Finite Group Databasebeta

← C2×C5×C7×D165 #37528753

Subgroups — C2×C5×C7×D165 #37528753

Order 23100.

192 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×C7×D165C212yesmaximal, direct product factor
2C2×C3×C52×C7×C11C211yesmaximal, characteristic, complemented
3C2×C5×C7×D55—31nomaximal, Hall
4C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
5C2×C7×D165C511yesmaximal, characteristic, direct product factor
6C2×C5×C7×D33—51nomaximal
7C5×C7×D55—32no—
8C2×C52×C7×C11D311yescharacteristic, complemented
9C2×C5×D165C711yesmaximal, characteristic, direct product factor, Hall
10C7×D165C2×C512yesdirect product factor
11C5×C7×D33—52no—
12C2×C3×C5×C7×C11—22no—
13C2×C3×C5×C7×C11D511yescharacteristic, complemented
14C2×C3×C5×C7×C11C2×C511yescharacteristic, complemented
15C2×C5×C7×D15—111nomaximal, Hall
16C52×C7×C11C2×D311yescharacteristic, complemented, Hall
17C2×C3×C52×C11C2×C711yescharacteristic, complemented
18C5×D165C2×C712yesdirect product factor
19C2×C7×D55—31no—
20C2×C5×C7×D11—151no—
21C3×C5×C7×C11—22no—
22C3×C5×C7×C11C2×D511yescharacteristic, complemented
23C3×C5×C7×C11C22×C511yescharacteristic, complemented
24C2×C5×D55—31noHall
25C2×C3×C52×C7D1111yescharacteristic, complemented
26C5×C7×D15—112no—
27C2×C7×D33—51noHall
28C3×C52×C11C22×C711yescharacteristic, complemented, Hall
29C2×C5×C7×C11—22no—
30C2×C5×C7×C11C5×D311yescharacteristic, complemented
31C2×C5×C7×C11D1511yescharacteristic, complemented
32C7×D55—32no—
33C5×C7×D11—152no—
34C2×C5×C7×D5—331noHall
35C2×D165C5×C711yescharacteristic, direct product factor
36C2×C5×D33—51no—
37C2×C52×C11D3×C711yescharacteristic, complemented
38C5×D55—32no—
39C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
40C2×C3×C7×C11C5×D511yescharacteristic, complemented
41C7×D33—52no—
42C2×C7×D15—111no—
43C2×C5×D3×C7—551no—
44C5×C7×C11—22no—
45C5×C7×C11C2×C5×D311yescharacteristic, complemented
46C5×C7×C11C2×D1511yescharacteristic, complemented
47C2×C52×C7D3311yescharacteristic, complemented
48C5×C7×D5—332no—
49C2×C3×C5×C11—22no—
50C2×C3×C5×C11C7×D511yescharacteristic, complemented
51C2×C3×C5×C11C2×C5×C711yescharacteristic, complemented
52D165C2×C5×C712yesdirect product factor
53C5×D33—52no—
54C2×C7×D11—151noHall
55C2×C5×D15—111noHall
56C52×C11C2×D3×C711yescharacteristic, complemented, Hall
57C3×C7×C11C2×C5×D511yescharacteristic, complemented, Hall
58C2×D55—31no—
59C2×C5×D11—151no—
60C2×C3×C5×C7—22no—
61C2×C3×C5×C7C5×D1111yescharacteristic, complemented
62C2×C3×C5×C7D5511yescharacteristic, complemented
63C7×D15—112no—
64C5×D3×C7—552no—
65C52×C7C2×D3311yescharacteristic, complemented, Hall
66C3×C5×C11—22no—
67C3×C5×C11C2×C7×D511yescharacteristic, complemented
68C3×C5×C11C22×C5×C711yescharacteristic, complemented
69C2×C7×C11C5×D1511yescharacteristic, complemented
70C7×D11—152no—
71C2×C3×C52C7×D1111yescharacteristic, complemented
72C5×D15—112no—
73C22×C5×C7—1651no—
74C2×C7×D5—331no—
75C2×D33—51noHall
76C2×C5×C11—22no—
77C2×C5×C11C5×D3×C711yescharacteristic, complemented
78C2×C5×C11C7×D1511yescharacteristic, complemented
79D55—32no—
80C5×D11—152no—
81C3×C5×C7—22no—
82C3×C5×C7C2×C5×D1111yescharacteristic, complemented
83C3×C5×C7C2×D5511yescharacteristic, complemented
84C2×C5×D5—331noHall
85C2×D3×C7—551noHall
86C7×C11C2×C5×D1511yescharacteristic, complemented, Hall
87C3×C52C2×C7×D1111yescharacteristic, complemented, Hall
88C2×C5×C7—22no—
89C2×C5×C7—1652no—
90C2×C5×C7C5×D3311yescharacteristic, complemented
91C2×C5×C7D16511yescharacteristic, direct product factor
92C7×D5—332no—
93C2×C3×C11C5×C7×D511yescharacteristic, complemented
94D33—52no—
95C2×D15—111no—
96C2×C5×D3—551no—
97C5×C11—22no—
98C5×C11C2×C5×D3×C711yescharacteristic, complemented
99C5×C11C2×C7×D1511yescharacteristic, complemented
100C2×C52C7×D3311yescharacteristic, complemented
101C5×D5—332no—
102C2×D11—151noHall
103C2×C3×C7C5×D5511yescharacteristic, complemented
104D3×C7—552no—
105C5×C7—22no—
106C5×C7C2×C5×D3311yescharacteristic, complemented
107C5×C7C2×D16511yescharacteristic, direct product factor
108C3×C11C2×C5×C7×D511yescharacteristic, complemented, Hall
109C2×C3×C5—22no—
110C2×C3×C5C5×C7×D1111yescharacteristic, complemented
111C2×C3×C5C7×D5511yescharacteristic, complemented
112D15—112no—
113C5×D3—552no—
114C22×C7—1651noHall
115C52C2×C7×D3311yescharacteristic, complemented, Sylow
116C2×C11C5×C7×D1511yescharacteristic, complemented
117D11—152no—
118C3×C7C2×C5×D5511yescharacteristic, complemented, Hall
119C22×C5—1651no—
120C2×D5—331no—
121C3×C5—22no—
122C3×C5C2×C5×C7×D1111yescharacteristic, complemented
123C3×C5C2×C7×D5511yescharacteristic, complemented
124C2×C7—1652no—
125C2×C7C5×D16511yescharacteristic, direct product factor
126C2×D3—551noHall
127C11C2×C5×C7×D1511yescharacteristic, complemented, Sylow
128C2×C5—22no—
129C2×C5—1652no—
130C2×C5C5×C7×D3311yescharacteristic, complemented
131C2×C5C7×D16511yescharacteristic, direct product factor
132D5—332no—
133C7C2×C5×D16511yescharacteristic, direct product factor, Sylow
134C2×C3C5×C7×D5511yescharacteristic, complemented
135D3—552no—
136C5—22no—
137C5C2×C5×C7×D3311yescharacteristic, complemented
138C5C2×C7×D16511yescharacteristic, direct product factor
139C22—1651noSylow
140C3C2×C5×C7×D5511yescharacteristic, complemented, Sylow
141C2—1652no—
142C2C5×C7×D16511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C7D165
commutator, cosocle, hypocenterC3×C5×C11C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C5×C7

