Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂²×F₅

Direct product G=N×Q with N=C₆ and Q=C₂²×F₅

		d	ρ	Label	ID
F₅×C₂²×C₆		120		F5xC2^2xC6	480,1205

Semidirect products G=N:Q with N=C₆ and Q=C₂²×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₂²×F₅) = C₂²×S₃×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60		C6:1(C2^2xF5)	480,1197
C₆⋊₂(C₂²×F₅) = C₂³×C₃⋊F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120		C6:2(C2^2xF5)	480,1206

Non-split extensions G=N.Q with N=C₆ and Q=C₂²×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₂²×F₅) = F₅×Dic₆	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8-	C6.1(C2^2xF5)	480,982
C₆.₂(C₂²×F₅) = C₄⋊F₅⋊₃S₃	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.2(C2^2xF5)	480,983
C₆.₃(C₂²×F₅) = Dic₆⋊₅F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8-	C6.3(C2^2xF5)	480,984
C₆.₄(C₂²×F₅) = (C₄×S₃)⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.4(C2^2xF5)	480,985
C₆.₅(C₂²×F₅) = S₃×D₅⋊C₈	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.5(C2^2xF5)	480,986
C₆.₆(C₂²×F₅) = D₁₂.₂F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240	8-	C6.6(C2^2xF5)	480,987
C₆.₇(C₂²×F₅) = S₃×C₄.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.7(C2^2xF5)	480,988
C₆.₈(C₂²×F₅) = D₁₂.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240	8-	C6.8(C2^2xF5)	480,989
C₆.₉(C₂²×F₅) = D₆₀.C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240	8+	C6.9(C2^2xF5)	480,990
C₆.₁₀(C₂²×F₅) = D₁₅⋊M₄(2)	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.10(C2^2xF5)	480,991
C₆.₁₁(C₂²×F₅) = Dic₆.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240	8+	C6.11(C2^2xF5)	480,992
C₆.₁₂(C₂²×F₅) = C₅⋊C₈⋊D₆	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.12(C2^2xF5)	480,993
C₆.₁₃(C₂²×F₅) = C₄×S₃×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8	C6.13(C2^2xF5)	480,994
C₆.₁₄(C₂²×F₅) = F₅×D₁₂	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8+	C6.14(C2^2xF5)	480,995
C₆.₁₅(C₂²×F₅) = S₃×C₄⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8	C6.15(C2^2xF5)	480,996
C₆.₁₆(C₂²×F₅) = D₆₀⋊₃C₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8+	C6.16(C2^2xF5)	480,997
C₆.₁₇(C₂²×F₅) = C₂×Dic₃×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120		C6.17(C2^2xF5)	480,998
C₆.₁₈(C₂²×F₅) = C₂²⋊F₅.S₃	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8-	C6.18(C2^2xF5)	480,999
C₆.₁₉(C₂²×F₅) = C₂×D₆⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120		C6.19(C2^2xF5)	480,1000
C₆.₂₀(C₂²×F₅) = C₂×Dic₃⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120		C6.20(C2^2xF5)	480,1001
C₆.₂₁(C₂²×F₅) = C₂×S₃×C₅⋊C₈	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240		C6.21(C2^2xF5)	480,1002
C₆.₂₂(C₂²×F₅) = C₅⋊C₈.D₆	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240	8	C6.22(C2^2xF5)	480,1003
C₆.₂₃(C₂²×F₅) = S₃×C₂².F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8-	C6.23(C2^2xF5)	480,1004
C₆.₂₄(C₂²×F₅) = D₁₅⋊C₈⋊C₂	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240	8	C6.24(C2^2xF5)	480,1005
C₆.₂₅(C₂²×F₅) = C₂×D₁₅⋊C₈	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240		C6.25(C2^2xF5)	480,1006
C₆.₂₆(C₂²×F₅) = D₁₅⋊₂M₄(2)	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8+	C6.26(C2^2xF5)	480,1007
