=== AGL25  |G| = 12000  (degree 25)
  method A: |F(G)| = 25, |E(G)| = 1, |F*(G)| = 25, h*(G/F*) = 2  =>  h*(G) = 3
  O_p(G) orders: p=2:1, p=3:1, p=5:25
  method B (intersection of H.C_G(H/L) over chief factors): F*-series orders [1, 25, 6000, 12000], h* = 3; F*_1 equal to method A: True
  s(G) = max h(K) over soluble K: -1 (lower bound), attained by None
  Theorem P, p = 2 (O_p(G)=1): max h(K/O_p(K)) = -1 (lower bound) vs h*(G) = 3 -> NOT FOUND  [None]
  Theorem P, p = 3 (O_p(G)=1): max h(K/O_p(K)) = -1 (lower bound) vs h*(G) = 3 -> NOT FOUND  [None]
  Theorem P, p = 7 (O_p(G)=1, p does not divide |G|): max h(K/O_p(K)) = -1 (lower bound) vs h*(G) = 3 -> NOT FOUND  [None]
  question (h*(G) <= s(G)): NOT FOUND;  time 3.0s
=== 3^4:S5  |G| = 9720  (degree 81)
  method A: |F(G)| = 81, |E(G)| = 1, |F*(G)| = 81, h*(G/F*) = 2  =>  h*(G) = 3
  O_p(G) orders: p=2:1, p=3:81, p=5:1
  method B (intersection of H.C_G(H/L) over chief factors): F*-series orders [1, 81, 4860, 9720], h* = 3; F*_1 equal to method A: True
  s(G) = max h(K) over soluble K: 4 (lower bound), attained by 3^4:S4 (order 648)
  Theorem P, p = 2 (O_p(G)=1): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [3^4:S4 (order 648)]
  Theorem P, p = 5 (O_p(G)=1): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [3^4:S4 (order 648)]
  Theorem P, p = 7 (O_p(G)=1, p does not divide |G|): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [3^4:S4 (order 648)]
  question (h*(G) <= s(G)): OK;  time 3.5s
=== S5wrC2  |G| = 28800  (degree 10)
  method A: |F(G)| = 1, |E(G)| = 3600, |F*(G)| = 3600, h*(G/F*) = 1  =>  h*(G) = 2
  O_p(G) orders: p=2:1, p=3:1, p=5:1
  method B (intersection of H.C_G(H/L) over chief factors): F*-series orders [1, 3600, 28800], h* = 2; F*_1 equal to method A: True
  s(G) = max h(K) over soluble K: 3 (lower bound), attained by S4 wr C2 (order 1152)
  Theorem P, p = 2 (O_p(G)=1): max h(K/O_p(K)) = 2 (lower bound) vs h*(G) = 2 -> OK  [S4 wr C2 (order 1152)]
  Theorem P, p = 3 (O_p(G)=1): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [S4 wr C2 (order 1152)]
  Theorem P, p = 5 (O_p(G)=1): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [S4 wr C2 (order 1152)]
  Theorem P, p = 7 (O_p(G)=1, p does not divide |G|): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [S4 wr C2 (order 1152)]
  question (h*(G) <= s(G)): OK;  time 2.6s
=== A5wrC3  |G| = 648000  (degree 15)
  method A: |F(G)| = 1, |E(G)| = 216000, |F*(G)| = 216000, h*(G/F*) = 1  =>  h*(G) = 2
  O_p(G) orders: p=2:1, p=3:1, p=5:1
  s(G) = max h(K) over soluble K: 3 (lower bound), attained by S3 wr C3 (order 648)
  Theorem P, p = 2 (O_p(G)=1): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [S3 wr C3 (order 648)]
  Theorem P, p = 3 (O_p(G)=1): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [D10 wr C3 (order 3000)]
  Theorem P, p = 5 (O_p(G)=1): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [S3 wr C3 (order 648)]
  Theorem P, p = 7 (O_p(G)=1, p does not divide |G|): max h(K/O_p(K)) = 3 (lower bound) vs h*(G) = 2 -> OK  [S3 wr C3 (order 648)]
  question (h*(G) <= s(G)): OK;  time 3.7s
=== A5wrS3  |G| = 1296000  (degree 15)
  method A: |F(G)| = 1, |E(G)| = 216000, |F*(G)| = 216000, h*(G/F*) = 2  =>  h*(G) = 3
  O_p(G) orders: p=2:1, p=3:1, p=5:1
  s(G) = max h(K) over soluble K: 4 (lower bound), attained by S3 wr S3 (order 1296)
  Theorem P, p = 2 (O_p(G)=1): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [S3 wr S3 (order 1296)]
  Theorem P, p = 3 (O_p(G)=1): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [D10 wr S3 (order 6000)]
  Theorem P, p = 5 (O_p(G)=1): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [S3 wr S3 (order 1296)]
  Theorem P, p = 7 (O_p(G)=1, p does not divide |G|): max h(K/O_p(K)) = 4 (lower bound) vs h*(G) = 3 -> OK  [S3 wr S3 (order 1296)]
  question (h*(G) <= s(G)): OK;  time 20.0s
