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Extensions 1→N→G→Q→1 with N=C2×C30 and Q=C2×C4

Direct product G=N×Q with N=C2×C30 and Q=C2×C4
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C2×C30 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C2×C30)⋊1(C2×C4) = F5×C3⋊D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30608(C2xC30):1(C2xC4)480,1010
(C2×C30)⋊2(C2×C4) = S3×C22⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30608+(C2xC30):2(C2xC4)480,1011
(C2×C30)⋊3(C2×C4) = C3⋊D4⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30608(C2xC30):3(C2xC4)480,1012
(C2×C30)⋊4(C2×C4) = C22×S3×F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C3060(C2xC30):4(C2xC4)480,1197
(C2×C30)⋊5(C2×C4) = D4×C3⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30608(C2xC30):5(C2xC4)480,1067
(C2×C30)⋊6(C2×C4) = C3×D4×F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30608(C2xC30):6(C2xC4)480,1054
(C2×C30)⋊7(C2×C4) = C2×D10.D6φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30):7(C2xC4)480,1072
(C2×C30)⋊8(C2×C4) = C23×C3⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30):8(C2xC4)480,1206
(C2×C30)⋊9(C2×C4) = C6×C22⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30):9(C2xC4)480,1059
(C2×C30)⋊10(C2×C4) = F5×C22×C6φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30):10(C2xC4)480,1205
(C2×C30)⋊11(C2×C4) = C22⋊C4×D15φ: C2×C4/C2 → C22 ⊆ Aut C2×C30120(C2xC30):11(C2xC4)480,845
(C2×C30)⋊12(C2×C4) = Dic15⋊19D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):12(C2xC4)480,846
(C2×C30)⋊13(C2×C4) = D4×Dic15φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):13(C2xC4)480,899
(C2×C30)⋊14(C2×C4) = D5×C6.D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30120(C2xC30):14(C2xC4)480,623
(C2×C30)⋊15(C2×C4) = Dic5×C3⋊D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):15(C2xC4)480,627
(C2×C30)⋊16(C2×C4) = C15⋊26(C4×D4)φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):16(C2xC4)480,628
(C2×C30)⋊17(C2×C4) = Dic3×C5⋊D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):17(C2xC4)480,629
(C2×C30)⋊18(C2×C4) = S3×C23.D5φ: C2×C4/C2 → C22 ⊆ Aut C2×C30120(C2xC30):18(C2xC4)480,630
(C2×C30)⋊19(C2×C4) = C15⋊28(C4×D4)φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):19(C2xC4)480,632
(C2×C30)⋊20(C2×C4) = Dic15⋊16D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):20(C2xC4)480,635
(C2×C30)⋊21(C2×C4) = Dic15⋊17D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):21(C2xC4)480,636
(C2×C30)⋊22(C2×C4) = D30.45D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30120(C2xC30):22(C2xC4)480,637
(C2×C30)⋊23(C2×C4) = C22×D5×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):23(C2xC4)480,1112
(C2×C30)⋊24(C2×C4) = C22×S3×Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):24(C2xC4)480,1115
(C2×C30)⋊25(C2×C4) = C22×D30.C2φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):25(C2xC4)480,1117
(C2×C30)⋊26(C2×C4) = C3×D5×C22⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30120(C2xC30):26(C2xC4)480,673
(C2×C30)⋊27(C2×C4) = C3×Dic5⋊4D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):27(C2xC4)480,674
(C2×C30)⋊28(C2×C4) = C3×D4×Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):28(C2xC4)480,727
(C2×C30)⋊29(C2×C4) = C5×S3×C22⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30120(C2xC30):29(C2xC4)480,759
(C2×C30)⋊30(C2×C4) = C5×Dic3⋊4D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):30(C2xC4)480,760
(C2×C30)⋊31(C2×C4) = C5×D4×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30):31(C2xC4)480,813
(C2×C30)⋊32(C2×C4) = D4×C60φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):32(C2xC4)480,923
(C2×C30)⋊33(C2×C4) = C4×C15⋊7D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):33(C2xC4)480,893
(C2×C30)⋊34(C2×C4) = C22×C4×D15φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):34(C2xC4)480,1166
