Extensions 1→N→G→Q→1 with N=C₂₀⋊₂D₄ and Q=C₂

Direct product G=N×Q with N=C₂₀⋊₂D₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₂₀⋊₂D₄		160		C2xC20:2D4	320,1472

Semidirect products G=N:Q with N=C₂₀⋊₂D₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₂₀⋊₂D₄⋊₁C₂ = D₁₀⋊D₈	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:1C2	320,402
C₂₀⋊₂D₄⋊₂C₂ = C₅⋊(C₈⋊₂D₄)	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:2C2	320,409
C₂₀⋊₂D₄⋊₃C₂ = D₂₀⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:3C2	320,783
C₂₀⋊₂D₄⋊₄C₂ = C₄₀⋊₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:4C2	320,784
C₂₀⋊₂D₄⋊₅C₂ = Dic₁₀⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:5C2	320,785
C₂₀⋊₂D₄⋊₆C₂ = C₄₀⋊₁₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:6C2	320,786
C₂₀⋊₂D₄⋊₇C₂ = D₂₀⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:7C2	320,799
C₂₀⋊₂D₄⋊₈C₂ = D₂₀⋊₂₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:8C2	320,1223
C₂₀⋊₂D₄⋊₉C₂ = C₄².₁₁₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:9C2	320,1230
C₂₀⋊₂D₄⋊₁₀C₂ = C₄².₁₁₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:10C2	320,1234
C₂₀⋊₂D₄⋊₁₁C₂ = C₄².₁₁₇D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:11C2	320,1235
C₂₀⋊₂D₄⋊₁₂C₂ = C₂⁴⋊₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:12C2	320,1261
C₂₀⋊₂D₄⋊₁₃C₂ = C₂⁴.₃₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:13C2	320,1263
C₂₀⋊₂D₄⋊₁₄C₂ = C₂⁴.₃₅D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:14C2	320,1265
C₂₀⋊₂D₄⋊₁₅C₂ = C₂⁴.₃₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:15C2	320,1267
C₂₀⋊₂D₄⋊₁₆C₂ = D₅×C₄⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:16C2	320,1276
C₂₀⋊₂D₄⋊₁₇C₂ = C₄⋊C₄⋊₂₁D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:17C2	320,1278
C₂₀⋊₂D₄⋊₁₈C₂ = C₁₀.₃₈2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:18C2	320,1279
C₂₀⋊₂D₄⋊₁₉C₂ = C₁₀.₃₉2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:19C2	320,1280
C₂₀⋊₂D₄⋊₂₀C₂ = C₁₀.₇₃2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:20C2	320,1283
C₂₀⋊₂D₄⋊₂₁C₂ = D₂₀⋊₂₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:21C2	320,1284
C₂₀⋊₂D₄⋊₂₂C₂ = C₁₀.₄₂2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:22C2	320,1285
C₂₀⋊₂D₄⋊₂₃C₂ = C₁₀.₄₃2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:23C2	320,1286
C₂₀⋊₂D₄⋊₂₄C₂ = C₁₀.₄₄2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:24C2	320,1287
C₂₀⋊₂D₄⋊₂₅C₂ = C₁₀.₄₅2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:25C2	320,1288
C₂₀⋊₂D₄⋊₂₆C₂ = C₁₀.₁₁₅2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:26C2	320,1290
C₂₀⋊₂D₄⋊₂₇C₂ = C₁₀.₄₇2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:27C2	320,1291
C₂₀⋊₂D₄⋊₂₈C₂ = C₁₀.₄₈2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:28C2	320,1292
C₂₀⋊₂D₄⋊₂₉C₂ = C₁₀.₇₄2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:29C2	320,1293
C₂₀⋊₂D₄⋊₃₀C₂ = C₁₀.₆₁2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:30C2	320,1329
C₂₀⋊₂D₄⋊₃₁C₂ = C₁₀.₆₄2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:31C2	320,1333
C₂₀⋊₂D₄⋊₃₂C₂ = C₁₀.₆₉2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:32C2	320,1339
C₂₀⋊₂D₄⋊₃₃C₂ = D₂₀⋊₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:33C2	320,1348
C₂₀⋊₂D₄⋊₃₄C₂ = Dic₁₀⋊₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:34C2	320,1349
C₂₀⋊₂D₄⋊₃₅C₂ = C₄².₂₃₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:35C2	320,1388
C₂₀⋊₂D₄⋊₃₆C₂ = D₂₀⋊₁₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:36C2	320,1389
C₂₀⋊₂D₄⋊₃₇C₂ = Dic₁₀⋊₁₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:37C2	320,1390
C₂₀⋊₂D₄⋊₃₈C₂ = C₄².₁₆₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:38C2	320,1391
C₂₀⋊₂D₄⋊₃₉C₂ = D₄×C₅⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:39C2	320,1473
C₂₀⋊₂D₄⋊₄₀C₂ = C₂⁴.₄₁D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:40C2	320,1477
C₂₀⋊₂D₄⋊₄₁C₂ = C₂⁴.₄₂D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4:41C2	320,1478
C₂₀⋊₂D₄⋊₄₂C₂ = C₁₀.₁₀₇2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:42C2	320,1503
C₂₀⋊₂D₄⋊₄₃C₂ = C₁₀.₁₄₇2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:43C2	320,1505
C₂₀⋊₂D₄⋊₄₄C₂ = C₁₀.₁₄₈2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4:44C2	320,1506
C₂₀⋊₂D₄⋊₄₅C₂ = C₄².₂₂₈D₁₀	φ: trivial image	160	C20:2D4:45C2	320,1220
C₂₀⋊₂D₄⋊₄₆C₂ = (C₂×C₂₀)⋊₁₅D₄	φ: trivial image	80	C20:2D4:46C2	320,1500

