Finite Group Databasebeta

← C2×C5×C11×D165 #49137828

Subgroups — C2×C5×C11×D165 #49137828

Order 36300.

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

normal subgroups only

This group has 352 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×C11×D165C212yesmaximal, direct product factor
2C2×C3×C52×C112C211yesmaximal, characteristic, complemented
3C2×C5×C11×D55—31nomaximal, Hall
4C3×C52×C112C2211yescharacteristic, complemented, Hall
5C2×C5×C11×D33—51nomaximal
6C2×C11×D165C511yesmaximal, characteristic, direct product factor
7C5×C11×D55—32no—
8C2×C52×C112D311yescharacteristic, complemented
9C11×D165C2×C512yesdirect product factor
10C5×C11×D33—52no—
11C2×C3×C5×C112—22no—
12C2×C3×C5×C112D511yescharacteristic, complemented
13C2×C3×C5×C112C2×C511yescharacteristic, complemented
14C2×C5×D165C1111yesmaximal, characteristic, direct product factor
15C2×C5×C11×D15—111nomaximal
16C52×C112C2×D311yescharacteristic, complemented, Hall
17C2×C11×D55—31no—
18C2×C5×C11×D11—151no—
19C3×C5×C112—22no—
20C3×C5×C112C2×D511yescharacteristic, complemented
21C3×C5×C112C22×C511yescharacteristic, complemented
22C2×C3×C52×C11—25no—
23C2×C3×C52×C11D1111yescharacteristic, complemented
24C2×C3×C52×C11C2×C1111yescharacteristic, complemented
25C5×D165C2×C1112yesdirect product factor
26C5×C11×D15—112no—
27C2×C11×D33—51noHall
28C2×C5×C112—22no—
29C2×C5×C112C5×D311yescharacteristic, complemented
30C2×C5×C112D1511yescharacteristic, complemented
31C11×D55—32no—
32C5×C11×D11—152no—
33C2×C5×D55—31no—
34C2×C5×D5×C11—331no—
35C3×C52×C11—25no—
36C3×C52×C11C2×D1111yescharacteristic, complemented
37C3×C52×C11C22×C1111yescharacteristic, complemented
38C2×C3×C112C5×D511yescharacteristic, complemented
39C11×D33—52no—
40C2×D165C5×C1111yescharacteristic, direct product factor
41C2×C11×D15—111no—
42C2×C5×D33—51no—
43C2×C5×D3×C11—551no—
44C5×C112—22no—
45C5×C112C2×C5×D311yescharacteristic, complemented
46C5×C112C2×D1511yescharacteristic, complemented
47C2×C52×C11—25no—
48C2×C52×C11D3×C1111yescharacteristic, complemented
49C2×C52×C11D3311yescharacteristic, complemented
50C5×D55—32no—
51C5×D5×C11—332no—
52C2×C11×D11—151noHall
53C3×C112C2×C5×D511yescharacteristic, complemented, Hall
54C2×C3×C5×C11—220no—
55C2×C3×C5×C11—25no—
56C2×C3×C5×C11—25no—
57C2×C3×C5×C11—22no—
58C2×C3×C5×C11—22no—
59C2×C3×C5×C11D5×C1111yescharacteristic, complemented
60C2×C3×C5×C11C5×D1111yescharacteristic, complemented
61C2×C3×C5×C11D5511yescharacteristic, complemented
62C2×C3×C5×C11C2×C5×C1111yescharacteristic, complemented
63D165C2×C5×C1112yesdirect product factor
64C11×D15—112no—
65C5×D33—52no—
66C5×D3×C11—552no—
67C2×C5×D15—111noHall
68C52×C11—25no—
69C52×C11C2×D3×C1111yescharacteristic, complemented
70C52×C11C2×D3311yescharacteristic, complemented
