Extensions 1→N→G→Q→1 with N=C₆ and Q=D₄×C₁₀

Direct product G=N×Q with N=C₆ and Q=D₄×C₁₀

		d	ρ	Label	ID
D₄×C₂×C₃₀		240		D4xC2xC30	480,1181

Semidirect products G=N:Q with N=C₆ and Q=D₄×C₁₀

extension	φ:Q→Aut N	d	Label	ID
C₆⋊₁(D₄×C₁₀) = C₂×C₁₀×D₁₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240	C6:1(D4xC10)	480,1152
C₆⋊₂(D₄×C₁₀) = S₃×D₄×C₁₀	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	120	C6:2(D4xC10)	480,1154
C₆⋊₃(D₄×C₁₀) = C₂×C₁₀×C₃⋊D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240	C6:3(D4xC10)	480,1164

Non-split extensions G=N.Q with N=C₆ and Q=D₄×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(D₄×C₁₀) = C₅×C₁₂⋊₂Q₈	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	480		C6.1(D4xC10)	480,748
C₆.₂(D₄×C₁₀) = C₂₀×D₁₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.2(D4xC10)	480,752
C₆.₃(D₄×C₁₀) = C₅×C₄⋊D₁₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.3(D4xC10)	480,753
C₆.₄(D₄×C₁₀) = C₅×C₄²⋊₇S₃	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.4(D4xC10)	480,754
C₆.₅(D₄×C₁₀) = C₅×D₆⋊D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	120		C6.5(D4xC10)	480,761
C₆.₆(D₄×C₁₀) = C₅×C₂³.₂₁D₆	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.6(D4xC10)	480,765
C₆.₇(D₄×C₁₀) = C₅×C₁₂⋊D₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.7(D4xC10)	480,774
C₆.₈(D₄×C₁₀) = C₅×C₄.D₁₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.8(D4xC10)	480,776
C₆.₉(D₄×C₁₀) = C₁₀×C₂₄⋊C₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.9(D4xC10)	480,781
C₆.₁₀(D₄×C₁₀) = C₁₀×D₂₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.10(D4xC10)	480,782
C₆.₁₁(D₄×C₁₀) = C₅×C₄○D₂₄	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240	2	C6.11(D4xC10)	480,783
C₆.₁₂(D₄×C₁₀) = C₁₀×Dic₁₂	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	480		C6.12(D4xC10)	480,784
C₆.₁₃(D₄×C₁₀) = C₅×C₈⋊D₆	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	120	4	C6.13(D4xC10)	480,787
C₆.₁₄(D₄×C₁₀) = C₅×C₈.D₆	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	240	4	C6.14(D4xC10)	480,788
C₆.₁₅(D₄×C₁₀) = C₁₀×C₄⋊Dic₃	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₆	480		C6.15(D4xC10)	480,804
C₆.₁₆(D₄×C₁₀) = C₅×Dic₃.D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.16(D4xC10)	480,757
C₆.₁₇(D₄×C₁₀) = C₅×S₃×C₂²⋊C₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	120		C6.17(D4xC10)	480,759
C₆.₁₈(D₄×C₁₀) = C₅×Dic₃⋊₄D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.18(D4xC10)	480,760
C₆.₁₉(D₄×C₁₀) = C₅×C₂³.₉D₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.19(D4xC10)	480,762
C₆.₂₀(D₄×C₁₀) = C₅×Dic₃⋊D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.20(D4xC10)	480,763
C₆.₂₁(D₄×C₁₀) = C₅×C₂³.₁₁D₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.21(D4xC10)	480,764
