Finite Group Databasebeta

← C3×C5×C7×D165 #46831667

Subgroups — C3×C5×C7×D165 #46831667

Order 34650.

192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C3×C5×C7×D55—31nomaximal
3C5×C7×D165C311yesmaximal, characteristic, direct product factor
4C3×C7×D165C511yesmaximal, characteristic, direct product factor
5C3×C5×C7×D33—51nomaximal
6C3×C52×C7×C11—21no—
7C3×C52×C7×C11D311yescharacteristic, complemented
8C3×C52×C7×C11C2×C311yescharacteristic, complemented
9C3×C5×D165C711yesmaximal, characteristic, direct product factor, Hall
10C5×C7×D55—31noHall
11C32×C5×C7×C11—22no—
12C32×C5×C7×C11D511yescharacteristic, complemented
13C32×C5×C7×C11C2×C511yescharacteristic, complemented
14C3×C5×C7×D15—111nomaximal, Hall
15C32×C52×C11C2×C711yescharacteristic, complemented, Hall
16C7×D165C3×C511yescharacteristic, direct product factor
17C5×C7×D33—51no—
18C3×C7×D55—31no—
19C3×C5×C7×D11—151no—
20C52×C7×C11C3×D311yescharacteristic, complemented, Hall
21C5×D165C3×C711yescharacteristic, direct product factor
22C3×C5×D55—31no—
23C32×C52×C7D1111yescharacteristic, complemented, Hall
24C3×C7×D33—51noHall
25C3×C5×C7×C11—24no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11—22no—
28C3×C5×C7×C11—21no—
29C3×C5×C7×C11—21no—
30C3×C5×C7×C11C5×D311yescharacteristic, complemented
31C3×C5×C7×C11C3×D511yescharacteristic, complemented
32C3×C5×C7×C11D1511yescharacteristic, complemented
33C3×C5×C7×C11C2×C3×C511yescharacteristic, complemented
34C5×C7×D15—111no—
35C3×C5×C7×D5—331no—
36C3×D165C5×C711yescharacteristic, direct product factor
37C3×C5×D33—51no—
38C3×C52×C11—21no—
39C3×C52×C11D3×C711yescharacteristic, complemented
40C3×C52×C11C2×C3×C711yescharacteristic, complemented
41C7×D55—31no—
42C5×C7×D11—151no—
43C32×C7×C11C5×D511yescharacteristic, complemented, Hall
44C3×C7×D15—111no—
45C3×C5×D3×C7—551no—
46C5×D55—31noHall
47C3×C52×C7—21no—
48C3×C52×C7C3×D1111yescharacteristic, complemented
49C3×C52×C7D3311yescharacteristic, complemented
50C32×C5×C11—22no—
51C32×C5×C11C7×D511yescharacteristic, complemented
52C32×C5×C11C2×C5×C711yescharacteristic, complemented
53C7×D33—51no—
54C3×C7×D11—151no—
55C3×C5×D15—111noHall
56C5×C7×C11—22no—
57C5×C7×C11C3×C5×D311yescharacteristic, complemented
58C5×C7×C11C3×D1511yescharacteristic, complemented
59C5×C7×D5—331noHall
60D165C3×C5×C711yescharacteristic, direct product factor
61C5×D33—51no—
62C3×D55—31no—
63C3×C5×D11—151no—
64C32×C5×C7—22no—
65C32×C5×C7C5×D1111yescharacteristic, complemented
66C32×C5×C7D5511yescharacteristic, complemented
67C52×C11C3×D3×C711yescharacteristic, complemented, Hall
68C3×C7×C11—21no—
69C3×C7×C11C3×C5×D511yescharacteristic, complemented
70C3×C7×C11C5×D1511yescharacteristic, complemented
