Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₂×F₅

Direct product G=N×Q with N=C₁₀ and Q=C₂×F₅

		d	ρ	Label	ID
F₅×C₂×C₁₀		80		F5xC2xC10	400,214

Semidirect products G=N:Q with N=C₁₀ and Q=C₂×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁(C₂×F₅) = C₂×D₅⋊F₅	φ: C₂×F₅/D₅ → C₄ ⊆ Aut C₁₀	20	8+	C10:1(C2xF5)	400,210
C₁₀⋊₂(C₂×F₅) = C₂²×C₅⋊F₅	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100		C10:2(C2xF5)	400,216
C₁₀⋊₃(C₂×F₅) = C₂²×C₅²⋊C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	40		C10:3(C2xF5)	400,217
C₁₀⋊₄(C₂×F₅) = C₂×D₅×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	40	8+	C10:4(C2xF5)	400,209
C₁₀⋊₅(C₂×F₅) = C₂²×D₅.D₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10:5(C2xF5)	400,215

Non-split extensions G=N.Q with N=C₁₀ and Q=C₂×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₂×F₅) = C₅²⋊₃C₄²	φ: C₂×F₅/D₅ → C₄ ⊆ Aut C₁₀	20	8+	C10.1(C2xF5)	400,124
C₁₀.₂(C₂×F₅) = D₁₀⋊F₅	φ: C₂×F₅/D₅ → C₄ ⊆ Aut C₁₀	20	8+	C10.2(C2xF5)	400,125
C₁₀.₃(C₂×F₅) = Dic₅⋊F₅	φ: C₂×F₅/D₅ → C₄ ⊆ Aut C₁₀	20	8+	C10.3(C2xF5)	400,126
C₁₀.₄(C₂×F₅) = D₁₀.₂F₅	φ: C₂×F₅/D₅ → C₄ ⊆ Aut C₁₀	80	8-	C10.4(C2xF5)	400,127
C₁₀.₅(C₂×F₅) = C₅²⋊₄M₄(2)	φ: C₂×F₅/D₅ → C₄ ⊆ Aut C₁₀	80	8-	C10.5(C2xF5)	400,128
C₁₀.₆(C₂×F₅) = D₂₅⋊C₈	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	200	4	C10.6(C2xF5)	400,28
C₁₀.₇(C₂×F₅) = C₁₀₀.C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	200	4	C10.7(C2xF5)	400,29
C₁₀.₈(C₂×F₅) = C₄×C₂₅⋊C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100	4	C10.8(C2xF5)	400,30
C₁₀.₉(C₂×F₅) = C₁₀₀⋊C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100	4	C10.9(C2xF5)	400,31
C₁₀.₁₀(C₂×F₅) = C₂×C₂₅⋊C₈	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	400		C10.10(C2xF5)	400,32
C₁₀.₁₁(C₂×F₅) = C₂₅⋊M₄(2)	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	200	4-	C10.11(C2xF5)	400,33
C₁₀.₁₂(C₂×F₅) = D₂₅.D₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100	4+	C10.12(C2xF5)	400,34
C₁₀.₁₃(C₂×F₅) = C₂²×C₂₅⋊C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100		C10.13(C2xF5)	400,53
C₁₀.₁₄(C₂×F₅) = C₂₀.F₅	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	200		C10.14(C2xF5)	400,149
C₁₀.₁₅(C₂×F₅) = C₅²⋊₇M₄(2)	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	200		C10.15(C2xF5)	400,150
C₁₀.₁₆(C₂×F₅) = C₄×C₅⋊F₅	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100		C10.16(C2xF5)	400,151
C₁₀.₁₇(C₂×F₅) = C₂₀⋊F₅	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100		C10.17(C2xF5)	400,152
C₁₀.₁₈(C₂×F₅) = C₂×C₅²⋊₄C₈	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	400		C10.18(C2xF5)	400,153
C₁₀.₁₉(C₂×F₅) = C₅²⋊₁₃M₄(2)	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	200		C10.19(C2xF5)	400,154
C₁₀.₂₀(C₂×F₅) = C₁₀²⋊C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	100		C10.20(C2xF5)	400,155
