2014 AMC 12B Problem 18

The numbers 1, 2, 3, 4, 5, are to be arranged in a circle. An arrangement is \textit{bad} if it is not true that for every n from 1 to 15 one can find a subset of the numbers that appear consecutively on the circle that sum to n. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?

\textbf{(A) }1\qquad\textbf{(B) }2\qquad\textbf{(C) }3\qquad\textbf{(D) }4\qquad\textbf{(E) }5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.