Finite Group Databasebeta

← C11×D7×C3⋊(C5⋊D5) #37528702

Subgroups — C11×D7×C3⋊(C5⋊D5) #37528702

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×C11×D7C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4C11×D7×C5⋊D5—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C11×D7×D15—56nomaximal
7C11×C5⋊D35—31no—
8C7×C11×C5⋊D5—31no—
9C52×C11×D7D311yescharacteristic, complemented
10C2×C11×C3⋊(C5⋊D5)—71nomaximal, Hall
11C11×D105—56no—
12C7×C11×D15—56no—
13C3×C5×C11×D7D516yescomplemented
14D7×C3⋊(C5⋊D5)C1111yesmaximal, characteristic, direct product factor, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C2×C3×C52×C11—71no—
17C11×C3⋊(C5⋊D5)—71no—
18C11×C3⋊(C5⋊D5)D711yescharacteristic, direct product factor
19D5×C11×D7—156no—
20C3×C5×C7×C11C2×D516yescomplemented
21C2×C11×C5⋊D5—211noHall
22C3⋊(C5⋊D35)C2×C1111yescharacteristic, complemented
23C7×C3⋊(C5⋊D5)C2×C1111yescharacteristic, complemented
24C3×C52×D7C2×C1111yescharacteristic, complemented
25D3×C11×D7—251noHall
26C3×C52×C11C2×D711yescharacteristic, complemented, Hall
27C11×D35—156no—
28C7×D5×C11—156no—
29C5×C11×D7D1516yescomplemented
30D7×C5⋊D5—31noHall
31C2×C11×D15—356no—
32C2×C52×C11—71no—
33C11×C5⋊D5—31no—
34C11×C5⋊D5—211no—
35C3×C52×C7C22×C1111yescharacteristic, complemented, Hall
36C11×D21—251no—
37D3×C7×C11—251no—
38C3×C11×D7C5⋊D511yescharacteristic, complemented
39D7×D15—56no—
40C5×C7×C11C2×D1516yescomplemented
41C5⋊D35—31no—
42C7×C5⋊D5—31no—
43C52×D7D3×C1111yescharacteristic, complemented
44C2×C3×C5×C11—76no—
45C11×D15—56no—
46C11×D15—356no—
47C2×C11×D7—751noHall
48C2×C3⋊(C5⋊D5)—71noHall
49C52×C11D3×D711yescharacteristic, complemented, Hall
50C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
51C2×D5×C11—1056no—
52D105—56no—
53C7×D15—56no—
54C3×C5×D7D5×C1116yescomplemented
55C52×C7C2×D3×C1111yescharacteristic, complemented, Hall
56C3×C5×C11D5×D716yescomplemented
57C2×C7×C11—751no—
58C11×D7—751no—
59C11×D7C3⋊(C5⋊D5)11yescharacteristic, direct product factor
60C2×C3×C52—71no—
61C3⋊(C5⋊D5)—71no—
62C3⋊(C5⋊D5)C11×D711yescharacteristic, direct product factor
63D5×D7—156no—
64C2×D3×C11—1751noHall
65C2×C5×C11—76no—
66D5×C11—156no—
67D5×C11—1056no—
68C3×C5×C7C2×D5×C1116yescomplemented
69C2×C5⋊D5—211noHall
70D3×D7—251noHall
71C7×C11C2×C3⋊(C5⋊D5)11yescharacteristic, complemented, Hall
72C3×C52C2×C11×D711yescharacteristic, complemented, Hall
73D35—156no—
74C5×D7C11×D1516yescomplemented
75C7×D5—156no—
76C2×C3×C11—71no—
77D3×C11—251no—
78D3×C11—1751no—
79C2×D15—356no—
80C5×C11D7×D1516yescomplemented
81C2×C52—71no—
82C5⋊D5—31no—
