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Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C5⋊D5

Direct product G=N×Q with N=C4 and Q=C2×C5⋊D5
dρLabelID
C2×C4×C5⋊D5200C2xC4xC5:D5400,192

Semidirect products G=N:Q with N=C4 and Q=C2×C5⋊D5
extensionφ:Q→Aut NdρLabelID
C4⋊1(C2×C5⋊D5) = D4×C5⋊D5φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4100C4:1(C2xC5:D5)400,195
C4⋊2(C2×C5⋊D5) = C2×C20⋊D5φ: C2×C5⋊D5/C5×C10 → C2 ⊆ Aut C4200C4:2(C2xC5:D5)400,193

Non-split extensions G=N.Q with N=C4 and Q=C2×C5⋊D5
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C5⋊D5) = C52⋊7D8φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4200C4.1(C2xC5:D5)400,103
C4.2(C2×C5⋊D5) = C52⋊8SD16φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4200C4.2(C2xC5:D5)400,104
C4.3(C2×C5⋊D5) = C52⋊10SD16φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4200C4.3(C2xC5:D5)400,105
C4.4(C2×C5⋊D5) = C52⋊7Q16φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4400C4.4(C2xC5:D5)400,106
C4.5(C2×C5⋊D5) = C20.D10φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4200C4.5(C2xC5:D5)400,196
C4.6(C2×C5⋊D5) = Q8×C5⋊D5φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4200C4.6(C2xC5:D5)400,197
C4.7(C2×C5⋊D5) = C20.26D10φ: C2×C5⋊D5/C5⋊D5 → C2 ⊆ Aut C4200C4.7(C2xC5:D5)400,198
C4.8(C2×C5⋊D5) = C40⋊2D5φ: C2×C5⋊D5/C5×C10 → C2 ⊆ Aut C4200C4.8(C2xC5:D5)400,94
C4.9(C2×C5⋊D5) = C52⋊5D8φ: C2×C5⋊D5/C5×C10 → C2 ⊆ Aut C4200C4.9(C2xC5:D5)400,95
C4.10(C2×C5⋊D5) = C40.D5φ: C2×C5⋊D5/C5×C10 → C2 ⊆ Aut C4400C4.10(C2xC5:D5)400,96
C4.11(C2×C5⋊D5) = C2×C52⋊4Q8φ: C2×C5⋊D5/C5×C10 → C2 ⊆ Aut C4400C4.11(C2xC5:D5)400,191
C4.12(C2×C5⋊D5) = C8×C5⋊D5central extension (φ=1)200C4.12(C2xC5:D5)400,92
C4.13(C2×C5⋊D5) = C40⋊D5central extension (φ=1)200C4.13(C2xC5:D5)400,93
C4.14(C2×C5⋊D5) = C2×C52⋊7C8central extension (φ=1)400C4.14(C2xC5:D5)400,97
C4.15(C2×C5⋊D5) = C20.59D10central extension (φ=1)200C4.15(C2xC5:D5)400,98
C4.16(C2×C5⋊D5) = C20.50D10central extension (φ=1)200C4.16(C2xC5:D5)400,194

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