q=17 (q mod 8 = 1): 21 soluble classes of S, 12 with PGL-invariant class; witnesses for (p=l, delta): NONE  [0.2s]
    X=17[1^1,17^16]                            b1=0 b2=0  O_l(N) != 1
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=18 |F|=9, beta trivial on N/F: 18 of 18
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=16 |F|=16, beta trivial on N/F: 16 of 16
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=16 |F|=16, beta trivial on N/F: 16 of 16
    X=9[1^1,3^2,9^6]                           b1=0 b2=0  |N_S|=18 |F|=9, beta trivial on N/F: 18 of 18
    X=6[1^1,2^3,3^2]                           b1=0 b2=0  |N_S|=6 |F|=3, beta trivial on N/F: 6 of 6
    X=8[1^1,2^1,4^2,8^4]                       b1=0 b2=0  |N_S|=16 |F|=16, beta trivial on N/F: 16 of 16
    X=16[1^1,2^9,4^2,8^4]                      b1=0 b2=0  |N_S|=16 |F|=16, beta trivial on N/F: 16 of 16
    X=18[1^1,2^9,3^2,9^6]                      b1=0 b2=0  |N_S|=18 |F|=9, beta trivial on N/F: 18 of 18
    X=34[1^1,2^17,17^16]                       b1=0 b2=0  O_l(N) != 1
    X=68[1^1,2^17,4^34,17^16]                  b1=0 b2=0  O_l(N) != 1
    X=136[1^1,2^17,4^34,8^68,17^16]            b1=0 b2=0  O_l(N) != 1
q=19 (q mod 8 = 3): 16 soluble classes of S, 13 with PGL-invariant class; witnesses for (p=l, delta): ['4[1^1,2^3]:b2', '12[1^1,2^3,3^8]:b2']  [0.2s]
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=18 |F|=9, beta trivial on N/F: 18 of 18
    X=5[1^1,5^4]                               b1=0 b2=0  |N_S|=20 |F|=10, beta trivial on N/F: 20 of 20
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=20 |F|=10, beta trivial on N/F: 20 of 20
    X=19[1^1,19^18]                            b1=0 b2=0  O_l(N) != 1
    X=10[1^1,2^1,5^4,10^4]                     b1=0 b2=0  |N_S|=20 |F|=10, beta trivial on N/F: 20 of 20
    X=4[1^1,2^3]                               b1=0 b2=1  |N_S|=12 |F|=4, beta trivial on N/F: 0 of 12
    X=6[1^1,2^3,3^2]                           b1=0 b2=0  |N_S|=6 |F|=3, beta trivial on N/F: 6 of 6
    X=9[1^1,3^2,9^6]                           b1=0 b2=0  |N_S|=18 |F|=9, beta trivial on N/F: 18 of 18
    X=12[1^1,2^3,3^8]                          b1=0 b2=1  |N_S|=12 |F|=4, beta trivial on N/F: 0 of 12
    X=18[1^1,2^9,3^2,9^6]                      b1=0 b2=0  |N_S|=18 |F|=9, beta trivial on N/F: 18 of 18
    X=20[1^1,2^11,5^4,10^4]                    b1=0 b2=0  |N_S|=20 |F|=10, beta trivial on N/F: 20 of 20
    X=57[1^1,3^38,19^18]                       b1=0 b2=0  O_l(N) != 1
    X=171[1^1,3^38,9^114,19^18]                b1=0 b2=0  O_l(N) != 1
q=23 (q mod 8 = 7): 22 soluble classes of S, 11 with PGL-invariant class; witnesses for (p=l, delta): NONE  [0.4s]
    X=11[1^1,11^10]                            b1=0 b2=0  |N_S|=22 |F|=11, beta trivial on N/F: 22 of 22
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=23[1^1,23^22]                            b1=0 b2=0  O_l(N) != 1
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=6[1^1,2^1,3^2,6^2]                       b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=12[1^1,2^1,3^2,4^2,6^2,12^4]             b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=8[1^1,2^5,4^2]                           b1=0 b2=0  |N_S|=8 |F|=8, beta trivial on N/F: 8 of 8
    X=22[1^1,2^11,11^10]                       b1=0 b2=0  |N_S|=22 |F|=11, beta trivial on N/F: 22 of 22
    X=24[1^1,2^13,3^2,4^2,6^2,12^4]            b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=253[1^1,11^230,23^22]                    b1=0 b2=0  O_l(N) != 1
q=25 (q mod 8 = 1): 32 soluble classes of S, 15 with PGL-invariant class; witnesses for (p=l, delta): NONE  [0.7s]
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=13[1^1,13^12]                            b1=0 b2=0  |N_S|=26 |F|=13, beta trivial on N/F: 26 of 26
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=6[1^1,2^1,3^2,6^2]                       b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=12[1^1,2^1,3^2,4^2,6^2,12^4]             b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=8[1^1,2^5,4^2]                           b1=0 b2=0  |N_S|=8 |F|=8, beta trivial on N/F: 8 of 8
    X=25[1^1,5^24]                             b1=0 b2=0  O_l(N) != 1
    X=24[1^1,2^13,3^2,4^2,6^2,12^4]            b1=0 b2=0  |N_S|=24 |F|=12, beta trivial on N/F: 24 of 24
    X=26[1^1,2^13,13^12]                       b1=0 b2=0  |N_S|=26 |F|=13, beta trivial on N/F: 26 of 26
