Finite Group Databasebeta

← C3×D11×D195 #38788203

Subgroups — C3×D11×D195 #38788203

Order 25740.

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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×C5×C13×D11C211yesmaximal, characteristic, complemented
2C3×C11×D195C211yesmaximal, characteristic, complemented
3C3×D2145C211yesmaximal, characteristic, complemented
4D11×D195C311yesmaximal, characteristic, direct product factor
5C3×D11×D65—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D11×D39—51nomaximal, Hall
8D2145C2×C311yescharacteristic, complemented
9C11×D195C2×C311yescharacteristic, complemented
10C3×D715—31no—
11C3×C11×D65—31no—
12C3×C5×C13×D11—21no—
13C3×C5×C13×D11D311yescharacteristic, complemented
14C3×C5×C13×D11C2×C311yescharacteristic, complemented
15D11×D65—31noHall
16C3×D429—51no—
17C3×C11×D39—51no—
18C32×C13×D11D511yescharacteristic, complemented
19C2×C3×D195—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D11×D15—131nomaximal, Hall
24D11×D39—51no—
25C3×D11×D13—151no—
26D715—31no—
27C11×D65—31no—
28C5×C13×D11C3×D311yescharacteristic, complemented
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C2×C32×C5×C13—111no—
31C3×D195—111no—
32C3×D195D1111yescharacteristic, direct product factor
33C3×D165—131no—
34C3×C11×D15—131no—
35C32×C5×D11D1311yescharacteristic, complemented
36D429—51no—
37C11×D39—51no—
38C3×D143—151no—
39C3×C13×D11—21no—
40C3×C13×D11C3×D511yescharacteristic, complemented
41C3×C13×D11D1511yescharacteristic, complemented
42C3×C11×D13—151no—
43C2×D195—111no—
44C2×C3×D65—331no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46D11×D15—131no—
47C3×D5×D11—391no—
48C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
49D11×D13—151noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51C2×C3×D39—551noHall
52C3×C11×C13—21no—
53C3×C11×C13C2×C3×D511yescharacteristic, complemented
54C3×C11×C13C2×D1511yescharacteristic, complemented
55C3×D3×D11—651noHall
56C2×C3×C5×C13—111no—
57C2×C3×C5×C13—111no—
58C2×C3×C5×C13—221no—
59D195—111no—
60D195C3×D1111yescharacteristic, direct product factor
61C3×D65—31no—
62C3×D65—331no—
63D165—131no—
64C11×D15—131no—
65C3×D55—391no—
66C3×D5×C11—391no—
67C3×C5×D11—21no—
68C3×C5×D11C3×D1311yescharacteristic, complemented
69C3×C5×D11D3911yescharacteristic, complemented
70D143—151no—
71C11×D13—151no—
72C13×D11C3×D1511yescharacteristic, complemented
73C2×D65—331noHall
74C2×C32×C13—111no—
75C3×D39—51no—
76C3×D39—551no—
77D5×D11—391noHall
78C3×D33—651no—
79C3×D3×C11—651no—
80C32×D11D6511yescharacteristic, complemented
81C3×C5×C13—21no—
82C3×C5×C13D3×D1111yescharacteristic, complemented
83C3×C5×C13C2×C3×D1111yescharacteristic, complemented
84C2×C3×D15—1431noHall
85C3×C5×C11—21no—
86C3×C5×C11C2×C3×D1311yescharacteristic, complemented
87C3×C5×C11C2×D3911yescharacteristic, complemented
88C2×D39—551no—
89C2×C3×D13—1651no—
90C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
91C2×C3×D11—1951no—
92D3×D11—651no—
93C2×C5×C13—111no—
94D65—31no—
95D65—331no—
96C32×C13D5×D1111yescharacteristic, complemented, Hall
97D55—391no—
98C5×D11C3×D3911yescharacteristic, complemented
99D5×C11—391no—
100C32×C11C2×D6511yescharacteristic, complemented, Hall
101C2×C32×C5—111no—
102C3×D15—131no—
103C3×D15—1431no—
104C2×C3×C13—111no—
105C2×C3×C13—111no—
106C2×C3×C13—221no—
107D39—51no—
108D39—551no—
109C3×D13—151no—
110C3×D13—1651no—
111C2×C3×C11—1951no—
112D33—651no—
113C3×D11—21no—
114C3×D11—1951no—
