Finite Group Databasebeta

← C23×C112×C25 #72201507

Subgroups — C23×C112×C25 #72201507

Order 24200.

672 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C112C511yesmaximal, characteristic
2C23×C11×C25C11112yesmaximal, direct product factor
3C22×C112×C25C217yesmaximal, direct product factor
4C2×C112×C25C2217yesdirect product factor
5C112×C25C2311yescharacteristic, direct product factor, Hall
6C22×C5×C112C2×C517yes—
7C2×C5×C112C22×C517yes—
8C22×C11×C25C2×C11184yesdirect product factor
9C23×C112C2511yescharacteristic, direct product factor, Hall
10C5×C112C23×C511yescharacteristic
11C2×C11×C25C22×C11184yesdirect product factor
12C22×C112C2×C2517yesdirect product factor
13C23×C5×C11C5×C11112yes—
14C11×C25C23×C11112yesdirect product factor
15C2×C112C22×C2517yesdirect product factor
16C22×C5×C11C2×C5×C11184yes—
17C23×C25C11211yescharacteristic, direct product factor, Hall
18C112C23×C2511yescharacteristic, direct product factor, Sylow
19C2×C5×C11C22×C5×C11184yes—
20C22×C25C2×C11217yesdirect product factor
21C23×C11C11×C25112yesdirect product factor
22C5×C11C23×C5×C11112yes—
23C2×C25C22×C11217yesdirect product factor
24C22×C11C2×C11×C25184yesdirect product factor
25C23×C5C5×C11211yescharacteristic
26C25C23×C11211yescharacteristic, direct product factor, Sylow
27C2×C11C22×C11×C25184yesdirect product factor
28C22×C5C2×C5×C11217yes—
29C11C23×C11×C25112yesdirect product factor
30C2×C5C22×C5×C11217yes—
31C23C112×C2511yescharacteristic, direct product factor, Sylow
32C5C23×C5×C11211yescharacteristic
33C22C2×C112×C2517yesdirect product factor
34C2C22×C112×C2517yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C23×C5×C112
socle, prime radicalC23×C5×C112C5
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C11×C25C11direct (N × H)
3. C22×C112×C25C2direct (N × H)
4. C2×C112×C25C22direct (N × H)
5. C112×C25C23direct (N × H)
8. C22×C11×C25C2×C11direct (N × H)
9. C23×C112C25direct (N × H)
11. C2×C11×C25C22×C11direct (N × H)
12. C22×C112C2×C25direct (N × H)
14. C11×C25C23×C11direct (N × H)
15. C2×C112C22×C25direct (N × H)
17. C23×C25C112direct (N × H)
18. C112C23×C25direct (N × H)
20. C22×C25C2×C112direct (N × H)
21. C23×C11C11×C25direct (N × H)
23. C2×C25C22×C112direct (N × H)
24. C22×C11C2×C11×C25direct (N × H)
26. C25C23×C112direct (N × H)
27. C2×C11C22×C11×C25direct (N × H)
29. C11C23×C11×C25direct (N × H)
31. C23C112×C25direct (N × H)
33. C22C2×C112×C25direct (N × H)
34. C2C22×C112×C25direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C1125
C23×C11×C2511
C22×C112×C252