Extensions 1→N→G→Q→1 with N=D₄×C₁₅ and Q=C₂²

Direct product G=N×Q with N=D₄×C₁₅ and Q=C₂²

		d	ρ	Label	ID
D₄×C₂×C₃₀		240		D4xC2xC30	480,1181

Semidirect products G=N:Q with N=D₄×C₁₅ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₁₅)⋊₁C₂² = D₅×D₄⋊S₃	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):1C2^2	480,553
(D₄×C₁₅)⋊₂C₂² = Dic₁₀⋊₃D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):2C2^2	480,554
(D₄×C₁₅)⋊₃C₂² = S₃×D₄⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):3C2^2	480,555
(D₄×C₁₅)⋊₄C₂² = D₆₀.C₂²	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):4C2^2	480,556
(D₄×C₁₅)⋊₅C₂² = D₁₅⋊D₈	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):5C2^2	480,557
(D₄×C₁₅)⋊₆C₂² = D₃₀.₈D₄	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15):6C2^2	480,558
(D₄×C₁₅)⋊₇C₂² = S₃×D₄×D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	60	8+	(D4xC15):7C2^2	480,1097
(D₄×C₁₅)⋊₈C₂² = D₅×D₄⋊₂S₃	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15):8C2^2	480,1098
(D₄×C₁₅)⋊₉C₂² = S₃×D₄⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15):9C2^2	480,1099
(D₄×C₁₅)⋊₁₀C₂² = D₃₀.C₂³	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):10C2^2	480,1100
(D₄×C₁₅)⋊₁₁C₂² = D₂₀⋊₁₃D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15):11C2^2	480,1101
(D₄×C₁₅)⋊₁₂C₂² = D₂₀⋊₁₄D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):12C2^2	480,1102
(D₄×C₁₅)⋊₁₃C₂² = D₁₂⋊₁₄D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15):13C2^2	480,1103
(D₄×C₁₅)⋊₁₄C₂² = D₈×D₁₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4+	(D4xC15):14C2^2	480,875
(D₄×C₁₅)⋊₁₅C₂² = D₈⋊D₁₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15):15C2^2	480,876
(D₄×C₁₅)⋊₁₆C₂² = C₃×D₅×D₈	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15):16C2^2	480,703
(D₄×C₁₅)⋊₁₇C₂² = C₃×D₈⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15):17C2^2	480,704
(D₄×C₁₅)⋊₁₈C₂² = C₅×S₃×D₈	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15):18C2^2	480,789
(D₄×C₁₅)⋊₁₉C₂² = C₅×D₈⋊S₃	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15):19C2^2	480,790
(D₄×C₁₅)⋊₂₀C₂² = C₂×D₄⋊D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):20C2^2	480,896
(D₄×C₁₅)⋊₂₁C₂² = D₄⋊D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4+	(D4xC15):21C2^2	480,914
(D₄×C₁₅)⋊₂₂C₂² = C₂×D₄×D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120		(D4xC15):22C2^2	480,1169
(D₄×C₁₅)⋊₂₃C₂² = C₂×D₄⋊₂D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):23C2^2	480,1170
(D₄×C₁₅)⋊₂₄C₂² = D₄⋊₆D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):24C2^2	480,1171
(D₄×C₁₅)⋊₂₅C₂² = C₄○D₄×D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):25C2^2	480,1175
(D₄×C₁₅)⋊₂₆C₂² = D₄⋊₈D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4+	(D4xC15):26C2^2	480,1176
(D₄×C₁₅)⋊₂₇C₂² = C₆×D₄⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):27C2^2	480,724
(D₄×C₁₅)⋊₂₈C₂² = C₃×D₄⋊D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):28C2^2	480,742
(D₄×C₁₅)⋊₂₉C₂² = C₆×D₄×D₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120		(D4xC15):29C2^2	480,1139
(D₄×C₁₅)⋊₃₀C₂² = C₆×D₄⋊₂D₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):30C2^2	480,1140
(D₄×C₁₅)⋊₃₁C₂² = C₃×D₄⋊₆D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):31C2^2	480,1141
(D₄×C₁₅)⋊₃₂C₂² = C₃×D₅×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):32C2^2	480,1145
(D₄×C₁₅)⋊₃₃C₂² = C₃×D₄⋊₈D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):33C2^2	480,1146
(D₄×C₁₅)⋊₃₄C₂² = C₁₀×D₄⋊S₃	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):34C2^2	480,810
(D₄×C₁₅)⋊₃₅C₂² = C₅×D₄⋊D₆	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):35C2^2	480,828
(D₄×C₁₅)⋊₃₆C₂² = S₃×D₄×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120		(D4xC15):36C2^2	480,1154
(D₄×C₁₅)⋊₃₇C₂² = C₁₀×D₄⋊₂S₃	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):37C2^2	480,1155
(D₄×C₁₅)⋊₃₈C₂² = C₅×D₄⋊₆D₆	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):38C2^2	480,1156
(D₄×C₁₅)⋊₃₉C₂² = C₅×S₃×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):39C2^2	480,1160
(D₄×C₁₅)⋊₄₀C₂² = C₅×D₄○D₁₂	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):40C2^2	480,1161
(D₄×C₁₅)⋊₄₁C₂² = D₈×C₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15):41C2^2	480,937
(D₄×C₁₅)⋊₄₂C₂² = C₁₅×C₈⋊C₂²	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15):42C2^2	480,941
(D₄×C₁₅)⋊₄₃C₂² = C₄○D₄×C₃₀	φ: trivial image	240		(D4xC15):43C2^2	480,1183
(D₄×C₁₅)⋊₄₄C₂² = C₁₅×2₊¹⁺⁴	φ: trivial image	120	4	(D4xC15):44C2^2	480,1184

