Finite Group Databasebeta

← C5×C3⋊(C3⋊(C5⋊(C7⋊D7))) #36348082

Subgroups — C5×C3⋊(C3⋊(C5⋊(C7⋊D7))) #36348082

Order 22050.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C72C211yesmaximal, characteristic, complemented, Hall
2C5×C3⋊(C5⋊(C7⋊D7))—34nomaximal
3C3⋊(C3⋊(C5⋊(C7⋊D7)))C511yesmaximal, characteristic, direct product factor
4C5×C3⋊(C3⋊(C7⋊D7))—51nomaximal
5C3×C52×C72D314yescomplemented
6C5×C3⋊D105—78nomaximal
7C5×C5⋊(C7⋊D7)—91noHall
8C32×C5×C72—22no—
9C32×C5×C72D511yescharacteristic, complemented
10C32×C5×C72C2×C511yescharacteristic, complemented
11C32×C52×C7D718yescomplemented
12C3⋊(C5⋊(C7⋊D7))—34no—
13C5×C3⋊(C7⋊D7)—154no—
14C52×C72C3⋊D311yescharacteristic, complemented, Hall
15C5×D105—2132no—
16C3⋊(C3⋊(C7⋊D7))—51noHall
17C3×C5×C72—28no—
18C3×C5×C72C5×D314yescomplemented
19C3×C5×C72D1514yescomplemented
20C3⋊D105—78no—
21C5×C3⋊D21—358no—
22C3×C52×C7D21132yescomplemented
23C5⋊(C7⋊D7)—91no—
24C5×C7⋊D7—451no—
25C5×C3⋊D15—491noHall
26C32×C72C5×D511yescharacteristic, complemented, Hall
27C5×D35—638no—
28C32×C5×C7—216no—
29C32×C5×C7C5×D718yescomplemented
30C32×C5×C7D3518yescomplemented
31C3⋊(C7⋊D7)—154no—
32C5×C72—22no—
33C5×C72C5×C3⋊D311yescharacteristic, complemented
34C5×C72C3⋊D1511yescharacteristic, complemented
35C32×C52C7⋊D711yescharacteristic, complemented, Hall
36D105—2132no—
37C5×D21—10532no—
38C52×C7C3⋊D2118yescomplemented
39C5×D15—1474no—
40C3×C72C5×D1514yescomplemented
41C3⋊D21—358no—
42C3×C5×C7—264no—
43C3×C5×C7C5×D21132yescomplemented
44C3×C5×C7D105132yescomplemented
45C7⋊D7—451noHall
46C3⋊D15—491no—
47C5×C3⋊D3—2451no—
48C3×C52C3⋊(C7⋊D7)14yescomplemented
49D35—638no—
50C5×D7—3158no—
51C32×C7C5×D3518yescomplemented
52C5×D5—4411noHall
53C72C5×C3⋊D1511yescharacteristic, complemented, Sylow
54C32×C5—22no—
55C32×C5C5×C7⋊D711yescharacteristic, complemented
56C32×C5C5⋊(C7⋊D7)11yescharacteristic, complemented
57D21—10532no—
58C5×C7—216no—
59C5×C7C5×C3⋊D2118yescomplemented
60C5×C7C3⋊D10518yescomplemented
61D15—1474no—
62C5×D3—7354no—
63C52C3⋊(C3⋊(C7⋊D7))11yescharacteristic, complemented, Sylow
64C3×C7C5×D105132yescomplemented
65C3⋊D3—2451noHall
66C3×C5—28no—
67C3×C5C5×C3⋊(C7⋊D7)14yescomplemented
68C3×C5C3⋊(C5⋊(C7⋊D7))14yescomplemented
69D7—3158no—
70C2×C5—22051no—
71D5—4411no—
72C32C5×C5⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
73C7C5×C3⋊D10518yescomplemented
74D3—7354no—
75C5—22no—
76C5C5×C3⋊(C3⋊(C7⋊D7))11yescharacteristic, complemented
77C5C3⋊(C3⋊(C5⋊(C7⋊D7)))11yescharacteristic, direct product factor
78C3C5×C3⋊(C5⋊(C7⋊D7))14yescomplemented
79C2—22051noSylow
subgroupG/H
center, hypercenterC5C3⋊(C3⋊(C5⋊(C7⋊D7)))
commutator, cosocle, hypocenterC32×C5×C72C2×C5
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C32×C5×C72
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
3. C3⋊(C3⋊(C5⋊(C7⋊D7)))C5direct (N × H)
5. C3×C52×C72D3semidirect
9. C32×C5×C72D5semidirect
10. C32×C5×C72C2×C5semidirect
11. C32×C52×C7D7semidirect
14. C52×C72C3⋊D3semidirect
18. C3×C5×C72C5×D3semidirect
19. C3×C5×C72D15semidirect
22. C3×C52×C7D21semidirect
26. C32×C72C5×D5semidirect
29. C32×C5×C7C5×D7semidirect
30. C32×C5×C7D35semidirect
33. C5×C72C5×C3⋊D3semidirect
34. C5×C72C3⋊D15semidirect
35. C32×C52C7⋊D7semidirect
38. C52×C7C3⋊D21semidirect
40. C3×C72C5×D15semidirect
43. C3×C5×C7C5×D21semidirect
44. C3×C5×C7D105semidirect
48. C3×C52C3⋊(C7⋊D7)semidirect
51. C32×C7C5×D35semidirect
53. C72C5×C3⋊D15semidirect
55. C32×C5C5×C7⋊D7semidirect
56. C32×C5C5⋊(C7⋊D7)semidirect
59. C5×C7C5×C3⋊D21semidirect
60. C5×C7C3⋊D105semidirect
63. C52C3⋊(C3⋊(C7⋊D7))semidirect
64. C3×C7C5×D105semidirect
67. C3×C5C5×C3⋊(C7⋊D7)semidirect
68. C3×C5C3⋊(C5⋊(C7⋊D7))semidirect
72. C32C5×C5⋊(C7⋊D7)semidirect
73. C7C5×C3⋊D105semidirect
76. C5C5×C3⋊(C3⋊(C7⋊D7))semidirect
77. C5C3⋊(C3⋊(C5⋊(C7⋊D7)))direct (N × H)
78. C3C5×C3⋊(C5⋊(C7⋊D7))semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C722
C5×C3⋊(C5⋊(C7⋊D7))3
C3⋊(C3⋊(C5⋊(C7⋊D7)))5
C5×C3⋊(C3⋊(C7⋊D7))5
C5×C3⋊D1057