Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₂×C₄²

Direct product G=N×Q with N=C₁₀ and Q=C₂×C₄²

		d	ρ	Label	ID
C₂²×C₄×C₂₀		320		C2^2xC4xC20	320,1513

Semidirect products G=N:Q with N=C₁₀ and Q=C₂×C₄²

extension	φ:Q→Aut N	d	Label	ID
C₁₀⋊(C₂×C₄²) = C₂²×C₄×F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80	C10:(C2xC4^2)	320,1590
C₁₀⋊₂(C₂×C₄²) = D₅×C₂×C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160	C10:2(C2xC4^2)	320,1143
C₁₀⋊₃(C₂×C₄²) = C₂²×C₄×Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320	C10:3(C2xC4^2)	320,1454

Non-split extensions G=N.Q with N=C₁₀ and Q=C₂×C₄²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₂×C₄²) = C₄×D₅⋊C₈	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	160		C10.1(C2xC4^2)	320,1013
C₁₀.₂(C₂×C₄²) = C₄².₅F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	160		C10.2(C2xC4^2)	320,1014
C₁₀.₃(C₂×C₄²) = C₄×C₄.F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	160		C10.3(C2xC4^2)	320,1015
C₁₀.₄(C₂×C₄²) = C₄²×F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.4(C2xC4^2)	320,1023
C₁₀.₅(C₂×C₄²) = C₄²⋊₄F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.5(C2xC4^2)	320,1024
C₁₀.₆(C₂×C₄²) = C₄×C₄⋊F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.6(C2xC4^2)	320,1025
C₁₀.₇(C₂×C₄²) = Dic₅.C₄²	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	160		C10.7(C2xC4^2)	320,1029
C₁₀.₈(C₂×C₄²) = C₂²⋊C₄×F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	40		C10.8(C2xC4^2)	320,1036
C₁₀.₉(C₂×C₄²) = D₁₀.C₄²	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	160		C10.9(C2xC4^2)	320,1039
C₁₀.₁₀(C₂×C₄²) = C₄⋊C₄×F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.10(C2xC4^2)	320,1048
C₁₀.₁₁(C₂×C₄²) = C₂×C₈×F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.11(C2xC4^2)	320,1054
C₁₀.₁₂(C₂×C₄²) = C₂×C₈⋊F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.12(C2xC4^2)	320,1055
C₁₀.₁₃(C₂×C₄²) = C₂₀.₁₂C₄²	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80	4	C10.13(C2xC4^2)	320,1056
C₁₀.₁₄(C₂×C₄²) = M₄(2)×F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	40	8	C10.14(C2xC4^2)	320,1064
C₁₀.₁₅(C₂×C₄²) = M₄(2)⋊₅F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80	8	C10.15(C2xC4^2)	320,1066
C₁₀.₁₆(C₂×C₄²) = C₂×C₄×C₅⋊C₈	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.16(C2xC4^2)	320,1084
C₁₀.₁₇(C₂×C₄²) = C₂×C₁₀.C₄²	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.17(C2xC4^2)	320,1087
C₁₀.₁₈(C₂×C₄²) = C₄×C₂².F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	160		C10.18(C2xC4^2)	320,1088
C₁₀.₁₉(C₂×C₄²) = C₂×D₁₀.₃Q₈	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.19(C2xC4^2)	320,1100
C₁₀.₂₀(C₂×C₄²) = C₄×C₂²⋊F₅	φ: C₂×C₄²/C₂×C₄ → C₄ ⊆ Aut C₁₀	80		C10.20(C2xC4^2)	320,1101
C₁₀.₂₁(C₂×C₄²) = Dic₅.₁₅C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	320		C10.21(C2xC4^2)	320,275
C₁₀.₂₂(C₂×C₄²) = Dic₅⋊₂C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	320		C10.22(C2xC4^2)	320,276
C₁₀.₂₃(C₂×C₄²) = D₅×C₂.C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.23(C2xC4^2)	320,290
C₁₀.₂₄(C₂×C₄²) = D₁₀⋊₂C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.24(C2xC4^2)	320,293
