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Extensions 1→N→G→Q→1 with N=C10 and Q=C22⋊C4

Direct product G=N×Q with N=C10 and Q=C22⋊C4
dρLabelID
C10×C22⋊C480C10xC2^2:C4160,176

Semidirect products G=N:Q with N=C10 and Q=C22⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊(C22⋊C4) = C2×C22⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C1040C10:(C2^2:C4)160,212
C10⋊2(C22⋊C4) = C2×D10⋊C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C1080C10:2(C2^2:C4)160,148
C10⋊3(C22⋊C4) = C2×C23.D5φ: C22⋊C4/C23 → C2 ⊆ Aut C1080C10:3(C2^2:C4)160,173

Non-split extensions G=N.Q with N=C10 and Q=C22⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(C22⋊C4) = D10.D4φ: C22⋊C4/C22 → C4 ⊆ Aut C10404+C10.1(C2^2:C4)160,74
C10.2(C22⋊C4) = D10⋊C8φ: C22⋊C4/C22 → C4 ⊆ Aut C1080C10.2(C2^2:C4)160,78
C10.3(C22⋊C4) = Dic5.D4φ: C22⋊C4/C22 → C4 ⊆ Aut C10804-C10.3(C2^2:C4)160,80
C10.4(C22⋊C4) = D10.3Q8φ: C22⋊C4/C22 → C4 ⊆ Aut C1040C10.4(C2^2:C4)160,81
C10.5(C22⋊C4) = D20⋊C4φ: C22⋊C4/C22 → C4 ⊆ Aut C10408+C10.5(C2^2:C4)160,82
C10.6(C22⋊C4) = D4⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C10408-C10.6(C2^2:C4)160,83
C10.7(C22⋊C4) = Q8⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C10408-C10.7(C2^2:C4)160,84
C10.8(C22⋊C4) = Q8⋊2F5φ: C22⋊C4/C22 → C4 ⊆ Aut C10408+C10.8(C2^2:C4)160,85
C10.9(C22⋊C4) = C23⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C10404C10.9(C2^2:C4)160,86
C10.10(C22⋊C4) = C23.2F5φ: C22⋊C4/C22 → C4 ⊆ Aut C1080C10.10(C2^2:C4)160,87
C10.11(C22⋊C4) = C23.F5φ: C22⋊C4/C22 → C4 ⊆ Aut C10404C10.11(C2^2:C4)160,88
C10.12(C22⋊C4) = D20⋊4C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10402C10.12(C2^2:C4)160,12
C10.13(C22⋊C4) = C23.1D10φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10404C10.13(C2^2:C4)160,13
C10.14(C22⋊C4) = D20⋊6C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C1080C10.14(C2^2:C4)160,16
C10.15(C22⋊C4) = C10.Q16φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10160C10.15(C2^2:C4)160,17
C10.16(C22⋊C4) = C20.44D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10160C10.16(C2^2:C4)160,23
C10.17(C22⋊C4) = D10⋊1C8φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C1080C10.17(C2^2:C4)160,27
C10.18(C22⋊C4) = D20⋊5C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C1080C10.18(C2^2:C4)160,28
C10.19(C22⋊C4) = C20.46D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10404+C10.19(C2^2:C4)160,30
C10.20(C22⋊C4) = C4.12D20φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10804-C10.20(C2^2:C4)160,31
C10.21(C22⋊C4) = D20⋊7C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10404C10.21(C2^2:C4)160,32
C10.22(C22⋊C4) = C10.10C42φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C10160C10.22(C2^2:C4)160,38
C10.23(C22⋊C4) = C20.55D4φ: C22⋊C4/C23 → C2 ⊆ Aut C1080C10.23(C2^2:C4)160,37
C10.24(C22⋊C4) = D4⋊Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C1080C10.24(C2^2:C4)160,39
C10.25(C22⋊C4) = C20.D4φ: C22⋊C4/C23 → C2 ⊆ Aut C10404C10.25(C2^2:C4)160,40
C10.26(C22⋊C4) = C23⋊Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C10404C10.26(C2^2:C4)160,41
C10.27(C22⋊C4) = Q8⋊Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C10160C10.27(C2^2:C4)160,42
C10.28(C22⋊C4) = C20.10D4φ: C22⋊C4/C23 → C2 ⊆ Aut C10804C10.28(C2^2:C4)160,43
C10.29(C22⋊C4) = D4⋊2Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C10404C10.29(C2^2:C4)160,44
C10.30(C22⋊C4) = C5×C2.C42central extension (φ=1)160C10.30(C2^2:C4)160,45
C10.31(C22⋊C4) = C5×C22⋊C8central extension (φ=1)80C10.31(C2^2:C4)160,48
C10.32(C22⋊C4) = C5×C23⋊C4central extension (φ=1)404C10.32(C2^2:C4)160,49
C10.33(C22⋊C4) = C5×C4.D4central extension (φ=1)404C10.33(C2^2:C4)160,50
C10.34(C22⋊C4) = C5×C4.10D4central extension (φ=1)804C10.34(C2^2:C4)160,51
C10.35(C22⋊C4) = C5×D4⋊C4central extension (φ=1)80C10.35(C2^2:C4)160,52
C10.36(C22⋊C4) = C5×Q8⋊C4central extension (φ=1)160C10.36(C2^2:C4)160,53
C10.37(C22⋊C4) = C5×C4≀C2central extension (φ=1)402C10.37(C2^2:C4)160,54

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