Complements

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

NH ≅ G/Ntype
1. C5×C7×D165C2direct (N × H)
2. C2×C3×C52×C7×C11C2semidirect
4. C3×C52×C7×C11C22semidirect
5. C2×C7×D165C5direct (N × H)
8. C2×C52×C7×C11D3semidirect
9. C2×C5×D165C7direct (N × H)
10. C7×D165C2×C5direct (N × H)
13. C2×C3×C5×C7×C11D5semidirect
14. C2×C3×C5×C7×C11C2×C5semidirect
16. C52×C7×C11C2×D3semidirect
17. C2×C3×C52×C11C2×C7semidirect
18. C5×D165C2×C7direct (N × H)
22. C3×C5×C7×C11C2×D5semidirect
23. C3×C5×C7×C11C22×C5semidirect
25. C2×C3×C52×C7D11semidirect
28. C3×C52×C11C22×C7semidirect
30. C2×C5×C7×C11C5×D3semidirect
31. C2×C5×C7×C11D15semidirect
35. C2×D165C5×C7direct (N × H)
37. C2×C52×C11D3×C7semidirect
39. C3×C52×C7C2×D11semidirect
40. C2×C3×C7×C11C5×D5semidirect
45. C5×C7×C11C2×C5×D3semidirect
46. C5×C7×C11C2×D15semidirect
47. C2×C52×C7D33semidirect
50. C2×C3×C5×C11C7×D5semidirect
51. C2×C3×C5×C11C2×C5×C7semidirect
52. D165C2×C5×C7direct (N × H)
56. C52×C11C2×D3×C7semidirect
57. C3×C7×C11C2×C5×D5semidirect
61. C2×C3×C5×C7C5×D11semidirect
62. C2×C3×C5×C7D55semidirect
65. C52×C7C2×D33semidirect
67. C3×C5×C11C2×C7×D5semidirect
68. C3×C5×C11C22×C5×C7semidirect
69. C2×C7×C11C5×D15semidirect
71. C2×C3×C52C7×D11semidirect
77. C2×C5×C11C5×D3×C7semidirect
78. C2×C5×C11C7×D15semidirect
82. C3×C5×C7C2×C5×D11semidirect
83. C3×C5×C7C2×D55semidirect
86. C7×C11C2×C5×D15semidirect
87. C3×C52C2×C7×D11semidirect
90. C2×C5×C7C5×D33semidirect
91. C2×C5×C7D165direct (N × H)
93. C2×C3×C11C5×C7×D5semidirect
98. C5×C11C2×C5×D3×C7semidirect
99. C5×C11C2×C7×D15semidirect
100. C2×C52C7×D33semidirect
103. C2×C3×C7C5×D55semidirect
106. C5×C7C2×C5×D33semidirect
107. C5×C7C2×D165direct (N × H)
108. C3×C11C2×C5×C7×D5semidirect
110. C2×C3×C5C5×C7×D11semidirect
111. C2×C3×C5C7×D55semidirect
115. C52C2×C7×D33semidirect
116. C2×C11C5×C7×D15semidirect
118. C3×C7C2×C5×D55semidirect
122. C3×C5C2×C5×C7×D11semidirect
123. C3×C5C2×C7×D55semidirect
125. C2×C7C5×D165direct (N × H)
127. C11C2×C5×C7×D15semidirect
130. C2×C5C5×C7×D33semidirect
131. C2×C5C7×D165direct (N × H)
133. C7C2×C5×D165direct (N × H)
134. C2×C3C5×C7×D55semidirect
137. C5C2×C5×C7×D33semidirect
138. C5C2×C7×D165direct (N × H)
140. C3C2×C5×C7×D55semidirect
142. C2C5×C7×D165direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×D1652
C2×C3×C52×C7×C112
C2×C5×C7×D553
C2×C7×D1655
C2×C5×C7×D335
C2×C5×D1657
C2×C5×C7×D1511