C₁₀.₂₁(C₂×F₅) = C₂₀.₁₁F₅	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	40	4	C10.21(C2xF5)	400,156
C₁₀.₂₂(C₂×F₅) = C₅²⋊₈M₄(2)	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	40	4	C10.22(C2xF5)	400,157
C₁₀.₂₃(C₂×F₅) = C₄×C₅²⋊C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	40	4	C10.23(C2xF5)	400,158
C₁₀.₂₄(C₂×F₅) = C₂₀⋊₂F₅	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	40	4	C10.24(C2xF5)	400,159
C₁₀.₂₅(C₂×F₅) = C₂×C₅²⋊₅C₈	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	80		C10.25(C2xF5)	400,160
C₁₀.₂₆(C₂×F₅) = C₅²⋊₁₄M₄(2)	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	40	4-	C10.26(C2xF5)	400,161
C₁₀.₂₇(C₂×F₅) = C₁₀²⋊₄C₄	φ: C₂×F₅/C₁₀ → C₄ ⊆ Aut C₁₀	20	4+	C10.27(C2xF5)	400,162
C₁₀.₂₈(C₂×F₅) = Dic₅×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	80	8-	C10.28(C2xF5)	400,117
C₁₀.₂₉(C₂×F₅) = D₅.D₂₀	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	40	8+	C10.29(C2xF5)	400,118
C₁₀.₃₀(C₂×F₅) = D₅.Dic₁₀	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	80	8-	C10.30(C2xF5)	400,119
C₁₀.₃₁(C₂×F₅) = D₅×C₅⋊C₈	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	80	8-	C10.31(C2xF5)	400,120
C₁₀.₃₂(C₂×F₅) = Dic₅.₄F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	40	8+	C10.32(C2xF5)	400,121
C₁₀.₃₃(C₂×F₅) = D₁₀.F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	80	8-	C10.33(C2xF5)	400,122
C₁₀.₃₄(C₂×F₅) = Dic₅.F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₀	40	8+	C10.34(C2xF5)	400,123
C₁₀.₃₅(C₂×F₅) = C₂₀.₁₄F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.35(C2xF5)	400,142
C₁₀.₃₆(C₂×F₅) = C₂₀.₁₂F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.36(C2xF5)	400,143
C₁₀.₃₇(C₂×F₅) = C₄×D₅.D₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.37(C2xF5)	400,144
C₁₀.₃₈(C₂×F₅) = C₂₀⋊₅F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.38(C2xF5)	400,145
C₁₀.₃₉(C₂×F₅) = C₂×C₅²⋊₃C₈	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10.39(C2xF5)	400,146
C₁₀.₄₀(C₂×F₅) = C₁₀².C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	40	4	C10.40(C2xF5)	400,147
C₁₀.₄₁(C₂×F₅) = D₁₀.D₁₀	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₀	40	4	C10.41(C2xF5)	400,148
C₁₀.₄₂(C₂×F₅) = C₅×D₅⋊C₈	central extension (φ=1)	80	4	C10.42(C2xF5)	400,135
C₁₀.₄₃(C₂×F₅) = C₅×C₄.F₅	central extension (φ=1)	80	4	C10.43(C2xF5)	400,136
C₁₀.₄₄(C₂×F₅) = C₂₀×F₅	central extension (φ=1)	80	4	C10.44(C2xF5)	400,137
C₁₀.₄₅(C₂×F₅) = C₅×C₄⋊F₅	central extension (φ=1)	80	4	C10.45(C2xF5)	400,138
C₁₀.₄₆(C₂×F₅) = C₁₀×C₅⋊C₈	central extension (φ=1)	80		C10.46(C2xF5)	400,139
C₁₀.₄₇(C₂×F₅) = C₅×C₂².F₅	central extension (φ=1)	40	4	C10.47(C2xF5)	400,140
C₁₀.₄₈(C₂×F₅) = C₅×C₂²⋊F₅	central extension (φ=1)	40	4	C10.48(C2xF5)	400,141

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Extensions 1→N→G→Q→1 with N=C10 and Q=C2×F5

Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₂×F₅