q=41 (q mod 8 = 1): 30 soluble classes of S, 19 with PGL-invariant class; witnesses for (p=l, delta): NONE  [3.0s]
    X=7[1^1,7^6]                               b1=0 b2=0  |N_S|=42 |F|=21, beta trivial on N/F: 42 of 42
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=42 |F|=21, beta trivial on N/F: 42 of 42
    X=5[1^1,5^4]                               b1=0 b2=0  |N_S|=40 |F|=20, beta trivial on N/F: 40 of 40
    X=41[1^1,41^40]                            b1=0 b2=0  O_l(N) != 1
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=40 |F|=20, beta trivial on N/F: 40 of 40
    X=10[1^1,2^1,5^4,10^4]                     b1=0 b2=0  |N_S|=40 |F|=20, beta trivial on N/F: 40 of 40
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=40 |F|=20, beta trivial on N/F: 40 of 40
    X=21[1^1,3^2,7^6,21^12]                    b1=0 b2=0  |N_S|=42 |F|=21, beta trivial on N/F: 42 of 42
    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[1^1,2^5,4^2]                           b1=0 b2=0  |N_S|=8 |F|=8, beta trivial on N/F: 8 of 8
    X=20[1^1,2^1,4^2,5^4,10^4,20^8]            b1=0 b2=0  |N_S|=40 |F|=20, beta trivial on N/F: 40 of 40
    X=14[1^1,2^7,7^6]                          b1=0 b2=0  |N_S|=14 |F|=7, beta trivial on N/F: 14 of 14
    X=40[1^1,2^21,4^2,5^4,10^4,20^8]           b1=0 b2=0  |N_S|=40 |F|=20, beta trivial on N/F: 40 of 40
    X=42[1^1,2^21,3^2,7^6,21^12]               b1=0 b2=0  |N_S|=42 |F|=21, beta trivial on N/F: 42 of 42
    X=205[1^1,5^164,41^40]                     b1=0 b2=0  O_l(N) != 1
    X=82[1^1,2^41,41^40]                       b1=0 b2=0  O_l(N) != 1
    X=164[1^1,2^41,4^82,41^40]                 b1=0 b2=0  O_l(N) != 1
    X=410[1^1,2^41,5^164,10^164,41^40]         b1=0 b2=0  O_l(N) != 1
    X=820[1^1,2^41,4^82,5^164,10^164,20^328,41^40] b1=0 b2=0  O_l(N) != 1
q=47 (q mod 8 = 7): 28 soluble classes of S, 13 with PGL-invariant class; witnesses for (p=l, delta): NONE  [4.3s]
    X=23[1^1,23^22]                            b1=0 b2=0  |N_S|=46 |F|=23, beta trivial on N/F: 46 of 46
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=47[1^1,47^46]                            b1=0 b2=0  O_l(N) != 1
    X=6[1^1,2^1,3^2,6^2]                       b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=12[1^1,2^1,3^2,4^2,6^2,12^4]             b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=8[1^1,2^1,4^2,8^4]                       b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    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=24[1^1,2^1,3^2,4^2,6^2,8^4,12^4,24^8]    b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=46[1^1,2^23,23^22]                       b1=0 b2=0  |N_S|=46 |F|=23, beta trivial on N/F: 46 of 46
    X=48[1^1,2^25,3^2,4^2,6^2,8^4,12^4,24^8]   b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=1081[1^1,23^1034,47^46]                  b1=0 b2=0  O_l(N) != 1
q=49 (q mod 8 = 1): 44 soluble classes of S, 21 with PGL-invariant class; witnesses for (p=l, delta): NONE  [7.3s]
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=5[1^1,5^4]                               b1=0 b2=0  |N_S|=50 |F|=25, beta trivial on N/F: 50 of 50
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=6[1^1,2^1,3^2,6^2]                       b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=12[1^1,2^1,3^2,4^2,6^2,12^4]             b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=8[1^1,2^1,4^2,8^4]                       b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=25[1^1,5^4,25^20]                        b1=0 b2=0  |N_S|=50 |F|=25, beta trivial on N/F: 50 of 50
    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=49[1^1,7^48]                             b1=0 b2=0  O_l(N) != 1
    X=24[1^1,2^1,3^2,4^2,6^2,8^4,12^4,24^8]    b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    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=48[1^1,2^25,3^2,4^2,6^2,8^4,12^4,24^8]   b1=0 b2=0  |N_S|=48 |F|=24, beta trivial on N/F: 48 of 48
    X=50[1^1,2^25,5^4,25^20]                   b1=0 b2=0  |N_S|=50 |F|=25, beta trivial on N/F: 50 of 50
    X=147[1^1,3^98,7^48]                       b1=0 b2=0  O_l(N) != 1
    X=98[1^1,2^49,7^48]                        b1=0 b2=0  O_l(N) != 1