(C2×C30)⋊35(C2×C4) = C12×C5⋊D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):35(C2xC4)480,721
(C2×C30)⋊36(C2×C4) = D5×C22×C12φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):36(C2xC4)480,1136
(C2×C30)⋊37(C2×C4) = C20×C3⋊D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):37(C2xC4)480,807
(C2×C30)⋊38(C2×C4) = S3×C22×C20φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30):38(C2xC4)480,1151
(C2×C30)⋊39(C2×C4) = C22⋊C4×C30φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30):39(C2xC4)480,920
(C2×C30)⋊40(C2×C4) = C2×C30.38D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30):40(C2xC4)480,917
(C2×C30)⋊41(C2×C4) = C23×Dic15φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30):41(C2xC4)480,1178
(C2×C30)⋊42(C2×C4) = C6×C23.D5φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30):42(C2xC4)480,745
(C2×C30)⋊43(C2×C4) = Dic5×C22×C6φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30):43(C2xC4)480,1148
(C2×C30)⋊44(C2×C4) = C10×C6.D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30):44(C2xC4)480,831
(C2×C30)⋊45(C2×C4) = Dic3×C22×C10φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30):45(C2xC4)480,1163

Non-split extensions G=N.Q with N=C2×C30 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C2×C30).1(C2×C4) = D10.20D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30120(C2xC30).1(C2xC4)480,243
(C2×C30).2(C2×C4) = Dic3×C5⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30480(C2xC30).2(C2xC4)480,244
(C2×C30).3(C2×C4) = C30.M4(2)φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30480(C2xC30).3(C2xC4)480,245
(C2×C30).4(C2×C4) = Dic5.22D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30240(C2xC30).4(C2xC4)480,246
(C2×C30).5(C2×C4) = D30⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30240(C2xC30).5(C2xC4)480,247
(C2×C30).6(C2×C4) = D10.D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C301208-(C2xC30).6(C2xC4)480,248
(C2×C30).7(C2×C4) = D10.4D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C301208+(C2xC30).7(C2xC4)480,249
(C2×C30).8(C2×C4) = Dic5.D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C301208+(C2xC30).8(C2xC4)480,250
(C2×C30).9(C2×C4) = Dic5.4D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C302408-(C2xC30).9(C2xC4)480,251
(C2×C30).10(C2×C4) = C30.4M4(2)φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30480(C2xC30).10(C2xC4)480,252
(C2×C30).11(C2×C4) = Dic15⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30480(C2xC30).11(C2xC4)480,253
(C2×C30).12(C2×C4) = C2×Dic3×F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30120(C2xC30).12(C2xC4)480,998
(C2×C30).13(C2×C4) = C22⋊F5.S3φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C301208-(C2xC30).13(C2xC4)480,999
(C2×C30).14(C2×C4) = C2×D6⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30120(C2xC30).14(C2xC4)480,1000
(C2×C30).15(C2×C4) = C2×Dic3⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30120(C2xC30).15(C2xC4)480,1001
(C2×C30).16(C2×C4) = C2×S3×C5⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30240(C2xC30).16(C2xC4)480,1002
(C2×C30).17(C2×C4) = C5⋊C8.D6φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C302408(C2xC30).17(C2xC4)480,1003
(C2×C30).18(C2×C4) = S3×C22.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C301208-(C2xC30).18(C2xC4)480,1004
(C2×C30).19(C2×C4) = D15⋊C8⋊C2φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C302408(C2xC30).19(C2xC4)480,1005
(C2×C30).20(C2×C4) = C2×D15⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30240(C2xC30).20(C2xC4)480,1006
(C2×C30).21(C2×C4) = D15⋊2M4(2)φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C301208+(C2xC30).21(C2xC4)480,1007
(C2×C30).22(C2×C4) = C2×D6.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30240(C2xC30).22(C2xC4)480,1008
(C2×C30).23(C2×C4) = C2×Dic3.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C30240(C2xC30).23(C2xC4)480,1009