115C3×D11C3×D6511yescharacteristic, complemented
116C3×D11D19511yescharacteristic, direct product factor
117D3×C11—651no—
118C5×C13C3×D3×D1111yescharacteristic, complemented, Hall
119C2×D15—1431no—
120C2×C3×D5—4291no—
121C5×C11C2×C3×D3911yescharacteristic, complemented, Hall
122C2×D13—1651noHall
123C32×C5D11×D1311yescharacteristic, complemented, Hall
124C2×D11—1951noHall
125C3×C13—21no—
126C3×C13C3×D5×D1111yescharacteristic, complemented
127C3×C13D11×D1511yescharacteristic, complemented
128C2×C3×D3—7151noHall
129C3×C11—21no—
130C3×C11C2×C3×D6511yescharacteristic, complemented
131C3×C11C2×D19511yescharacteristic, complemented
132C2×C3×C5—111no—
133C2×C3×C5—111no—
134C2×C3×C5—221no—
135D15—131no—
136D15—1431no—
137C3×D5—391no—
138C3×D5—4291no—
139C2×C13—111no—
140D13—151no—
141D13—1651no—
142C2×C11—1951no—
143D11—1951no—
144D11C3×D19511yescharacteristic, direct product factor
145C2×D5—4291noHall
146C2×C32—111no—
147C3×D3—651no—
148C3×D3—7151no—
149C3×C5—21no—
150C3×C5C3×D11×D1311yescharacteristic, complemented
151C3×C5D11×D3911yescharacteristic, complemented
152C13C3×D11×D1511yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11C2×C3×D19511yescharacteristic, complemented, Sylow
156C2×C5—111no—
157D5—391no—
158D5—4291no—
159C32D11×D6511yescharacteristic, complemented, Sylow
160C2×C3—111no—
161C2×C3—111no—
162C2×C3—221no—
163C2×C3—21451no—
164C2×C3—1951no—
165D3—651no—
166D3—7151no—
167C5C3×D11×D3911yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—21no—
170C3C3×D11×D6511yescharacteristic, complemented
171C3D11×D19511yescharacteristic, direct product factor
172C2—111no—
173C2—21451no—
174C2—1951no—
subgroupG/H
center, hypercenterC3D11×D195
commutator, cosocle, hypocenterC3×C5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D11C2semidirect
2. C3×C11×D195C2semidirect
3. C3×D2145C2semidirect
4. D11×D195C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. D2145C2×C3semidirect
9. C11×D195C2×C3semidirect
13. C3×C5×C13×D11D3semidirect
14. C3×C5×C13×D11C2×C3semidirect
18. C32×C13×D11D5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
28. C5×C13×D11C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
32. C3×D195D11direct (N × H)
35. C32×C5×D11D13semidirect
40. C3×C13×D11C3×D5semidirect
41. C3×C13×D11D15semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13C2×C3×D5semidirect
54. C3×C11×C13C2×D15semidirect
60. D195C3×D11direct (N × H)
68. C3×C5×D11C3×D13semidirect
69. C3×C5×D11D39semidirect
72. C13×D11C3×D15semidirect
80. C32×D11D65semidirect
82. C3×C5×C13D3×D11semidirect
83. C3×C5×C13C2×C3×D11semidirect
86. C3×C5×C11C2×C3×D13semidirect
87. C3×C5×C11C2×D39semidirect
90. C11×C13C2×C3×D15semidirect
96. C32×C13D5×D11semidirect
98. C5×D11C3×D39semidirect
100. C32×C11C2×D65semidirect
115. C3×D11C3×D65semidirect
116. C3×D11D195direct (N × H)
118. C5×C13C3×D3×D11semidirect
121. C5×C11C2×C3×D39semidirect
123. C32×C5D11×D13semidirect
126. C3×C13C3×D5×D11semidirect
127. C3×C13D11×D15semidirect
130. C3×C11C2×C3×D65semidirect
131. C3×C11C2×D195semidirect
144. D11C3×D195direct (N × H)
150. C3×C5C3×D11×D13semidirect
151. C3×C5D11×D39semidirect
152. C13C3×D11×D15semidirect
155. C11C2×C3×D195semidirect
159. C32D11×D65semidirect
167. C5C3×D11×D39semidirect
170. C3C3×D11×D65semidirect
171. C3D11×D195direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C13×D112
C3×C11×D1952
C3×D21452
D11×D1953
C3×D11×D653
C3×D11×D395
C2×C3×D19511
C3×D11×D1513