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Extensions 1→N→G→Q→1 with N=C30 and Q=C2×Q8

Direct product G=N×Q with N=C30 and Q=C2×Q8
dρLabelID
Q8×C2×C30480Q8xC2xC30480,1182

Semidirect products G=N:Q with N=C30 and Q=C2×Q8
extensionφ:Q→Aut NdρLabelID
C30⋊1(C2×Q8) = C2×D5×Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30:1(C2xQ8)480,1073
C30⋊2(C2×Q8) = C2×S3×Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30:2(C2xQ8)480,1078
C30⋊3(C2×Q8) = C2×D15⋊Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30:3(C2xQ8)480,1082
C30⋊4(C2×Q8) = C22×C15⋊Q8φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30:4(C2xQ8)480,1121
C30⋊5(C2×Q8) = C22×Dic30φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30:5(C2xQ8)480,1165
C30⋊6(C2×Q8) = C2×C6×Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30:6(C2xQ8)480,1135
C30⋊7(C2×Q8) = C2×C10×Dic6φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30:7(C2xQ8)480,1150
C30⋊8(C2×Q8) = C2×Q8×D15φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30:8(C2xQ8)480,1172
C30⋊9(C2×Q8) = C6×Q8×D5φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30:9(C2xQ8)480,1142
C30⋊10(C2×Q8) = S3×Q8×C10φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30:10(C2xQ8)480,1157

Non-split extensions G=N.Q with N=C30 and Q=C2×Q8
extensionφ:Q→Aut NdρLabelID
C30.1(C2×Q8) = Dic5⋊5Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.1(C2xQ8)480,399
C30.2(C2×Q8) = Dic3⋊5Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.2(C2xQ8)480,400
C30.3(C2×Q8) = Dic15⋊5Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.3(C2xQ8)480,401
C30.4(C2×Q8) = Dic15⋊1Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.4(C2xQ8)480,403
C30.5(C2×Q8) = Dic3⋊Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.5(C2xQ8)480,404
C30.6(C2×Q8) = Dic15⋊Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.6(C2xQ8)480,405
C30.7(C2×Q8) = Dic3×Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.7(C2xQ8)480,406
C30.8(C2×Q8) = Dic15⋊6Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.8(C2xQ8)480,407
C30.9(C2×Q8) = Dic5×Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.9(C2xQ8)480,408
C30.10(C2×Q8) = Dic30⋊17C4φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.10(C2xQ8)480,409
C30.11(C2×Q8) = Dic5.1Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.11(C2xQ8)480,410
C30.12(C2×Q8) = Dic5.2Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.12(C2xQ8)480,411
C30.13(C2×Q8) = Dic15.Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.13(C2xQ8)480,412
C30.14(C2×Q8) = Dic15.2Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.14(C2xQ8)480,415
C30.15(C2×Q8) = Dic30⋊14C4φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.15(C2xQ8)480,416
C30.16(C2×Q8) = Dic3.Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.16(C2xQ8)480,419
C30.17(C2×Q8) = Dic15⋊7Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.17(C2xQ8)480,420
C30.18(C2×Q8) = Dic3.2Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.18(C2xQ8)480,422
C30.19(C2×Q8) = D10⋊Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.19(C2xQ8)480,425
C30.20(C2×Q8) = D6⋊Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.20(C2xQ8)480,428
C30.21(C2×Q8) = C60.67D4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.21(C2xQ8)480,435
C30.22(C2×Q8) = C60.68D4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.22(C2xQ8)480,436
C30.23(C2×Q8) = C60.45D4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.23(C2xQ8)480,441
C30.24(C2×Q8) = C60.46D4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.24(C2xQ8)480,445
C30.25(C2×Q8) = Dic5⋊Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.25(C2xQ8)480,452
C30.26(C2×Q8) = D30⋊8Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.26(C2xQ8)480,453
C30.27(C2×Q8) = Dic5.7Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.27(C2xQ8)480,454
C30.28(C2×Q8) = Dic3.3Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.28(C2xQ8)480,455
C30.29(C2×Q8) = Dic15.4Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.29(C2xQ8)480,458
C30.30(C2×Q8) = D30⋊9Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.30(C2xQ8)480,459
C30.31(C2×Q8) = Dic15⋊8Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.31(C2xQ8)480,461