71C2×C112C5×D1511yescharacteristic, complemented
72C11×D11—152no—
73C22×C5×C11—1651no—
74C2×D55—31no—
75C2×D5×C11—331no—
76C2×C5×D11—151no—
77C3×C5×C11—220no—
78C3×C5×C11—22no—
79C3×C5×C11—22no—
80C3×C5×C11—25no—
81C3×C5×C11—25no—
82C3×C5×C11C2×C5×D1111yescharacteristic, complemented
83C3×C5×C11C2×D5×C1111yescharacteristic, complemented
84C3×C5×C11C2×D5511yescharacteristic, complemented
85C3×C5×C11C22×C5×C1111yescharacteristic, complemented
86C2×C3×C52C11×D1111yescharacteristic, complemented
87C5×D15—112no—
88C2×D33—51no—
89C2×D3×C11—551no—
90C112C2×C5×D1511yescharacteristic, complemented, Sylow
91C2×C5×C11—220no—
92C2×C5×C11—22no—
93C2×C5×C11—22no—
94C2×C5×C11—25no—
95C2×C5×C11—25no—
96C2×C5×C11—1652no—
97C2×C5×C11C5×D3×C1111yescharacteristic, complemented
98C2×C5×C11C5×D3311yescharacteristic, complemented
99C2×C5×C11C11×D1511yescharacteristic, complemented
100C2×C5×C11D16511yescharacteristic, direct product factor
101D55—32no—
102C5×D11—152no—
103D5×C11—332no—
104C2×C5×D5—331noHall
105C3×C52C2×C11×D1111yescharacteristic, complemented, Hall
106C2×C3×C11—25no—
107C2×C3×C11C5×D5×C1111yescharacteristic, complemented
108C2×C3×C11C5×D5511yescharacteristic, complemented
109D33—52no—
110D3×C11—552no—
111C2×D15—111no—
112C2×C5×D3—551no—
113C5×C11—220no—
114C5×C11—22no—
115C5×C11—22no—
116C5×C11—25no—
117C5×C11—25no—
118C5×C11C2×C5×D3×C1111yescharacteristic, complemented
119C5×C11C2×C5×D3311yescharacteristic, complemented
120C5×C11C2×C11×D1511yescharacteristic, complemented
121C5×C11C2×D16511yescharacteristic, direct product factor
122C2×C52C11×D3311yescharacteristic, complemented
123C5×D5—332no—
124C22×C11—1651no—
125C2×D11—151no—
126C3×C11—25no—
127C3×C11C2×C5×D5×C1111yescharacteristic, complemented
128C3×C11C2×C5×D5511yescharacteristic, complemented
129C2×C3×C5—22no—
130C2×C3×C5C5×C11×D1111yescharacteristic, complemented
131C2×C3×C5C11×D5511yescharacteristic, complemented
132D15—112no—
133C5×D3—552no—
134C52C2×C11×D3311yescharacteristic, complemented, Sylow
135C2×C11—25no—
136C2×C11—1652no—
137C2×C11C5×C11×D1511yescharacteristic, complemented
138C2×C11C5×D16511yescharacteristic, direct product factor
139D11—152no—
140C22×C5—1651no—
141C2×D5—331no—
142C3×C5—22no—
143C3×C5C2×C5×C11×D1111yescharacteristic, complemented
144C3×C5C2×C11×D5511yescharacteristic, complemented
145C2×D3—551noHall
146C11—25no—
147C11C2×C5×C11×D1511yescharacteristic, complemented
148C11C2×C5×D16511yescharacteristic, direct product factor
149C2×C5—22no—
150C2×C5—1652no—
151C2×C5C5×C11×D3311yescharacteristic, complemented
152C2×C5C11×D16511yescharacteristic, direct product factor
153D5—332no—
154C2×C3C5×C11×D5511yescharacteristic, complemented
155D3—552no—
156C5—22no—
157C5C2×C11×D16511yescharacteristic, direct product factor
