Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₅×D₄

Direct product G=N×Q with N=C₂³ and Q=C₅×D₄

		d	ρ	Label	ID
D₄×C₂²×C₁₀		160		D4xC2^2xC10	320,1629

Semidirect products G=N:Q with N=C₂³ and Q=C₅×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₅×D₄) = C₅×C₂≀C₂²	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	40	4	C2^3:(C5xD4)	320,958
C₂³⋊₂(C₅×D₄) = C₅×C₂³⋊₂D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3:2(C5xD4)	320,893
C₂³⋊₃(C₅×D₄) = C₅×C₂³⋊₃D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	80		C2^3:3(C5xD4)	320,1536
C₂³⋊₄(C₅×D₄) = C₁₀×C₄⋊D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3:4(C5xD4)	320,1524
C₂³⋊₅(C₅×D₄) = C₁₀×C₂²≀C₂	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3:5(C5xD4)	320,1523

Non-split extensions G=N.Q with N=C₂³ and Q=C₅×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₅×D₄) = C₅×C₂≀C₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	40	4	C2^3.1(C5xD4)	320,156
C₂³.₂(C₅×D₄) = C₅×C₂³.D₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	80	4	C2^3.2(C5xD4)	320,157
C₂³.₃(C₅×D₄) = C₅×C₄²⋊C₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	40	4	C2^3.3(C5xD4)	320,158
C₂³.₄(C₅×D₄) = C₅×C₄²⋊₃C₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	80	4	C2^3.4(C5xD4)	320,159
C₂³.₅(C₅×D₄) = C₅×D₄⋊₄D₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	40	4	C2^3.5(C5xD4)	320,954
C₂³.₆(C₅×D₄) = C₅×D₄.₉D₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	80	4	C2^3.6(C5xD4)	320,956
C₂³.₇(C₅×D₄) = C₅×C₂³.₇D₄	φ: C₅×D₄/C₅ → D₄ ⊆ Aut C₂³	80	4	C2^3.7(C5xD4)	320,959
C₂³.₈(C₅×D₄) = C₅×C₄.₉C₄²	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	80	4	C2^3.8(C5xD4)	320,142
C₂³.₉(C₅×D₄) = C₅×C₂³.₁₀D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.9(C5xD4)	320,895
C₂³.₁₀(C₅×D₄) = C₅×C₂³.₁₁D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.10(C5xD4)	320,898
C₂³.₁₁(C₅×D₄) = C₁₀×C₂³⋊C₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	80		C2^3.11(C5xD4)	320,910
C₂³.₁₂(C₅×D₄) = C₅×C₄²⋊C₂²	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	80	4	C2^3.12(C5xD4)	320,922
C₂³.₁₃(C₅×D₄) = C₅×D₄⋊D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.13(C5xD4)	320,950
C₂³.₁₄(C₅×D₄) = C₅×D₄.₇D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.14(C5xD4)	320,953
C₂³.₁₅(C₅×D₄) = C₅×C₈⋊D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.15(C5xD4)	320,969
C₂³.₁₆(C₅×D₄) = C₅×C₈⋊₂D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.16(C5xD4)	320,970
C₂³.₁₇(C₅×D₄) = C₅×C₈.D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.17(C5xD4)	320,971
C₂³.₁₈(C₅×D₄) = C₅×C₂³.₁₉D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.18(C5xD4)	320,983
C₂³.₁₉(C₅×D₄) = C₅×C₂³.₂₀D₄	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.19(C5xD4)	320,986
C₂³.₂₀(C₅×D₄) = C₅×D₈⋊C₂²	φ: C₅×D₄/C₁₀ → C₂² ⊆ Aut C₂³	80	4	C2^3.20(C5xD4)	320,1577
C₂³.₂₁(C₅×D₄) = C₅×C₂³.₇Q₈	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.21(C5xD4)	320,881
C₂³.₂₂(C₅×D₄) = C₅×C₂³.₂₃D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.22(C5xD4)	320,887
C₂³.₂₃(C₅×D₄) = C₅×C₂³.₂₄D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.23(C5xD4)	320,917
C₂³.₂₄(C₅×D₄) = C₅×C₂³.₂₅D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.24(C5xD4)	320,928
C₂³.₂₅(C₅×D₄) = C₅×C₈⋊₈D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.25(C5xD4)	320,966
C₂³.₂₆(C₅×D₄) = C₅×C₈⋊₇D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.26(C5xD4)	320,967