71C32×C52C7×D1111yescharacteristic, complemented, Hall
72C2×C3×C5×C7—1651no—
73C7×D15—111no—
74C5×D3×C7—551no—
75C3×C7×D5—331no—
76C3×D33—51noHall
77C52×C7C3×D3311yescharacteristic, complemented, Hall
78C3×C5×C11—24no—
79C3×C5×C11—22no—
80C3×C5×C11—22no—
81C3×C5×C11—21no—
82C3×C5×C11—21no—
83C3×C5×C11C3×C7×D511yescharacteristic, complemented
84C3×C5×C11C5×D3×C711yescharacteristic, complemented
85C3×C5×C11C7×D1511yescharacteristic, complemented
86C3×C5×C11C2×C3×C5×C711yescharacteristic, complemented
87C7×D11—151noHall
88C5×D15—111no—
89C3×C5×D5—331no—
90C3×D3×C7—551noHall
91D55—31no—
92C5×D11—151no—
93C3×C5×C7—24no—
94C3×C5×C7—21no—
95C3×C5×C7—21no—
96C3×C5×C7—22no—
97C3×C5×C7—22no—
98C3×C5×C7C3×C5×D1111yescharacteristic, complemented
99C3×C5×C7C3×D5511yescharacteristic, complemented
100C3×C5×C7C5×D3311yescharacteristic, complemented
101C3×C5×C7D16511yescharacteristic, direct product factor
102C32×C11C5×C7×D511yescharacteristic, complemented, Hall
103C3×D15—111no—
104C3×C5×D3—551no—
105C7×C11C3×C5×D1511yescharacteristic, complemented, Hall
106C3×C52—21no—
107C3×C52C3×C7×D1111yescharacteristic, complemented
108C3×C52C7×D3311yescharacteristic, complemented
109C2×C5×C7—1651no—
110C7×D5—331no—
111D33—51no—
112C3×D11—151no—
113C32×C7C5×D5511yescharacteristic, complemented, Hall
114C5×C11—22no—
115C5×C11C3×C5×D3×C711yescharacteristic, complemented
116C5×C11C3×C7×D1511yescharacteristic, complemented
117C5×D5—331noHall
118C32×C5—22no—
119C32×C5C5×C7×D1111yescharacteristic, complemented
120C32×C5C7×D5511yescharacteristic, complemented
121C2×C3×C7—1651no—
122D3×C7—551no—
123C5×C7—22no—
124C5×C7C3×C5×D3311yescharacteristic, complemented
125C5×C7C3×D16511yescharacteristic, direct product factor
126C3×C11—21no—
127C3×C11C3×C5×C7×D511yescharacteristic, complemented
128C3×C11C5×C7×D1511yescharacteristic, complemented
129C2×C3×C5—1651no—
130D15—111no—
131C3×D5—331no—
132C5×D3—551no—
133C52C3×C7×D3311yescharacteristic, complemented, Sylow
134D11—151noHall
135C3×C7—21no—
136C3×C7C3×C5×D5511yescharacteristic, complemented
137C3×C7C5×D16511yescharacteristic, direct product factor
138C3×D3—551noHall
139C3×C5—24no—
140C3×C5—21no—
141C3×C5—21no—
142C3×C5—22no—
143C3×C5—22no—
144C3×C5C3×C5×C7×D1111yescharacteristic, complemented
145C3×C5C3×C7×D5511yescharacteristic, complemented
146C3×C5C5×C7×D3311yescharacteristic, complemented
147C3×C5C7×D16511yescharacteristic, direct product factor
148C2×C7—1651noHall
149C11C3×C5×C7×D1511yescharacteristic, complemented, Sylow
150C2×C5—1651no—
151D5—331no—
152C32C5×C7×D5511yescharacteristic, complemented, Sylow
153C7C3×C5×D16511yescharacteristic, direct product factor, Sylow
154C2×C3—1651no—
