Finite Group Databasebeta

← C32×C5×C167 #21418933

Subgroups — C32×C5×C167 #21418933

Order 7515.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C167C314yesmaximal, direct product factor
2C32×C167C511yesmaximal, characteristic, direct product factor, Hall
3C5×C167C3211yescharacteristic, direct product factor, Hall
4C3×C167C3×C514yesdirect product factor
5C167C32×C511yescharacteristic, direct product factor, Sylow
6C32×C5C16711yesmaximal, characteristic, direct product factor, Hall
7C3×C5C3×C16714yesdirect product factor
8C32C5×C16711yescharacteristic, direct product factor, Sylow
9C5C32×C16711yescharacteristic, direct product factor, Sylow
10C3C3×C5×C16714yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×C167C3direct (N × H)
2. C32×C167C5direct (N × H)
3. C5×C167C32direct (N × H)
4. C3×C167C3×C5direct (N × H)
5. C167C32×C5direct (N × H)
6. C32×C5C167direct (N × H)
7. C3×C5C3×C167direct (N × H)
8. C32C5×C167direct (N × H)
9. C5C32×C167direct (N × H)
10. C3C3×C5×C167direct (N × H)