C30.32(C2×Q8) = C60.48D4φ: C2×Q8/C4 → C22 ⊆ Aut C30480C30.32(C2xQ8)480,465
C30.33(C2×Q8) = D30⋊10Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.33(C2xQ8)480,466
C30.34(C2×Q8) = D5×Dic3⋊C4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.34(C2xQ8)480,468
C30.35(C2×Q8) = S3×C10.D4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.35(C2xQ8)480,475
C30.36(C2×Q8) = D30.Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.36(C2xQ8)480,480
C30.37(C2×Q8) = D6⋊1Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.37(C2xQ8)480,486
C30.38(C2×Q8) = D30⋊Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.38(C2xQ8)480,487
C30.39(C2×Q8) = D5×C4⋊Dic3φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.39(C2xQ8)480,488
C30.40(C2×Q8) = D6⋊2Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.40(C2xQ8)480,493
C30.41(C2×Q8) = D30⋊2Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.41(C2xQ8)480,495
C30.42(C2×Q8) = D10⋊1Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.42(C2xQ8)480,497
C30.43(C2×Q8) = D10⋊2Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.43(C2xQ8)480,498
C30.44(C2×Q8) = D30⋊3Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.44(C2xQ8)480,500
C30.45(C2×Q8) = S3×C4⋊Dic5φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.45(C2xQ8)480,502
C30.46(C2×Q8) = D30⋊4Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.46(C2xQ8)480,505
C30.47(C2×Q8) = Dic15.D4φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.47(C2xQ8)480,506
C30.48(C2×Q8) = D10⋊4Dic6φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.48(C2xQ8)480,507
C30.49(C2×Q8) = D6⋊3Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.49(C2xQ8)480,508
C30.50(C2×Q8) = D6⋊4Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.50(C2xQ8)480,512
C30.51(C2×Q8) = D30.2Q8φ: C2×Q8/C4 → C22 ⊆ Aut C30240C30.51(C2xQ8)480,513
C30.52(C2×Q8) = C60.6Q8φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.52(C2xQ8)480,457
C30.53(C2×Q8) = C12.Dic10φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.53(C2xQ8)480,460
C30.54(C2×Q8) = C20.Dic6φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.54(C2xQ8)480,464
C30.55(C2×Q8) = C4×C15⋊Q8φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.55(C2xQ8)480,543
C30.56(C2×Q8) = C60⋊Q8φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.56(C2xQ8)480,544
C30.57(C2×Q8) = C20⋊4Dic6φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.57(C2xQ8)480,545
C30.58(C2×Q8) = C20⋊Dic6φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.58(C2xQ8)480,546
C30.59(C2×Q8) = C2×C30.Q8φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.59(C2xQ8)480,617
C30.60(C2×Q8) = C2×Dic15⋊5C4φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.60(C2xQ8)480,620
C30.61(C2×Q8) = C2×C6.Dic10φ: C2×Q8/C22 → C22 ⊆ Aut C30480C30.61(C2xQ8)480,621
C30.62(C2×Q8) = (C2×C30)⋊Q8φ: C2×Q8/C22 → C22 ⊆ Aut C30240C30.62(C2xQ8)480,650
C30.63(C2×Q8) = (C2×C10)⋊8Dic6φ: C2×Q8/C22 → C22 ⊆ Aut C30240C30.63(C2xQ8)480,651
C30.64(C2×Q8) = Dic15.48D4φ: C2×Q8/C22 → C22 ⊆ Aut C30240C30.64(C2xQ8)480,652
C30.65(C2×Q8) = C4×Dic30φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.65(C2xQ8)480,833
C30.66(C2×Q8) = C60⋊8Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.66(C2xQ8)480,834
C30.67(C2×Q8) = C60.24Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.67(C2xQ8)480,835
C30.68(C2×Q8) = C22⋊2Dic30φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30240C30.68(C2xQ8)480,843
C30.69(C2×Q8) = C4.Dic30φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.69(C2xQ8)480,855
C30.70(C2×Q8) = C2×C30.4Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.70(C2xQ8)480,888
C30.71(C2×Q8) = C60.205D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30240C30.71(C2xQ8)480,889
C30.72(C2×Q8) = C2×C60⋊5C4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.72(C2xQ8)480,890
C30.73(C2×Q8) = C12×Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.73(C2xQ8)480,661
C30.74(C2×Q8) = C3×C20⋊2Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.74(C2xQ8)480,662
C30.75(C2×Q8) = C3×C20.6Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.75(C2xQ8)480,663
C30.76(C2×Q8) = C3×Dic5.14D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30240C30.76(C2xQ8)480,671