(C2×C30).24(C2×C4) = Dic10.Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C302408(C2xC30).24(C2xC4)480,1066
(C2×C30).25(C2×C4) = C3×D4.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C2×C302408(C2xC30).25(C2xC4)480,1053
(C2×C30).26(C2×C4) = (C2×C60)⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).26(C2xC4)480,304
(C2×C30).27(C2×C4) = C4×C15⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).27(C2xC4)480,305
(C2×C30).28(C2×C4) = C60⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).28(C2xC4)480,306
(C2×C30).29(C2×C4) = C30.11C42φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).29(C2xC4)480,307
(C2×C30).30(C2×C4) = C30.7M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).30(C2xC4)480,308
(C2×C30).31(C2×C4) = Dic5.13D12φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).31(C2xC4)480,309
(C2×C30).32(C2×C4) = (C2×C60).C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C302404(C2xC30).32(C2xC4)480,310
(C2×C30).33(C2×C4) = D10.10D12φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30).33(C2xC4)480,311
(C2×C30).34(C2×C4) = C3⋊(C23⋊F5)φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).34(C2xC4)480,316
(C2×C30).35(C2×C4) = C30.22M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).35(C2xC4)480,317
(C2×C30).36(C2×C4) = C5⋊(C12.D4)φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).36(C2xC4)480,318
(C2×C30).37(C2×C4) = C2×C60.C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).37(C2xC4)480,1060
(C2×C30).38(C2×C4) = C2×C12.F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).38(C2xC4)480,1061
(C2×C30).39(C2×C4) = C60.59(C2×C4)φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).39(C2xC4)480,1062
(C2×C30).40(C2×C4) = C2×C4×C3⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30).40(C2xC4)480,1063
(C2×C30).41(C2×C4) = C2×C60⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30).41(C2xC4)480,1064
(C2×C30).42(C2×C4) = (C2×C12)⋊6F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).42(C2xC4)480,1065
(C2×C30).43(C2×C4) = C22×C15⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).43(C2xC4)480,1070
(C2×C30).44(C2×C4) = C2×C15⋊8M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).44(C2xC4)480,1071
(C2×C30).45(C2×C4) = C3×D10.D4φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).45(C2xC4)480,279
(C2×C30).46(C2×C4) = C12×C5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).46(C2xC4)480,280
(C2×C30).47(C2×C4) = C3×C20⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).47(C2xC4)480,281
(C2×C30).48(C2×C4) = C3×C10.C42φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).48(C2xC4)480,282
(C2×C30).49(C2×C4) = C3×D10⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).49(C2xC4)480,283
(C2×C30).50(C2×C4) = C3×Dic5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).50(C2xC4)480,284
(C2×C30).51(C2×C4) = C3×Dic5.D4φ: C2×C4/C2 → C4 ⊆ Aut C2×C302404(C2xC30).51(C2xC4)480,285
(C2×C30).52(C2×C4) = C3×D10.3Q8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30).52(C2xC4)480,286
(C2×C30).53(C2×C4) = C3×C23⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).53(C2xC4)480,291
(C2×C30).54(C2×C4) = C3×C23.2F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).54(C2xC4)480,292
(C2×C30).55(C2×C4) = C3×C23.F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).55(C2xC4)480,293
(C2×C30).56(C2×C4) = C6×D5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).56(C2xC4)480,1047
(C2×C30).57(C2×C4) = C6×C4.F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).57(C2xC4)480,1048
(C2×C30).58(C2×C4) = C3×D5⋊M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).58(C2xC4)480,1049
(C2×C30).59(C2×C4) = F5×C2×C12φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30).59(C2xC4)480,1050
(C2×C30).60(C2×C4) = C6×C4⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30120(C2xC30).60(C2xC4)480,1051