155D3—551no—
156C5—22no—
157C5C3×C5×C7×D3311yescharacteristic, complemented
158C5C3×C7×D16511yescharacteristic, direct product factor
159C3—21no—
160C3C5×C7×D16511yescharacteristic, direct product factor
161C3C3×C5×C7×D5511yescharacteristic, complemented
162C2—1651noSylow
subgroupG/H
center, hypercenterC3×C5×C7D165
commutator, cosocle, hypocenterC3×C5×C11C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C5×C7×D165C3direct (N × H)
4. C3×C7×D165C5direct (N × H)
7. C3×C52×C7×C11D3semidirect
8. C3×C52×C7×C11C2×C3semidirect
9. C3×C5×D165C7direct (N × H)
12. C32×C5×C7×C11D5semidirect
13. C32×C5×C7×C11C2×C5semidirect
15. C32×C52×C11C2×C7semidirect
16. C7×D165C3×C5direct (N × H)
20. C52×C7×C11C3×D3semidirect
21. C5×D165C3×C7direct (N × H)
23. C32×C52×C7D11semidirect
30. C3×C5×C7×C11C5×D3semidirect
31. C3×C5×C7×C11C3×D5semidirect
32. C3×C5×C7×C11D15semidirect
33. C3×C5×C7×C11C2×C3×C5semidirect
36. C3×D165C5×C7direct (N × H)
39. C3×C52×C11D3×C7semidirect
40. C3×C52×C11C2×C3×C7semidirect
43. C32×C7×C11C5×D5semidirect
48. C3×C52×C7C3×D11semidirect
49. C3×C52×C7D33semidirect
51. C32×C5×C11C7×D5semidirect
52. C32×C5×C11C2×C5×C7semidirect
57. C5×C7×C11C3×C5×D3semidirect
58. C5×C7×C11C3×D15semidirect
60. D165C3×C5×C7direct (N × H)
65. C32×C5×C7C5×D11semidirect
66. C32×C5×C7D55semidirect
67. C52×C11C3×D3×C7semidirect
69. C3×C7×C11C3×C5×D5semidirect
70. C3×C7×C11C5×D15semidirect
71. C32×C52C7×D11semidirect
77. C52×C7C3×D33semidirect
83. C3×C5×C11C3×C7×D5semidirect
84. C3×C5×C11C5×D3×C7semidirect
85. C3×C5×C11C7×D15semidirect
86. C3×C5×C11C2×C3×C5×C7semidirect
98. C3×C5×C7C3×C5×D11semidirect
99. C3×C5×C7C3×D55semidirect
100. C3×C5×C7C5×D33semidirect
101. C3×C5×C7D165direct (N × H)
102. C32×C11C5×C7×D5semidirect
105. C7×C11C3×C5×D15semidirect
107. C3×C52C3×C7×D11semidirect
108. C3×C52C7×D33semidirect
113. C32×C7C5×D55semidirect
115. C5×C11C3×C5×D3×C7semidirect
116. C5×C11C3×C7×D15semidirect
119. C32×C5C5×C7×D11semidirect
120. C32×C5C7×D55semidirect
124. C5×C7C3×C5×D33semidirect
125. C5×C7C3×D165direct (N × H)
127. C3×C11C3×C5×C7×D5semidirect
128. C3×C11C5×C7×D15semidirect
133. C52C3×C7×D33semidirect
136. C3×C7C3×C5×D55semidirect
137. C3×C7C5×D165direct (N × H)
144. C3×C5C3×C5×C7×D11semidirect
145. C3×C5C3×C7×D55semidirect
146. C3×C5C5×C7×D33semidirect
147. C3×C5C7×D165direct (N × H)
149. C11C3×C5×C7×D15semidirect
152. C32C5×C7×D55semidirect
153. C7C3×C5×D165direct (N × H)
157. C5C3×C5×C7×D33semidirect
158. C5C3×C7×D165direct (N × H)
160. C3C5×C7×D165direct (N × H)
161. C3C3×C5×C7×D55semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C3×C5×C7×D553
C5×C7×D1653
C3×C7×D1655
C3×C5×C7×D335
C3×C5×D1657
C3×C5×C7×D1511