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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×F5

Direct product G=N×Q with N=C2×C6 and Q=C2×F5
dρLabelID
F5×C22×C6120F5xC2^2xC6480,1205

Semidirect products G=N:Q with N=C2×C6 and Q=C2×F5
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C2×F5) = S3×C22⋊F5φ: C2×F5/D5 → C22 ⊆ Aut C2×C6608+(C2xC6):1(C2xF5)480,1011
(C2×C6)⋊2(C2×F5) = C3⋊D4⋊F5φ: C2×F5/D5 → C22 ⊆ Aut C2×C6608(C2xC6):2(C2xF5)480,1012
(C2×C6)⋊3(C2×F5) = D4×C3⋊F5φ: C2×F5/D5 → C22 ⊆ Aut C2×C6608(C2xC6):3(C2xF5)480,1067
(C2×C6)⋊4(C2×F5) = C3×D4×F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C6608(C2xC6):4(C2xF5)480,1054
(C2×C6)⋊5(C2×F5) = F5×C3⋊D4φ: C2×F5/F5 → C2 ⊆ Aut C2×C6608(C2xC6):5(C2xF5)480,1010
(C2×C6)⋊6(C2×F5) = C22×S3×F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C660(C2xC6):6(C2xF5)480,1197
(C2×C6)⋊7(C2×F5) = C6×C22⋊F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C6120(C2xC6):7(C2xF5)480,1059
(C2×C6)⋊8(C2×F5) = C2×D10.D6φ: C2×F5/D10 → C2 ⊆ Aut C2×C6120(C2xC6):8(C2xF5)480,1072
(C2×C6)⋊9(C2×F5) = C23×C3⋊F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C6120(C2xC6):9(C2xF5)480,1206