(C2×C30).61(C2×C4) = C3×D10.C23φ: C2×C4/C2 → C4 ⊆ Aut C2×C301204(C2xC30).61(C2xC4)480,1052
(C2×C30).62(C2×C4) = C2×C6×C5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2×C30480(C2xC30).62(C2xC4)480,1057
(C2×C30).63(C2×C4) = C6×C22.F5φ: C2×C4/C2 → C4 ⊆ Aut C2×C30240(C2xC30).63(C2xC4)480,1058
(C2×C30).64(C2×C4) = C23.6D30φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).64(C2xC4)480,166
(C2×C30).65(C2×C4) = M4(2)⋊D15φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204+(C2xC30).65(C2xC4)480,183
(C2×C30).66(C2×C4) = C4.D60φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404-(C2xC30).66(C2xC4)480,184
(C2×C30).67(C2×C4) = C23.15D30φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).67(C2xC4)480,842
(C2×C30).68(C2×C4) = M4(2)×D15φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).68(C2xC4)480,871
(C2×C30).69(C2×C4) = D60.3C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).69(C2xC4)480,872
(C2×C30).70(C2×C4) = D4.Dic15φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).70(C2xC4)480,913
(C2×C30).71(C2×C4) = Dic5×C3⋊C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).71(C2xC4)480,25
(C2×C30).72(C2×C4) = Dic3×C5⋊2C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).72(C2xC4)480,26
(C2×C30).73(C2×C4) = Dic15⋊4C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).73(C2xC4)480,27
(C2×C30).74(C2×C4) = C30.21C42φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).74(C2xC4)480,28
(C2×C30).75(C2×C4) = C30.22C42φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).75(C2xC4)480,29
(C2×C30).76(C2×C4) = C30.23C42φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).76(C2xC4)480,30
(C2×C30).77(C2×C4) = C60.93D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).77(C2xC4)480,31
(C2×C30).78(C2×C4) = C60.94D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).78(C2xC4)480,32
(C2×C30).79(C2×C4) = D30⋊4C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).79(C2xC4)480,33
(C2×C30).80(C2×C4) = C60.28D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).80(C2xC4)480,34
(C2×C30).81(C2×C4) = C20.5D12φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).81(C2xC4)480,35
(C2×C30).82(C2×C4) = C60.29D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204+(C2xC30).82(C2xC4)480,36
(C2×C30).83(C2×C4) = C12.6D20φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).83(C2xC4)480,37
(C2×C30).84(C2×C4) = C60.54D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).84(C2xC4)480,38
(C2×C30).85(C2×C4) = C60.31D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404-(C2xC30).85(C2xC4)480,39
(C2×C30).86(C2×C4) = C60.13Q8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).86(C2xC4)480,58
(C2×C30).87(C2×C4) = C60.14Q8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).87(C2xC4)480,59
(C2×C30).88(C2×C4) = C60.15Q8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).88(C2xC4)480,60
(C2×C30).89(C2×C4) = C30.24C42φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).89(C2xC4)480,70
(C2×C30).90(C2×C4) = (C2×C6).D20φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).90(C2xC4)480,71
(C2×C30).91(C2×C4) = C15⋊8(C23⋊C4)φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).91(C2xC4)480,72
(C2×C30).92(C2×C4) = C15⋊9(C23⋊C4)φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).92(C2xC4)480,73
(C2×C30).93(C2×C4) = C2×D5×C3⋊C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).93(C2xC4)480,357
(C2×C30).94(C2×C4) = D5×C4.Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).94(C2xC4)480,358
(C2×C30).95(C2×C4) = D20.3Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).95(C2xC4)480,359
(C2×C30).96(C2×C4) = D20.2Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).96(C2xC4)480,360
(C2×C30).97(C2×C4) = C2×S3×C5⋊2C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).97(C2xC4)480,361
(C2×C30).98(C2×C4) = D12.2Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).98(C2xC4)480,362
