Let n ≥ 1 be an integer, and ℓ a prime number with ℓ ∤ 2n. For a prime number p of the form p = 2nℓ^f + 1, let K_t be the cyclic field of degree ℓ^t contained in the real p th cyclotomic field Q(ζ_p)⁺, and let h_t be the class number of K_t in the ordinary sense. For a prime number r ≠ℓ, we study whether or not the ratio h_t /h_t−1 is divisible by r with the help of computer. One of our typical results asserts that when ℓ = 3 and 1 ≤ n ≤ 29 with 3 ∤ n, h_f⋅/h_f−1 is not divisible by a prime number r with r ≡ 2, 5 mod 9 for every prime number p = 2n⋅3^f + 1 with f ≥ 2.