83C5⋊D5—211no—
84C22×C11—5251noHall
85D21—251no—
86C3×D7C11×C5⋊D511yescharacteristic, complemented
87D3×C7—251no—
88C5×C7C2×C11×D1516yescomplemented
89C3×C11D7×C5⋊D511yescharacteristic, complemented, Hall
90C2×C3×C5—76no—
91D15—56no—
92D15—356no—
93C2×D7—751noHall
94C52D3×C11×D711yescharacteristic, complemented, Sylow
95C2×C11—71no—
96C2×C11—5251no—
97C2×C11—751no—
98C3×C7C2×C11×C5⋊D511yescharacteristic, complemented, Hall
99C2×D5—1056no—
100C3×C5D5×C11×D716yescomplemented
101C2×C7—751no—
102D7—751no—
103D7C11×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
104C2×D3—1751noHall
105C11D7×C3⋊(C5⋊D5)11yescharacteristic, direct product factor, Sylow
106C2×C5—76no—
107D5—156no—
108D5—1056no—
109C7C2×C11×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
110C2×C3—71no—
111D3—251no—
112D3—1751no—
113C5C11×D7×D1516yescomplemented
114C22—5251noSylow
115C3C11×D7×C5⋊D511yescharacteristic, complemented, Sylow
116C2—71no—
117C2—5251no—
118C2—751no—
subgroupG/H
center, hypercenterC11D7×C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C7C22×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D7C2semidirect
2. C7×C11×C3⋊(C5⋊D5)C2semidirect
3. C11×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C11C22semidirect
9. C52×C11×D7D3semidirect
13. C3×C5×C11×D7D5semidirect
14. D7×C3⋊(C5⋊D5)C11direct (N × H)
15. C52×C7×C11C2×D3semidirect
18. C11×C3⋊(C5⋊D5)D7direct (N × H)
20. C3×C5×C7×C11C2×D5semidirect
22. C3⋊(C5⋊D35)C2×C11semidirect
23. C7×C3⋊(C5⋊D5)C2×C11semidirect
24. C3×C52×D7C2×C11semidirect
26. C3×C52×C11C2×D7semidirect
29. C5×C11×D7D15semidirect
35. C3×C52×C7C22×C11semidirect
38. C3×C11×D7C5⋊D5semidirect
40. C5×C7×C11C2×D15semidirect
43. C52×D7D3×C11semidirect
49. C52×C11D3×D7semidirect
50. C3×C7×C11C2×C5⋊D5semidirect
54. C3×C5×D7D5×C11semidirect
55. C52×C7C2×D3×C11semidirect
56. C3×C5×C11D5×D7semidirect
59. C11×D7C3⋊(C5⋊D5)direct (N × H)
62. C3⋊(C5⋊D5)C11×D7direct (N × H)
68. C3×C5×C7C2×D5×C11semidirect
71. C7×C11C2×C3⋊(C5⋊D5)semidirect
72. C3×C52C2×C11×D7semidirect
74. C5×D7C11×D15semidirect
80. C5×C11D7×D15semidirect
86. C3×D7C11×C5⋊D5semidirect
88. C5×C7C2×C11×D15semidirect
89. C3×C11D7×C5⋊D5semidirect
94. C52D3×C11×D7semidirect
98. C3×C7C2×C11×C5⋊D5semidirect
100. C3×C5D5×C11×D7semidirect
103. D7C11×C3⋊(C5⋊D5)direct (N × H)
105. C11D7×C3⋊(C5⋊D5)direct (N × H)
109. C7C2×C11×C3⋊(C5⋊D5)semidirect
113. C5C11×D7×D15semidirect
115. C3C11×D7×C5⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C11×D72
C7×C11×C3⋊(C5⋊D5)2
C11×C3⋊(C5⋊D35)2
C11×D7×C5⋊D53
C11×D7×D155
C2×C11×C3⋊(C5⋊D5)7
D7×C3⋊(C5⋊D5)11