Finite Group Databasebeta

← #37528713

Subgroups — #37528713

Order 23100.

320 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 79 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×C7×C5⋊D55C211yesmaximal, characteristic, complemented
2C52×D231C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D77⋊(C5⋊D5)—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D55⋊D21—56nomaximal
7C11×C5⋊D35—31no—
8C7×C5⋊D55D311yescharacteristic, complemented
9C52×D77—31no—
10D33⋊(C5⋊D5)—71nomaximal, Hall
11C11×D105—56no—
12C5×D231D516yescomplemented
13C3×C7×D55—56no—
14D21×C5⋊D5—111nomaximal, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C11×C3⋊(C5⋊D5)—71no—
17C52×D33—71no—
18C3×C5⋊D55D711yescharacteristic, complemented
19D35⋊D11—156no—
20C3×C5×C7×C11C2×D516yescomplemented
21D11×C5⋊D5—211noHall
22C3⋊(C5⋊D35)D1111yescharacteristic, complemented
23C52×D21—111no—
24C3×C7×C5⋊D5—111no—
25D11×D21—251noHall
26C3×C52×C11C2×D711yescharacteristic, complemented, Hall
27C11×D35—156no—
28C7×D55—56no—
29C5×D77—36no—
30D7×C5⋊D5—331noHall
31D15⋊D11—356no—
32C5⋊D55D2111yescharacteristic, complemented
33C11×C5⋊D5—211no—
34C52×D11—211no—
35C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
36D231C5⋊D511yescharacteristic, complemented
37C11×D21—251no—
38C3×C7×D11—251no—
39D5×D21—556no—
40C5×C7×C11D3×D516yescomplemented
41C5⋊D35—31no—
42C7×C5⋊D5—111no—
43C52×D7—331no—
44C11×D15—356no—
45C5×D33—76no—
46C3×D55—56no—
47D7×D11—751noHall
48D3×C5⋊D5—771noHall
49C52×C11C2×D2111yescharacteristic, complemented, Hall
50C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
51D5×D11—1056no—
52D105—56no—
53C5×D21—116no—
54C3×C7×D5—556no—
55C52×C7D3×D1111yescharacteristic, complemented, Hall
56C3×C5×C11D5×D716yescomplemented
57D77—31no—
58C7×D11—251no—
59C11×D7—751no—
60C3⋊(C5⋊D5)—71no—
61C52×D3—771no—
62C3×C5⋊D5—111no—
63D5×D7—1656no—
64D3×D11—1751noHall
65D55—56no—
66C5×D11—216no—
67D5×C11—1056no—
68C3×C5×C7D5×D1116yescomplemented
69C2×C5⋊D5—2311noHall
70C2×D21—2751noHall
71C7×C11D3×C5⋊D511yescharacteristic, complemented, Hall
72C3×C52D7×D1111yescharacteristic, complemented, Hall
73D35—156no—
74C5×D7—336no—
75C7×D5—556no—
76D33—71no—
77C3×D11—251no—
78D3×C11—1751no—
79D3×D5—3856no—
80C5×C11D5×D2116yescomplemented
81C2×C52—2311no—
82C5⋊D5—111no—
83C5⋊D5—211no—
84C2×D11—5251noHall
85C2×C3×C7—2751no—
86D21—111no—
87D21—251no—
88C5×C7D15⋊D1116yescomplemented
89C3×C11D7×C5⋊D511yescharacteristic, complemented, Hall
90D15—356no—
91C3×D5—556no—
92C5×D3—776no—
93C2×D7—8251noHall
94C52D11×D2111yescharacteristic, complemented, Sylow
95C2×C11—5251no—
96D11—211no—
97D11—251no—
98C3×C7D11×C5⋊D511yescharacteristic, complemented, Hall
99C2×D5—11556no—
100C3×C5D35⋊D1116yescomplemented
101C2×C7—2751no—
102D7—331no—
103D7—751no—
104C2×D3—19251noHall
105C11D21×C5⋊D511yescharacteristic, complemented, Sylow
106C2×C5—2316no—
107D5—556no—
108D5—1056no—
109C7D33⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
110C2×C3—2751no—
111D3—771no—
112D3—1751no—
113C5D55⋊D2116yescomplemented
114C22—57751noSylow
115C3D77⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
116C2—5251no—
117C2—2751no—
118C2—2311no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C5⋊D55C2semidirect
2. C52×D231C2semidirect
3. C11×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C11C22semidirect
8. C7×C5⋊D55D3semidirect
12. C5×D231D5semidirect
15. C52×C7×C11C2×D3semidirect
18. C3×C5⋊D55D7semidirect
20. C3×C5×C7×C11C2×D5semidirect
22. C3⋊(C5⋊D35)D11semidirect
26. C3×C52×C11C2×D7semidirect
32. C5⋊D55D21semidirect
35. C3×C52×C7C2×D11semidirect
36. D231C5⋊D5semidirect
40. C5×C7×C11D3×D5semidirect
49. C52×C11C2×D21semidirect
50. C3×C7×C11C2×C5⋊D5semidirect
55. C52×C7D3×D11semidirect
56. C3×C5×C11D5×D7semidirect
68. C3×C5×C7D5×D11semidirect
71. C7×C11D3×C5⋊D5semidirect
72. C3×C52D7×D11semidirect
80. C5×C11D5×D21semidirect
88. C5×C7D15⋊D11semidirect
89. C3×C11D7×C5⋊D5semidirect
94. C52D11×D21semidirect
98. C3×C7D11×C5⋊D5semidirect
100. C3×C5D35⋊D11semidirect
105. C11D21×C5⋊D5semidirect
109. C7D33⋊(C5⋊D5)semidirect
113. C5D55⋊D21semidirect
115. C3D77⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C5⋊D552
C52×D2312
C11×C3⋊(C5⋊D35)2
D77⋊(C5⋊D5)3
D55⋊D215
D33⋊(C5⋊D5)7
D21×C5⋊D511