# Extensions 1→N→G→Q→1 with N=C4○D20 and Q=C2

Direct product G=N×Q with N=C4○D20 and Q=C2
dρLabelID
C2×C4○D2080C2xC4oD20160,216

Semidirect products G=N:Q with N=C4○D20 and Q=C2
extensionφ:Q→Out NdρLabelID
C4○D201C2 = D407C2φ: C2/C1C2 ⊆ Out C4○D20802C4oD20:1C2160,125
C4○D202C2 = C8⋊D10φ: C2/C1C2 ⊆ Out C4○D20404+C4oD20:2C2160,129
C4○D203C2 = D4.D10φ: C2/C1C2 ⊆ Out C4○D20404C4oD20:3C2160,153
C4○D204C2 = D4.8D10φ: C2/C1C2 ⊆ Out C4○D20804C4oD20:4C2160,171
C4○D205C2 = D46D10φ: C2/C1C2 ⊆ Out C4○D20404C4oD20:5C2160,219
C4○D206C2 = Q8.10D10φ: C2/C1C2 ⊆ Out C4○D20804C4oD20:6C2160,222
C4○D207C2 = D5×C4○D4φ: C2/C1C2 ⊆ Out C4○D20404C4oD20:7C2160,223
C4○D208C2 = D48D10φ: C2/C1C2 ⊆ Out C4○D20404+C4oD20:8C2160,224
C4○D209C2 = D4.10D10φ: C2/C1C2 ⊆ Out C4○D20804-C4oD20:9C2160,225

Non-split extensions G=N.Q with N=C4○D20 and Q=C2
extensionφ:Q→Out NdρLabelID
C4○D20.1C2 = D204C4φ: C2/C1C2 ⊆ Out C4○D20402C4oD20.1C2160,12
C4○D20.2C2 = D207C4φ: C2/C1C2 ⊆ Out C4○D20404C4oD20.2C2160,32
C4○D20.3C2 = D20.2C4φ: C2/C1C2 ⊆ Out C4○D20804C4oD20.3C2160,128
C4○D20.4C2 = C8.D10φ: C2/C1C2 ⊆ Out C4○D20804-C4oD20.4C2160,130
C4○D20.5C2 = C20.C23φ: C2/C1C2 ⊆ Out C4○D20804C4oD20.5C2160,163
C4○D20.6C2 = D20.3C4φ: trivial image802C4oD20.6C2160,122

׿
×
𝔽