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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×C6

Direct product G=N×Q with N=C2×C10 and Q=C2×C6
dρLabelID
C23×C30240C2^3xC30240,208

Semidirect products G=N:Q with N=C2×C10 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C2×C6) = C2×D5×A4φ: C2×C6/C2 → C6 ⊆ Aut C2×C10306+(C2xC10):(C2xC6)240,198
(C2×C10)⋊2(C2×C6) = C3×D4×D5φ: C2×C6/C3 → C22 ⊆ Aut C2×C10604(C2xC10):2(C2xC6)240,159
(C2×C10)⋊3(C2×C6) = A4×C2×C10φ: C2×C6/C22 → C3 ⊆ Aut C2×C1060(C2xC10):3(C2xC6)240,203
(C2×C10)⋊4(C2×C6) = D4×C30φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10):4(C2xC6)240,186
(C2×C10)⋊5(C2×C6) = C6×C5⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10):5(C2xC6)240,164
(C2×C10)⋊6(C2×C6) = D5×C22×C6φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10):6(C2xC6)240,205

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C2×C10).(C2×C6) = C3×D4⋊2D5φ: C2×C6/C3 → C22 ⊆ Aut C2×C101204(C2xC10).(C2xC6)240,160
(C2×C10).2(C2×C6) = C15×C4○D4φ: C2×C6/C6 → C2 ⊆ Aut C2×C101202(C2xC10).2(C2xC6)240,188
(C2×C10).3(C2×C6) = C12×Dic5φ: C2×C6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).3(C2xC6)240,40
(C2×C10).4(C2×C6) = C3×C10.D4φ: C2×C6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).4(C2xC6)240,41
(C2×C10).5(C2×C6) = C3×C4⋊Dic5φ: C2×C6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).5(C2xC6)240,42
(C2×C10).6(C2×C6) = C3×D10⋊C4φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).6(C2xC6)240,43
(C2×C10).7(C2×C6) = C3×C23.D5φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).7(C2xC6)240,48
(C2×C10).8(C2×C6) = C6×Dic10φ: C2×C6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).8(C2xC6)240,155
(C2×C10).9(C2×C6) = D5×C2×C12φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).9(C2xC6)240,156
(C2×C10).10(C2×C6) = C6×D20φ: C2×C6/C6 → C2 ⊆ Aut C2×C10120(C2xC10).10(C2xC6)240,157
(C2×C10).11(C2×C6) = C3×C4○D20φ: C2×C6/C6 → C2 ⊆ Aut C2×C101202(C2xC10).11(C2xC6)240,158
(C2×C10).12(C2×C6) = C2×C6×Dic5φ: C2×C6/C6 → C2 ⊆ Aut C2×C10240(C2xC10).12(C2xC6)240,163
(C2×C10).13(C2×C6) = C15×C22⋊C4central extension (φ=1)120(C2xC10).13(C2xC6)240,82
(C2×C10).14(C2×C6) = C15×C4⋊C4central extension (φ=1)240(C2xC10).14(C2xC6)240,83
(C2×C10).15(C2×C6) = Q8×C30central extension (φ=1)240(C2xC10).15(C2xC6)240,187

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