Finite Group Databasebeta

← C7×C3⋊(C3⋊(C5⋊D35)) #36348084

Subgroups — C7×C3⋊(C3⋊(C5⋊D35)) #36348084

Order 22050.

528 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C72C211yesmaximal, characteristic, complemented, Hall
2C7×C3⋊(C5⋊D35)—34nomaximal
3C7×C3⋊D105—56nomaximal
4C3×C52×C72D314yescomplemented
5C3⋊(C3⋊(C5⋊D35))C711yesmaximal, characteristic, direct product factor
6C7×C3⋊(C3⋊(C5⋊D5))—71nomaximal
7C7×C5⋊D35—91noHall
8C32×C5×C72D516yescomplemented
9C32×C52×C7—23no—
10C32×C52×C7D711yescharacteristic, complemented
11C32×C52×C7C2×C711yescharacteristic, complemented
12C7×D105—1524no—
13C52×C72C3⋊D311yescharacteristic, complemented, Hall
14C3⋊(C5⋊D35)—34no—
15C7×C3⋊(C5⋊D5)—214no—
16C7×C3⋊D21—251noHall
17C3×C5×C72D15124yescomplemented
18C3⋊D105—56no—
19C7×C3⋊D15—356no—
20C3×C52×C7—212no—
21C3×C52×C7D3×C714yescomplemented
22C3×C52×C7D2114yescomplemented
23C7×D35—456no—
24C3⋊(C3⋊(C5⋊D5))—71noHall
25C32×C72C5⋊D511yescharacteristic, complemented, Hall
26C5⋊D35—91no—
27C7×C5⋊D5—631no—
28C32×C5×C7—218no—
29C32×C5×C7C7×D516yescomplemented
30C32×C5×C7D3516yescomplemented
31C7×D21—754no—
32C5×C72C3⋊D1516yescomplemented
33C32×C52C7×D711yescharacteristic, complemented, Hall
34D105—1524no—
35C7×D15—10524no—
36C52×C7—23no—
37C52×C7C7×C3⋊D311yescharacteristic, complemented
38C52×C7C3⋊D2111yescharacteristic, complemented
39C3⋊(C5⋊D5)—214no—
40C3×C72C3⋊(C5⋊D5)14yescomplemented
41C3⋊D21—251no—
42C7×C3⋊D3—1751no—
43C3×C5×C7—272no—
44C3×C5×C7C7×D15124yescomplemented
45C3×C5×C7D105124yescomplemented
46C7×D7—2251noHall
47C3⋊D15—356no—
48C3×C52C7×D2114yescomplemented
49D35—456no—
50C7×D5—3156no—
51C32×C7—23no—
52C32×C7C7×C5⋊D511yescharacteristic, complemented
53C32×C7C5⋊D3511yescharacteristic, complemented
54C5⋊D5—631noHall
55C72C3⋊(C3⋊(C5⋊D5))11yescharacteristic, complemented, Sylow
56C32×C5C7×D3516yescomplemented
57D21—754no—
58D3×C7—5254no—
59C5×C7—218no—
60C5×C7C7×C3⋊D1516yescomplemented
61C5×C7C3⋊D10516yescomplemented
62D15—10524no—
63C52C7×C3⋊D2111yescharacteristic, complemented, Sylow
64C3×C7—212no—
65C3×C7C7×C3⋊(C5⋊D5)14yescomplemented
66C3×C7C3⋊(C5⋊D35)14yescomplemented
67C3⋊D3—1751noHall
68C3×C5C7×D105124yescomplemented
69C2×C7—15751no—
70D7—2251no—
71D5—3156no—
72C32C7×C5⋊D3511yescharacteristic, complemented, Sylow
73C7—23no—
74C7C7×C3⋊(C3⋊(C5⋊D5))11yescharacteristic, complemented
75C7C3⋊(C3⋊(C5⋊D35))11yescharacteristic, direct product factor
76D3—5254no—
77C5C7×C3⋊D10516yescomplemented
78C3C7×C3⋊(C5⋊D35)14yescomplemented
79C2—15751noSylow
subgroupG/H
center, hypercenterC7C3⋊(C3⋊(C5⋊D35))
commutator, cosocle, hypocenterC32×C52×C7C2×C7
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C32×C52×C7
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
4. C3×C52×C72D3semidirect
5. C3⋊(C3⋊(C5⋊D35))C7direct (N × H)
8. C32×C5×C72D5semidirect
10. C32×C52×C7D7semidirect
11. C32×C52×C7C2×C7semidirect
13. C52×C72C3⋊D3semidirect
17. C3×C5×C72D15semidirect
21. C3×C52×C7D3×C7semidirect
22. C3×C52×C7D21semidirect
25. C32×C72C5⋊D5semidirect
29. C32×C5×C7C7×D5semidirect
30. C32×C5×C7D35semidirect
32. C5×C72C3⋊D15semidirect
33. C32×C52C7×D7semidirect
37. C52×C7C7×C3⋊D3semidirect
38. C52×C7C3⋊D21semidirect
40. C3×C72C3⋊(C5⋊D5)semidirect
44. C3×C5×C7C7×D15semidirect
45. C3×C5×C7D105semidirect
48. C3×C52C7×D21semidirect
52. C32×C7C7×C5⋊D5semidirect
53. C32×C7C5⋊D35semidirect
55. C72C3⋊(C3⋊(C5⋊D5))semidirect
56. C32×C5C7×D35semidirect
60. C5×C7C7×C3⋊D15semidirect
61. C5×C7C3⋊D105semidirect
63. C52C7×C3⋊D21semidirect
65. C3×C7C7×C3⋊(C5⋊D5)semidirect
66. C3×C7C3⋊(C5⋊D35)semidirect
68. C3×C5C7×D105semidirect
72. C32C7×C5⋊D35semidirect
74. C7C7×C3⋊(C3⋊(C5⋊D5))semidirect
75. C7C3⋊(C3⋊(C5⋊D35))direct (N × H)
77. C5C7×C3⋊D105semidirect
78. C3C7×C3⋊(C5⋊D35)semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C722
C7×C3⋊(C5⋊D35)3
C7×C3⋊D1055
C3⋊(C3⋊(C5⋊D35))7
C7×C3⋊(C3⋊(C5⋊D5))7