Extensions 1→N→G→Q→1 with N=C₅×C₄²⋊C₂ and Q=C₂

Direct product G=N×Q with N=C₅×C₄²⋊C₂ and Q=C₂

		d	ρ	Label	ID
C₁₀×C₄²⋊C₂		160		C10xC4^2:C2	320,1516

Semidirect products G=N:Q with N=C₅×C₄²⋊C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₄²⋊C₂)⋊₁C₂ = C₄⋊C₄⋊₃₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):1C2	320,628
(C₅×C₄²⋊C₂)⋊₂C₂ = C₄○D₂₀⋊₁₀C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):2C2	320,629
(C₅×C₄²⋊C₂)⋊₃C₂ = C₄⋊C₄.₂₃₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):3C2	320,630
(C₅×C₄²⋊C₂)⋊₄C₂ = C₄²⋊₄D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2):4C2	320,632
(C₅×C₄²⋊C₂)⋊₅C₂ = (C₂×D₂₀)⋊₂₅C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2):5C2	320,633
(C₅×C₄²⋊C₂)⋊₆C₂ = D₅×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):6C2	320,1192
(C₅×C₄²⋊C₂)⋊₇C₂ = C₄²⋊₇D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):7C2	320,1193
(C₅×C₄²⋊C₂)⋊₈C₂ = C₄².₁₈₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):8C2	320,1194
(C₅×C₄²⋊C₂)⋊₉C₂ = C₄².₉₁D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):9C2	320,1195
(C₅×C₄²⋊C₂)⋊₁₀C₂ = C₄²⋊₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):10C2	320,1196
(C₅×C₄²⋊C₂)⋊₁₁C₂ = C₄²⋊₉D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):11C2	320,1197
(C₅×C₄²⋊C₂)⋊₁₂C₂ = C₄².₉₂D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):12C2	320,1198
(C₅×C₄²⋊C₂)⋊₁₃C₂ = C₄²⋊₁₀D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):13C2	320,1199
(C₅×C₄²⋊C₂)⋊₁₄C₂ = C₄².₉₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):14C2	320,1200
(C₅×C₄²⋊C₂)⋊₁₅C₂ = C₄².₉₄D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):15C2	320,1201
(C₅×C₄²⋊C₂)⋊₁₆C₂ = C₄².₉₅D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):16C2	320,1202
(C₅×C₄²⋊C₂)⋊₁₇C₂ = C₄².₉₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):17C2	320,1203
(C₅×C₄²⋊C₂)⋊₁₈C₂ = C₄².₉₇D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):18C2	320,1204
(C₅×C₄²⋊C₂)⋊₁₉C₂ = C₄².₉₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):19C2	320,1205
(C₅×C₄²⋊C₂)⋊₂₀C₂ = C₄².₉₉D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):20C2	320,1206
(C₅×C₄²⋊C₂)⋊₂₁C₂ = C₄².₁₀₀D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):21C2	320,1207
(C₅×C₄²⋊C₂)⋊₂₂C₂ = C₅×C₂³.C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2):22C2	320,911
(C₅×C₄²⋊C₂)⋊₂₃C₂ = C₅×C₂³.₂₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):23C2	320,917
(C₅×C₄²⋊C₂)⋊₂₄C₂ = C₅×C₂³.₃₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):24C2	320,919
(C₅×C₄²⋊C₂)⋊₂₅C₂ = C₅×C₄²⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2):25C2	320,922
(C₅×C₄²⋊C₂)⋊₂₆C₂ = C₅×C₂³.₁₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):26C2	320,983
(C₅×C₄²⋊C₂)⋊₂₇C₂ = C₅×C₂².₁₁C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):27C2	320,1520
(C₅×C₄²⋊C₂)⋊₂₈C₂ = C₅×C₂³.₃₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):28C2	320,1522
(C₅×C₄²⋊C₂)⋊₂₉C₂ = C₅×C₂².₁₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):29C2	320,1527
(C₅×C₄²⋊C₂)⋊₃₀C₂ = C₅×C₂³.₃₆C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):30C2	320,1531
(C₅×C₄²⋊C₂)⋊₃₁C₂ = C₅×C₂².₂₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):31C2	320,1537
(C₅×C₄²⋊C₂)⋊₃₂C₂ = C₅×C₂³.₃₈C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):32C2	320,1538
(C₅×C₄²⋊C₂)⋊₃₃C₂ = C₅×C₂².₃₄C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):33C2	320,1542
(C₅×C₄²⋊C₂)⋊₃₄C₂ = C₅×C₂².₃₆C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):34C2	320,1544
(C₅×C₄²⋊C₂)⋊₃₅C₂ = C₅×C₂².₄₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2):35C2	320,1553
(C₅×C₄²⋊C₂)⋊₃₆C₂ = C₅×C₂².₄₆C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):36C2	320,1554
(C₅×C₄²⋊C₂)⋊₃₇C₂ = C₅×C₂².₄₇C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):37C2	320,1555
(C₅×C₄²⋊C₂)⋊₃₈C₂ = C₅×C₂².₄₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):38C2	320,1557
(C₅×C₄²⋊C₂)⋊₃₉C₂ = C₅×C₂².₅₀C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2):39C2	320,1558
(C₅×C₄²⋊C₂)⋊₄₀C₂ = C₄○D₄×C₂₀	φ: trivial image	160		(C5xC4^2:C2):40C2	320,1519