(C2×C30).99(C2×C4) = S3×C4.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).99(C2xC4)480,363
(C2×C30).100(C2×C4) = D12.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).100(C2xC4)480,364
(C2×C30).101(C2×C4) = C2×D15⋊2C8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).101(C2xC4)480,365
(C2×C30).102(C2×C4) = D60.5C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).102(C2xC4)480,366
(C2×C30).103(C2×C4) = D60.4C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).103(C2xC4)480,367
(C2×C30).104(C2×C4) = D15⋊4M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).104(C2xC4)480,368
(C2×C30).105(C2×C4) = C2×C20.32D6φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).105(C2xC4)480,369
(C2×C30).106(C2×C4) = C2×D6.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).106(C2xC4)480,370
(C2×C30).107(C2×C4) = C2×D30.5C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).107(C2xC4)480,371
(C2×C30).108(C2×C4) = C2×Dic3×Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).108(C2xC4)480,603
(C2×C30).109(C2×C4) = (C6×Dic5)⋊7C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).109(C2xC4)480,604
(C2×C30).110(C2×C4) = C23.26(S3×D5)φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).110(C2xC4)480,605
(C2×C30).111(C2×C4) = C23.48(S3×D5)φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).111(C2xC4)480,608
(C2×C30).112(C2×C4) = C2×D10⋊Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).112(C2xC4)480,611
(C2×C30).113(C2×C4) = C2×D6⋊Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).113(C2xC4)480,614
(C2×C30).114(C2×C4) = C2×D30⋊4C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).114(C2xC4)480,616
(C2×C30).115(C2×C4) = C2×C30.Q8φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).115(C2xC4)480,617
(C2×C30).116(C2×C4) = C2×Dic15⋊5C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).116(C2xC4)480,620
(C2×C30).117(C2×C4) = C2×C6.Dic10φ: C2×C4/C2 → C22 ⊆ Aut C2×C30480(C2xC30).117(C2xC4)480,621
(C2×C30).118(C2×C4) = C3×C23.1D10φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).118(C2xC4)480,84
(C2×C30).119(C2×C4) = C3×C20.46D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).119(C2xC4)480,101
(C2×C30).120(C2×C4) = C3×C4.12D20φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).120(C2xC4)480,102
(C2×C30).121(C2×C4) = C3×C23.11D10φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).121(C2xC4)480,670
(C2×C30).122(C2×C4) = C3×D5×M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).122(C2xC4)480,699
(C2×C30).123(C2×C4) = C3×D20.2C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).123(C2xC4)480,700
(C2×C30).124(C2×C4) = C3×D4.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).124(C2xC4)480,741
(C2×C30).125(C2×C4) = C5×C23.6D6φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).125(C2xC4)480,125
(C2×C30).126(C2×C4) = C5×C12.46D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).126(C2xC4)480,142
(C2×C30).127(C2×C4) = C5×C12.47D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).127(C2xC4)480,143
(C2×C30).128(C2×C4) = C5×C23.16D6φ: C2×C4/C2 → C22 ⊆ Aut C2×C30240(C2xC30).128(C2xC4)480,756
(C2×C30).129(C2×C4) = C5×S3×M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2×C301204(C2xC30).129(C2xC4)480,785
(C2×C30).130(C2×C4) = C5×D12.C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).130(C2xC4)480,786
(C2×C30).131(C2×C4) = C5×D4.Dic3φ: C2×C4/C2 → C22 ⊆ Aut C2×C302404(C2xC30).131(C2xC4)480,827
(C2×C30).132(C2×C4) = C15×C8○D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C302402(C2xC30).132(C2xC4)480,936
(C2×C30).133(C2×C4) = C8×Dic15φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).133(C2xC4)480,173
(C2×C30).134(C2×C4) = C60.26Q8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).134(C2xC4)480,174