C30.77(C2×Q8) = C3×C20⋊Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.77(C2xQ8)480,681
C30.78(C2×Q8) = C3×C4.Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.78(C2xQ8)480,683
C30.79(C2×Q8) = C6×C10.D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.79(C2xQ8)480,716
C30.80(C2×Q8) = C3×C20.48D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30240C30.80(C2xQ8)480,717
C30.81(C2×Q8) = C6×C4⋊Dic5φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.81(C2xQ8)480,718
C30.82(C2×Q8) = C20×Dic6φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.82(C2xQ8)480,747
C30.83(C2×Q8) = C5×C12⋊2Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.83(C2xQ8)480,748
C30.84(C2×Q8) = C5×C12.6Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.84(C2xQ8)480,749
C30.85(C2×Q8) = C5×Dic3.D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30240C30.85(C2xQ8)480,757
C30.86(C2×Q8) = C5×C12⋊Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.86(C2xQ8)480,767
C30.87(C2×Q8) = C5×C4.Dic6φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.87(C2xQ8)480,769
C30.88(C2×Q8) = C10×Dic3⋊C4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.88(C2xQ8)480,802
C30.89(C2×Q8) = C5×C12.48D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30240C30.89(C2xQ8)480,803
C30.90(C2×Q8) = C10×C4⋊Dic3φ: C2×Q8/C2×C4 → C2 ⊆ Aut C30480C30.90(C2xQ8)480,804
C30.91(C2×Q8) = Dic15⋊10Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.91(C2xQ8)480,852
C30.92(C2×Q8) = C4⋊Dic30φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.92(C2xQ8)480,853
C30.93(C2×Q8) = Dic15.3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.93(C2xQ8)480,854
C30.94(C2×Q8) = C4⋊C4×D15φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.94(C2xQ8)480,856
C30.95(C2×Q8) = D30⋊5Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.95(C2xQ8)480,861
C30.96(C2×Q8) = D30⋊6Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.96(C2xQ8)480,862
C30.97(C2×Q8) = Dic15⋊4Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.97(C2xQ8)480,909
C30.98(C2×Q8) = Q8×Dic15φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.98(C2xQ8)480,910
C30.99(C2×Q8) = D30⋊7Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.99(C2xQ8)480,911
C30.100(C2×Q8) = C3×Dic5⋊3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.100(C2xQ8)480,680
C30.101(C2×Q8) = C3×Dic5.Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.101(C2xQ8)480,682
C30.102(C2×Q8) = C3×D5×C4⋊C4φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.102(C2xQ8)480,684
C30.103(C2×Q8) = C3×D10⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.103(C2xQ8)480,689
C30.104(C2×Q8) = C3×D10⋊2Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.104(C2xQ8)480,690
C30.105(C2×Q8) = C3×Dic5⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.105(C2xQ8)480,737
C30.106(C2×Q8) = C3×Q8×Dic5φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.106(C2xQ8)480,738
C30.107(C2×Q8) = C3×D10⋊3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.107(C2xQ8)480,739
C30.108(C2×Q8) = C5×Dic6⋊C4φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.108(C2xQ8)480,766
C30.109(C2×Q8) = C5×Dic3.Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.109(C2xQ8)480,768
C30.110(C2×Q8) = C5×S3×C4⋊C4φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.110(C2xQ8)480,770
C30.111(C2×Q8) = C5×D6⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.111(C2xQ8)480,775
C30.112(C2×Q8) = C5×C4.D12φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.112(C2xQ8)480,776
C30.113(C2×Q8) = C5×Dic3⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.113(C2xQ8)480,823
C30.114(C2×Q8) = C5×Q8×Dic3φ: C2×Q8/Q8 → C2 ⊆ Aut C30480C30.114(C2xQ8)480,824
C30.115(C2×Q8) = C5×D6⋊3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C30240C30.115(C2xQ8)480,825
C30.116(C2×Q8) = C4⋊C4×C30central extension (φ=1)480C30.116(C2xQ8)480,921
C30.117(C2×Q8) = Q8×C60central extension (φ=1)480C30.117(C2xQ8)480,924
C30.118(C2×Q8) = C15×C22⋊Q8central extension (φ=1)240C30.118(C2xQ8)480,927
C30.119(C2×Q8) = C15×C42.C2central extension (φ=1)480C30.119(C2xQ8)480,930
C30.120(C2×Q8) = C15×C4⋊Q8central extension (φ=1)480C30.120(C2xQ8)480,933

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