Finite Group Databasebeta

← C7×D11×C3⋊(C5⋊D5) #37528700

Subgroups — C7×D11×C3⋊(C5⋊D5) #37528700

Order 23100.

320 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×C7×D11C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
4C7×D11×C5⋊D5—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C7×D11×D15—56nomaximal
7C7×C5⋊D55—31no—
8C7×C11×C5⋊D5—31no—
9C52×C7×D11D311yescharacteristic, complemented
10D11×C3⋊(C5⋊D5)C711yesmaximal, characteristic, direct product factor, Hall
11C7×D165—56no—
12C7×C11×D15—56no—
13C3×C5×C7×D11D516yescomplemented
14C2×C7×C3⋊(C5⋊D5)—111nomaximal, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C3⋊(C5⋊D55)C2×C711yescharacteristic, complemented
17C11×C3⋊(C5⋊D5)C2×C711yescharacteristic, complemented
18C3×C52×D11C2×C711yescharacteristic, complemented
19C7×D5×D11—156no—
20C3×C5×C7×C11C2×D516yescomplemented
21D11×C5⋊D5—31noHall
22C2×C3×C52×C7—111no—
23C7×C3⋊(C5⋊D5)—111no—
24C7×C3⋊(C5⋊D5)D1111yescharacteristic, direct product factor
25D3×C7×D11—251noHall
26C3×C52×C11C22×C711yescharacteristic, complemented, Hall
27C7×D55—156no—
28C7×D5×C11—156no—
29C5×C7×D11D1516yescomplemented
30C2×C7×C5⋊D5—331noHall
31D11×D15—56no—
32C5⋊D55—31no—
33C11×C5⋊D5—31no—
34C52×D11D3×C711yescharacteristic, complemented
35C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
36C7×D33—251no—
37D3×C7×C11—251no—
38C3×C7×D11C5⋊D511yescharacteristic, complemented
39C2×C7×D15—556no—
40C5×C7×C11C2×D1516yescomplemented
41C2×C52×C7—111no—
42C7×C5⋊D5—31no—
43C7×C5⋊D5—331no—
44D165—56no—
45C11×D15—56no—
46C3×C5×D11C7×D516yescomplemented
47C2×C7×D11—751noHall
48C2×C3⋊(C5⋊D5)—111noHall
49C52×C11C2×D3×C711yescharacteristic, complemented, Hall
50C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
51D5×D11—156no—
52C2×C3×C5×C7—116no—
53C7×D15—56no—
54C7×D15—556no—
55C52×C7D3×D1111yescharacteristic, complemented, Hall
56C3×C5×C11C2×C7×D516yescomplemented
57C2×C7×C11—751no—
58C7×D11—751no—
59C7×D11C3⋊(C5⋊D5)11yescharacteristic, direct product factor
60C2×C3×C52—111no—
61C3⋊(C5⋊D5)—111no—
62C3⋊(C5⋊D5)C7×D1111yescharacteristic, direct product factor
63C2×C7×D5—1656no—
64D3×D11—251noHall
65D55—156no—
66C5×D11C7×D1516yescomplemented
67D5×C11—156no—
68C3×C5×C7D5×D1116yescomplemented
69C2×C5⋊D5—331noHall
70C2×D3×C7—2751noHall
71C7×C11C2×C3⋊(C5⋊D5)11yescharacteristic, complemented, Hall
72C3×C52C2×C7×D1111yescharacteristic, complemented, Hall
73C2×C5×C7—116no—
74C7×D5—156no—
75C7×D5—1656no—
76D33—251no—
77C3×D11C7×C5⋊D511yescharacteristic, complemented
78D3×C11—251no—
79C2×D15—556no—
80C5×C11C2×C7×D1516yescomplemented
