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Extensions 1→N→G→Q→1 with N=C50 and Q=C2×C4

Direct product G=N×Q with N=C50 and Q=C2×C4
dρLabelID
C22×C100400C2^2xC100400,45

Semidirect products G=N:Q with N=C50 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C50⋊(C2×C4) = C22×C25⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C50100C50:(C2xC4)400,53
C50⋊2(C2×C4) = C2×C4×D25φ: C2×C4/C4 → C2 ⊆ Aut C50200C50:2(C2xC4)400,36
C50⋊3(C2×C4) = C22×Dic25φ: C2×C4/C22 → C2 ⊆ Aut C50400C50:3(C2xC4)400,43

Non-split extensions G=N.Q with N=C50 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C50.1(C2×C4) = D25⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C502004C50.1(C2xC4)400,28
C50.2(C2×C4) = C100.C4φ: C2×C4/C2 → C4 ⊆ Aut C502004C50.2(C2xC4)400,29
C50.3(C2×C4) = C4×C25⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C501004C50.3(C2xC4)400,30
C50.4(C2×C4) = C100⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C501004C50.4(C2xC4)400,31
C50.5(C2×C4) = C2×C25⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C50400C50.5(C2xC4)400,32
C50.6(C2×C4) = C25⋊M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C502004-C50.6(C2xC4)400,33
C50.7(C2×C4) = D25.D4φ: C2×C4/C2 → C4 ⊆ Aut C501004+C50.7(C2xC4)400,34
C50.8(C2×C4) = C8×D25φ: C2×C4/C4 → C2 ⊆ Aut C502002C50.8(C2xC4)400,5
C50.9(C2×C4) = C8⋊D25φ: C2×C4/C4 → C2 ⊆ Aut C502002C50.9(C2xC4)400,6
C50.10(C2×C4) = C4×Dic25φ: C2×C4/C4 → C2 ⊆ Aut C50400C50.10(C2xC4)400,11
C50.11(C2×C4) = C50.D4φ: C2×C4/C4 → C2 ⊆ Aut C50400C50.11(C2xC4)400,12
C50.12(C2×C4) = D50⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C50200C50.12(C2xC4)400,14
C50.13(C2×C4) = C2×C25⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C50400C50.13(C2xC4)400,9
C50.14(C2×C4) = C4.Dic25φ: C2×C4/C22 → C2 ⊆ Aut C502002C50.14(C2xC4)400,10
C50.15(C2×C4) = C4⋊Dic25φ: C2×C4/C22 → C2 ⊆ Aut C50400C50.15(C2xC4)400,13
C50.16(C2×C4) = C23.D25φ: C2×C4/C22 → C2 ⊆ Aut C50200C50.16(C2xC4)400,19
C50.17(C2×C4) = C22⋊C4×C25central extension (φ=1)200C50.17(C2xC4)400,21
C50.18(C2×C4) = C4⋊C4×C25central extension (φ=1)400C50.18(C2xC4)400,22
C50.19(C2×C4) = M4(2)×C25central extension (φ=1)2002C50.19(C2xC4)400,24

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