C₆.₂₂(D₄×C₁₀) = C₅×C₁₂⋊Q₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	480		C6.22(D4xC10)	480,767
C₆.₂₃(D₄×C₁₀) = C₅×S₃×C₄⋊C₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.23(D4xC10)	480,770
C₆.₂₄(D₄×C₁₀) = C₅×Dic₃⋊₅D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.24(D4xC10)	480,772
C₆.₂₅(D₄×C₁₀) = C₅×D₆.D₄	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.25(D4xC10)	480,773
C₆.₂₆(D₄×C₁₀) = C₅×D₆⋊Q₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.26(D4xC10)	480,775
C₆.₂₇(D₄×C₁₀) = C₅×S₃×D₈	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	120	4	C6.27(D4xC10)	480,789
C₆.₂₈(D₄×C₁₀) = C₅×D₈⋊S₃	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	120	4	C6.28(D4xC10)	480,790
C₆.₂₉(D₄×C₁₀) = C₅×D₈⋊₃S₃	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.29(D4xC10)	480,791
C₆.₃₀(D₄×C₁₀) = C₅×S₃×SD₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	120	4	C6.30(D4xC10)	480,792
C₆.₃₁(D₄×C₁₀) = C₅×Q₈⋊₃D₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	120	4	C6.31(D4xC10)	480,793
C₆.₃₂(D₄×C₁₀) = C₅×D₄.D₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.32(D4xC10)	480,794
C₆.₃₃(D₄×C₁₀) = C₅×Q₈.₇D₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.33(D4xC10)	480,795
C₆.₃₄(D₄×C₁₀) = C₅×S₃×Q₁₆	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.34(D4xC10)	480,796
C₆.₃₅(D₄×C₁₀) = C₅×Q₁₆⋊S₃	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.35(D4xC10)	480,797
C₆.₃₆(D₄×C₁₀) = C₅×D₂₄⋊C₂	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.36(D4xC10)	480,798
C₆.₃₇(D₄×C₁₀) = C₅×D₄×Dic₃	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.37(D4xC10)	480,813
C₆.₃₈(D₄×C₁₀) = C₁₀×Dic₃⋊C₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	480		C6.38(D4xC10)	480,802
C₆.₃₉(D₄×C₁₀) = C₅×C₁₂.₄₈D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.39(D4xC10)	480,803
C₆.₄₀(D₄×C₁₀) = C₁₀×D₆⋊C₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.40(D4xC10)	480,806
C₆.₄₁(D₄×C₁₀) = C₂₀×C₃⋊D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.41(D4xC10)	480,807
C₆.₄₂(D₄×C₁₀) = C₅×C₂³.₂₈D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.42(D4xC10)	480,808
C₆.₄₃(D₄×C₁₀) = C₅×C₁₂⋊₇D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.43(D4xC10)	480,809
C₆.₄₄(D₄×C₁₀) = C₁₀×D₄⋊S₃	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.44(D4xC10)	480,810
C₆.₄₅(D₄×C₁₀) = C₅×D₁₂⋊₆C₂²	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.45(D4xC10)	480,811
C₆.₄₆(D₄×C₁₀) = C₁₀×D₄.S₃	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.46(D4xC10)	480,812
C₆.₄₇(D₄×C₁₀) = C₅×C₂³.₂₃D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.47(D4xC10)	480,814
C₆.₄₈(D₄×C₁₀) = C₅×C₂³.₁₂D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.48(D4xC10)	480,815
C₆.₄₉(D₄×C₁₀) = C₅×C₂³⋊₂D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	120		C6.49(D4xC10)	480,816
