Finite Group Databasebeta

← C25×C4×C199 #38766659

Subgroups — C25×C4×C199 #38766659

Order 25472.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C199C211yesmaximal, characteristic
2C24×C4×C199C2162yesmaximal, direct product factor
3C25×C199C4132yesdirect product factor
4C25×C199C22131yes—
5C23×C4×C199C221620yesdirect product factor
6C24×C199C2×C41496yesdirect product factor
7C24×C199C231155yes—
8C22×C4×C199C2311240yesdirect product factor
9C23×C199C22×C411240yesdirect product factor
10C23×C199C241155yes—
11C2×C4×C199C241496yesdirect product factor
12C22×C199C23×C41620yesdirect product factor
13C22×C199C25131yes—
14C4×C199C25132yesdirect product factor
15C2×C199C24×C4162yesdirect product factor
16C2×C199C2611yescharacteristic
17C199C25×C411yescharacteristic, direct product factor, Sylow
18C25×C4C19911yesmaximal, characteristic, direct product factor, Sylow
19C26C2×C19911yescharacteristic
20C24×C4C2×C199162yesdirect product factor
21C25C4×C199132yesdirect product factor
22C25C22×C199131yes—
23C23×C4C22×C1991620yesdirect product factor
24C24C2×C4×C1991496yesdirect product factor
25C24C23×C1991155yes—
26C22×C4C23×C19911240yesdirect product factor
27C23C22×C4×C19911240yesdirect product factor
28C23C24×C1991155yes—
29C2×C4C24×C1991496yesdirect product factor
30C22C23×C4×C1991620yesdirect product factor
31C22C25×C199131yes—
32C4C25×C199132yesdirect product factor
33C2C24×C4×C199162yesdirect product factor
34C2C26×C19911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C26×C199
socle, prime radicalC26×C199C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C24×C4×C199C2direct (N × H)
3. C25×C199C4direct (N × H)
5. C23×C4×C199C22direct (N × H)
6. C24×C199C2×C4direct (N × H)
8. C22×C4×C199C23direct (N × H)
9. C23×C199C22×C4direct (N × H)
11. C2×C4×C199C24direct (N × H)
12. C22×C199C23×C4direct (N × H)
14. C4×C199C25direct (N × H)
15. C2×C199C24×C4direct (N × H)
17. C199C25×C4direct (N × H)
18. C25×C4C199direct (N × H)
20. C24×C4C2×C199direct (N × H)
21. C25C4×C199direct (N × H)
23. C23×C4C22×C199direct (N × H)
24. C24C2×C4×C199direct (N × H)
26. C22×C4C23×C199direct (N × H)
27. C23C22×C4×C199direct (N × H)
29. C2×C4C24×C199direct (N × H)
30. C22C23×C4×C199direct (N × H)
32. C4C25×C199direct (N × H)
33. C2C24×C4×C199direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C1992
C24×C4×C1992
C25×C4199