Extensions 1→N→G→Q→1 with N=C₂² and Q=C₂²⋊F₅

Direct product G=N×Q with N=C₂² and Q=C₂²⋊F₅

		d	ρ	Label	ID
C₂²×C₂²⋊F₅		80		C2^2xC2^2:F5	320,1607

Semidirect products G=N:Q with N=C₂² and Q=C₂²⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊₁(C₂²⋊F₅) = (C₂×F₅)⋊D₄	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	40		C2^2:1(C2^2:F5)	320,1117
C₂²⋊₂(C₂²⋊F₅) = C₂⁴⋊₄F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40		C2^2:2(C2^2:F5)	320,1138

Non-split extensions G=N.Q with N=C₂² and Q=C₂²⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₂²⋊F₅) = (C₂×D₄)⋊₇F₅	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	40	8+	C2^2.1(C2^2:F5)	320,1108
C₂².₂(C₂²⋊F₅) = (C₂×D₄).₇F₅	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	160		C2^2.2(C2^2:F5)	320,1113
C₂².₃(C₂²⋊F₅) = (C₂×D₄).₉F₅	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.3(C2^2:F5)	320,1115
C₂².₄(C₂²⋊F₅) = D₅⋊C₄≀C₂	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	40	8	C2^2.4(C2^2:F5)	320,1130
C₂².₅(C₂²⋊F₅) = C₄○D₄⋊F₅	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	40	8	C2^2.5(C2^2:F5)	320,1131
C₂².₆(C₂²⋊F₅) = C₄○D₂₀⋊C₄	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	80	8	C2^2.6(C2^2:F5)	320,1132
C₂².₇(C₂²⋊F₅) = D₄⋊F₅⋊C₂	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₂²	80	8	C2^2.7(C2^2:F5)	320,1133
C₂².₈(C₂²⋊F₅) = C₄²⋊F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	4+	C2^2.8(C2^2:F5)	320,191
C₂².₉(C₂²⋊F₅) = C₄²⋊₂F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	4	C2^2.9(C2^2:F5)	320,192
C₂².₁₀(C₂²⋊F₅) = C₄².F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	4-	C2^2.10(C2^2:F5)	320,193
C₂².₁₁(C₂²⋊F₅) = C₄².₂F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	4	C2^2.11(C2^2:F5)	320,194
C₂².₁₂(C₂²⋊F₅) = C₄²⋊₆F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	4	C2^2.12(C2^2:F5)	320,200
C₂².₁₃(C₂²⋊F₅) = C₄²⋊₃F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	4	C2^2.13(C2^2:F5)	320,201
C₂².₁₄(C₂²⋊F₅) = C₅⋊C₂≀C₄	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	8+	C2^2.14(C2^2:F5)	320,202
C₂².₁₅(C₂²⋊F₅) = C₂²⋊C₄⋊F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.15(C2^2:F5)	320,203
C₂².₁₆(C₂²⋊F₅) = (C₂²×F₅)⋊C₄	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	8+	C2^2.16(C2^2:F5)	320,204
C₂².₁₇(C₂²⋊F₅) = C₂²⋊C₄.F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.17(C2^2:F5)	320,205
C₂².₁₈(C₂²⋊F₅) = (C₂²×C₄)⋊F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	4	C2^2.18(C2^2:F5)	320,254
C₂².₁₉(C₂²⋊F₅) = (C₂×D₄)⋊F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	8+	C2^2.19(C2^2:F5)	320,260
C₂².₂₀(C₂²⋊F₅) = (D₄×C₁₀).C₄	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.20(C2^2:F5)	320,261
C₂².₂₁(C₂²⋊F₅) = (C₂×Q₈)⋊F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8+	C2^2.21(C2^2:F5)	320,266
C₂².₂₂(C₂²⋊F₅) = (Q₈×C₁₀).C₄	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.22(C2^2:F5)	320,267
C₂².₂₃(C₂²⋊F₅) = C₂⁴⋊₂F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	4	C2^2.23(C2^2:F5)	320,272
C₂².₂₄(C₂²⋊F₅) = D₁₀⋊₉M₄(2)	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80		C2^2.24(C2^2:F5)	320,1093
C₂².₂₅(C₂²⋊F₅) = (C₂²×C₄)⋊₇F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80		C2^2.25(C2^2:F5)	320,1102
C₂².₂₆(C₂²⋊F₅) = (D₄×C₁₀)⋊C₄	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	40	8+	C2^2.26(C2^2:F5)	320,1105
