Extensions 1→N→G→Q→1 with N=C₄ and Q=D₄×C₁₀

Direct product G=N×Q with N=C₄ and Q=D₄×C₁₀

		d	ρ	Label	ID
D₄×C₂×C₂₀		160		D4xC2xC20	320,1517

Semidirect products G=N:Q with N=C₄ and Q=D₄×C₁₀

extension	φ:Q→Aut N	d	Label	ID
C₄⋊₁(D₄×C₁₀) = C₁₀×C₄⋊₁D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160	C4:1(D4xC10)	320,1532
C₄⋊₂(D₄×C₁₀) = C₅×D₄²	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	C4:2(D4xC10)	320,1547
C₄⋊₃(D₄×C₁₀) = C₁₀×C₄⋊D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160	C4:3(D4xC10)	320,1524

Non-split extensions G=N.Q with N=C₄ and Q=D₄×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(D₄×C₁₀) = C₅×C₈⋊₅D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.1(D4xC10)	320,993
C₄.₂(D₄×C₁₀) = C₅×C₈⋊₄D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.2(D4xC10)	320,994
C₄.₃(D₄×C₁₀) = C₅×C₄⋊Q₁₆	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.3(D4xC10)	320,995
C₄.₄(D₄×C₁₀) = C₅×C₈.₁₂D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.4(D4xC10)	320,996
C₄.₅(D₄×C₁₀) = C₅×C₈⋊₃D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.5(D4xC10)	320,997
C₄.₆(D₄×C₁₀) = C₅×C₈.₂D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.6(D4xC10)	320,998
C₄.₇(D₄×C₁₀) = C₁₀×D₁₆	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.7(D4xC10)	320,1006
C₄.₈(D₄×C₁₀) = C₁₀×SD₃₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.8(D4xC10)	320,1007
C₄.₉(D₄×C₁₀) = C₁₀×Q₃₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.9(D4xC10)	320,1008
C₄.₁₀(D₄×C₁₀) = C₅×C₄○D₁₆	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160	2	C4.10(D4xC10)	320,1009
C₄.₁₁(D₄×C₁₀) = C₅×C₁₆⋊C₂²	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	80	4	C4.11(D4xC10)	320,1010
C₄.₁₂(D₄×C₁₀) = C₅×Q₃₂⋊C₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160	4	C4.12(D4xC10)	320,1011
C₄.₁₃(D₄×C₁₀) = C₁₀×C₄.₄D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.13(D4xC10)	320,1528
C₄.₁₄(D₄×C₁₀) = C₁₀×C₄⋊Q₈	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.14(D4xC10)	320,1533
C₄.₁₅(D₄×C₁₀) = C₅×C₂².₂₆C₂⁴	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.15(D4xC10)	320,1534
C₄.₁₆(D₄×C₁₀) = C₅×C₂².₂₉C₂⁴	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	80		C4.16(D4xC10)	320,1537
C₄.₁₇(D₄×C₁₀) = C₅×C₂³.₃₈C₂³	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.17(D4xC10)	320,1538
C₄.₁₈(D₄×C₁₀) = D₈×C₂×C₁₀	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.18(D4xC10)	320,1571
C₄.₁₉(D₄×C₁₀) = SD₁₆×C₂×C₁₀	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.19(D4xC10)	320,1572
C₄.₂₀(D₄×C₁₀) = Q₁₆×C₂×C₁₀	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.20(D4xC10)	320,1573
C₄.₂₁(D₄×C₁₀) = C₅×C₂²⋊D₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80		C4.21(D4xC10)	320,948
C₄.₂₂(D₄×C₁₀) = C₅×Q₈⋊D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.22(D4xC10)	320,949
C₄.₂₃(D₄×C₁₀) = C₅×D₄⋊D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.23(D4xC10)	320,950
