Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂²×F₅

Direct product G=N×Q with N=C₄ and Q=C₂²×F₅

		d	ρ	Label	ID
C₂²×C₄×F₅		80		C2^2xC4xF5	320,1590

Semidirect products G=N:Q with N=C₄ and Q=C₂²×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂²×F₅) = C₂×D₄×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40		C4:1(C2^2xF5)	320,1595
C₄⋊₂(C₂²×F₅) = C₂²×C₄⋊F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80		C4:2(C2^2xF5)	320,1591

Non-split extensions G=N.Q with N=C₄ and Q=C₂²×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂²×F₅) = D₈×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8+	C4.1(C2^2xF5)	320,1068
C₄.₂(C₂²×F₅) = D₄₀⋊C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8+	C4.2(C2^2xF5)	320,1069
C₄.₃(C₂²×F₅) = D₈⋊₅F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.3(C2^2xF5)	320,1070
C₄.₄(C₂²×F₅) = D₈⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.4(C2^2xF5)	320,1071
C₄.₅(C₂²×F₅) = SD₁₆×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.5(C2^2xF5)	320,1072
C₄.₆(C₂²×F₅) = SD₁₆⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.6(C2^2xF5)	320,1073
C₄.₇(C₂²×F₅) = SD₁₆⋊₃F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.7(C2^2xF5)	320,1074
C₄.₈(C₂²×F₅) = SD₁₆⋊₂F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.8(C2^2xF5)	320,1075
C₄.₉(C₂²×F₅) = Q₁₆×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.9(C2^2xF5)	320,1076
C₄.₁₀(C₂²×F₅) = Dic₂₀⋊C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.10(C2^2xF5)	320,1077
C₄.₁₁(C₂²×F₅) = Q₁₆⋊₅F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8+	C4.11(C2^2xF5)	320,1078
C₄.₁₂(C₂²×F₅) = Q₁₆⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8+	C4.12(C2^2xF5)	320,1079
C₄.₁₃(C₂²×F₅) = C₂×D₂₀⋊C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.13(C2^2xF5)	320,1104
C₄.₁₄(C₂²×F₅) = (D₄×C₁₀)⋊C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8+	C4.14(C2^2xF5)	320,1105
C₄.₁₅(C₂²×F₅) = C₂×D₄⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.15(C2^2xF5)	320,1106
C₄.₁₆(C₂²×F₅) = (C₂×D₄)⋊₆F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.16(C2^2xF5)	320,1107
C₄.₁₇(C₂²×F₅) = C₂×Q₈⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.17(C2^2xF5)	320,1119
C₄.₁₈(C₂²×F₅) = (C₂×Q₈)⋊₄F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.18(C2^2xF5)	320,1120
C₄.₁₉(C₂²×F₅) = C₂×Q₈⋊₂F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.19(C2^2xF5)	320,1121
C₄.₂₀(C₂²×F₅) = (C₂×Q₈)⋊₆F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8+	C4.20(C2^2xF5)	320,1122
C₄.₂₁(C₂²×F₅) = D₅⋊C₄≀C₂	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.21(C2^2xF5)	320,1130
C₄.₂₂(C₂²×F₅) = C₄○D₄⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.22(C2^2xF5)	320,1131
C₄.₂₃(C₂²×F₅) = C₄○D₂₀⋊C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.23(C2^2xF5)	320,1132
C₄.₂₄(C₂²×F₅) = D₄⋊F₅⋊C₂	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.24(C2^2xF5)	320,1133
C₄.₂₅(C₂²×F₅) = C₂×D₄.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	160		C4.25(C2^2xF5)	320,1593
C₄.₂₆(C₂²×F₅) = Dic₅.C₂⁴	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.26(C2^2xF5)	320,1594
C₄.₂₇(C₂²×F₅) = D₁₀.C₂⁴	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8+	C4.27(C2^2xF5)	320,1596
