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Extensions 1→N→G→Q→1 with N=C10 and Q=C2×C4

Direct product G=N×Q with N=C10 and Q=C2×C4
dρLabelID
C22×C2080C2^2xC2080,45

Semidirect products G=N:Q with N=C10 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C10⋊(C2×C4) = C22×F5φ: C2×C4/C2 → C4 ⊆ Aut C1020C10:(C2xC4)80,50
C10⋊2(C2×C4) = C2×C4×D5φ: C2×C4/C4 → C2 ⊆ Aut C1040C10:2(C2xC4)80,36
C10⋊3(C2×C4) = C22×Dic5φ: C2×C4/C22 → C2 ⊆ Aut C1080C10:3(C2xC4)80,43

Non-split extensions G=N.Q with N=C10 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C4) = D5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C10404C10.1(C2xC4)80,28
C10.2(C2×C4) = C4.F5φ: C2×C4/C2 → C4 ⊆ Aut C10404C10.2(C2xC4)80,29
C10.3(C2×C4) = C4×F5φ: C2×C4/C2 → C4 ⊆ Aut C10204C10.3(C2xC4)80,30
C10.4(C2×C4) = C4⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C10204C10.4(C2xC4)80,31
C10.5(C2×C4) = C2×C5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C1080C10.5(C2xC4)80,32
C10.6(C2×C4) = C22.F5φ: C2×C4/C2 → C4 ⊆ Aut C10404-C10.6(C2xC4)80,33
C10.7(C2×C4) = C22⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C10204+C10.7(C2xC4)80,34
C10.8(C2×C4) = C8×D5φ: C2×C4/C4 → C2 ⊆ Aut C10402C10.8(C2xC4)80,4
C10.9(C2×C4) = C8⋊D5φ: C2×C4/C4 → C2 ⊆ Aut C10402C10.9(C2xC4)80,5
C10.10(C2×C4) = C4×Dic5φ: C2×C4/C4 → C2 ⊆ Aut C1080C10.10(C2xC4)80,11
C10.11(C2×C4) = C10.D4φ: C2×C4/C4 → C2 ⊆ Aut C1080C10.11(C2xC4)80,12
C10.12(C2×C4) = D10⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C1040C10.12(C2xC4)80,14
C10.13(C2×C4) = C2×C5⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C1080C10.13(C2xC4)80,9
C10.14(C2×C4) = C4.Dic5φ: C2×C4/C22 → C2 ⊆ Aut C10402C10.14(C2xC4)80,10
C10.15(C2×C4) = C4⋊Dic5φ: C2×C4/C22 → C2 ⊆ Aut C1080C10.15(C2xC4)80,13
C10.16(C2×C4) = C23.D5φ: C2×C4/C22 → C2 ⊆ Aut C1040C10.16(C2xC4)80,19
C10.17(C2×C4) = C5×C22⋊C4central extension (φ=1)40C10.17(C2xC4)80,21
C10.18(C2×C4) = C5×C4⋊C4central extension (φ=1)80C10.18(C2xC4)80,22
C10.19(C2×C4) = C5×M4(2)central extension (φ=1)402C10.19(C2xC4)80,24

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