C₄.₂₄(D₄×C₁₀) = C₅×C₂²⋊SD₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80		C4.24(D4xC10)	320,951
C₄.₂₅(D₄×C₁₀) = C₅×C₂²⋊Q₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.25(D4xC10)	320,952
C₄.₂₆(D₄×C₁₀) = C₅×D₄.₇D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.26(D4xC10)	320,953
C₄.₂₇(D₄×C₁₀) = C₅×D₄⋊₄D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	40	4	C4.27(D4xC10)	320,954
C₄.₂₈(D₄×C₁₀) = C₅×D₄.₈D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.28(D4xC10)	320,955
C₄.₂₉(D₄×C₁₀) = C₅×D₄.₉D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.29(D4xC10)	320,956
C₄.₃₀(D₄×C₁₀) = C₅×D₄.₁₀D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.30(D4xC10)	320,957
C₄.₃₁(D₄×C₁₀) = C₅×C₄⋊D₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.31(D4xC10)	320,960
C₄.₃₂(D₄×C₁₀) = C₅×C₄⋊SD₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.32(D4xC10)	320,961
C₄.₃₃(D₄×C₁₀) = C₅×D₄.D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.33(D4xC10)	320,962
C₄.₃₄(D₄×C₁₀) = C₅×C₄⋊₂Q₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	320		C4.34(D4xC10)	320,963
C₄.₃₅(D₄×C₁₀) = C₅×D₄.₂D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.35(D4xC10)	320,964
C₄.₃₆(D₄×C₁₀) = C₅×Q₈.D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.36(D4xC10)	320,965
C₄.₃₇(D₄×C₁₀) = C₅×D₄.₃D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.37(D4xC10)	320,972
C₄.₃₈(D₄×C₁₀) = C₅×D₄.₄D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.38(D4xC10)	320,973
C₄.₃₉(D₄×C₁₀) = C₅×D₄.₅D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160	4	C4.39(D4xC10)	320,974
C₄.₄₀(D₄×C₁₀) = C₅×D₄⋊₅D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80		C4.40(D4xC10)	320,1548
C₄.₄₁(D₄×C₁₀) = C₅×D₄⋊₆D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.41(D4xC10)	320,1549
C₄.₄₂(D₄×C₁₀) = C₅×Q₈⋊₅D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.42(D4xC10)	320,1550
C₄.₄₃(D₄×C₁₀) = C₅×D₄×Q₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.43(D4xC10)	320,1551
C₄.₄₄(D₄×C₁₀) = C₅×Q₈⋊₆D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160		C4.44(D4xC10)	320,1552
C₄.₄₅(D₄×C₁₀) = C₅×D₄○D₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.45(D4xC10)	320,1578
C₄.₄₆(D₄×C₁₀) = C₅×D₄○SD₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	80	4	C4.46(D4xC10)	320,1579
C₄.₄₇(D₄×C₁₀) = C₅×Q₈○D₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₄	160	4	C4.47(D4xC10)	320,1580
C₄.₄₈(D₄×C₁₀) = C₁₀×C₄.D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80		C4.48(D4xC10)	320,912
C₄.₄₉(D₄×C₁₀) = C₁₀×C₄.₁₀D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.49(D4xC10)	320,913
C₄.₅₀(D₄×C₁₀) = C₅×M₄(2).₈C₂²	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80	4	C4.50(D4xC10)	320,914
C₄.₅₁(D₄×C₁₀) = C₁₀×D₄⋊C₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.51(D4xC10)	320,915
C₄.₅₂(D₄×C₁₀) = C₁₀×Q₈⋊C₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	320		C4.52(D4xC10)	320,916
C₄.₅₃(D₄×C₁₀) = C₅×C₂³.₂₄D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.53(D4xC10)	320,917
