Extensions 1→N→G→Q→1 with N=C5×2+ 1+4 and Q=C2

Direct product G=N×Q with N=C5×2+ 1+4 and Q=C2
dρLabelID
C10×2+ 1+480C10xES+(2,2)320,1632

Semidirect products G=N:Q with N=C5×2+ 1+4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C5×2+ 1+4)⋊1C2 = 2+ 1+4⋊D5φ: C2/C1C2 ⊆ Out C5×2+ 1+4408+(C5xES+(2,2)):1C2320,868
(C5×2+ 1+4)⋊2C2 = D20.32C23φ: C2/C1C2 ⊆ Out C5×2+ 1+4808+(C5xES+(2,2)):2C2320,1507
(C5×2+ 1+4)⋊3C2 = D20.33C23φ: C2/C1C2 ⊆ Out C5×2+ 1+4808-(C5xES+(2,2)):3C2320,1508
(C5×2+ 1+4)⋊4C2 = D5×2+ 1+4φ: C2/C1C2 ⊆ Out C5×2+ 1+4408+(C5xES+(2,2)):4C2320,1622
(C5×2+ 1+4)⋊5C2 = D20.37C23φ: C2/C1C2 ⊆ Out C5×2+ 1+4808-(C5xES+(2,2)):5C2320,1623
(C5×2+ 1+4)⋊6C2 = 2+ 1+42D5φ: C2/C1C2 ⊆ Out C5×2+ 1+4408+(C5xES+(2,2)):6C2320,871
(C5×2+ 1+4)⋊7C2 = C5×D44D4φ: C2/C1C2 ⊆ Out C5×2+ 1+4404(C5xES+(2,2)):7C2320,954
(C5×2+ 1+4)⋊8C2 = C5×C2≀C22φ: C2/C1C2 ⊆ Out C5×2+ 1+4404(C5xES+(2,2)):8C2320,958
(C5×2+ 1+4)⋊9C2 = C5×D4○D8φ: C2/C1C2 ⊆ Out C5×2+ 1+4804(C5xES+(2,2)):9C2320,1578
(C5×2+ 1+4)⋊10C2 = C5×D4○SD16φ: C2/C1C2 ⊆ Out C5×2+ 1+4804(C5xES+(2,2)):10C2320,1579
(C5×2+ 1+4)⋊11C2 = C5×C2.C25φ: trivial image804(C5xES+(2,2)):11C2320,1634

Non-split extensions G=N.Q with N=C5×2+ 1+4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C5×2+ 1+4).1C2 = 2+ 1+4.D5φ: C2/C1C2 ⊆ Out C5×2+ 1+4808-(C5xES+(2,2)).1C2320,869
(C5×2+ 1+4).2C2 = 2+ 1+4.2D5φ: C2/C1C2 ⊆ Out C5×2+ 1+4808-(C5xES+(2,2)).2C2320,870
(C5×2+ 1+4).3C2 = C5×D4.9D4φ: C2/C1C2 ⊆ Out C5×2+ 1+4804(C5xES+(2,2)).3C2320,956
(C5×2+ 1+4).4C2 = C5×C23.7D4φ: C2/C1C2 ⊆ Out C5×2+ 1+4804(C5xES+(2,2)).4C2320,959

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