Finite Group Databasebeta

← C11×D23×C11⋊C5 #42123710

Subgroups — C11×D23×C11⋊C5 #42123710

Order 27830.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C23×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C112×D23C511yesmaximal, characteristic, complemented, Hall
3C112×C23C2×C511yescharacteristic, complemented, Hall
4D23×C11⋊C5C1111yesmaximal, characteristic, direct product factor
5C5×C11×D23—111nomaximal
6C5×C11×C23—111no—
7C23×C11⋊C5C2×C1111yescharacteristic, complemented
8C2×C11×C11⋊C5—231nomaximal, Hall
9C11×C11⋊C5D2311yescharacteristic, direct product factor, Hall
10C11×D23—52no—
11C11×D23C11⋊C511yescharacteristic, direct product factor
12C11×D23C5×C1111yescharacteristic, complemented
13C11×C23—52no—
14C11×C23C2×C11⋊C511yescharacteristic, complemented
15C11×C23C2×C5×C1111yescharacteristic, complemented
16C2×C112—231noHall
17C5×D23—111noHall
18C112C5×D2311yescharacteristic, complemented, Sylow
19C5×C23—111noHall
20C2×C5×C11—2531no—
21C2×C11⋊C5—231no—
22C5×C11—111no—
23C11⋊C5C11×D2311yescharacteristic, direct product factor
24D23C11×C11⋊C511yescharacteristic, direct product factor, Hall
25C23C2×C11×C11⋊C511yescharacteristic, complemented, Sylow
26C2×C11—231no—
27C2×C11—231no—
28C2×C11—1152no—
29C11—52no—
30C11C5×C11×D2311yescharacteristic, complemented
31C11D23×C11⋊C511yescharacteristic, direct product factor
32C2×C5—2531noHall
33C5—111noSylow
34C2—231noSylow
subgroupG/H
center, hypercenterC11D23×C11⋊C5
commutator, cosocle, hypocenterC11×C23C2×C5×C11
FrattiniC1G
Fitting, socleC112×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C23×C11⋊C5C2semidirect
2. C112×D23C5semidirect
3. C112×C23C2×C5semidirect
4. D23×C11⋊C5C11direct (N × H)
7. C23×C11⋊C5C2×C11semidirect
9. C11×C11⋊C5D23direct (N × H)
11. C11×D23C11⋊C5direct (N × H)
12. C11×D23C5×C11semidirect
14. C11×C23C2×C11⋊C5semidirect
15. C11×C23C2×C5×C11semidirect
18. C112C5×D23semidirect
23. C11⋊C5C11×D23direct (N × H)
24. D23C11×C11⋊C5direct (N × H)
25. C23C2×C11×C11⋊C5semidirect
30. C11C5×C11×D23semidirect
31. C11D23×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C23×C11⋊C52
C112×D235
D23×C11⋊C511
C5×C11×D2311
C2×C11×C11⋊C523