Non-split extensions G=N.Q with N=C₅×C₄²⋊C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₄²⋊C₂).₁C₂ = C₄²⋊₁Dic₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2).1C2	320,89
(C₅×C₄²⋊C₂).₂C₂ = C₂₀.₃₂C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2).2C2	320,90
(C₅×C₄²⋊C₂).₃C₂ = C₂₀.₆₀(C₄⋊C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2).3C2	320,91
(C₅×C₄²⋊C₂).₄C₂ = C₂₀.₆₄(C₄⋊C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).4C2	320,622
(C₅×C₄²⋊C₂).₅C₂ = C₄⋊C₄.₂₃₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).5C2	320,623
(C₅×C₄²⋊C₂).₆C₂ = C₂₀.₃₅C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).6C2	320,624
(C₅×C₄²⋊C₂).₇C₂ = C₂₀.₇₆(C₄⋊C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).7C2	320,625
(C₅×C₄²⋊C₂).₈C₂ = C₄².₄₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).8C2	320,626
(C₅×C₄²⋊C₂).₉C₂ = C₄².₁₈₇D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).9C2	320,627
(C₅×C₄²⋊C₂).₁₀C₂ = C₄.(C₂×D₂₀)	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).10C2	320,631
(C₅×C₄²⋊C₂).₁₁C₂ = C₄².₈₇D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).11C2	320,1188
(C₅×C₄²⋊C₂).₁₂C₂ = C₄².₈₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).12C2	320,1189
(C₅×C₄²⋊C₂).₁₃C₂ = C₄².₈₉D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).13C2	320,1190
(C₅×C₄²⋊C₂).₁₄C₂ = C₄².₉₀D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).14C2	320,1191
(C₅×C₄²⋊C₂).₁₅C₂ = C₅×C₄.₉C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2).15C2	320,142
(C₅×C₄²⋊C₂).₁₆C₂ = C₅×C₄²⋊₆C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80		(C5xC4^2:C2).16C2	320,144
(C₅×C₄²⋊C₂).₁₇C₂ = C₅×M₄(2)⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	80	4	(C5xC4^2:C2).17C2	320,149
(C₅×C₄²⋊C₂).₁₈C₂ = C₅×C₂³.₃₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).18C2	320,920
(C₅×C₄²⋊C₂).₁₉C₂ = C₅×C₄².₆C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).19C2	320,925
(C₅×C₄²⋊C₂).₂₀C₂ = C₅×C₂³.₂₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).20C2	320,928
(C₅×C₄²⋊C₂).₂₁C₂ = C₅×M₄(2)⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).21C2	320,929
(C₅×C₄²⋊C₂).₂₂C₂ = C₅×C₄².₇C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).22C2	320,934
(C₅×C₄²⋊C₂).₂₃C₂ = C₅×C₂³.₂₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).23C2	320,986
(C₅×C₄²⋊C₂).₂₄C₂ = C₅×C₂³.₃₂C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).24C2	320,1521
(C₅×C₄²⋊C₂).₂₅C₂ = C₅×C₂³.₃₇C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).25C2	320,1535
(C₅×C₄²⋊C₂).₂₆C₂ = C₅×C₂².₃₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).26C2	320,1543
(C₅×C₄²⋊C₂).₂₇C₂ = C₅×C₂³.₄₁C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₄²⋊C₂	160		(C5xC4^2:C2).27C2	320,1546
(C₅×C₄²⋊C₂).₂₈C₂ = C₅×C₈○₂M₄(2)	φ: trivial image	160		(C5xC4^2:C2).28C2	320,906

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5×C42⋊C2 and Q=C2

Extensions 1→N→G→Q→1 with N=C₅×C₄²⋊C₂ and Q=C₂