directly, iff none of the letters are members of the set {F, G, J, L, P, Q, R}.
[letters exhibiting flip symmetry with vertical axis: A, H, I, M, O, T, U, V, W, X, Y
letters exhibiting flip symmetry with horizontal axis: B, C, D, E, H, I, K, O, X
letters exhibiting rotational symmetry: H, I, N, O, S, X, Z]
[in case people are curious: my initial guess (disproven with F and L) was forbidding letters written in uppercase that contains both straight as well as curved parts, though already that leaves J and U somewhat ambiguous. Expanding guess to individual letters was needed to see if it only matters that the forbidden letter is the first letter in the word (disproven with NOOG).]
