Finite Group Databasebeta

← C13×C3⋊(C5⋊(C7⋊D7)) #34062186

Subgroups — C13×C3⋊(C5⋊(C7⋊D7)) #34062186

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C72×C13C211yesmaximal, characteristic, complemented, Hall
2C13×C5⋊(C7⋊D7)—31nomaximal, Hall
3C13×C3⋊(C7⋊D7)—51nomaximal, Hall
4C5×C72×C13D311yescharacteristic, complemented, Hall
5C13×D105—78nomaximal
6C3×C72×C13D511yescharacteristic, complemented, Hall
7C3⋊(C5⋊(C7⋊D7))C1311yesmaximal, characteristic, direct product factor, Hall
8C3×C5×C7×C13D718yescomplemented
9C13×C7⋊D7—151noHall
10C13×D35—218no—
11C3×C5×C72C2×C1311yescharacteristic, complemented, Hall
12C72×C13D1511yescharacteristic, complemented, Hall
13C13×D21—358no—
14C5⋊(C7⋊D7)—31noHall
15C5×C7×C13D2118yescomplemented
16C13×D15—491noHall
17C3⋊(C7⋊D7)—51noHall
18C3×C7×C13D3518yescomplemented
19C5×C72D3×C1311yescharacteristic, complemented, Hall
20D105—78no—
21C3×C5×C13C7⋊D711yescharacteristic, complemented, Hall
22C13×D7—1058no—
23C3×C72D5×C1311yescharacteristic, complemented, Hall
24D5×C13—1471noHall
25C3×C5×C7C13×D718yescomplemented
26C7⋊D7—151noHall
27C7×C13D10518yescomplemented
28D3×C13—2451noHall
29D35—218no—
30C5×C13C3⋊(C7⋊D7)11yescharacteristic, complemented, Hall
31C72C13×D1511yescharacteristic, complemented, Sylow
32D21—358no—
33C3×C13C5⋊(C7⋊D7)11yescharacteristic, complemented, Hall
34C5×C7C13×D2118yescomplemented
35D15—491noHall
36C2×C13—7351noHall
37C3×C7C13×D3518yescomplemented
38C3×C5C13×C7⋊D711yescharacteristic, complemented, Hall
39D7—1058no—
40C13C3⋊(C5⋊(C7⋊D7))11yescharacteristic, direct product factor, Sylow
41D5—1471noHall
42C7C13×D10518yescomplemented
43D3—2451noHall
44C5C13×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
45C3C13×C5⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
46C2—7351noSylow
subgroupG/H
center, hypercenterC13C3⋊(C5⋊(C7⋊D7))
commutator, cosocle, hypocenterC3×C5×C72C2×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C2
LCSG ▷ C3×C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×C13C2semidirect
4. C5×C72×C13D3semidirect
6. C3×C72×C13D5semidirect
7. C3⋊(C5⋊(C7⋊D7))C13direct (N × H)
8. C3×C5×C7×C13D7semidirect
11. C3×C5×C72C2×C13semidirect
12. C72×C13D15semidirect
15. C5×C7×C13D21semidirect
18. C3×C7×C13D35semidirect
19. C5×C72D3×C13semidirect
21. C3×C5×C13C7⋊D7semidirect
23. C3×C72D5×C13semidirect
25. C3×C5×C7C13×D7semidirect
27. C7×C13D105semidirect
30. C5×C13C3⋊(C7⋊D7)semidirect
31. C72C13×D15semidirect
33. C3×C13C5⋊(C7⋊D7)semidirect
34. C5×C7C13×D21semidirect
37. C3×C7C13×D35semidirect
38. C3×C5C13×C7⋊D7semidirect
40. C13C3⋊(C5⋊(C7⋊D7))direct (N × H)
42. C7C13×D105semidirect
44. C5C13×C3⋊(C7⋊D7)semidirect
45. C3C13×C5⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C72×C132
C13×C5⋊(C7⋊D7)3
C13×C3⋊(C7⋊D7)5
C13×D1057
C3⋊(C5⋊(C7⋊D7))13