Finite Group Databasebeta

← C25×C11×C41 #72192607

Subgroups — C25×C11×C41 #72192607

Order 14432.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C11×C41C2131yesmaximal, direct product factor
2C23×C11×C41C221155yesdirect product factor
3C22×C11×C41C231155yesdirect product factor
4C25×C41C1111yesmaximal, characteristic, direct product factor, Hall
5C2×C11×C41C24131yesdirect product factor
6C24×C41C2×C11131yesdirect product factor
7C11×C41C2511yescharacteristic, direct product factor, Hall
8C25×C11C4111yesmaximal, characteristic, direct product factor, Hall
9C23×C41C22×C111155yesdirect product factor
10C24×C11C2×C41131yesdirect product factor
11C22×C41C23×C111155yesdirect product factor
12C23×C11C22×C411155yesdirect product factor
13C2×C41C24×C11131yesdirect product factor
14C22×C11C23×C411155yesdirect product factor
15C41C25×C1111yescharacteristic, direct product factor, Sylow
16C25C11×C4111yescharacteristic, direct product factor, Sylow
17C2×C11C24×C41131yesdirect product factor
18C24C2×C11×C41131yesdirect product factor
19C11C25×C4111yescharacteristic, direct product factor, Sylow
20C23C22×C11×C411155yesdirect product factor
21C22C23×C11×C411155yesdirect product factor
22C2C24×C11×C41131yesdirect 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. C24×C11×C41C2direct (N × H)
2. C23×C11×C41C22direct (N × H)
3. C22×C11×C41C23direct (N × H)
4. C25×C41C11direct (N × H)
5. C2×C11×C41C24direct (N × H)
6. C24×C41C2×C11direct (N × H)
7. C11×C41C25direct (N × H)
8. C25×C11C41direct (N × H)
9. C23×C41C22×C11direct (N × H)
10. C24×C11C2×C41direct (N × H)
11. C22×C41C23×C11direct (N × H)
12. C23×C11C22×C41direct (N × H)
13. C2×C41C24×C11direct (N × H)
14. C22×C11C23×C41direct (N × H)
15. C41C25×C11direct (N × H)
16. C25C11×C41direct (N × H)
17. C2×C11C24×C41direct (N × H)
18. C24C2×C11×C41direct (N × H)
19. C11C25×C41direct (N × H)
20. C23C22×C11×C41direct (N × H)
21. C22C23×C11×C41direct (N × H)
22. C2C24×C11×C41direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C11×C412
C25×C4111
C25×C1141