Finite Group Databasebeta

← C5⋊((C13⋊C3)⋊(C7⋊D7)) #34062172

Subgroups — C5⋊((C13⋊C3)⋊(C7⋊D7)) #34062172

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C72×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5⋊(C7⋊D91)C311yesmaximal, characteristic, complemented, Hall
3(C13⋊C3)⋊(C7⋊D7)—51nomaximal, Hall
4C5×C72×C13C2×C311yescharacteristic, complemented, Hall
5C5⋊((C13⋊C3)⋊D7)—78nomaximal
6C72×C13⋊C3D511yescharacteristic, complemented, Hall
7C3×C5⋊(C7⋊D7)—131nomaximal, Hall
8C5×C7×C13⋊C3D718yescomplemented
9C7⋊D91—51noHall
10D455—78no—
11C3×C5×C72—131noHall
12C72×C13C3×D511yescharacteristic, complemented, Hall
13(C13⋊C3)⋊D7—358no—
14C5⋊(C7⋊D7)—131noHall
15C5×C7×C13C3×D718yescomplemented
16C5⋊(D13⋊C3)—491noHall
17C3×C7⋊D7—651noHall
18C7×C13⋊C3D3518yescomplemented
19C5×C72D13⋊C311yescharacteristic, complemented, Hall
20C3×D35—918no—
21C5×C13⋊C3C7⋊D711yescharacteristic, complemented, Hall
22D91—358no—
23C3×C72—131noHall
24D65—491noHall
25C3×C5×C7—138no—
26C7⋊D7—651noHall
27C7×C13C3×D3518yescomplemented
28D13⋊C3—2451noHall
29D35—918no—
30C5×C13C3×C7⋊D711yescharacteristic, complemented, Hall
31C72C5⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
32C3×D7—4558no—
33C13⋊C3C5⋊(C7⋊D7)11yescharacteristic, complemented, Hall
34C5×C7(C13⋊C3)⋊D718yescomplemented
35C3×D5—6371noHall
36D13—2451noHall
37C3×C7—138no—
38C3×C5—131noHall
39D7—4558no—
40C13C3×C5⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
41D5—6371noHall
42C7C5⋊((C13⋊C3)⋊D7)18yescomplemented
43C2×C3—31851noHall
44C5(C13⋊C3)⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
45C3—131noSylow
46C2—31851noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C72×C13⋊C3C2semidirect
2. C5⋊(C7⋊D91)C3semidirect
4. C5×C72×C13C2×C3semidirect
6. C72×C13⋊C3D5semidirect
8. C5×C7×C13⋊C3D7semidirect
12. C72×C13C3×D5semidirect
15. C5×C7×C13C3×D7semidirect
18. C7×C13⋊C3D35semidirect
19. C5×C72D13⋊C3semidirect
21. C5×C13⋊C3C7⋊D7semidirect
27. C7×C13C3×D35semidirect
30. C5×C13C3×C7⋊D7semidirect
31. C72C5⋊(D13⋊C3)semidirect
33. C13⋊C3C5⋊(C7⋊D7)semidirect
34. C5×C7(C13⋊C3)⋊D7semidirect
40. C13C3×C5⋊(C7⋊D7)semidirect
42. C7C5⋊((C13⋊C3)⋊D7)semidirect
44. C5(C13⋊C3)⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C5×C72×C13⋊C32
C5⋊(C7⋊D91)3
(C13⋊C3)⋊(C7⋊D7)5
C5⋊((C13⋊C3)⋊D7)7
C3×C5⋊(C7⋊D7)13