Finite Group Databasebeta

← C3×C71×(C5⋊D5)⋊C3 #44544069

Subgroups — C3×C71×(C5⋊D5)⋊C3 #44544069

Order 31950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C71×C52⋊C3C211yesmaximal, characteristic, complemented, Hall
2C3×C5⋊D5×C71C311yesmaximal, characteristic, complemented
3C71×(C5⋊D5)⋊C3C313yesmaximal, direct product factor
4C71×C52⋊C3C2×C313yescomplemented
5C3×C52×C71C2×C311yescharacteristic, complemented
6C5⋊D5×C71C3211yescharacteristic, complemented, Hall
7C3×D5×C71—152no—
8C52×C71C2×C3211yescharacteristic, complemented, Hall
9C2×C32×C71—251nomaximal, Hall
10C3×C5×C71—32no—
11D5×C71—152no—
12C32×C71—251noHall
13C3×(C5⋊D5)⋊C3C7111yesmaximal, characteristic, direct product factor, Hall
14C2×C3×C71—253no—
15C2×C3×C71—251no—
16C5×C71—32no—
17C3×C52⋊C3C2×C7111yescharacteristic, complemented, Hall
18C3×C71—253no—
19C3×C71(C5⋊D5)⋊C311yescharacteristic, direct product factor
20C3×C5⋊D5C3×C7111yescharacteristic, complemented
21(C5⋊D5)⋊C3C3×C7113yesdirect product factor
22C2×C71—251noHall
23C3×C52C2×C3×C7111yescharacteristic, complemented
24C52⋊C3C2×C3×C7113yescomplemented
25C71C3×(C5⋊D5)⋊C311yescharacteristic, direct product factor, Sylow
26C5⋊D5C32×C7111yescharacteristic, complemented, Hall
27C3×D5—152no—
28C52C2×C32×C7111yescharacteristic, complemented, Sylow
29C2×C32—251noHall
30C3×C5—32no—
31D5—152no—
32C32—251noSylow
33C2×C3—253no—
34C2×C3—251no—
35C5—32no—
36C3—253no—
37C3C71×(C5⋊D5)⋊C311yescharacteristic, direct product factor
38C2—251noSylow
subgroupG/H
center, hypercenterC3×C71(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C2×C32×C71
FrattiniC1G
Fitting, socleC3×C52×C71C2×C3
LCSG ▷ C52
UCSC1 ◁ C3×C71

Complements

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

NH ≅ G/Ntype
1. C3×C71×C52⋊C3C2semidirect
2. C3×C5⋊D5×C71C3semidirect
3. C71×(C5⋊D5)⋊C3C3direct (N × H)
4. C71×C52⋊C3C2×C3semidirect
5. C3×C52×C71C2×C3semidirect
6. C5⋊D5×C71C32semidirect
8. C52×C71C2×C32semidirect
13. C3×(C5⋊D5)⋊C3C71direct (N × H)
17. C3×C52⋊C3C2×C71semidirect
19. C3×C71(C5⋊D5)⋊C3direct (N × H)
20. C3×C5⋊D5C3×C71semidirect
21. (C5⋊D5)⋊C3C3×C71direct (N × H)
23. C3×C52C2×C3×C71semidirect
24. C52⋊C3C2×C3×C71semidirect
25. C71C3×(C5⋊D5)⋊C3direct (N × H)
26. C5⋊D5C32×C71semidirect
28. C52C2×C32×C71semidirect
37. C3C71×(C5⋊D5)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C71×C52⋊C32
C3×C5⋊D5×C713
C71×(C5⋊D5)⋊C33
C2×C32×C7125
C3×(C5⋊D5)⋊C371