Extensions 1→N→G→Q→1 with N=C₅×SL₂(𝔽₃) and Q=C₂²

Direct product G=N×Q with N=C₅×SL₂(𝔽₃) and Q=C₂²

		d	ρ	Label	ID
C₂×C₁₀×SL₂(𝔽₃)		160		C2xC10xSL(2,3)	480,1128

Semidirect products G=N:Q with N=C₅×SL₂(𝔽₃) and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×SL₂(𝔽₃))⋊₁C₂² = GL₂(𝔽₃)⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	80	4+	(C5xSL(2,3)):1C2^2	480,970
(C₅×SL₂(𝔽₃))⋊₂C₂² = D₅×GL₂(𝔽₃)	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	40	4	(C5xSL(2,3)):2C2^2	480,974
(C₅×SL₂(𝔽₃))⋊₃C₂² = C₂×Q₈⋊D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80		(C5xSL(2,3)):3C2^2	480,1028
(C₅×SL₂(𝔽₃))⋊₄C₂² = C₂₀.₃S₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4+	(C5xSL(2,3)):4C2^2	480,1032
(C₅×SL₂(𝔽₃))⋊₅C₂² = C₂×Dic₅.A₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	160		(C5xSL(2,3)):5C2^2	480,1038
(C₅×SL₂(𝔽₃))⋊₆C₂² = C₂×D₅×SL₂(𝔽₃)	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80		(C5xSL(2,3)):6C2^2	480,1039
(C₅×SL₂(𝔽₃))⋊₇C₂² = Dic₁₀.A₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	120	4+	(C5xSL(2,3)):7C2^2	480,1041
(C₅×SL₂(𝔽₃))⋊₈C₂² = D₅×C₄.A₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)):8C2^2	480,1042
(C₅×SL₂(𝔽₃))⋊₉C₂² = C₁₀×GL₂(𝔽₃)	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80		(C5xSL(2,3)):9C2^2	480,1017
(C₅×SL₂(𝔽₃))⋊₁₀C₂² = C₅×C₄.₃S₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)):10C2^2	480,1021
(C₅×SL₂(𝔽₃))⋊₁₁C₂² = C₁₀×C₄.A₄	φ: trivial image	160		(C5xSL(2,3)):11C2^2	480,1130
(C₅×SL₂(𝔽₃))⋊₁₂C₂² = C₅×Q₈.A₄	φ: trivial image	120	4	(C5xSL(2,3)):12C2^2	480,1131

Non-split extensions G=N.Q with N=C₅×SL₂(𝔽₃) and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×SL₂(𝔽₃)).₁C₂² = CSU₂(𝔽₃)⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	160	4	(C5xSL(2,3)).1C2^2	480,967
(C₅×SL₂(𝔽₃)).₂C₂² = Dic₅.₆S₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)).2C2^2	480,968
(C₅×SL₂(𝔽₃)).₃C₂² = Dic₅.₇S₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	80	4+	(C5xSL(2,3)).3C2^2	480,969
(C₅×SL₂(𝔽₃)).₄C₂² = D₅×CSU₂(𝔽₃)	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	80	4-	(C5xSL(2,3)).4C2^2	480,971
(C₅×SL₂(𝔽₃)).₅C₂² = D₁₀.₁S₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	80	4-	(C5xSL(2,3)).5C2^2	480,972
(C₅×SL₂(𝔽₃)).₆C₂² = D₁₀.₂S₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)).6C2^2	480,973
(C₅×SL₂(𝔽₃)).₇C₂² = C₂×Q₈.D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	160		(C5xSL(2,3)).7C2^2	480,1027
(C₅×SL₂(𝔽₃)).₈C₂² = Q₈.D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)).8C2^2	480,1029
(C₅×SL₂(𝔽₃)).₉C₂² = C₂₀.₂S₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	160	4-	(C5xSL(2,3)).9C2^2	480,1030
(C₅×SL₂(𝔽₃)).₁₀C₂² = C₂₀.₆S₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)).10C2^2	480,1031
(C₅×SL₂(𝔽₃)).₁₁C₂² = SL₂(𝔽₃).₁₁D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)).11C2^2	480,1040
(C₅×SL₂(𝔽₃)).₁₂C₂² = D₂₀.A₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4-	(C5xSL(2,3)).12C2^2	480,1043
(C₅×SL₂(𝔽₃)).₁₃C₂² = C₁₀×CSU₂(𝔽₃)	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	160		(C5xSL(2,3)).13C2^2	480,1016
(C₅×SL₂(𝔽₃)).₁₄C₂² = C₅×Q₈.D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	4	(C5xSL(2,3)).14C2^2	480,1018
(C₅×SL₂(𝔽₃)).₁₅C₂² = C₅×C₄.S₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	160	4	(C5xSL(2,3)).15C2^2	480,1019
(C₅×SL₂(𝔽₃)).₁₆C₂² = C₅×C₄.₆S₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅×SL₂(𝔽₃)	80	2	(C5xSL(2,3)).16C2^2	480,1020
(C₅×SL₂(𝔽₃)).₁₇C₂² = C₅×D₄.A₄	φ: trivial image	80	4	(C5xSL(2,3)).17C2^2	480,1132

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