# Extensions 1→N→G→Q→1 with N=C2×M5(2) and Q=C2

Direct product G=N×Q with N=C2×M5(2) and Q=C2
dρLabelID
C22×M5(2)64C2^2xM5(2)128,2137

Semidirect products G=N:Q with N=C2×M5(2) and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×M5(2))⋊1C2 = C16⋊D4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):1C2128,950
(C2×M5(2))⋊2C2 = C162D4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):2C2128,952
(C2×M5(2))⋊3C2 = C2×C16⋊C22φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)):3C2128,2144
(C2×M5(2))⋊4C2 = C2×Q32⋊C2φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):4C2128,2145
(C2×M5(2))⋊5C2 = D16⋊C22φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):5C2128,2146
(C2×M5(2))⋊6C2 = C24.5C8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)):6C2128,844
(C2×M5(2))⋊7C2 = (C2×D4).5C8φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):7C2128,845
(C2×M5(2))⋊8C2 = C2×C23.C8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)):8C2128,846
(C2×M5(2))⋊9C2 = M5(2).19C22φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):9C2128,847
(C2×M5(2))⋊10C2 = C2×D4.C8φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):10C2128,848
(C2×M5(2))⋊11C2 = M5(2)⋊12C22φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):11C2128,849
(C2×M5(2))⋊12C2 = C23.39D8φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):12C2128,871
(C2×M5(2))⋊13C2 = C23.40D8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)):13C2128,872
(C2×M5(2))⋊14C2 = C23.20SD16φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):14C2128,875
(C2×M5(2))⋊15C2 = C2×D82C4φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)):15C2128,876
(C2×M5(2))⋊16C2 = C23.13D8φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):16C2128,877
(C2×M5(2))⋊17C2 = C2×M5(2)⋊C2φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)):17C2128,878
(C2×M5(2))⋊18C2 = C23.21SD16φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):18C2128,880
(C2×M5(2))⋊19C2 = C169D4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):19C2128,900
(C2×M5(2))⋊20C2 = C166D4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)):20C2128,901
(C2×M5(2))⋊21C2 = Q8○M5(2)φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)):21C2128,2139
(C2×M5(2))⋊22C2 = C2×D4○C16φ: trivial image64(C2xM5(2)):22C2128,2138

Non-split extensions G=N.Q with N=C2×M5(2) and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×M5(2)).1C2 = M5(2)⋊1C4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).1C2128,891
(C2×M5(2)).2C2 = M5(2).1C4φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).2C2128,893
(C2×M5(2)).3C2 = C16.D4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).3C2128,951
(C2×M5(2)).4C2 = C2×C8.Q8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).4C2128,886
(C2×M5(2)).5C2 = M5(2)⋊3C4φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).5C2128,887
(C2×M5(2)).6C2 = C42.2C8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).6C2128,107
(C2×M5(2)).7C2 = C42.7C8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).7C2128,108
(C2×M5(2)).8C2 = M5(2)⋊C4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).8C2128,109
(C2×M5(2)).9C2 = M4(2).C8φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).9C2128,110
(C2×M5(2)).10C2 = M5(2)⋊7C4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).10C2128,111
(C2×M5(2)).11C2 = C8.11C42φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).11C2128,115
(C2×M5(2)).12C2 = C23.9D8φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).12C2128,116
(C2×M5(2)).13C2 = C8.13C42φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).13C2128,117
(C2×M5(2)).14C2 = C8.C42φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).14C2128,118
(C2×M5(2)).15C2 = C8.2C42φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).15C2128,119
(C2×M5(2)).16C2 = M5(2).C4φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).16C2128,120
(C2×M5(2)).17C2 = C8.4C42φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).17C2128,121
(C2×M5(2)).18C2 = C23.C16φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).18C2128,132
(C2×M5(2)).19C2 = C2×C16⋊C4φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).19C2128,841
(C2×M5(2)).20C2 = C8.23C42φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).20C2128,842
(C2×M5(2)).21C2 = C23.41D8φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).21C2128,873
(C2×M5(2)).22C2 = C2×C8.17D4φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).22C2128,879
(C2×M5(2)).23C2 = C4⋊M5(2)φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).23C2128,882
(C2×M5(2)).24C2 = C4⋊C4.7C8φ: C2/C1C2 ⊆ Out C2×M5(2)64(C2xM5(2)).24C2128,883
(C2×M5(2)).25C2 = C2×C8.C8φ: C2/C1C2 ⊆ Out C2×M5(2)32(C2xM5(2)).25C2128,884
(C2×M5(2)).26C2 = M4(2).1C8φ: C2/C1C2 ⊆ Out C2×M5(2)324(C2xM5(2)).26C2128,885
(C2×M5(2)).27C2 = C4×M5(2)φ: trivial image64(C2xM5(2)).27C2128,839
(C2×M5(2)).28C2 = C162M5(2)φ: trivial image64(C2xM5(2)).28C2128,840

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