Finite Group Databasebeta

← C2×(C5⋊D5)⋊(C31⋊C3) #22604884

Subgroups — C2×(C5⋊D5)⋊(C31⋊C3) #22604884

Order 9300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C52⋊(C31⋊C3)C211yesmaximal, characteristic, complemented
2(C5⋊D5)⋊(C31⋊C3)C212yesmaximal, direct product factor
3C2×C31×C5⋊D5C311yesmaximal, characteristic, complemented, Hall
4C52⋊(C31⋊C3)C2211yescharacteristic, complemented, Hall
5C2×C52×C31C2×C311yescharacteristic, complemented
6C31×C5⋊D5C2×C312yescomplemented
7C52×C31C22×C311yescharacteristic, complemented, Hall
8C2×D5×C31—152no—
9C22×C31⋊C3—251nomaximal, Hall
10C2×C5×C31—32no—
11D5×C31—154no—
12C2×(C5⋊D5)⋊C3—311nomaximal, Hall
13C2×C31⋊C3—252no—
14C2×C31⋊C3—251no—
15C5×C31—32no—
16C2×C52⋊C3—311no—
17(C5⋊D5)⋊C3—312no—
18C22×C31—251noHall
19C2×C5⋊D5C31⋊C311yescharacteristic, complemented, Hall
20C31⋊C3—251noHall
21C52⋊C3—311noHall
22C2×C31—252no—
23C2×C31(C5⋊D5)⋊C311yescharacteristic, complemented
24C2×C52C2×C31⋊C311yescharacteristic, complemented
25C5⋊D5C2×C31⋊C312yescomplemented
26C31C2×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
27C52C22×C31⋊C311yescharacteristic, complemented, Sylow
28C2×D5—152no—
29C22×C3—7751noHall
30C2×C5—32no—
31D5—154no—
32C2×C3—7752no—
33C2×C3—7751no—
34C5—32no—
35C22—251noSylow
36C3—7751noSylow
37C2—252no—
38C2(C5⋊D5)⋊(C31⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2(C5⋊D5)⋊(C31⋊C3)
commutator, hypocenterC52×C31C22×C3
FrattiniC1G
Fitting, socleC2×C52×C31C2×C3
LCSG ▷ C52×C31
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C52⋊(C31⋊C3)C2semidirect
2. (C5⋊D5)⋊(C31⋊C3)C2direct (N × H)
3. C2×C31×C5⋊D5C3semidirect
4. C52⋊(C31⋊C3)C22semidirect
5. C2×C52×C31C2×C3semidirect
6. C31×C5⋊D5C2×C3semidirect
7. C52×C31C22×C3semidirect
19. C2×C5⋊D5C31⋊C3semidirect
23. C2×C31(C5⋊D5)⋊C3semidirect
24. C2×C52C2×C31⋊C3semidirect
25. C5⋊D5C2×C31⋊C3semidirect
26. C31C2×(C5⋊D5)⋊C3semidirect
27. C52C22×C31⋊C3semidirect
38. C2(C5⋊D5)⋊(C31⋊C3)direct (N × H)