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×F5
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C2×F5) = D10.D12φ: C2×F5/D5 → C22 ⊆ Aut C2×C61208-(C2xC6).1(C2xF5)480,248
(C2×C6).2(C2×F5) = D10.4D12φ: C2×F5/D5 → C22 ⊆ Aut C2×C61208+(C2xC6).2(C2xF5)480,249
(C2×C6).3(C2×F5) = Dic5.D12φ: C2×F5/D5 → C22 ⊆ Aut C2×C61208+(C2xC6).3(C2xF5)480,250
(C2×C6).4(C2×F5) = Dic5.4D12φ: C2×F5/D5 → C22 ⊆ Aut C2×C62408-(C2xC6).4(C2xF5)480,251
(C2×C6).5(C2×F5) = C22⋊F5.S3φ: C2×F5/D5 → C22 ⊆ Aut C2×C61208-(C2xC6).5(C2xF5)480,999
(C2×C6).6(C2×F5) = S3×C22.F5φ: C2×F5/D5 → C22 ⊆ Aut C2×C61208-(C2xC6).6(C2xF5)480,1004
(C2×C6).7(C2×F5) = D15⋊C8⋊C2φ: C2×F5/D5 → C22 ⊆ Aut C2×C62408(C2xC6).7(C2xF5)480,1005
(C2×C6).8(C2×F5) = D15⋊2M4(2)φ: C2×F5/D5 → C22 ⊆ Aut C2×C61208+(C2xC6).8(C2xF5)480,1007
(C2×C6).9(C2×F5) = Dic10.Dic3φ: C2×F5/D5 → C22 ⊆ Aut C2×C62408(C2xC6).9(C2xF5)480,1066
(C2×C6).10(C2×F5) = C3×D4.F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C62408(C2xC6).10(C2xF5)480,1053
(C2×C6).11(C2×F5) = D10.20D12φ: C2×F5/F5 → C2 ⊆ Aut C2×C6120(C2xC6).11(C2xF5)480,243
(C2×C6).12(C2×F5) = Dic3×C5⋊C8φ: C2×F5/F5 → C2 ⊆ Aut C2×C6480(C2xC6).12(C2xF5)480,244
(C2×C6).13(C2×F5) = C30.M4(2)φ: C2×F5/F5 → C2 ⊆ Aut C2×C6480(C2xC6).13(C2xF5)480,245
(C2×C6).14(C2×F5) = Dic5.22D12φ: C2×F5/F5 → C2 ⊆ Aut C2×C6240(C2xC6).14(C2xF5)480,246
(C2×C6).15(C2×F5) = D30⋊C8φ: C2×F5/F5 → C2 ⊆ Aut C2×C6240(C2xC6).15(C2xF5)480,247
(C2×C6).16(C2×F5) = C30.4M4(2)φ: C2×F5/F5 → C2 ⊆ Aut C2×C6480(C2xC6).16(C2xF5)480,252
(C2×C6).17(C2×F5) = Dic15⋊C8φ: C2×F5/F5 → C2 ⊆ Aut C2×C6480(C2xC6).17(C2xF5)480,253
(C2×C6).18(C2×F5) = C2×Dic3×F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C6120(C2xC6).18(C2xF5)480,998
(C2×C6).19(C2×F5) = C2×D6⋊F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C6120(C2xC6).19(C2xF5)480,1000
(C2×C6).20(C2×F5) = C2×Dic3⋊F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C6120(C2xC6).20(C2xF5)480,1001
(C2×C6).21(C2×F5) = C2×S3×C5⋊C8φ: C2×F5/F5 → C2 ⊆ Aut C2×C6240(C2xC6).21(C2xF5)480,1002
(C2×C6).22(C2×F5) = C5⋊C8.D6φ: C2×F5/F5 → C2 ⊆ Aut C2×C62408(C2xC6).22(C2xF5)480,1003
(C2×C6).23(C2×F5) = C2×D15⋊C8φ: C2×F5/F5 → C2 ⊆ Aut C2×C6240(C2xC6).23(C2xF5)480,1006
(C2×C6).24(C2×F5) = C2×D6.F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C6240(C2xC6).24(C2xF5)480,1008
(C2×C6).25(C2×F5) = C2×Dic3.F5φ: C2×F5/F5 → C2 ⊆ Aut C2×C6240(C2xC6).25(C2xF5)480,1009
(C2×C6).26(C2×F5) = C3×D10.D4φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).26(C2xF5)480,279
(C2×C6).27(C2×F5) = C3×Dic5.D4φ: C2×F5/D10 → C2 ⊆ Aut C2×C62404(C2xC6).27(C2xF5)480,285
(C2×C6).28(C2×F5) = C3×C23⋊F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).28(C2xF5)480,291
(C2×C6).29(C2×F5) = C3×C23.F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).29(C2xF5)480,293
(C2×C6).30(C2×F5) = C3×D5⋊M4(2)φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).30(C2xF5)480,1049
(C2×C6).31(C2×F5) = C3×D10.C23φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).31(C2xF5)480,1052
(C2×C6).32(C2×F5) = (C2×C60)⋊C4φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).32(C2xF5)480,304
(C2×C6).33(C2×F5) = C4×C15⋊C8φ: C2×F5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).33(C2xF5)480,305
(C2×C6).34(C2×F5) = C60⋊C8φ: C2×F5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).34(C2xF5)480,306
(C2×C6).35(C2×F5) = C30.11C42φ: C2×F5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).35(C2xF5)480,307
(C2×C6).36(C2×F5) = C30.7M4(2)φ: C2×F5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).36(C2xF5)480,308
(C2×C6).37(C2×F5) = Dic5.13D12φ: C2×F5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).37(C2xF5)480,309
(C2×C6).38(C2×F5) = (C2×C60).C4φ: C2×F5/D10 → C2 ⊆ Aut C2×C62404(C2xC6).38(C2xF5)480,310
(C2×C6).39(C2×F5) = D10.10D12φ: C2×F5/D10 → C2 ⊆ Aut C2×C6120(C2xC6).39(C2xF5)480,311
(C2×C6).40(C2×F5) = C3⋊(C23⋊F5)φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).40(C2xF5)480,316
(C2×C6).41(C2×F5) = C30.22M4(2)φ: C2×F5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).41(C2xF5)480,317
(C2×C6).42(C2×F5) = C5⋊(C12.D4)φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).42(C2xF5)480,318
(C2×C6).43(C2×F5) = C2×C60.C4φ: C2×F5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).43(C2xF5)480,1060
(C2×C6).44(C2×F5) = C2×C12.F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).44(C2xF5)480,1061
(C2×C6).45(C2×F5) = C60.59(C2×C4)φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).45(C2xF5)480,1062
(C2×C6).46(C2×F5) = C2×C4×C3⋊F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C6120(C2xC6).46(C2xF5)480,1063
(C2×C6).47(C2×F5) = C2×C60⋊C4φ: C2×F5/D10 → C2 ⊆ Aut C2×C6120(C2xC6).47(C2xF5)480,1064
(C2×C6).48(C2×F5) = (C2×C12)⋊6F5φ: C2×F5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).48(C2xF5)480,1065
(C2×C6).49(C2×F5) = C22×C15⋊C8φ: C2×F5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).49(C2xF5)480,1070
(C2×C6).50(C2×F5) = C2×C15⋊8M4(2)φ: C2×F5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).50(C2xF5)480,1071
(C2×C6).51(C2×F5) = C12×C5⋊C8central extension (φ=1)480(C2xC6).51(C2xF5)480,280
(C2×C6).52(C2×F5) = C3×C20⋊C8central extension (φ=1)480(C2xC6).52(C2xF5)480,281
(C2×C6).53(C2×F5) = C3×C10.C42central extension (φ=1)480(C2xC6).53(C2xF5)480,282
(C2×C6).54(C2×F5) = C3×D10⋊C8central extension (φ=1)240(C2xC6).54(C2xF5)480,283
(C2×C6).55(C2×F5) = C3×Dic5⋊C8central extension (φ=1)480(C2xC6).55(C2xF5)480,284
(C2×C6).56(C2×F5) = C3×D10.3Q8central extension (φ=1)120(C2xC6).56(C2xF5)480,286
(C2×C6).57(C2×F5) = C3×C23.2F5central extension (φ=1)240(C2xC6).57(C2xF5)480,292
(C2×C6).58(C2×F5) = C6×D5⋊C8central extension (φ=1)240(C2xC6).58(C2xF5)480,1047
(C2×C6).59(C2×F5) = C6×C4.F5central extension (φ=1)240(C2xC6).59(C2xF5)480,1048
(C2×C6).60(C2×F5) = F5×C2×C12central extension (φ=1)120(C2xC6).60(C2xF5)480,1050
(C2×C6).61(C2×F5) = C6×C4⋊F5central extension (φ=1)120(C2xC6).61(C2xF5)480,1051
(C2×C6).62(C2×F5) = C2×C6×C5⋊C8central extension (φ=1)480(C2xC6).62(C2xF5)480,1057
(C2×C6).63(C2×F5) = C6×C22.F5central extension (φ=1)240(C2xC6).63(C2xF5)480,1058

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