Finite Group Databasebeta

← C24×C5×C172 #72200488

Subgroups — C24×C5×C172 #72200488

Order 23120.

2680 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C172C2115yesmaximal, direct product factor
2C24×C172C511yesmaximal, characteristic, direct product factor, Hall
3C23×C172C2×C5115yesdirect product factor
4C22×C5×C172C22135yesdirect product factor
5C2×C5×C172C23115yesdirect product factor
6C5×C172C2411yescharacteristic, direct product factor, Hall
7C24×C5×C17C17118yesmaximal, direct product factor
8C22×C172C22×C5135yesdirect product factor
9C23×C5×C17C2×C171270yesdirect product factor
10C2×C172C23×C5115yesdirect product factor
11C22×C5×C17C22×C171630yesdirect product factor
12C172C24×C511yescharacteristic, direct product factor, Sylow
13C24×C17C5×C17118yesdirect product factor
14C2×C5×C17C23×C171270yesdirect product factor
15C23×C17C2×C5×C171270yesdirect product factor
16C5×C17C24×C17118yesdirect product factor
17C24×C5C17211yescharacteristic, direct product factor, Hall
18C22×C17C22×C5×C171630yesdirect product factor
19C23×C5C2×C172115yesdirect product factor
20C2×C17C23×C5×C171270yesdirect product factor
21C22×C5C22×C172135yesdirect product factor
22C17C24×C5×C17118yesdirect product factor
23C24C5×C17211yescharacteristic, direct product factor, Sylow
24C2×C5C23×C172115yesdirect product factor
25C23C2×C5×C172115yesdirect product factor
26C5C24×C17211yescharacteristic, direct product factor, Sylow
27C22C22×C5×C172135yesdirect product factor
28C2C23×C5×C172115yesdirect 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. C23×C5×C172C2direct (N × H)
2. C24×C172C5direct (N × H)
3. C23×C172C2×C5direct (N × H)
4. C22×C5×C172C22direct (N × H)
5. C2×C5×C172C23direct (N × H)
6. C5×C172C24direct (N × H)
7. C24×C5×C17C17direct (N × H)
8. C22×C172C22×C5direct (N × H)
9. C23×C5×C17C2×C17direct (N × H)
10. C2×C172C23×C5direct (N × H)
11. C22×C5×C17C22×C17direct (N × H)
12. C172C24×C5direct (N × H)
13. C24×C17C5×C17direct (N × H)
14. C2×C5×C17C23×C17direct (N × H)
15. C23×C17C2×C5×C17direct (N × H)
16. C5×C17C24×C17direct (N × H)
17. C24×C5C172direct (N × H)
18. C22×C17C22×C5×C17direct (N × H)
19. C23×C5C2×C172direct (N × H)
20. C2×C17C23×C5×C17direct (N × H)
21. C22×C5C22×C172direct (N × H)
22. C17C24×C5×C17direct (N × H)
23. C24C5×C172direct (N × H)
24. C2×C5C23×C172direct (N × H)
25. C23C2×C5×C172direct (N × H)
26. C5C24×C172direct (N × H)
27. C22C22×C5×C172direct (N × H)
28. C2C23×C5×C172direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C1722
C24×C1725
C24×C5×C1717