C₄.₅₄(D₄×C₁₀) = C₅×C₂³.₃₆D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.54(D4xC10)	320,918
C₄.₅₅(D₄×C₁₀) = C₅×C₂³.₃₇D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80		C4.55(D4xC10)	320,919
C₄.₅₆(D₄×C₁₀) = C₅×C₂³.₃₈D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.56(D4xC10)	320,920
C₄.₅₇(D₄×C₁₀) = C₅×C₈⋊₈D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.57(D4xC10)	320,966
C₄.₅₈(D₄×C₁₀) = C₅×C₈⋊₇D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.58(D4xC10)	320,967
C₄.₅₉(D₄×C₁₀) = C₅×C₈.₁₈D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.59(D4xC10)	320,968
C₄.₆₀(D₄×C₁₀) = C₅×C₈⋊D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.60(D4xC10)	320,969
C₄.₆₁(D₄×C₁₀) = C₅×C₈⋊₂D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.61(D4xC10)	320,970
C₄.₆₂(D₄×C₁₀) = C₅×C₈.D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.62(D4xC10)	320,971
C₄.₆₃(D₄×C₁₀) = C₁₀×C₂²⋊Q₈	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.63(D4xC10)	320,1525
C₄.₆₄(D₄×C₁₀) = C₅×C₂².₁₉C₂⁴	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80		C4.64(D4xC10)	320,1527
C₄.₆₅(D₄×C₁₀) = C₅×C₂².₃₁C₂⁴	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.65(D4xC10)	320,1539
C₄.₆₆(D₄×C₁₀) = C₁₀×C₈⋊C₂²	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80		C4.66(D4xC10)	320,1575
C₄.₆₇(D₄×C₁₀) = C₁₀×C₈.C₂²	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.67(D4xC10)	320,1576
C₄.₆₈(D₄×C₁₀) = C₅×D₈⋊C₂²	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80	4	C4.68(D4xC10)	320,1577
C₄.₆₉(D₄×C₁₀) = C₁₀×C₂²⋊C₈	central extension (φ=1)	160		C4.69(D4xC10)	320,907
C₄.₇₀(D₄×C₁₀) = C₅×C₂⁴.₄C₄	central extension (φ=1)	80		C4.70(D4xC10)	320,908
C₄.₇₁(D₄×C₁₀) = C₅×(C₂²×C₈)⋊C₂	central extension (φ=1)	160		C4.71(D4xC10)	320,909
C₄.₇₂(D₄×C₁₀) = C₁₀×C₄≀C₂	central extension (φ=1)	80		C4.72(D4xC10)	320,921
C₄.₇₃(D₄×C₁₀) = C₅×C₄²⋊C₂²	central extension (φ=1)	80	4	C4.73(D4xC10)	320,922
C₄.₇₄(D₄×C₁₀) = C₁₀×C₄⋊C₈	central extension (φ=1)	320		C4.74(D4xC10)	320,923
C₄.₇₅(D₄×C₁₀) = C₅×C₄⋊M₄(2)	central extension (φ=1)	160		C4.75(D4xC10)	320,924
C₄.₇₆(D₄×C₁₀) = C₅×C₄².₆C₂²	central extension (φ=1)	160		C4.76(D4xC10)	320,925
C₄.₇₇(D₄×C₁₀) = C₁₀×C₈.C₄	central extension (φ=1)	160		C4.77(D4xC10)	320,930
C₄.₇₈(D₄×C₁₀) = C₅×M₄(2).C₄	central extension (φ=1)	80	4	C4.78(D4xC10)	320,931
C₄.₇₉(D₄×C₁₀) = D₄×C₄₀	central extension (φ=1)	160		C4.79(D4xC10)	320,935
C₄.₈₀(D₄×C₁₀) = C₅×C₈⋊₉D₄	central extension (φ=1)	160		C4.80(D4xC10)	320,936
C₄.₈₁(D₄×C₁₀) = C₅×C₈⋊₆D₄	central extension (φ=1)	160		C4.81(D4xC10)	320,937
C₄.₈₂(D₄×C₁₀) = C₅×C₈○D₈	central extension (φ=1)	80	2	C4.82(D4xC10)	320,944
C₄.₈₃(D₄×C₁₀) = C₅×C₈.₂₆D₄	central extension (φ=1)	80	4	C4.83(D4xC10)	320,945
C₄.₈₄(D₄×C₁₀) = C₁₀×C₄○D₈	central extension (φ=1)	160		C4.84(D4xC10)	320,1574

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Extensions 1→N→G→Q→1 with N=C4 and Q=D4×C10

Extensions 1→N→G→Q→1 with N=C₄ and Q=D₄×C₁₀