Non-split extensions G=N.Q with N=D₄×C₁₅ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₁₅).₁C₂² = D₅×D₄.S₃	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15).1C2^2	480,559
(D₄×C₁₅).₂C₂² = C₆₀.₈C₂³	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).2C2^2	480,560
(D₄×C₁₅).₃C₂² = S₃×D₄.D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15).3C2^2	480,561
(D₄×C₁₅).₄C₂² = C₆₀.₁₀C₂³	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).4C2^2	480,562
(D₄×C₁₅).₅C₂² = Dic₁₀⋊D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15).5C2^2	480,563
(D₄×C₁₅).₆C₂² = D₃₀.₉D₄	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).6C2^2	480,564
(D₄×C₁₅).₇C₂² = D₁₂⋊₁₀D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15).7C2^2	480,565
(D₄×C₁₅).₈C₂² = D₁₂.₂₄D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).8C2^2	480,566
(D₄×C₁₅).₉C₂² = D₂₀.₉D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15).9C2^2	480,567
(D₄×C₁₅).₁₀C₂² = C₆₀.₁₆C₂³	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8+	(D4xC15).10C2^2	480,568
(D₄×C₁₅).₁₁C₂² = D₂₀.₂₄D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).11C2^2	480,569
(D₄×C₁₅).₁₂C₂² = D₂₀⋊₁₀D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8-	(D4xC15).12C2^2	480,570
(D₄×C₁₅).₁₃C₂² = C₆₀.₁₉C₂³	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8+	(D4xC15).13C2^2	480,571
(D₄×C₁₅).₁₄C₂² = D₁₂.₉D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15).14C2^2	480,572
(D₄×C₁₅).₁₅C₂² = D₂₀.₁₀D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).15C2^2	480,573
(D₄×C₁₅).₁₆C₂² = Dic₆⋊D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15).16C2^2	480,574
(D₄×C₁₅).₁₇C₂² = D₃₀.₁₁D₄	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).17C2^2	480,575
(D₄×C₁₅).₁₈C₂² = D₁₂⋊₅D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	8+	(D4xC15).18C2^2	480,576
(D₄×C₁₅).₁₉C₂² = C₁₅⋊2_-¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	8-	(D4xC15).19C2^2	480,1096
(D₄×C₁₅).₂₀C₂² = D₈⋊₃D₁₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4-	(D4xC15).20C2^2	480,877
(D₄×C₁₅).₂₁C₂² = SD₁₆×D₁₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15).21C2^2	480,878
(D₄×C₁₅).₂₂C₂² = Q₈⋊₃D₃₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4+	(D4xC15).22C2^2	480,879
(D₄×C₁₅).₂₃C₂² = SD₁₆⋊D₁₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4-	(D4xC15).23C2^2	480,880
(D₄×C₁₅).₂₄C₂² = D₄.₅D₃₀	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).24C2^2	480,881
(D₄×C₁₅).₂₅C₂² = C₃×D₈⋊₃D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).25C2^2	480,705
(D₄×C₁₅).₂₆C₂² = C₃×D₅×SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15).26C2^2	480,706
(D₄×C₁₅).₂₇C₂² = C₃×D₄₀⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15).27C2^2	480,707
