Finite Group Databasebeta

← C2×C3×C11×D195 #38788313

Subgroups — C2×C3×C11×D195 #38788313

Order 25740.

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

normal subgroups only

This group has 176 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
1C3×C11×D195C212yesmaximal, direct product factor
2C2×C32×C5×C11×C13C211yesmaximal, characteristic, complemented
3C2×C3×C11×D65—31nomaximal
4C2×C11×D195C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C3×C11×D39—51nomaximal, Hall
7C11×D195C2×C312yesdirect product factor
8C3×C11×D65—32no—
9C2×C3×C5×C11×C13—21no—
10C2×C3×C5×C11×C13D311yescharacteristic, complemented
11C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
12C2×C11×D65—31noHall
13C3×C11×D39—52no—
14C2×C32×C11×C13D511yescharacteristic, complemented
15C2×C3×D195C1111yesmaximal, characteristic, direct product factor, Hall
16C3×C5×C11×C13—21no—
17C3×C5×C11×C13C2×D311yescharacteristic, complemented
18C3×C5×C11×C13C22×C311yescharacteristic, complemented
19C2×C3×C11×D15—131nomaximal, Hall
20C2×C11×D39—51no—
21C2×C3×C11×D13—151no—
22C2×C5×C11×C13C3×D311yescharacteristic, complemented
23C11×D65—32no—
24C32×C11×C13C2×D511yescharacteristic, complemented, Hall
25C2×C32×C5×C13C2×C1111yescharacteristic, complemented
26C3×D195C2×C1112yesdirect product factor
27C2×C32×C5×C11D1311yescharacteristic, complemented
28C3×C11×D15—132no—
29C2×C3×C11×C13—21no—
30C2×C3×C11×C13C3×D511yescharacteristic, complemented
31C2×C3×C11×C13D1511yescharacteristic, complemented
32C11×D39—52no—
33C3×C11×D13—152no—
34C2×D195C3×C1111yescharacteristic, direct product factor
35C2×C3×D65—31no—
36C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
37C2×C11×D15—131no—
38C2×C3×D5×C11—391no—
39C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
40C2×C11×D13—151noHall
41C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
42C2×C3×D39—51noHall
43C3×C11×C13—21no—
44C3×C11×C13C2×C3×D511yescharacteristic, complemented
45C3×C11×C13C2×D1511yescharacteristic, complemented
46C2×C3×D3×C11—651noHall
47C2×C3×C5×C13—21no—
48C2×C3×C5×C13D3×C1111yescharacteristic, complemented
49C2×C3×C5×C13C2×C3×C1111yescharacteristic, complemented
50D195C2×C3×C1112yesdirect product factor
51C3×D65—32no—
52C2×C3×C5×C11—21no—
53C2×C3×C5×C11C3×D1311yescharacteristic, complemented
54C2×C3×C5×C11D3911yescharacteristic, complemented
55C11×D15—132no—
56C3×D5×C11—392no—
57C2×C11×C13C3×D1511yescharacteristic, complemented
58C11×D13—152no—
59C2×D65—31noHall
60C2×C32×C13D5×C1111yescharacteristic, complemented
61C3×D39—52no—
62C2×D5×C11—391noHall
63C2×C32×C11D6511yescharacteristic, complemented
64C3×D3×C11—652no—
65C3×C5×C13—21no—
66C3×C5×C13C2×D3×C1111yescharacteristic, complemented
67C3×C5×C13C22×C3×C1111yescharacteristic, complemented
68C2×C3×D15—131noHall
69C3×C5×C11—21no—
70C3×C5×C11C2×C3×D1311yescharacteristic, complemented
71C3×C5×C11C2×D3911yescharacteristic, complemented
72C2×D39—51no—
73C2×C3×D13—151no—
74C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
75C22×C3×C11—1951no—
76C2×D3×C11—651no—
77C2×C5×C13C3×D3×C1111yescharacteristic, complemented
78D65—32no—
79C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
80C2×C5×C11C3×D3911yescharacteristic, complemented
81D5×C11—392no—
82C32×C11C2×D6511yescharacteristic, complemented, Hall
83C2×C32×C5C11×D1311yescharacteristic, complemented
84C3×D15—132no—
85C2×C3×C13—21no—
86C2×C3×C13C3×D5×C1111yescharacteristic, complemented
87C2×C3×C13C11×D1511yescharacteristic, complemented
88D39—52no—
89C3×D13—152no—
90C2×C3×C11—21no—
91C2×C3×C11—1952no—
92C2×C3×C11C3×D6511yescharacteristic, complemented
93C2×C3×C11D19511yescharacteristic, direct product factor
94D3×C11—652no—
95C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
96C2×D15—131no—
97C2×C3×D5—391no—
98C5×C11C2×C3×D3911yescharacteristic, complemented, Hall
99C2×D13—151noHall
100C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
101C22×C11—1951noHall
102C3×C13—21no—
