Finite Group Databasebeta

← C25×C4×C257 #45662129

Subgroups — C25×C4×C257 #45662129

Order 32896.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C257C211yesmaximal, characteristic
2C24×C4×C257C2162yesmaximal, direct product factor
3C25×C257C4132yesdirect product factor
4C25×C257C22131yes—
5C23×C4×C257C221620yesdirect product factor
6C24×C257C2×C41496yesdirect product factor
7C24×C257C231155yes—
8C22×C4×C257C2311240yesdirect product factor
9C23×C257C22×C411240yesdirect product factor
10C23×C257C241155yes—
11C2×C4×C257C241496yesdirect product factor
12C22×C257C23×C41620yesdirect product factor
13C22×C257C25131yes—
14C4×C257C25132yesdirect product factor
15C2×C257C24×C4162yesdirect product factor
16C2×C257C2611yescharacteristic
17C257C25×C411yescharacteristic, direct product factor, Sylow
18C25×C4C25711yesmaximal, characteristic, direct product factor, Sylow
19C26C2×C25711yescharacteristic
20C24×C4C2×C257162yesdirect product factor
21C25C4×C257132yesdirect product factor
22C25C22×C257131yes—
23C23×C4C22×C2571620yesdirect product factor
24C24C2×C4×C2571496yesdirect product factor
25C24C23×C2571155yes—
26C22×C4C23×C25711240yesdirect product factor
27C23C22×C4×C25711240yesdirect product factor
28C23C24×C2571155yes—
29C2×C4C24×C2571496yesdirect product factor
30C22C23×C4×C2571620yesdirect product factor
31C22C25×C257131yes—
32C4C25×C257132yesdirect product factor
33C2C24×C4×C257162yesdirect product factor
34C2C26×C25711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C26×C257
socle, prime radicalC26×C257C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C24×C4×C257C2direct (N × H)
3. C25×C257C4direct (N × H)
5. C23×C4×C257C22direct (N × H)
6. C24×C257C2×C4direct (N × H)
8. C22×C4×C257C23direct (N × H)
9. C23×C257C22×C4direct (N × H)
11. C2×C4×C257C24direct (N × H)
12. C22×C257C23×C4direct (N × H)
14. C4×C257C25direct (N × H)
15. C2×C257C24×C4direct (N × H)
17. C257C25×C4direct (N × H)
18. C25×C4C257direct (N × H)
20. C24×C4C2×C257direct (N × H)
21. C25C4×C257direct (N × H)
23. C23×C4C22×C257direct (N × H)
24. C24C2×C4×C257direct (N × H)
26. C22×C4C23×C257direct (N × H)
27. C23C22×C4×C257direct (N × H)
29. C2×C4C24×C257direct (N × H)
30. C22C23×C4×C257direct (N × H)
32. C4C25×C257direct (N × H)
33. C2C24×C4×C257direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C2572
C24×C4×C2572
C25×C4257