C₆.₅₀(D₄×C₁₀) = C₅×D₆⋊₃D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.50(D4xC10)	480,817
C₆.₅₁(D₄×C₁₀) = C₅×C₂³.₁₄D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.51(D4xC10)	480,818
C₆.₅₂(D₄×C₁₀) = C₅×C₁₂⋊₃D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.52(D4xC10)	480,819
C₆.₅₃(D₄×C₁₀) = C₁₀×Q₈⋊₂S₃	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.53(D4xC10)	480,820
C₆.₅₄(D₄×C₁₀) = C₅×Q₈.₁₁D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240	4	C6.54(D4xC10)	480,821
C₆.₅₅(D₄×C₁₀) = C₁₀×C₃⋊Q₁₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	480		C6.55(D4xC10)	480,822
C₆.₅₆(D₄×C₁₀) = C₅×Dic₃⋊Q₈	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	480		C6.56(D4xC10)	480,823
C₆.₅₇(D₄×C₁₀) = C₅×D₆⋊₃Q₈	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.57(D4xC10)	480,825
C₆.₅₈(D₄×C₁₀) = C₅×C₁₂.₂₃D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.58(D4xC10)	480,826
C₆.₅₉(D₄×C₁₀) = C₅×D₄⋊D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.59(D4xC10)	480,828
C₆.₆₀(D₄×C₁₀) = C₅×Q₈.₁₃D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240	4	C6.60(D4xC10)	480,829
C₆.₆₁(D₄×C₁₀) = C₅×Q₈.₁₄D₆	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240	4	C6.61(D4xC10)	480,830
C₆.₆₂(D₄×C₁₀) = C₁₀×C₆.D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	240		C6.62(D4xC10)	480,831
C₆.₆₃(D₄×C₁₀) = C₅×C₂⁴⋊₄S₃	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₆	120		C6.63(D4xC10)	480,832
C₆.₆₄(D₄×C₁₀) = C₂²⋊C₄×C₃₀	central extension (φ=1)	240		C6.64(D4xC10)	480,920
C₆.₆₅(D₄×C₁₀) = C₄⋊C₄×C₃₀	central extension (φ=1)	480		C6.65(D4xC10)	480,921
C₆.₆₆(D₄×C₁₀) = D₄×C₆₀	central extension (φ=1)	240		C6.66(D4xC10)	480,923
C₆.₆₇(D₄×C₁₀) = C₁₅×C₂²≀C₂	central extension (φ=1)	120		C6.67(D4xC10)	480,925
C₆.₆₈(D₄×C₁₀) = C₁₅×C₄⋊D₄	central extension (φ=1)	240		C6.68(D4xC10)	480,926
C₆.₆₉(D₄×C₁₀) = C₁₅×C₂²⋊Q₈	central extension (φ=1)	240		C6.69(D4xC10)	480,927
C₆.₇₀(D₄×C₁₀) = C₁₅×C₂².D₄	central extension (φ=1)	240		C6.70(D4xC10)	480,928
C₆.₇₁(D₄×C₁₀) = C₁₅×C₄.₄D₄	central extension (φ=1)	240		C6.71(D4xC10)	480,929
C₆.₇₂(D₄×C₁₀) = C₁₅×C₄⋊₁D₄	central extension (φ=1)	240		C6.72(D4xC10)	480,932
C₆.₇₃(D₄×C₁₀) = C₁₅×C₄⋊Q₈	central extension (φ=1)	480		C6.73(D4xC10)	480,933
C₆.₇₄(D₄×C₁₀) = D₈×C₃₀	central extension (φ=1)	240		C6.74(D4xC10)	480,937
C₆.₇₅(D₄×C₁₀) = SD₁₆×C₃₀	central extension (φ=1)	240		C6.75(D4xC10)	480,938
C₆.₇₆(D₄×C₁₀) = Q₁₆×C₃₀	central extension (φ=1)	480		C6.76(D4xC10)	480,939
C₆.₇₇(D₄×C₁₀) = C₁₅×C₄○D₈	central extension (φ=1)	240	2	C6.77(D4xC10)	480,940
C₆.₇₈(D₄×C₁₀) = C₁₅×C₈⋊C₂²	central extension (φ=1)	120	4	C6.78(D4xC10)	480,941
C₆.₇₉(D₄×C₁₀) = C₁₅×C₈.C₂²	central extension (φ=1)	240	4	C6.79(D4xC10)	480,942

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Extensions 1→N→G→Q→1 with N=C6 and Q=D4×C10

Extensions 1→N→G→Q→1 with N=C₆ and Q=D₄×C₁₀