(D₄×C₁₅).₂₈C₂² = C₃×SD₁₆⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).28C2^2	480,708
(D₄×C₁₅).₂₉C₂² = C₃×SD₁₆⋊₃D₅	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).29C2^2	480,709
(D₄×C₁₅).₃₀C₂² = C₅×D₈⋊₃S₃	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).30C2^2	480,791
(D₄×C₁₅).₃₁C₂² = C₅×S₃×SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15).31C2^2	480,792
(D₄×C₁₅).₃₂C₂² = C₅×Q₈⋊₃D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	120	4	(D4xC15).32C2^2	480,793
(D₄×C₁₅).₃₃C₂² = C₅×D₄.D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).33C2^2	480,794
(D₄×C₁₅).₃₄C₂² = C₅×Q₈.₇D₆	φ: C₂²/C₁ → C₂² ⊆ Out D₄×C₁₅	240	4	(D4xC15).34C2^2	480,795
(D₄×C₁₅).₃₅C₂² = D₄.D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15).35C2^2	480,897
(D₄×C₁₅).₃₆C₂² = C₂×D₄.D₁₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15).36C2^2	480,898
(D₄×C₁₅).₃₇C₂² = D₄.₈D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).37C2^2	480,915
(D₄×C₁₅).₃₈C₂² = D₄.₉D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4-	(D4xC15).38C2^2	480,916
(D₄×C₁₅).₃₉C₂² = D₄.₁₀D₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4-	(D4xC15).39C2^2	480,1177
(D₄×C₁₅).₄₀C₂² = C₃×D₄.D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15).40C2^2	480,725
(D₄×C₁₅).₄₁C₂² = C₆×D₄.D₅	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15).41C2^2	480,726
(D₄×C₁₅).₄₂C₂² = C₃×D₄.₈D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).42C2^2	480,743
(D₄×C₁₅).₄₃C₂² = C₃×D₄.₉D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).43C2^2	480,744
(D₄×C₁₅).₄₄C₂² = C₃×D₄.₁₀D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).44C2^2	480,1147
(D₄×C₁₅).₄₅C₂² = C₅×D₁₂⋊₆C₂²	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	120	4	(D4xC15).45C2^2	480,811
(D₄×C₁₅).₄₆C₂² = C₁₀×D₄.S₃	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15).46C2^2	480,812
(D₄×C₁₅).₄₇C₂² = C₅×Q₈.₁₃D₆	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).47C2^2	480,829
(D₄×C₁₅).₄₈C₂² = C₅×Q₈.₁₄D₆	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).48C2^2	480,830
(D₄×C₁₅).₄₉C₂² = C₅×Q₈○D₁₂	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).49C2^2	480,1162
(D₄×C₁₅).₅₀C₂² = SD₁₆×C₃₀	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240		(D4xC15).50C2^2	480,938
(D₄×C₁₅).₅₁C₂² = C₁₅×C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	2	(D4xC15).51C2^2	480,940
(D₄×C₁₅).₅₂C₂² = C₁₅×C₈.C₂²	φ: C₂²/C₂ → C₂ ⊆ Out D₄×C₁₅	240	4	(D4xC15).52C2^2	480,942
(D₄×C₁₅).₅₃C₂² = C₁₅×2_-¹⁺⁴	φ: trivial image	240	4	(D4xC15).53C2^2	480,1185

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4×C15 and Q=C22

Extensions 1→N→G→Q→1 with N=D₄×C₁₅ and Q=C₂²