81C2×C52—111no—
82C5⋊D5—31no—
83C5⋊D5—331no—
84C2×D11—751noHall
85C2×C3×C7—111no—
86D3×C7—2751no—
87D3×C7—251no—
88C5×C7D11×D1516yescomplemented
89C3×C11C2×C7×C5⋊D511yescharacteristic, complemented, Hall
90C2×C3×C5—116no—
91D15—56no—
92D15—556no—
93C22×C7—8251noHall
94C52D3×C7×D1111yescharacteristic, complemented, Sylow
95C2×C11—751no—
96D11—751no—
97D11C7×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
98C3×C7D11×C5⋊D511yescharacteristic, complemented, Hall
99C2×D5—1656no—
100C3×C5C7×D5×D1116yescomplemented
101C2×C7—111no—
102C2×C7—8251no—
103C2×C7—751no—
104C2×D3—2751noHall
105C11C2×C7×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
106C2×C5—116no—
107D5—156no—
108D5—1656no—
109C7D11×C3⋊(C5⋊D5)11yescharacteristic, direct product factor, Sylow
110C2×C3—111no—
111D3—2751no—
112D3—251no—
113C5C7×D11×D1516yescomplemented
114C22—8251noSylow
115C3C7×D11×C5⋊D511yescharacteristic, complemented, Sylow
116C2—111no—
117C2—8251no—
118C2—751no—
subgroupG/H
center, hypercenterC7D11×C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C11C22×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C52×C7×D11C2semidirect
2. C7×C11×C3⋊(C5⋊D5)C2semidirect
3. C7×C3⋊(C5⋊D55)C2semidirect
5. C3×C52×C7×C11C22semidirect
9. C52×C7×D11D3semidirect
10. D11×C3⋊(C5⋊D5)C7direct (N × H)
13. C3×C5×C7×D11D5semidirect
15. C52×C7×C11C2×D3semidirect
16. C3⋊(C5⋊D55)C2×C7semidirect
17. C11×C3⋊(C5⋊D5)C2×C7semidirect
18. C3×C52×D11C2×C7semidirect
20. C3×C5×C7×C11C2×D5semidirect
24. C7×C3⋊(C5⋊D5)D11direct (N × H)
26. C3×C52×C11C22×C7semidirect
29. C5×C7×D11D15semidirect
34. C52×D11D3×C7semidirect
35. C3×C52×C7C2×D11semidirect
38. C3×C7×D11C5⋊D5semidirect
40. C5×C7×C11C2×D15semidirect
46. C3×C5×D11C7×D5semidirect
49. C52×C11C2×D3×C7semidirect
50. C3×C7×C11C2×C5⋊D5semidirect
55. C52×C7D3×D11semidirect
56. C3×C5×C11C2×C7×D5semidirect
59. C7×D11C3⋊(C5⋊D5)direct (N × H)
62. C3⋊(C5⋊D5)C7×D11direct (N × H)
66. C5×D11C7×D15semidirect
68. C3×C5×C7D5×D11semidirect
71. C7×C11C2×C3⋊(C5⋊D5)semidirect
72. C3×C52C2×C7×D11semidirect
77. C3×D11C7×C5⋊D5semidirect
80. C5×C11C2×C7×D15semidirect
88. C5×C7D11×D15semidirect
89. C3×C11C2×C7×C5⋊D5semidirect
94. C52D3×C7×D11semidirect
97. D11C7×C3⋊(C5⋊D5)direct (N × H)
98. C3×C7D11×C5⋊D5semidirect
100. C3×C5C7×D5×D11semidirect
105. C11C2×C7×C3⋊(C5⋊D5)semidirect
109. C7D11×C3⋊(C5⋊D5)direct (N × H)
113. C5C7×D11×D15semidirect
115. C3C7×D11×C5⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C7×D112
C7×C11×C3⋊(C5⋊D5)2
C7×C3⋊(C5⋊D55)2
C7×D11×C5⋊D53
C7×D11×D155
D11×C3⋊(C5⋊D5)7
C2×C7×C3⋊(C5⋊D5)11