C₆.₂₇(C₂²×F₅) = C₂×D₆.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240		C6.27(C2^2xF5)	480,1008
C₆.₂₈(C₂²×F₅) = C₂×Dic₃.F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	240		C6.28(C2^2xF5)	480,1009
C₆.₂₉(C₂²×F₅) = F₅×C₃⋊D₄	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8	C6.29(C2^2xF5)	480,1010
C₆.₃₀(C₂²×F₅) = S₃×C₂²⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8+	C6.30(C2^2xF5)	480,1011
C₆.₃₁(C₂²×F₅) = C₃⋊D₄⋊F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	60	8	C6.31(C2^2xF5)	480,1012
C₆.₃₂(C₂²×F₅) = C₂×C₆₀.C₄	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	240		C6.32(C2^2xF5)	480,1060
C₆.₃₃(C₂²×F₅) = C₂×C₁₂.F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	240		C6.33(C2^2xF5)	480,1061
C₆.₃₄(C₂²×F₅) = C₆₀.₅₉(C₂×C₄)	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120	4	C6.34(C2^2xF5)	480,1062
C₆.₃₅(C₂²×F₅) = C₂×C₄×C₃⋊F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120		C6.35(C2^2xF5)	480,1063
C₆.₃₆(C₂²×F₅) = C₂×C₆₀⋊C₄	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120		C6.36(C2^2xF5)	480,1064
C₆.₃₇(C₂²×F₅) = (C₂×C₁₂)⋊₆F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120	4	C6.37(C2^2xF5)	480,1065
C₆.₃₈(C₂²×F₅) = Dic₁₀.Dic₃	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	240	8	C6.38(C2^2xF5)	480,1066
C₆.₃₉(C₂²×F₅) = D₄×C₃⋊F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	60	8	C6.39(C2^2xF5)	480,1067
C₆.₄₀(C₂²×F₅) = D₂₀.Dic₃	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	240	8	C6.40(C2^2xF5)	480,1068
C₆.₄₁(C₂²×F₅) = Q₈×C₃⋊F₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120	8	C6.41(C2^2xF5)	480,1069
C₆.₄₂(C₂²×F₅) = C₂²×C₁₅⋊C₈	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	480		C6.42(C2^2xF5)	480,1070
C₆.₄₃(C₂²×F₅) = C₂×C₁₅⋊₈M₄(2)	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	240		C6.43(C2^2xF5)	480,1071
C₆.₄₄(C₂²×F₅) = C₂×D₁₀.D₆	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₆	120		C6.44(C2^2xF5)	480,1072
C₆.₄₅(C₂²×F₅) = C₆×D₅⋊C₈	central extension (φ=1)	240		C6.45(C2^2xF5)	480,1047
C₆.₄₆(C₂²×F₅) = C₆×C₄.F₅	central extension (φ=1)	240		C6.46(C2^2xF5)	480,1048
C₆.₄₇(C₂²×F₅) = C₃×D₅⋊M₄(2)	central extension (φ=1)	120	4	C6.47(C2^2xF5)	480,1049
C₆.₄₈(C₂²×F₅) = F₅×C₂×C₁₂	central extension (φ=1)	120		C6.48(C2^2xF5)	480,1050
C₆.₄₉(C₂²×F₅) = C₆×C₄⋊F₅	central extension (φ=1)	120		C6.49(C2^2xF5)	480,1051
C₆.₅₀(C₂²×F₅) = C₃×D₁₀.C₂³	central extension (φ=1)	120	4	C6.50(C2^2xF5)	480,1052
C₆.₅₁(C₂²×F₅) = C₃×D₄.F₅	central extension (φ=1)	240	8	C6.51(C2^2xF5)	480,1053
C₆.₅₂(C₂²×F₅) = C₃×D₄×F₅	central extension (φ=1)	60	8	C6.52(C2^2xF5)	480,1054
C₆.₅₃(C₂²×F₅) = C₃×Q₈.F₅	central extension (φ=1)	240	8	C6.53(C2^2xF5)	480,1055
C₆.₅₄(C₂²×F₅) = C₃×Q₈×F₅	central extension (φ=1)	120	8	C6.54(C2^2xF5)	480,1056
C₆.₅₅(C₂²×F₅) = C₂×C₆×C₅⋊C₈	central extension (φ=1)	480		C6.55(C2^2xF5)	480,1057
C₆.₅₆(C₂²×F₅) = C₆×C₂².F₅	central extension (φ=1)	240		C6.56(C2^2xF5)	480,1058
C₆.₅₇(C₂²×F₅) = C₆×C₂²⋊F₅	central extension (φ=1)	120		C6.57(C2^2xF5)	480,1059

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Extensions 1→N→G→Q→1 with N=C6 and Q=C22×F5

Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂²×F₅