C₂².₂₇(C₂²⋊F₅) = (C₂×D₄)⋊₆F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.27(C2^2:F5)	320,1107
C₂².₂₈(C₂²⋊F₅) = (C₂×Q₈)⋊₄F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8-	C2^2.28(C2^2:F5)	320,1120
C₂².₂₉(C₂²⋊F₅) = (C₂×Q₈)⋊₆F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80	8+	C2^2.29(C2^2:F5)	320,1122
C₂².₃₀(C₂²⋊F₅) = C₂⁴.₄F₅	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₂²	80		C2^2.30(C2^2:F5)	320,1136
C₂².₃₁(C₂²⋊F₅) = D₂₀⋊C₈	central extension (φ=1)	160		C2^2.31(C2^2:F5)	320,209
C₂².₃₂(C₂²⋊F₅) = Dic₁₀⋊₁C₈	central extension (φ=1)	320		C2^2.32(C2^2:F5)	320,210
C₂².₃₃(C₂²⋊F₅) = D₁₀.₁₈D₈	central extension (φ=1)	80		C2^2.33(C2^2:F5)	320,212
C₂².₃₄(C₂²⋊F₅) = C₂₀.C₄²	central extension (φ=1)	80		C2^2.34(C2^2:F5)	320,213
C₂².₃₅(C₂²⋊F₅) = (C₂×C₂₀)⋊₁C₈	central extension (φ=1)	160		C2^2.35(C2^2:F5)	320,251
C₂².₃₆(C₂²⋊F₅) = (C₂²×C₄).F₅	central extension (φ=1)	160		C2^2.36(C2^2:F5)	320,252
C₂².₃₇(C₂²⋊F₅) = C₅⋊(C₂³⋊C₈)	central extension (φ=1)	80		C2^2.37(C2^2:F5)	320,253
C₂².₃₈(C₂²⋊F₅) = C₂²⋊F₅⋊C₄	central extension (φ=1)	80		C2^2.38(C2^2:F5)	320,255
C₂².₃₉(C₂²⋊F₅) = C₁₀.(C₄⋊C₈)	central extension (φ=1)	320		C2^2.39(C2^2:F5)	320,256
C₂².₄₀(C₂²⋊F₅) = C₂².F₅⋊C₄	central extension (φ=1)	160		C2^2.40(C2^2:F5)	320,257
C₂².₄₁(C₂²⋊F₅) = Dic₅.₂₃D₈	central extension (φ=1)	160		C2^2.41(C2^2:F5)	320,262
C₂².₄₂(C₂²⋊F₅) = Dic₅.₁₂Q₁₆	central extension (φ=1)	320		C2^2.42(C2^2:F5)	320,268
C₂².₄₃(C₂²⋊F₅) = C₂⁴.F₅	central extension (φ=1)	80		C2^2.43(C2^2:F5)	320,271
C₂².₄₄(C₂²⋊F₅) = C₂×D₁₀.D₄	central extension (φ=1)	80		C2^2.44(C2^2:F5)	320,1082
C₂².₄₅(C₂²⋊F₅) = C₂×D₁₀⋊C₈	central extension (φ=1)	160		C2^2.45(C2^2:F5)	320,1089
C₂².₄₆(C₂²⋊F₅) = C₂×Dic₅.D₄	central extension (φ=1)	160		C2^2.46(C2^2:F5)	320,1098
C₂².₄₇(C₂²⋊F₅) = C₂×D₁₀.₃Q₈	central extension (φ=1)	80		C2^2.47(C2^2:F5)	320,1100
C₂².₄₈(C₂²⋊F₅) = C₂×D₂₀⋊C₄	central extension (φ=1)	80		C2^2.48(C2^2:F5)	320,1104
C₂².₄₉(C₂²⋊F₅) = C₂×D₄⋊F₅	central extension (φ=1)	80		C2^2.49(C2^2:F5)	320,1106
C₂².₅₀(C₂²⋊F₅) = C₂×Q₈⋊F₅	central extension (φ=1)	80		C2^2.50(C2^2:F5)	320,1119
C₂².₅₁(C₂²⋊F₅) = C₂×Q₈⋊₂F₅	central extension (φ=1)	80		C2^2.51(C2^2:F5)	320,1121
C₂².₅₂(C₂²⋊F₅) = C₂×C₂³⋊F₅	central extension (φ=1)	80		C2^2.52(C2^2:F5)	320,1134
C₂².₅₃(C₂²⋊F₅) = C₂×C₂³.₂F₅	central extension (φ=1)	160		C2^2.53(C2^2:F5)	320,1135
C₂².₅₄(C₂²⋊F₅) = C₂×C₂³.F₅	central extension (φ=1)	80		C2^2.54(C2^2:F5)	320,1137
C₂².₅₅(C₂²⋊F₅) = D₁₀.₁D₈	central stem extension (φ=1)	80		C2^2.55(C2^2:F5)	320,206
C₂².₅₆(C₂²⋊F₅) = D₁₀.₁Q₁₆	central stem extension (φ=1)	80		C2^2.56(C2^2:F5)	320,207
C₂².₅₇(C₂²⋊F₅) = C₁₀.C₄≀C₂	central stem extension (φ=1)	320		C2^2.57(C2^2:F5)	320,208
C₂².₅₈(C₂²⋊F₅) = Dic₅.D₈	central stem extension (φ=1)	320		C2^2.58(C2^2:F5)	320,211
C₂².₅₉(C₂²⋊F₅) = D₁₀.SD₁₆	central stem extension (φ=1)	80		C2^2.59(C2^2:F5)	320,258
C₂².₆₀(C₂²⋊F₅) = (C₂×D₄).F₅	central stem extension (φ=1)	160		C2^2.60(C2^2:F5)	320,259
C₂².₆₁(C₂²⋊F₅) = Dic₅.SD₁₆	central stem extension (φ=1)	160		C2^2.61(C2^2:F5)	320,263
C₂².₆₂(C₂²⋊F₅) = D₁₀.Q₁₆	central stem extension (φ=1)	80		C2^2.62(C2^2:F5)	320,264
C₂².₆₃(C₂²⋊F₅) = (C₂×Q₈).F₅	central stem extension (φ=1)	160		C2^2.63(C2^2:F5)	320,265
C₂².₆₄(C₂²⋊F₅) = Dic₅.Q₁₆	central stem extension (φ=1)	320		C2^2.64(C2^2:F5)	320,269

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Extensions 1→N→G→Q→1 with N=C22 and Q=C22⋊F5

Extensions 1→N→G→Q→1 with N=C₂² and Q=C₂²⋊F₅