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Extensions 1→N→G→Q→1 with N=C10 and Q=C3×C4⋊C4

Direct product G=N×Q with N=C10 and Q=C3×C4⋊C4
dρLabelID
C4⋊C4×C30480C4:C4xC30480,921

Semidirect products G=N:Q with N=C10 and Q=C3×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊(C3×C4⋊C4) = C6×C4⋊F5φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C10120C10:(C3xC4:C4)480,1051
C10⋊2(C3×C4⋊C4) = C6×C10.D4φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10:2(C3xC4:C4)480,716
C10⋊3(C3×C4⋊C4) = C6×C4⋊Dic5φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10:3(C3xC4:C4)480,718

Non-split extensions G=N.Q with N=C10 and Q=C3×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(C3×C4⋊C4) = C3×C40⋊C4φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C101204C10.1(C3xC4:C4)480,273
C10.2(C3×C4⋊C4) = C3×D5.D8φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C101204C10.2(C3xC4:C4)480,274
C10.3(C3×C4⋊C4) = C3×C40.C4φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C102404C10.3(C3xC4:C4)480,275
C10.4(C3×C4⋊C4) = C3×D10.Q8φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C102404C10.4(C3xC4:C4)480,276
C10.5(C3×C4⋊C4) = C3×C20⋊C8φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C10480C10.5(C3xC4:C4)480,281
C10.6(C3×C4⋊C4) = C3×Dic5⋊C8φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C10480C10.6(C3xC4:C4)480,284
C10.7(C3×C4⋊C4) = C3×D10.3Q8φ: C3×C4⋊C4/C12 → C4 ⊆ Aut C10120C10.7(C3xC4:C4)480,286
C10.8(C3×C4⋊C4) = C3×C20⋊3C8φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.8(C3xC4:C4)480,82
C10.9(C3×C4⋊C4) = C3×C10.D8φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.9(C3xC4:C4)480,85
C10.10(C3×C4⋊C4) = C3×C20.Q8φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.10(C3xC4:C4)480,86
C10.11(C3×C4⋊C4) = C3×C20.8Q8φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.11(C3xC4:C4)480,92
C10.12(C3×C4⋊C4) = C3×C40⋊6C4φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.12(C3xC4:C4)480,95
C10.13(C3×C4⋊C4) = C3×C40⋊5C4φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.13(C3xC4:C4)480,96
C10.14(C3×C4⋊C4) = C3×C40.6C4φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C102402C10.14(C3xC4:C4)480,97
C10.15(C3×C4⋊C4) = C3×C20.53D4φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C102404C10.15(C3xC4:C4)480,100
C10.16(C3×C4⋊C4) = C3×C10.10C42φ: C3×C4⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.16(C3xC4:C4)480,109
C10.17(C3×C4⋊C4) = C15×C2.C42central extension (φ=1)480C10.17(C3xC4:C4)480,198
C10.18(C3×C4⋊C4) = C15×C4⋊C8central extension (φ=1)480C10.18(C3xC4:C4)480,208
C10.19(C3×C4⋊C4) = C15×C4.Q8central extension (φ=1)480C10.19(C3xC4:C4)480,209
C10.20(C3×C4⋊C4) = C15×C2.D8central extension (φ=1)480C10.20(C3xC4:C4)480,210
C10.21(C3×C4⋊C4) = C15×C8.C4central extension (φ=1)2402C10.21(C3xC4:C4)480,211

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