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

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

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C30
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C30) = C15×C22≀C2φ: C2×C30/C15 → C22 ⊆ Aut C2×C4120(C2xC4):1(C2xC30)480,925
(C2×C4)⋊2(C2×C30) = C15×2+ 1+4φ: C2×C30/C15 → C22 ⊆ Aut C2×C41204(C2xC4):2(C2xC30)480,1184
(C2×C4)⋊3(C2×C30) = C22⋊C4×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4):3(C2xC30)480,920
(C2×C4)⋊4(C2×C30) = D4×C2×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4):4(C2xC30)480,1181
(C2×C4)⋊5(C2×C30) = C4○D4×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4):5(C2xC30)480,1183

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C30
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C30) = C15×C4.D4φ: C2×C30/C15 → C22 ⊆ Aut C2×C41204(C2xC4).1(C2xC30)480,203
(C2×C4).2(C2×C30) = C15×C4.10D4φ: C2×C30/C15 → C22 ⊆ Aut C2×C42404(C2xC4).2(C2xC30)480,204
(C2×C4).3(C2×C30) = C15×C4⋊D4φ: C2×C30/C15 → C22 ⊆ Aut C2×C4240(C2xC4).3(C2xC30)480,926
(C2×C4).4(C2×C30) = C15×C22⋊Q8φ: C2×C30/C15 → C22 ⊆ Aut C2×C4240(C2xC4).4(C2xC30)480,927
(C2×C4).5(C2×C30) = C15×C22.D4φ: C2×C30/C15 → C22 ⊆ Aut C2×C4240(C2xC4).5(C2xC30)480,928
(C2×C4).6(C2×C30) = C15×C4⋊Q8φ: C2×C30/C15 → C22 ⊆ Aut C2×C4480(C2xC4).6(C2xC30)480,933
(C2×C4).7(C2×C30) = C15×C8⋊C22φ: C2×C30/C15 → C22 ⊆ Aut C2×C41204(C2xC4).7(C2xC30)480,941
(C2×C4).8(C2×C30) = C15×C8.C22φ: C2×C30/C15 → C22 ⊆ Aut C2×C42404(C2xC4).8(C2xC30)480,942
(C2×C4).9(C2×C30) = C15×2- 1+4φ: C2×C30/C15 → C22 ⊆ Aut C2×C42404(C2xC4).9(C2xC30)480,1185
(C2×C4).10(C2×C30) = C4⋊C4×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).10(C2xC30)480,921
(C2×C4).11(C2×C30) = D4×C60φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).11(C2xC30)480,923
(C2×C4).12(C2×C30) = Q8×C60φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).12(C2xC30)480,924
(C2×C4).13(C2×C30) = C15×C4.4D4φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).13(C2xC30)480,929
(C2×C4).14(C2×C30) = C15×C42.C2φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).14(C2xC30)480,930
(C2×C4).15(C2×C30) = C15×C42⋊2C2φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).15(C2xC30)480,931
(C2×C4).16(C2×C30) = C15×D4⋊C4φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).16(C2xC30)480,205
(C2×C4).17(C2×C30) = C15×Q8⋊C4φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).17(C2xC30)480,206
(C2×C4).18(C2×C30) = C15×C4≀C2φ: C2×C30/C30 → C2 ⊆ Aut C2×C41202(C2xC4).18(C2xC30)480,207
(C2×C4).19(C2×C30) = C15×C4.Q8φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).19(C2xC30)480,209
(C2×C4).20(C2×C30) = C15×C2.D8φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).20(C2xC30)480,210
(C2×C4).21(C2×C30) = C15×C8.C4φ: C2×C30/C30 → C2 ⊆ Aut C2×C42402(C2xC4).21(C2xC30)480,211
(C2×C4).22(C2×C30) = C15×C42⋊C2φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).22(C2xC30)480,922
(C2×C4).23(C2×C30) = C15×C4⋊1D4φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).23(C2xC30)480,932
(C2×C4).24(C2×C30) = M4(2)×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).24(C2xC30)480,935
(C2×C4).25(C2×C30) = C15×C8○D4φ: C2×C30/C30 → C2 ⊆ Aut C2×C42402(C2xC4).25(C2xC30)480,936
(C2×C4).26(C2×C30) = D8×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).26(C2xC30)480,937
(C2×C4).27(C2×C30) = SD16×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4240(C2xC4).27(C2xC30)480,938
(C2×C4).28(C2×C30) = Q16×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).28(C2xC30)480,939
(C2×C4).29(C2×C30) = C15×C4○D8φ: C2×C30/C30 → C2 ⊆ Aut C2×C42402(C2xC4).29(C2xC30)480,940
(C2×C4).30(C2×C30) = Q8×C2×C30φ: C2×C30/C30 → C2 ⊆ Aut C2×C4480(C2xC4).30(C2xC30)480,1182
(C2×C4).31(C2×C30) = C15×C8⋊C4central extension (φ=1)480(C2xC4).31(C2xC30)480,200
(C2×C4).32(C2×C30) = C15×C22⋊C8central extension (φ=1)240(C2xC4).32(C2xC30)480,201
(C2×C4).33(C2×C30) = C15×C4⋊C8central extension (φ=1)480(C2xC4).33(C2xC30)480,208

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