    X=294[1^1,2^49,3^98,6^98,7^48]             b1=0 b2=0  O_l(N) != 1
    X=196[1^1,2^49,4^98,7^48]                  b1=0 b2=0  O_l(N) != 1
    X=588[1^1,2^49,3^98,4^98,6^98,7^48,12^196] b1=0 b2=0  O_l(N) != 1
    X=392[1^1,2^49,4^98,7^48,8^196]            b1=0 b2=0  O_l(N) != 1
    X=1176[1^1,2^49,3^98,4^98,6^98,7^48,8^196,12^196,24^392] b1=0 b2=0  O_l(N) != 1
q=71 (q mod 8 = 7): 36 soluble classes of S, 21 with PGL-invariant class; witnesses for (p=l, delta): NONE  [23.1s]
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=71[1^1,71^70]                            b1=0 b2=0  O_l(N) != 1
    X=7[1^1,7^6]                               b1=0 b2=0  |N_S|=70 |F|=35, beta trivial on N/F: 70 of 70
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=5[1^1,5^4]                               b1=0 b2=0  |N_S|=70 |F|=35, beta trivial on N/F: 70 of 70
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=6[1^1,2^1,3^2,6^2]                       b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=9[1^1,3^2,9^6]                           b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    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=12[1^1,2^1,3^2,4^2,6^2,12^4]             b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=35[1^1,5^4,7^6,35^24]                    b1=0 b2=0  |N_S|=70 |F|=35, beta trivial on N/F: 70 of 70
    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=18[1^1,2^1,3^2,6^2,9^6,18^6]             b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=14[1^1,2^7,7^6]                          b1=0 b2=0  |N_S|=14 |F|=7, beta trivial on N/F: 14 of 14
    X=36[1^1,2^1,3^2,4^2,6^2,9^6,12^4,18^6,36^12] b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    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=70[1^1,2^35,5^4,7^6,35^24]               b1=0 b2=0  |N_S|=70 |F|=35, beta trivial on N/F: 70 of 70
    X=72[1^1,2^37,3^2,4^2,6^2,9^6,12^4,18^6,36^12] b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=497[1^1,7^426,71^70]                     b1=0 b2=0  O_l(N) != 1
    X=355[1^1,5^284,71^70]                     b1=0 b2=0  O_l(N) != 1
    X=2485[1^1,5^284,7^426,35^1704,71^70]      b1=0 b2=0  O_l(N) != 1
q=73 (q mod 8 = 1): 37 soluble classes of S, 22 with PGL-invariant class; witnesses for (p=l, delta): NONE  [23.2s]
    X=37[1^1,37^36]                            b1=0 b2=0  |N_S|=74 |F|=37, beta trivial on N/F: 74 of 74
    X=2[1^1,2^1]                               b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=73[1^1,73^72]                            b1=0 b2=0  O_l(N) != 1
    X=3[1^1,3^2]                               b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=4[1^1,2^1,4^2]                           b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=6[1^1,2^1,3^2,6^2]                       b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=9[1^1,3^2,9^6]                           b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    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=12[1^1,2^1,3^2,4^2,6^2,12^4]             b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=18[1^1,2^1,3^2,6^2,9^6,18^6]             b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    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=36[1^1,2^1,3^2,4^2,6^2,9^6,12^4,18^6,36^12] b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=72[1^1,2^37,3^2,4^2,6^2,9^6,12^4,18^6,36^12] b1=0 b2=0  |N_S|=72 |F|=36, beta trivial on N/F: 72 of 72
    X=74[1^1,2^37,37^36]                       b1=0 b2=0  |N_S|=74 |F|=37, beta trivial on N/F: 74 of 74
    X=219[1^1,3^146,73^72]                     b1=0 b2=0  O_l(N) != 1
    X=146[1^1,2^73,73^72]                      b1=0 b2=0  O_l(N) != 1
    X=292[1^1,2^73,4^146,73^72]                b1=0 b2=0  O_l(N) != 1
    X=438[1^1,2^73,3^146,6^146,73^72]          b1=0 b2=0  O_l(N) != 1
    X=657[1^1,3^146,9^438,73^72]               b1=0 b2=0  O_l(N) != 1
    X=876[1^1,2^73,3^146,4^146,6^146,12^292,73^72] b1=0 b2=0  O_l(N) != 1
    X=1314[1^1,2^73,3^146,6^146,9^438,18^438,73^72] b1=0 b2=0  O_l(N) != 1
    X=2628[1^1,2^73,3^146,4^146,6^146,9^438,12^292,18^438,36^876,73^72] b1=0 b2=0  O_l(N) != 1