(C2×C30).135(C2×C4) = C120⋊13C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).135(C2xC4)480,175
(C2×C30).136(C2×C4) = D30⋊3C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).136(C2xC4)480,180
(C2×C30).137(C2×C4) = C30.29C42φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).137(C2xC4)480,191
(C2×C30).138(C2×C4) = C2×C8×D15φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).138(C2xC4)480,864
(C2×C30).139(C2×C4) = C2×C40⋊S3φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).139(C2xC4)480,865
(C2×C30).140(C2×C4) = D60.6C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C302402(C2xC30).140(C2xC4)480,866
(C2×C30).141(C2×C4) = C2×C30.4Q8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).141(C2xC4)480,888
(C2×C30).142(C2×C4) = C2×D30⋊3C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).142(C2xC4)480,892
(C2×C30).143(C2×C4) = Dic5×C24φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).143(C2xC4)480,91
(C2×C30).144(C2×C4) = C3×C20.8Q8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).144(C2xC4)480,92
(C2×C30).145(C2×C4) = C3×C40⋊8C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).145(C2xC4)480,93
(C2×C30).146(C2×C4) = C3×D10⋊1C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).146(C2xC4)480,98
(C2×C30).147(C2×C4) = C3×C10.10C42φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).147(C2xC4)480,109
(C2×C30).148(C2×C4) = D5×C2×C24φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).148(C2xC4)480,692
(C2×C30).149(C2×C4) = C6×C8⋊D5φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).149(C2xC4)480,693
(C2×C30).150(C2×C4) = C3×D20.3C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C302402(C2xC30).150(C2xC4)480,694
(C2×C30).151(C2×C4) = Dic5×C2×C12φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).151(C2xC4)480,715
(C2×C30).152(C2×C4) = C6×C10.D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).152(C2xC4)480,716
(C2×C30).153(C2×C4) = C6×D10⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).153(C2xC4)480,720
(C2×C30).154(C2×C4) = Dic3×C40φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).154(C2xC4)480,132
(C2×C30).155(C2×C4) = C5×Dic3⋊C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).155(C2xC4)480,133
(C2×C30).156(C2×C4) = C5×C24⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).156(C2xC4)480,134
(C2×C30).157(C2×C4) = C5×D6⋊C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).157(C2xC4)480,139
(C2×C30).158(C2×C4) = C5×C6.C42φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).158(C2xC4)480,150
(C2×C30).159(C2×C4) = S3×C2×C40φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).159(C2xC4)480,778
(C2×C30).160(C2×C4) = C10×C8⋊S3φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).160(C2xC4)480,779
(C2×C30).161(C2×C4) = C5×C8○D12φ: C2×C4/C4 → C2 ⊆ Aut C2×C302402(C2xC30).161(C2xC4)480,780
(C2×C30).162(C2×C4) = C10×Dic3⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30480(C2xC30).162(C2xC4)480,802
(C2×C30).163(C2×C4) = C10×D6⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C30240(C2xC30).163(C2xC4)480,806
(C2×C30).164(C2×C4) = C15×C23⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).164(C2xC4)480,202
(C2×C30).165(C2×C4) = C15×C4.D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).165(C2xC4)480,203
(C2×C30).166(C2×C4) = C15×C4.10D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C302404(C2xC30).166(C2xC4)480,204
(C2×C30).167(C2×C4) = C15×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).167(C2xC4)480,922
(C2×C30).168(C2×C4) = M4(2)×C30φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).168(C2xC4)480,935
(C2×C30).169(C2×C4) = C4×C15⋊3C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).169(C2xC4)480,162
(C2×C30).170(C2×C4) = C42.D15φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).170(C2xC4)480,163
(C2×C30).171(C2×C4) = C60⋊5C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).171(C2xC4)480,164