Non-split extensions G=N.Q with N=C₂₀⋊₂D₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₂₀⋊₂D₄.₁C₂ = D₁₀.SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	80	C20:2D4.1C2	320,258
C₂₀⋊₂D₄.₂C₂ = D₁₀.₁₂D₈	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.2C2	320,401
C₂₀⋊₂D₄.₃C₂ = D₁₀.₁₆SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.3C2	320,404
C₂₀⋊₂D₄.₄C₂ = D₁₀⋊SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.4C2	320,405
C₂₀⋊₂D₄.₅C₂ = C₄₀⋊₆C₄⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.5C2	320,406
C₂₀⋊₂D₄.₆C₂ = C₅⋊₂C₈⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.6C2	320,407
C₂₀⋊₂D₄.₇C₂ = C₄₀⋊₅C₄⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.7C2	320,411
C₂₀⋊₂D₄.₈C₂ = D₁₀⋊₈SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.8C2	320,797
C₂₀⋊₂D₄.₉C₂ = C₄₀⋊₁₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.9C2	320,798
C₂₀⋊₂D₄.₁₀C₂ = C₄₀⋊₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.10C2	320,801
C₂₀⋊₂D₄.₁₁C₂ = C₄².₁₁₅D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.11C2	320,1233
C₂₀⋊₂D₄.₁₂C₂ = C₁₀.₆₃2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.12C2	320,1332
C₂₀⋊₂D₄.₁₃C₂ = C₄².₂₃₄D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.13C2	320,1352
C₂₀⋊₂D₄.₁₄C₂ = C₄².₁₄₄D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂₀⋊₂D₄	160	C20:2D4.14C2	320,1354
C₂₀⋊₂D₄.₁₅C₂ = C₄².₂₂₉D₁₀	φ: trivial image	160	C20:2D4.15C2	320,1229

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C20⋊2D4 and Q=C2

Extensions 1→N→G→Q→1 with N=C₂₀⋊₂D₄ and Q=C₂