158C5C2×C5×C11×D3311yescharacteristic, complemented
159C22—1651noSylow
160C3C2×C5×C11×D5511yescharacteristic, complemented, Sylow
161C2—1652no—
162C2C5×C11×D16511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C11D165
commutator, cosocle, hypocenterC3×C5×C11C22×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C112C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C5×C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×D165C2direct (N × H)
2. C2×C3×C52×C112C2semidirect
4. C3×C52×C112C22semidirect
6. C2×C11×D165C5direct (N × H)
8. C2×C52×C112D3semidirect
9. C11×D165C2×C5direct (N × H)
12. C2×C3×C5×C112D5semidirect
13. C2×C3×C5×C112C2×C5semidirect
14. C2×C5×D165C11direct (N × H)
16. C52×C112C2×D3semidirect
20. C3×C5×C112C2×D5semidirect
21. C3×C5×C112C22×C5semidirect
23. C2×C3×C52×C11D11semidirect
24. C2×C3×C52×C11C2×C11semidirect
25. C5×D165C2×C11direct (N × H)
29. C2×C5×C112C5×D3semidirect
30. C2×C5×C112D15semidirect
36. C3×C52×C11C2×D11semidirect
37. C3×C52×C11C22×C11semidirect
38. C2×C3×C112C5×D5semidirect
40. C2×D165C5×C11direct (N × H)
45. C5×C112C2×C5×D3semidirect
46. C5×C112C2×D15semidirect
48. C2×C52×C11D3×C11semidirect
49. C2×C52×C11D33semidirect
53. C3×C112C2×C5×D5semidirect
59. C2×C3×C5×C11D5×C11semidirect
60. C2×C3×C5×C11C5×D11semidirect
61. C2×C3×C5×C11D55semidirect
62. C2×C3×C5×C11C2×C5×C11semidirect
63. D165C2×C5×C11direct (N × H)
69. C52×C11C2×D3×C11semidirect
70. C52×C11C2×D33semidirect
71. C2×C112C5×D15semidirect
82. C3×C5×C11C2×C5×D11semidirect
83. C3×C5×C11C2×D5×C11semidirect
84. C3×C5×C11C2×D55semidirect
85. C3×C5×C11C22×C5×C11semidirect
86. C2×C3×C52C11×D11semidirect
90. C112C2×C5×D15semidirect
97. C2×C5×C11C5×D3×C11semidirect
98. C2×C5×C11C5×D33semidirect
99. C2×C5×C11C11×D15semidirect
100. C2×C5×C11D165direct (N × H)
105. C3×C52C2×C11×D11semidirect
107. C2×C3×C11C5×D5×C11semidirect
108. C2×C3×C11C5×D55semidirect
118. C5×C11C2×C5×D3×C11semidirect
119. C5×C11C2×C5×D33semidirect
120. C5×C11C2×C11×D15semidirect
121. C5×C11C2×D165direct (N × H)
122. C2×C52C11×D33semidirect
127. C3×C11C2×C5×D5×C11semidirect
128. C3×C11C2×C5×D55semidirect
130. C2×C3×C5C5×C11×D11semidirect
131. C2×C3×C5C11×D55semidirect
134. C52C2×C11×D33semidirect
137. C2×C11C5×C11×D15semidirect
138. C2×C11C5×D165direct (N × H)
143. C3×C5C2×C5×C11×D11semidirect
144. C3×C5C2×C11×D55semidirect
147. C11C2×C5×C11×D15semidirect
148. C11C2×C5×D165direct (N × H)
151. C2×C5C5×C11×D33semidirect
152. C2×C5C11×D165direct (N × H)
154. C2×C3C5×C11×D55semidirect
157. C5C2×C11×D165direct (N × H)
158. C5C2×C5×C11×D33semidirect
160. C3C2×C5×C11×D55semidirect
162. C2C5×C11×D165direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×D1652
C2×C3×C52×C1122
C2×C5×C11×D553
C2×C5×C11×D335
C2×C11×D1655
C2×C5×D16511
C2×C5×C11×D1511