Finite Group Databasebeta

← C11⋊C5×D73⋊C3 #37562814

Subgroups — C11⋊C5×D73⋊C3 #37562814

Order 24090.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×C73⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11⋊C5×D73C311yesmaximal, characteristic, complemented, Hall
3C11×D73⋊C3C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C73C2×C311yescharacteristic, complemented, Hall
5C11×C73⋊C3C2×C511yescharacteristic, complemented, Hall
6C5×D73⋊C3—111nomaximal, Hall
7C11×D73C3×C511yescharacteristic, complemented, Hall
8C5×C73⋊C3—111noHall
9C11×C73C2×C3×C511yescharacteristic, complemented, Hall
10C5×D73—111noHall
11D73⋊C3C11⋊C511yescharacteristic, direct product factor, Hall
12C5×C73—111noHall
13C2×C3×C11⋊C5—731nomaximal, Hall
14C73⋊C3C2×C11⋊C511yescharacteristic, complemented, Hall
15C3×C11⋊C5—731noHall
16D73C3×C11⋊C511yescharacteristic, complemented, Hall
17C2×C11⋊C5—731noHall
18C73C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
19C2×C3×C11—731noHall
20C11⋊C5D73⋊C311yescharacteristic, direct product factor, Hall
21C3×C11—731noHall
22C2×C3×C5—8031noHall
23C2×C11—731noHall
24C3×C5—8031noHall
25C11C5×D73⋊C311yescharacteristic, complemented, Sylow
26C2×C5—8031noHall
27C2×C3—731noHall
28C5—111noSylow
29C3—731noSylow
30C2—731noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C73C2×C3×C5
LCSG ▷ C11×C73
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C73⋊C3C2semidirect
2. C11⋊C5×D73C3semidirect
3. C11×D73⋊C3C5semidirect
4. C11⋊C5×C73C2×C3semidirect
5. C11×C73⋊C3C2×C5semidirect
7. C11×D73C3×C5semidirect
9. C11×C73C2×C3×C5semidirect
11. D73⋊C3C11⋊C5direct (N × H)
14. C73⋊C3C2×C11⋊C5semidirect
16. D73C3×C11⋊C5semidirect
18. C73C2×C3×C11⋊C5semidirect
20. C11⋊C5D73⋊C3direct (N × H)
25. C11C5×D73⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×C73⋊C32
C11⋊C5×D733
C11×D73⋊C35
C5×D73⋊C311
C2×C3×C11⋊C573