C₄.₂₈(C₂²×F₅) = C₂×Q₈.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	160		C4.28(C2^2xF5)	320,1597
C₄.₂₉(C₂²×F₅) = Dic₅.₂₀C₂⁴	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8+	C4.29(C2^2xF5)	320,1598
C₄.₃₀(C₂²×F₅) = C₂×Q₈×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.30(C2^2xF5)	320,1599
C₄.₃₁(C₂²×F₅) = D₅.2_-¹⁺⁴	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8-	C4.31(C2^2xF5)	320,1600
C₄.₃₂(C₂²×F₅) = Dic₅.₂₁C₂⁴	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.32(C2^2xF5)	320,1601
C₄.₃₃(C₂²×F₅) = C₄○D₄×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.33(C2^2xF5)	320,1603
C₄.₃₄(C₂²×F₅) = D₅.2₊¹⁺⁴	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.34(C2^2xF5)	320,1604
C₄.₃₅(C₂²×F₅) = C₂×C₄₀⋊C₄	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80		C4.35(C2^2xF5)	320,1057
C₄.₃₆(C₂²×F₅) = C₂×D₅.D₈	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80		C4.36(C2^2xF5)	320,1058
C₄.₃₇(C₂²×F₅) = (C₂×C₈)⋊₆F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80	4	C4.37(C2^2xF5)	320,1059
C₄.₃₈(C₂²×F₅) = C₂×C₄₀.C₄	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	160		C4.38(C2^2xF5)	320,1060
C₄.₃₉(C₂²×F₅) = C₂×D₁₀.Q₈	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	160		C4.39(C2^2xF5)	320,1061
C₄.₄₀(C₂²×F₅) = (C₈×D₅).C₄	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80	4	C4.40(C2^2xF5)	320,1062
C₄.₄₁(C₂²×F₅) = M₄(2)⋊₁F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	40	8	C4.41(C2^2xF5)	320,1065
C₄.₄₂(C₂²×F₅) = M₄(2).₁F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80	8	C4.42(C2^2xF5)	320,1067
C₄.₄₃(C₂²×F₅) = C₂²×C₄.F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	160		C4.43(C2^2xF5)	320,1588
C₄.₄₄(C₂²×F₅) = Dic₅.₂₂C₂⁴	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₄	80	8	C4.44(C2^2xF5)	320,1602
C₄.₄₅(C₂²×F₅) = C₂×D₅⋊C₁₆	central extension (φ=1)	160		C4.45(C2^2xF5)	320,1051
C₄.₄₆(C₂²×F₅) = C₂×C₈.F₅	central extension (φ=1)	160		C4.46(C2^2xF5)	320,1052
C₄.₄₇(C₂²×F₅) = D₅⋊M₅(2)	central extension (φ=1)	80	4	C4.47(C2^2xF5)	320,1053
C₄.₄₈(C₂²×F₅) = C₂×C₈×F₅	central extension (φ=1)	80		C4.48(C2^2xF5)	320,1054
C₄.₄₉(C₂²×F₅) = C₂×C₈⋊F₅	central extension (φ=1)	80		C4.49(C2^2xF5)	320,1055
C₄.₅₀(C₂²×F₅) = C₂₀.₁₂C₄²	central extension (φ=1)	80	4	C4.50(C2^2xF5)	320,1056
C₄.₅₁(C₂²×F₅) = Dic₁₀.C₈	central extension (φ=1)	160	8	C4.51(C2^2xF5)	320,1063
C₄.₅₂(C₂²×F₅) = M₄(2)×F₅	central extension (φ=1)	40	8	C4.52(C2^2xF5)	320,1064
C₄.₅₃(C₂²×F₅) = M₄(2)⋊₅F₅	central extension (φ=1)	80	8	C4.53(C2^2xF5)	320,1066
C₄.₅₄(C₂²×F₅) = C₂²×C₅⋊C₁₆	central extension (φ=1)	320		C4.54(C2^2xF5)	320,1080
C₄.₅₅(C₂²×F₅) = C₂×C₂₀.C₈	central extension (φ=1)	160		C4.55(C2^2xF5)	320,1081
C₄.₅₆(C₂²×F₅) = C₅⋊C₁₆.C₂²	central extension (φ=1)	160	8	C4.56(C2^2xF5)	320,1129
C₄.₅₇(C₂²×F₅) = C₂²×D₅⋊C₈	central extension (φ=1)	160		C4.57(C2^2xF5)	320,1587
C₄.₅₈(C₂²×F₅) = C₂×D₅⋊M₄(2)	central extension (φ=1)	80		C4.58(C2^2xF5)	320,1589
C₄.₅₉(C₂²×F₅) = C₂×D₁₀.C₂³	central extension (φ=1)	80		C4.59(C2^2xF5)	320,1592

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Extensions 1→N→G→Q→1 with N=C4 and Q=C22×F5

Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂²×F₅