Finite Group Databasebeta

← C2×C31×(C5⋊D5)⋊C3 #22604882

Subgroups — C2×C31×(C5⋊D5)⋊C3 #22604882

Order 9300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×C52⋊C3C211yesmaximal, characteristic, complemented
2C31×(C5⋊D5)⋊C3C212yesmaximal, direct product factor
3C2×C31×C5⋊D5C311yesmaximal, characteristic, complemented, Hall
4C31×C52⋊C3C2211yescharacteristic, complemented, Hall
5C2×C52×C31C2×C311yescharacteristic, complemented
6C31×C5⋊D5C2×C312yescomplemented
7C52×C31C22×C311yescharacteristic, complemented, Hall
8C2×D5×C31—152no—
9C22×C3×C31—251nomaximal, Hall
10C2×C5×C31—32no—
11D5×C31—154no—
12C2×(C5⋊D5)⋊C3C3111yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C31—252no—
14C2×C3×C31—251no—
15C5×C31—32no—
16C2×C52⋊C3C2×C3111yescharacteristic, complemented
17(C5⋊D5)⋊C3C2×C3112yesdirect product factor
18C22×C31—251noHall
19C2×C5⋊D5C3×C3111yescharacteristic, complemented, Hall
20C3×C31—251noHall
21C52⋊C3C22×C3111yescharacteristic, complemented, Hall
22C2×C31—252no—
23C2×C31(C5⋊D5)⋊C311yescharacteristic, direct product factor
24C2×C52C2×C3×C3111yescharacteristic, complemented
25C5⋊D5C2×C3×C3112yescomplemented
26C31C2×(C5⋊D5)⋊C311yescharacteristic, direct product factor, Sylow
27C52C22×C3×C3111yescharacteristic, complemented, Sylow
28C2×D5—152no—
29C22×C3—251noHall
30C2×C5—32no—
31D5—154no—
32C2×C3—252no—
33C2×C3—251no—
34C5—32no—
35C22—251noSylow
36C3—251noSylow
37C2—252no—
38C2C31×(C5⋊D5)⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C31(C5⋊D5)⋊C3
commutator, hypocenterC52C22×C3×C31
FrattiniC1G
Fitting, socleC2×C52×C31C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C31

Complements

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

NH ≅ G/Ntype
1. C2×C31×C52⋊C3C2semidirect
2. C31×(C5⋊D5)⋊C3C2direct (N × H)
3. C2×C31×C5⋊D5C3semidirect
4. C31×C52⋊C3C22semidirect
5. C2×C52×C31C2×C3semidirect
6. C31×C5⋊D5C2×C3semidirect
7. C52×C31C22×C3semidirect
12. C2×(C5⋊D5)⋊C3C31direct (N × H)
16. C2×C52⋊C3C2×C31semidirect
17. (C5⋊D5)⋊C3C2×C31direct (N × H)
19. C2×C5⋊D5C3×C31semidirect
21. C52⋊C3C22×C31semidirect
23. C2×C31(C5⋊D5)⋊C3direct (N × H)
24. C2×C52C2×C3×C31semidirect
25. C5⋊D5C2×C3×C31semidirect
26. C31C2×(C5⋊D5)⋊C3direct (N × H)
27. C52C22×C3×C31semidirect
38. C2C31×(C5⋊D5)⋊C3direct (N × H)