Finite Group Databasebeta

← C3⋊(C3⋊(C5⋊(D71⋊C5))) #44544064

Subgroups — C3⋊(C3⋊(C5⋊(D71⋊C5))) #44544064

Order 31950.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C71⋊C5C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C5⋊(D71⋊C5))—34nomaximal
3C3⋊D1065C511yesmaximal, characteristic, complemented
4C3⋊(C3⋊(D71⋊C5))—51nomaximal
5C3×C5×C71⋊C5D314yescomplemented
6C5⋊(D71⋊C5)—91noHall
7C32×C71⋊C5—22no—
8C32×C71⋊C5D511yescharacteristic, complemented
9C32×C5×C71C2×C511yescharacteristic, complemented
10C3⋊(D71⋊C5)—154no—
11D1065—34no—
12C5×C71⋊C5C3⋊D311yescharacteristic, complemented, Hall
13C3⋊D213—51noHall
14C3×C5×C71C5×D314yescomplemented
15C3×C71⋊C5—28no—
16C3×C71⋊C5D1514yescomplemented
17D355—91no—
18D71⋊C5—451no—
19C32×C71C5×D511yescharacteristic, complemented, Hall
20C5×C3⋊D15—711nomaximal, Hall
21D213—154no—
22C5×C71C5×C3⋊D311yescharacteristic, complemented
23C71⋊C5—22no—
24C71⋊C5C3⋊D1511yescharacteristic, complemented
25C32×C52—711noHall
26C3×C71C5×D1514yescomplemented
27C5×D15—2134no—
28D71—451noHall
29C3⋊D15—711no—
30C5×C3⋊D3—3551no—
31C3×C52—714no—
32C71C5×C3⋊D1511yescharacteristic, complemented, Sylow
33C5×D5—6391noHall
34C32×C5—711no—
35C32×C5—1422no—
36C32×C5D71⋊C511yescharacteristic, complemented
37D15—2134no—
38C5×D3—10654no—
39C52—711noSylow
40C3⋊D3—3551noHall
41C3×C5—714no—
42C3×C5—1428no—
43C3×C5C3⋊(D71⋊C5)14yescomplemented
44C2×C5—31951no—
45D5—6391no—
46C32C5⋊(D71⋊C5)11yescharacteristic, complemented, Sylow
47D3—10654no—
48C5—711no—
49C5—1422no—
50C5C3⋊(C3⋊(D71⋊C5))11yescharacteristic, complemented
51C3C3⋊(C5⋊(D71⋊C5))14yescomplemented
52C2—31951noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C71C2×C5
LCSG ▷ C32×C5×C71
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×C71⋊C5C2semidirect
3. C3⋊D1065C5semidirect
5. C3×C5×C71⋊C5D3semidirect
8. C32×C71⋊C5D5semidirect
9. C32×C5×C71C2×C5semidirect
12. C5×C71⋊C5C3⋊D3semidirect
14. C3×C5×C71C5×D3semidirect
16. C3×C71⋊C5D15semidirect
19. C32×C71C5×D5semidirect
22. C5×C71C5×C3⋊D3semidirect
24. C71⋊C5C3⋊D15semidirect
26. C3×C71C5×D15semidirect
32. C71C5×C3⋊D15semidirect
36. C32×C5D71⋊C5semidirect
43. C3×C5C3⋊(D71⋊C5)semidirect
46. C32C5⋊(D71⋊C5)semidirect
50. C5C3⋊(C3⋊(D71⋊C5))semidirect
51. C3C3⋊(C5⋊(D71⋊C5))semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C71⋊C52
C3⋊(C5⋊(D71⋊C5))3
C3⋊D10655
C3⋊(C3⋊(D71⋊C5))5
C5×C3⋊D1571