    X=75[1^1,3^50,5^24]                        b1=0 b2=0  O_l(N) != 1
    X=50[1^1,2^25,5^24]                        b1=0 b2=0  O_l(N) != 1
    X=150[1^1,2^25,3^50,5^24,6^50]             b1=0 b2=0  O_l(N) != 1
    X=100[1^1,2^25,4^50,5^24]                  b1=0 b2=0  O_l(N) != 1
    X=300[1^1,2^25,3^50,4^50,5^24,6^50,12^100] b1=0 b2=0  O_l(N) != 1
q=27 (q mod 8 = 3): 15 soluble classes of S, 12 with PGL-invariant class; witnesses for (p=l, delta): ['4[1^1,2^3]:b2', '12[1^1,2^3,3^8]:b2']  [0.5s]
    X=7[1^1,7^6]                               b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=13[1^1,13^12]                            b1=0 b2=0  |N_S|=26 |F|=13, beta trivial on N/F: 26 of 26
    X=3[1^1,3^2]                               b1=0 b2=0  O_l(N) != 1
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=14[1^1,2^1,7^6,14^6]                     b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=4[1^1,2^3]                               b1=0 b2=1  |N_S|=12 |F|=4, beta trivial on N/F: 0 of 12
    X=9[1^1,3^8]                               b1=0 b2=0  O_l(N) != 1
    X=12[1^1,2^3,3^8]                          b1=0 b2=1  |N_S|=12 |F|=4, beta trivial on N/F: 0 of 12
    X=27[1^1,3^26]                             b1=0 b2=0  O_l(N) != 1
    X=26[1^1,2^13,13^12]                       b1=0 b2=0  |N_S|=26 |F|=13, beta trivial on N/F: 26 of 26
    X=28[1^1,2^15,7^6,14^6]                    b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=351[1^1,3^26,13^324]                     b1=0 b2=0  O_l(N) != 1
q=29 (q mod 8 = 5): 19 soluble classes of S, 16 with PGL-invariant class; witnesses for (p=l, delta): ['4[1^1,2^3]:b2', '12[1^1,2^3,3^8]:b2']  [0.7s]
    X=7[1^1,7^6]                               b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=5[1^1,5^4]                               b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=29[1^1,29^28]                            b1=0 b2=0  O_l(N) != 1
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=4[1^1,2^3]                               b1=0 b2=1  |N_S|=12 |F|=4, beta trivial on N/F: 0 of 12
    X=14[1^1,2^1,7^6,14^6]                     b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=15[1^1,3^2,5^4,15^8]                     b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=6[1^1,2^3,3^2]                           b1=0 b2=0  |N_S|=6 |F|=3, beta trivial on N/F: 6 of 6
    X=12[1^1,2^3,3^8]                          b1=0 b2=1  |N_S|=12 |F|=4, beta trivial on N/F: 0 of 12
    X=10[1^1,2^5,5^4]                          b1=0 b2=0  |N_S|=10 |F|=5, beta trivial on N/F: 10 of 10
    X=28[1^1,2^15,7^6,14^6]                    b1=0 b2=0  |N_S|=28 |F|=14, beta trivial on N/F: 28 of 28
    X=30[1^1,2^15,3^2,5^4,15^8]                b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=203[1^1,7^174,29^28]                     b1=0 b2=0  O_l(N) != 1
    X=58[1^1,2^29,29^28]                       b1=0 b2=0  O_l(N) != 1
    X=406[1^1,2^29,7^174,14^174,29^28]         b1=0 b2=0  O_l(N) != 1
q=31 (q mod 8 = 7): 26 soluble classes of S, 15 with PGL-invariant class; witnesses for (p=l, delta): NONE  [1.1s]
    X=5[1^1,5^4]                               b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=32 |F|=32, beta trivial on N/F: 32 of 32
    X=31[1^1,31^30]                            b1=0 b2=0  O_l(N) != 1
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=32 |F|=32, beta trivial on N/F: 32 of 32
    X=15[1^1,3^2,5^4,15^8]                     b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=6[1^1,2^3,3^2]                           b1=0 b2=0  |N_S|=6 |F|=3, beta trivial on N/F: 6 of 6
    X=8[1^1,2^1,4^2,8^4]                       b1=0 b2=0  |N_S|=32 |F|=32, beta trivial on N/F: 32 of 32
    X=10[1^1,2^5,5^4]                          b1=0 b2=0  |N_S|=10 |F|=5, beta trivial on N/F: 10 of 10
    X=16[1^1,2^1,4^2,8^4,16^8]                 b1=0 b2=0  |N_S|=32 |F|=32, beta trivial on N/F: 32 of 32
    X=30[1^1,2^15,3^2,5^4,15^8]                b1=0 b2=0  |N_S|=30 |F|=15, beta trivial on N/F: 30 of 30
    X=32[1^1,2^17,4^2,8^4,16^8]                b1=0 b2=0  |N_S|=32 |F|=32, beta trivial on N/F: 32 of 32
    X=155[1^1,5^124,31^30]                     b1=0 b2=0  O_l(N) != 1
    X=93[1^1,3^62,31^30]                       b1=0 b2=0  O_l(N) != 1
    X=465[1^1,3^62,5^124,15^248,31^30]         b1=0 b2=0  O_l(N) != 1