C₂³.₂₇(C₅×D₄) = C₅×C₈.₁₈D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.27(C5xD4)	320,968
C₂³.₂₈(C₅×D₄) = C₁₀×C₄○D₈	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.28(C5xD4)	320,1574
C₂³.₂₉(C₅×D₄) = C₅×C₂².SD₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.29(C5xD4)	320,132
C₂³.₃₀(C₅×D₄) = C₅×C₂³.₃₁D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.30(C5xD4)	320,133
C₂³.₃₁(C₅×D₄) = C₅×C₄²⋊₆C₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.31(C5xD4)	320,144
C₂³.₃₂(C₅×D₄) = C₅×C₂³.₉D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.32(C5xD4)	320,147
C₂³.₃₃(C₅×D₄) = C₅×C₂⁴⋊₃C₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.33(C5xD4)	320,880
C₂³.₃₄(C₅×D₄) = C₅×C₂³.₃₄D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.34(C5xD4)	320,882
C₂³.₃₅(C₅×D₄) = C₅×C₂³.₈Q₈	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.35(C5xD4)	320,886
C₂³.₃₆(C₅×D₄) = C₅×C₂³.₃₆D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.36(C5xD4)	320,918
C₂³.₃₇(C₅×D₄) = C₅×C₂³.₃₇D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.37(C5xD4)	320,919
C₂³.₃₈(C₅×D₄) = C₅×C₂³.₃₈D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.38(C5xD4)	320,920
C₂³.₃₉(C₅×D₄) = C₁₀×C₄≀C₂	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.39(C5xD4)	320,921
C₂³.₄₀(C₅×D₄) = C₅×M₄(2)⋊C₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.40(C5xD4)	320,929
C₂³.₄₁(C₅×D₄) = C₅×C₂²⋊D₈	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.41(C5xD4)	320,948
C₂³.₄₂(C₅×D₄) = C₅×Q₈⋊D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.42(C5xD4)	320,949
C₂³.₄₃(C₅×D₄) = C₅×C₂²⋊SD₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.43(C5xD4)	320,951
C₂³.₄₄(C₅×D₄) = C₅×C₂²⋊Q₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.44(C5xD4)	320,952
C₂³.₄₅(C₅×D₄) = C₅×C₂².D₈	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.45(C5xD4)	320,981
C₂³.₄₆(C₅×D₄) = C₅×C₂³.₄₆D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.46(C5xD4)	320,982
C₂³.₄₇(C₅×D₄) = C₅×C₂³.₄₇D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.47(C5xD4)	320,984
C₂³.₄₈(C₅×D₄) = C₅×C₂³.₄₈D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.48(C5xD4)	320,985
C₂³.₄₉(C₅×D₄) = C₁₀×C₂².D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.49(C5xD4)	320,1526
C₂³.₅₀(C₅×D₄) = C₁₀×C₈⋊C₂²	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.50(C5xD4)	320,1575
C₂³.₅₁(C₅×D₄) = C₁₀×C₈.C₂²	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₂³	160		C2^3.51(C5xD4)	320,1576
C₂³.₅₂(C₅×D₄) = C₅×C₂².₄Q₁₆	central extension (φ=1)	320		C2^3.52(C5xD4)	320,145
C₂³.₅₃(C₅×D₄) = C₁₀×C₂.C₄²	central extension (φ=1)	320		C2^3.53(C5xD4)	320,876
C₂³.₅₄(C₅×D₄) = C₁₀×D₄⋊C₄	central extension (φ=1)	160		C2^3.54(C5xD4)	320,915
C₂³.₅₅(C₅×D₄) = C₁₀×Q₈⋊C₄	central extension (φ=1)	320		C2^3.55(C5xD4)	320,916
C₂³.₅₆(C₅×D₄) = C₁₀×C₄.Q₈	central extension (φ=1)	320		C2^3.56(C5xD4)	320,926
C₂³.₅₇(C₅×D₄) = C₁₀×C₂.D₈	central extension (φ=1)	320		C2^3.57(C5xD4)	320,927
C₂³.₅₈(C₅×D₄) = C₂²⋊C₄×C₂×C₁₀	central extension (φ=1)	160		C2^3.58(C5xD4)	320,1514
C₂³.₅₉(C₅×D₄) = C₄⋊C₄×C₂×C₁₀	central extension (φ=1)	320		C2^3.59(C5xD4)	320,1515
C₂³.₆₀(C₅×D₄) = D₈×C₂×C₁₀	central extension (φ=1)	160		C2^3.60(C5xD4)	320,1571
C₂³.₆₁(C₅×D₄) = SD₁₆×C₂×C₁₀	central extension (φ=1)	160		C2^3.61(C5xD4)	320,1572
C₂³.₆₂(C₅×D₄) = Q₁₆×C₂×C₁₀	central extension (φ=1)	320		C2^3.62(C5xD4)	320,1573

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Extensions 1→N→G→Q→1 with N=C23 and Q=C5×D4

Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₅×D₄