103C3×C13C2×C3×D5×C1111yescharacteristic, complemented
104C3×C13C2×C11×D1511yescharacteristic, complemented
105C2×C3×D3—651noHall
106C3×C11—21no—
107C3×C11C2×C3×D6511yescharacteristic, complemented
108C3×C11C2×D19511yescharacteristic, direct product factor
109C2×C3×C5—21no—
110C2×C3×C5C3×C11×D1311yescharacteristic, complemented
111C2×C3×C5C11×D3911yescharacteristic, complemented
112D15—132no—
113C3×D5—392no—
114C2×C13C3×C11×D1511yescharacteristic, complemented
115D13—152no—
116C2×C11—1952no—
117C2×C11C3×D19511yescharacteristic, direct product factor
118C2×D5—391noHall
119C2×C32C11×D6511yescharacteristic, complemented
120C3×D3—652no—
121C3×C5—21no—
122C3×C5C2×C3×C11×D1311yescharacteristic, complemented
123C3×C5C2×C11×D3911yescharacteristic, complemented
124C13C2×C3×C11×D1511yescharacteristic, complemented, Sylow
125C22×C3—1951no—
126C2×D3—651no—
127C11C2×C3×D19511yescharacteristic, direct product factor, Sylow
128C2×C5C3×C11×D3911yescharacteristic, complemented
129D5—392no—
130C32C2×C11×D6511yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—1952no—
133C2×C3C3×C11×D6511yescharacteristic, complemented
134C2×C3C11×D19511yescharacteristic, direct product factor
135D3—652no—
136C5C2×C3×C11×D3911yescharacteristic, complemented, Sylow
137C22—1951noSylow
138C3—21no—
139C3C2×C11×D19511yescharacteristic, direct product factor
140C3C2×C3×C11×D6511yescharacteristic, complemented
141C2—1952no—
142C2C3×C11×D19511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11D195
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×D195C2direct (N × H)
2. C2×C32×C5×C11×C13C2semidirect
4. C2×C11×D195C3direct (N × H)
5. C32×C5×C11×C13C22semidirect
7. C11×D195C2×C3direct (N × H)
10. C2×C3×C5×C11×C13D3semidirect
11. C2×C3×C5×C11×C13C2×C3semidirect
14. C2×C32×C11×C13D5semidirect
15. C2×C3×D195C11direct (N × H)
17. C3×C5×C11×C13C2×D3semidirect
18. C3×C5×C11×C13C22×C3semidirect
22. C2×C5×C11×C13C3×D3semidirect
24. C32×C11×C13C2×D5semidirect
25. C2×C32×C5×C13C2×C11semidirect
26. C3×D195C2×C11direct (N × H)
27. C2×C32×C5×C11D13semidirect
30. C2×C3×C11×C13C3×D5semidirect
31. C2×C3×C11×C13D15semidirect
34. C2×D195C3×C11direct (N × H)
36. C5×C11×C13C2×C3×D3semidirect
39. C32×C5×C13C22×C11semidirect
41. C32×C5×C11C2×D13semidirect
44. C3×C11×C13C2×C3×D5semidirect
45. C3×C11×C13C2×D15semidirect
48. C2×C3×C5×C13D3×C11semidirect
49. C2×C3×C5×C13C2×C3×C11semidirect
50. D195C2×C3×C11direct (N × H)
53. C2×C3×C5×C11C3×D13semidirect
54. C2×C3×C5×C11D39semidirect
57. C2×C11×C13C3×D15semidirect
60. C2×C32×C13D5×C11semidirect
63. C2×C32×C11D65semidirect
66. C3×C5×C13C2×D3×C11semidirect
67. C3×C5×C13C22×C3×C11semidirect
70. C3×C5×C11C2×C3×D13semidirect
71. C3×C5×C11C2×D39semidirect
74. C11×C13C2×C3×D15semidirect
77. C2×C5×C13C3×D3×C11semidirect
79. C32×C13C2×D5×C11semidirect
80. C2×C5×C11C3×D39semidirect
82. C32×C11C2×D65semidirect
83. C2×C32×C5C11×D13semidirect
86. C2×C3×C13C3×D5×C11semidirect
87. C2×C3×C13C11×D15semidirect
92. C2×C3×C11C3×D65semidirect
93. C2×C3×C11D195direct (N × H)
95. C5×C13C2×C3×D3×C11semidirect
98. C5×C11C2×C3×D39semidirect
100. C32×C5C2×C11×D13semidirect
103. C3×C13C2×C3×D5×C11semidirect
104. C3×C13C2×C11×D15semidirect
107. C3×C11C2×C3×D65semidirect
108. C3×C11C2×D195direct (N × H)
110. C2×C3×C5C3×C11×D13semidirect
111. C2×C3×C5C11×D39semidirect
114. C2×C13C3×C11×D15semidirect
117. C2×C11C3×D195direct (N × H)
119. C2×C32C11×D65semidirect
122. C3×C5C2×C3×C11×D13semidirect
123. C3×C5C2×C11×D39semidirect
124. C13C2×C3×C11×D15semidirect
127. C11C2×C3×D195direct (N × H)
128. C2×C5C3×C11×D39semidirect
130. C32C2×C11×D65semidirect
133. C2×C3C3×C11×D65semidirect
134. C2×C3C11×D195direct (N × H)
136. C5C2×C3×C11×D39semidirect
139. C3C2×C11×D195direct (N × H)
140. C3C2×C3×C11×D65semidirect
142. C2C3×C11×D195direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×D1952
C2×C32×C5×C11×C132
C2×C3×C11×D653
C2×C11×D1953
C2×C3×C11×D395
C2×C3×D19511
C2×C3×C11×D1513