Finite Group Databasebeta

← C23×C32×C5 #67232

Subgroups — C23×C32×C5 #67232

Order 360.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C5C217yesmaximal, direct product factor
2C23×C3×C5C314yesmaximal, direct product factor
3C2×C32×C5C2217yesdirect product factor
4C23×C32C511yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5C2×C3128yesdirect product factor
6C32×C5C2311yescharacteristic, direct product factor, Hall
7C23×C5C3211yescharacteristic, direct product factor, Hall
8C22×C32C2×C517yesdirect product factor
9C2×C3×C5C22×C3128yesdirect product factor
10C23×C3C3×C514yesdirect product factor
11C22×C5C2×C3217yesdirect product factor
12C2×C32C22×C517yesdirect product factor
13C3×C5C23×C314yesdirect product factor
14C22×C3C2×C3×C5128yesdirect product factor
15C2×C5C22×C3217yesdirect product factor
16C32C23×C511yescharacteristic, direct product factor, Sylow
17C23C32×C511yescharacteristic, direct product factor, Sylow
18C2×C3C22×C3×C5128yesdirect product factor
19C5C23×C3211yescharacteristic, direct product factor, Sylow
20C22C2×C32×C517yesdirect product factor
21C3C23×C3×C514yesdirect product factor
22C2C22×C32×C517yesdirect 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. C22×C32×C5C2direct (N × H)
2. C23×C3×C5C3direct (N × H)
3. C2×C32×C5C22direct (N × H)
4. C23×C32C5direct (N × H)
5. C22×C3×C5C2×C3direct (N × H)
6. C32×C5C23direct (N × H)
7. C23×C5C32direct (N × H)
8. C22×C32C2×C5direct (N × H)
9. C2×C3×C5C22×C3direct (N × H)
10. C23×C3C3×C5direct (N × H)
11. C22×C5C2×C32direct (N × H)
12. C2×C32C22×C5direct (N × H)
13. C3×C5C23×C3direct (N × H)
14. C22×C3C2×C3×C5direct (N × H)
15. C2×C5C22×C32direct (N × H)
16. C32C23×C5direct (N × H)
17. C23C32×C5direct (N × H)
18. C2×C3C22×C3×C5direct (N × H)
19. C5C23×C32direct (N × H)
20. C22C2×C32×C5direct (N × H)
21. C3C23×C3×C5direct (N × H)
22. C2C22×C32×C5direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C32×C52
C23×C3×C53
C23×C325