A catalyst includes at least one element X selected from the group consisting of Groups 3 to 6 of the Periodic Table, and at least one element Z selected from the group consisting of Group 14 elements. At least one diffraction peak is observed in a low angle range of θ=6° or less in an X-ray diffraction profile observed using X-ray diffraction. The at least one diffraction peak has a ratio (I/H) of a peak intensity I to a half width at half maximum H of the diffraction peak of 5000 or more.