Extensions 1→N→G→Q→1 with N=Dic₆ and Q=C₂×C₁₀

Direct product G=N×Q with N=Dic₆ and Q=C₂×C₁₀

		d	ρ	Label	ID
C₂×C₁₀×Dic₆		480		C2xC10xDic6	480,1150

Semidirect products G=N:Q with N=Dic₆ and Q=C₂×C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₆⋊₁(C₂×C₁₀) = C₅×D₈⋊S₃	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	120	4	Dic6:1(C2xC10)	480,790
Dic₆⋊₂(C₂×C₁₀) = C₅×S₃×SD₁₆	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	120	4	Dic6:2(C2xC10)	480,792
Dic₆⋊₃(C₂×C₁₀) = C₁₀×C₂₄⋊C₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240		Dic6:3(C2xC10)	480,781
Dic₆⋊₄(C₂×C₁₀) = C₅×C₈⋊D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	120	4	Dic6:4(C2xC10)	480,787
Dic₆⋊₅(C₂×C₁₀) = C₅×D₁₂⋊₆C₂²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	120	4	Dic6:5(C2xC10)	480,811
Dic₆⋊₆(C₂×C₁₀) = C₁₀×D₄.S₃	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240		Dic6:6(C2xC10)	480,812
Dic₆⋊₇(C₂×C₁₀) = C₁₀×D₄⋊₂S₃	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240		Dic6:7(C2xC10)	480,1155
Dic₆⋊₈(C₂×C₁₀) = C₅×D₄⋊₆D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	120	4	Dic6:8(C2xC10)	480,1156
Dic₆⋊₉(C₂×C₁₀) = S₃×Q₈×C₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240		Dic6:9(C2xC10)	480,1157
Dic₆⋊₁₀(C₂×C₁₀) = C₅×S₃×C₄○D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	120	4	Dic6:10(C2xC10)	480,1160
Dic₆⋊₁₁(C₂×C₁₀) = C₁₀×C₄○D₁₂	φ: trivial image	240		Dic6:11(C2xC10)	480,1153
Dic₆⋊₁₂(C₂×C₁₀) = C₅×D₄○D₁₂	φ: trivial image	120	4	Dic6:12(C2xC10)	480,1161

Non-split extensions G=N.Q with N=Dic₆ and Q=C₂×C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₆.₁(C₂×C₁₀) = C₅×D₈⋊₃S₃	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	240	4	Dic6.1(C2xC10)	480,791
Dic₆.₂(C₂×C₁₀) = C₅×D₄.D₆	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	240	4	Dic6.2(C2xC10)	480,794
Dic₆.₃(C₂×C₁₀) = C₅×Q₈.₇D₆	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	240	4	Dic6.3(C2xC10)	480,795
Dic₆.₄(C₂×C₁₀) = C₅×S₃×Q₁₆	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	240	4	Dic6.4(C2xC10)	480,796
Dic₆.₅(C₂×C₁₀) = C₅×Q₁₆⋊S₃	φ: C₂×C₁₀/C₅ → C₂² ⊆ Out Dic₆	240	4	Dic6.5(C2xC10)	480,797
Dic₆.₆(C₂×C₁₀) = C₅×C₄○D₂₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	2	Dic6.6(C2xC10)	480,783
Dic₆.₇(C₂×C₁₀) = C₁₀×Dic₁₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	480		Dic6.7(C2xC10)	480,784
Dic₆.₈(C₂×C₁₀) = C₅×C₈.D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	4	Dic6.8(C2xC10)	480,788
Dic₆.₉(C₂×C₁₀) = C₅×Q₈.₁₁D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	4	Dic6.9(C2xC10)	480,821
Dic₆.₁₀(C₂×C₁₀) = C₁₀×C₃⋊Q₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	480		Dic6.10(C2xC10)	480,822
Dic₆.₁₁(C₂×C₁₀) = C₅×Q₈.₁₃D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	4	Dic6.11(C2xC10)	480,829
Dic₆.₁₂(C₂×C₁₀) = C₅×Q₈.₁₄D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	4	Dic6.12(C2xC10)	480,830
Dic₆.₁₃(C₂×C₁₀) = C₅×Q₈.₁₅D₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	4	Dic6.13(C2xC10)	480,1159
Dic₆.₁₄(C₂×C₁₀) = C₅×Q₈○D₁₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Dic₆	240	4	Dic6.14(C2xC10)	480,1162

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