(C2×C30).172(C2×C4) = C60.212D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).172(C2xC4)480,190
(C2×C30).173(C2×C4) = C60.8D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).173(C2xC4)480,193
(C2×C30).174(C2×C4) = C23.7D30φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).174(C2xC4)480,194
(C2×C30).175(C2×C4) = C60.10D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C302404(C2xC30).175(C2xC4)480,196
(C2×C30).176(C2×C4) = C22×C15⋊3C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).176(C2xC4)480,885
(C2×C30).177(C2×C4) = C2×C60.7C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).177(C2xC4)480,886
(C2×C30).178(C2×C4) = C2×C4×Dic15φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).178(C2xC4)480,887
(C2×C30).179(C2×C4) = C2×C60⋊5C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).179(C2xC4)480,890
(C2×C30).180(C2×C4) = C23.26D30φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).180(C2xC4)480,891
(C2×C30).181(C2×C4) = C12×C5⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).181(C2xC4)480,80
(C2×C30).182(C2×C4) = C3×C42.D5φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).182(C2xC4)480,81
(C2×C30).183(C2×C4) = C3×C20⋊3C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).183(C2xC4)480,82
(C2×C30).184(C2×C4) = C3×C20.55D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).184(C2xC4)480,108
(C2×C30).185(C2×C4) = C3×C20.D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).185(C2xC4)480,111
(C2×C30).186(C2×C4) = C3×C23⋊Dic5φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).186(C2xC4)480,112
(C2×C30).187(C2×C4) = C3×C20.10D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C302404(C2xC30).187(C2xC4)480,114
(C2×C30).188(C2×C4) = C2×C6×C5⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).188(C2xC4)480,713
(C2×C30).189(C2×C4) = C6×C4.Dic5φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).189(C2xC4)480,714
(C2×C30).190(C2×C4) = C6×C4⋊Dic5φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).190(C2xC4)480,718
(C2×C30).191(C2×C4) = C3×C23.21D10φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).191(C2xC4)480,719
(C2×C30).192(C2×C4) = C20×C3⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).192(C2xC4)480,121
(C2×C30).193(C2×C4) = C5×C42.S3φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).193(C2xC4)480,122
(C2×C30).194(C2×C4) = C5×C12⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).194(C2xC4)480,123
(C2×C30).195(C2×C4) = C5×C12.55D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).195(C2xC4)480,149
(C2×C30).196(C2×C4) = C5×C12.D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).196(C2xC4)480,152
(C2×C30).197(C2×C4) = C5×C23.7D6φ: C2×C4/C22 → C2 ⊆ Aut C2×C301204(C2xC30).197(C2xC4)480,153
(C2×C30).198(C2×C4) = C5×C12.10D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C302404(C2xC30).198(C2xC4)480,155
(C2×C30).199(C2×C4) = C2×C10×C3⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).199(C2xC4)480,799
(C2×C30).200(C2×C4) = C10×C4.Dic3φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).200(C2xC4)480,800
(C2×C30).201(C2×C4) = Dic3×C2×C20φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).201(C2xC4)480,801
(C2×C30).202(C2×C4) = C10×C4⋊Dic3φ: C2×C4/C22 → C2 ⊆ Aut C2×C30480(C2xC30).202(C2xC4)480,804
(C2×C30).203(C2×C4) = C5×C23.26D6φ: C2×C4/C22 → C2 ⊆ Aut C2×C30240(C2xC30).203(C2xC4)480,805
(C2×C30).204(C2×C4) = C15×C2.C42central extension (φ=1)480(C2xC30).204(C2xC4)480,198
(C2×C30).205(C2×C4) = C15×C8⋊C4central extension (φ=1)480(C2xC30).205(C2xC4)480,200
(C2×C30).206(C2×C4) = C15×C22⋊C8central extension (φ=1)240(C2xC30).206(C2xC4)480,201
(C2×C30).207(C2×C4) = C15×C4⋊C8central extension (φ=1)480(C2xC30).207(C2xC4)480,208
(C2×C30).208(C2×C4) = C4⋊C4×C30central extension (φ=1)480(C2xC30).208(C2xC4)480,921

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