Extensions 1→N→G→Q→1 with N=C₃⋊D₂₀ and Q=C₂²

Direct product G=N×Q with N=C₃⋊D₂₀ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₃⋊D₂₀		240		C2^2xC3:D20	480,1119

Semidirect products G=N:Q with N=C₃⋊D₂₀ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊D₂₀⋊₁C₂² = D₂₀⋊₂₅D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	120	4	C3:D20:1C2^2	480,1093
C₃⋊D₂₀⋊₂C₂² = D₂₀⋊₂₉D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	120	4+	C3:D20:2C2^2	480,1095
C₃⋊D₂₀⋊₃C₂² = S₃×D₄×D₅	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	60	8+	C3:D20:3C2^2	480,1097
C₃⋊D₂₀⋊₄C₂² = D₅×D₄⋊₂S₃	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	120	8-	C3:D20:4C2^2	480,1098
C₃⋊D₂₀⋊₅C₂² = D₃₀.C₂³	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	120	8+	C3:D20:5C2^2	480,1100
C₃⋊D₂₀⋊₆C₂² = S₃×Q₈⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	120	8+	C3:D20:6C2^2	480,1109
C₃⋊D₂₀⋊₇C₂² = C₁₅⋊2₊¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	120	4	C3:D20:7C2^2	480,1125
C₃⋊D₂₀⋊₈C₂² = C₂×D₂₀⋊S₃	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	240		C3:D20:8C2^2	480,1075
C₃⋊D₂₀⋊₉C₂² = C₂×C₁₂.₂₈D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	240		C3:D20:9C2^2	480,1085
C₃⋊D₂₀⋊₁₀C₂² = C₂×S₃×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120		C3:D20:10C2^2	480,1088
C₃⋊D₂₀⋊₁₁C₂² = D₅×C₄○D₁₂	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120	4	C3:D20:11C2^2	480,1090
C₃⋊D₂₀⋊₁₂C₂² = S₃×C₄○D₂₀	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120	4	C3:D20:12C2^2	480,1091
C₃⋊D₂₀⋊₁₃C₂² = D₂₀⋊₂₄D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120	4	C3:D20:13C2^2	480,1092
C₃⋊D₂₀⋊₁₄C₂² = D₂₀⋊₁₃D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120	8-	C3:D20:14C2^2	480,1101
C₃⋊D₂₀⋊₁₅C₂² = D₁₂⋊₁₄D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120	8+	C3:D20:15C2^2	480,1103
C₃⋊D₂₀⋊₁₆C₂² = D₂₀⋊₁₇D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120	8+	C3:D20:16C2^2	480,1111
C₃⋊D₂₀⋊₁₇C₂² = C₂×Dic₅.D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	240		C3:D20:17C2^2	480,1113
C₃⋊D₂₀⋊₁₈C₂² = C₂×D₅×C₃⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120		C3:D20:18C2^2	480,1122
C₃⋊D₂₀⋊₁₉C₂² = C₂×D₁₀⋊D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	120		C3:D20:19C2^2	480,1124
C₃⋊D₂₀⋊₂₀C₂² = C₂×D₆.D₁₀	φ: trivial image	240		C3:D20:20C2^2	480,1083
C₃⋊D₂₀⋊₂₁C₂² = D₂₀⋊₁₄D₆	φ: trivial image	120	8+	C3:D20:21C2^2	480,1102

Non-split extensions G=N.Q with N=C₃⋊D₂₀ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊D₂₀.C₂² = D₂₀.₃₈D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₃⋊D₂₀	240	4	C3:D20.C2^2	480,1076
C₃⋊D₂₀.₂C₂² = C₁₅⋊2_-¹⁺⁴	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	240	8-	C3:D20.2C2^2	480,1096
C₃⋊D₂₀.₃C₂² = D₂₀.₂₉D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	240	8-	C3:D20.3C2^2	480,1104
C₃⋊D₂₀.₄C₂² = C₃₀.₃₃C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out C₃⋊D₂₀	240	8+	C3:D20.4C2^2	480,1105
C₃⋊D₂₀.₅C₂² = D₁₂.₂₉D₁₀	φ: trivial image	240	8-	C3:D20.5C2^2	480,1106

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Extensions 1→N→G→Q→1 with N=C3⋊D20 and Q=C22

Extensions 1→N→G→Q→1 with N=C₃⋊D₂₀ and Q=C₂²