Extensions 1→N→G→Q→1 with N=C₄² and Q=C₃×D₅

Direct product G=N×Q with N=C₄² and Q=C₃×D₅

		d	ρ	Label	ID
D₅×C₄×C₁₂		240		D5xC4xC12	480,664

Semidirect products G=N:Q with N=C₄² and Q=C₃×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄²⋊₁(C₃×D₅) = (C₄×C₂₀)⋊C₆	φ: C₃×D₅/C₅ → C₆ ⊆ Aut C₄²	80	6	C4^2:1(C3xD5)	480,263
C₄²⋊₂(C₃×D₅) = C₂₀⋊₄D₄⋊C₃	φ: C₃×D₅/C₅ → C₆ ⊆ Aut C₄²	60	6+	C4^2:2(C3xD5)	480,262
C₄²⋊₃(C₃×D₅) = D₅×C₄²⋊C₃	φ: C₃×D₅/D₅ → C₃ ⊆ Aut C₄²	60	6	C4^2:3(C3xD5)	480,264
C₄²⋊₄(C₃×D₅) = C₃×C₄²⋊D₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:4(C3xD5)	480,665
C₄²⋊₅(C₃×D₅) = C₃×C₄²⋊₂D₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:5(C3xD5)	480,669
C₄²⋊₆(C₃×D₅) = C₃×D₂₀⋊₄C₄	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	120	2	C4^2:6(C3xD5)	480,83
C₄²⋊₇(C₃×D₅) = C₁₂×D₂₀	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:7(C3xD5)	480,666
C₄²⋊₈(C₃×D₅) = C₃×C₂₀⋊₄D₄	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:8(C3xD5)	480,667
C₄²⋊₉(C₃×D₅) = C₃×C₄.D₂₀	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:9(C3xD5)	480,668

Non-split extensions G=N.Q with N=C₄² and Q=C₃×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄².₁(C₃×D₅) = C₃×C₄².D₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.1(C3xD5)	480,81
C₄².₂(C₃×D₅) = C₃×C₂₀⋊₃C₈	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.2(C3xD5)	480,82
C₄².₃(C₃×D₅) = C₁₂×Dic₁₀	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.3(C3xD5)	480,661
C₄².₄(C₃×D₅) = C₃×C₂₀⋊₂Q₈	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.4(C3xD5)	480,662
C₄².₅(C₃×D₅) = C₃×C₂₀.₆Q₈	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.5(C3xD5)	480,663
C₄².₆(C₃×D₅) = C₁₂×C₅⋊₂C₈	central extension (φ=1)	480		C4^2.6(C3xD5)	480,80

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