C₁₀.₂₅(C₂×C₄²) = D₅×C₄×C₈	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.25(C2xC4^2)	320,311
C₁₀.₂₆(C₂×C₄²) = C₄×C₈⋊D₅	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.26(C2xC4^2)	320,314
C₁₀.₂₇(C₂×C₄²) = D₁₀.₅C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.27(C2xC4^2)	320,316
C₁₀.₂₈(C₂×C₄²) = D₅×C₈⋊C₄	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.28(C2xC4^2)	320,331
C₁₀.₂₉(C₂×C₄²) = D₁₀.₆C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.29(C2xC4^2)	320,334
C₁₀.₃₀(C₂×C₄²) = D₁₀.₇C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.30(C2xC4^2)	320,335
C₁₀.₃₁(C₂×C₄²) = C₄×C₁₀.D₄	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	320		C10.31(C2xC4^2)	320,558
C₁₀.₃₂(C₂×C₄²) = C₄×D₁₀⋊C₄	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₁₀	160		C10.32(C2xC4^2)	320,565
C₁₀.₃₃(C₂×C₄²) = C₂×C₄×C₅⋊₂C₈	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.33(C2xC4^2)	320,547
C₁₀.₃₄(C₂×C₄²) = C₂×C₄².D₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.34(C2xC4^2)	320,548
C₁₀.₃₅(C₂×C₄²) = C₄×C₄.Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.35(C2xC4^2)	320,549
C₁₀.₃₆(C₂×C₄²) = C₄²×Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.36(C2xC4^2)	320,557
C₁₀.₃₇(C₂×C₄²) = C₄²⋊₄Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.37(C2xC4^2)	320,559
C₁₀.₃₈(C₂×C₄²) = C₄×C₄⋊Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.38(C2xC4^2)	320,561
C₁₀.₃₉(C₂×C₄²) = C₂²⋊C₄×Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.39(C2xC4^2)	320,568
C₁₀.₄₀(C₂×C₄²) = C₄⋊C₄×Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.40(C2xC4^2)	320,602
C₁₀.₄₁(C₂×C₄²) = C₂₀.₃₅C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.41(C2xC4^2)	320,624
C₁₀.₄₂(C₂×C₄²) = C₂×C₈×Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.42(C2xC4^2)	320,725
C₁₀.₄₃(C₂×C₄²) = C₂×C₄₀⋊₈C₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.43(C2xC4^2)	320,727
C₁₀.₄₄(C₂×C₄²) = C₂₀.₄₂C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.44(C2xC4^2)	320,728
C₁₀.₄₅(C₂×C₄²) = M₄(2)×Dic₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.45(C2xC4^2)	320,744
C₁₀.₄₆(C₂×C₄²) = C₂₀.₃₇C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.46(C2xC4^2)	320,749
C₁₀.₄₇(C₂×C₄²) = C₂×C₁₀.₁₀C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	320		C10.47(C2xC4^2)	320,835
C₁₀.₄₈(C₂×C₄²) = C₄×C₂³.D₅	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₁₀	160		C10.48(C2xC4^2)	320,836
C₁₀.₄₉(C₂×C₄²) = C₁₀×C₂.C₄²	central extension (φ=1)	320		C10.49(C2xC4^2)	320,876
C₁₀.₅₀(C₂×C₄²) = C₅×C₄²⋊₄C₄	central extension (φ=1)	320		C10.50(C2xC4^2)	320,877
C₁₀.₅₁(C₂×C₄²) = C₂²⋊C₄×C₂₀	central extension (φ=1)	160		C10.51(C2xC4^2)	320,878
C₁₀.₅₂(C₂×C₄²) = C₄⋊C₄×C₂₀	central extension (φ=1)	320		C10.52(C2xC4^2)	320,879
C₁₀.₅₃(C₂×C₄²) = C₁₀×C₈⋊C₄	central extension (φ=1)	320		C10.53(C2xC4^2)	320,904
C₁₀.₅₄(C₂×C₄²) = M₄(2)×C₂₀	central extension (φ=1)	160		C10.54(C2xC4^2)	320,905
C₁₀.₅₅(C₂×C₄²) = C₅×C₈○₂M₄(2)	central extension (φ=1)	160		C10.55(C2xC4^2)	320,906

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Extensions 1→N→G→Q→1 with N=C10 and Q=C2×C42

Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₂×C₄²