Finite Group Databasebeta

← C3×(C5⋊D5)⋊(C31⋊C3) #28358481

Subgroups — C3×(C5⋊D5)⋊(C31⋊C3) #28358481

Order 13950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52⋊(C31⋊C3)C211yesmaximal, characteristic, complemented, Hall
2C3×C31×C5⋊D5C311yesmaximal, characteristic, complemented
3(C5⋊D5)⋊(C31⋊C3)C313yesmaximal, direct product factor
4C52⋊(C31⋊C3)C2×C313yescomplemented
5C3×C52×C31C2×C311yescharacteristic, complemented
6C31×C5⋊D5C3211yescharacteristic, complemented, Hall
7C3×D5×C31—152no—
8C52×C31C2×C3211yescharacteristic, complemented, Hall
9C2×C3×C31⋊C3—251nomaximal, Hall
10C3×C5×C31—32no—
11C3×(C5⋊D5)⋊C3—311nomaximal, Hall
12D5×C31—152no—
13C3×C31⋊C3—251noHall
14C3×C52⋊C3—311noHall
15C2×C3×C31—251no—
16C2×C31⋊C3—253no—
17C5×C31—32no—
18C3×C5⋊D5C31⋊C311yescharacteristic, complemented
19(C5⋊D5)⋊C3—313no—
20C3×C31(C5⋊D5)⋊C311yescharacteristic, complemented
21C31⋊C3—253no—
22C3×C52C2×C31⋊C311yescharacteristic, complemented
23C52⋊C3—313no—
24C2×C31—251noHall
25C5⋊D5C3×C31⋊C311yescharacteristic, complemented, Hall
26C31C3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
27C3×D5—152no—
28C52C2×C3×C31⋊C311yescharacteristic, complemented, Sylow
29C2×C32—7751noHall
30C3×C5—32no—
31D5—152no—
32C32—7751noSylow
33C2×C3—7753no—
34C2×C3—251no—
35C5—32no—
36C3—7753no—
37C3(C5⋊D5)⋊(C31⋊C3)11yescharacteristic, direct product factor
38C2—251noSylow
subgroupG/H
center, hypercenterC3(C5⋊D5)⋊(C31⋊C3)
commutator, cosocle, hypocenterC52×C31C2×C32
FrattiniC1G
Fitting, socleC3×C52×C31C2×C3
LCSG ▷ C52×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C52⋊(C31⋊C3)C2semidirect
2. C3×C31×C5⋊D5C3semidirect
3. (C5⋊D5)⋊(C31⋊C3)C3direct (N × H)
4. C52⋊(C31⋊C3)C2×C3semidirect
5. C3×C52×C31C2×C3semidirect
6. C31×C5⋊D5C32semidirect
8. C52×C31C2×C32semidirect
18. C3×C5⋊D5C31⋊C3semidirect
20. C3×C31(C5⋊D5)⋊C3semidirect
22. C3×C52C2×C31⋊C3semidirect
25. C5⋊D5C3×C31⋊C3semidirect
26. C31C3×(C5⋊D5)⋊C3semidirect
28. C52C2×C3×C31⋊C3semidirect
37. C3(C5⋊D5)⋊(C31⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52⋊(C31⋊C3)2
C3×C31×C5⋊D53
(C5⋊D5)⋊(C31⋊C3)3
C2×C3×C31⋊C325
C3×(C5⋊D5)⋊C331