Finite Group Databasebeta

← C3×D55⋊D39 #38788219

Subgroups — C3×D55⋊D39 #38788219

Order 25740.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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×C13×D55C211yesmaximal, characteristic, complemented
2C3×C5×D429C211yesmaximal, characteristic, complemented
3C3×C11×D195C211yesmaximal, characteristic, complemented
4D55⋊D39C311yesmaximal, characteristic, direct product factor
5C3×D55⋊D13—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D11×D39—51nomaximal, Hall
8C11×D195C2×C311yescharacteristic, complemented
9C5×D429C2×C311yescharacteristic, complemented
10C3×C13×D55—21no—
11C3×C13×D55D311yescharacteristic, complemented
12C3×C13×D55C2×C311yescharacteristic, complemented
13C3×C11×D65—31no—
14C3×C5×D143—31no—
15D55⋊D13—31noHall
16C3×D429D511yescharacteristic, complemented
17C3×C11×D39—51no—
18C32×C13×D11—51no—
19C3×D5×D39—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D15⋊D11—131nomaximal, Hall
24D11×D39—51no—
25C3×D11×D13—151no—
26C13×D55C3×D311yescharacteristic, complemented
27C11×D65—31no—
28C5×D143—31no—
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×D195D1111yescharacteristic, complemented
31C3×C5×D39—111no—
32C32×D5×C13—111no—
33C3×C11×D15—131no—
34C3×C5×D33—131no—
35C32×D55D1311yescharacteristic, complemented
36D429C3×D511yescharacteristic, complemented
37C11×D39—51no—
38C3×D143—31no—
39C3×C13×D11—51no—
40C3×C13×D11—51no—
41C3×C13×D11—101no—
42C3×C11×D13—151no—
43D5×D39—111no—
44C3×D5×D13—331no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46D15⋊D11—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×C13D3×D511yescharacteristic, complemented
54C3×C11×C13C2×C3×D511yescharacteristic, complemented
55C3×D3×D11—651noHall
56D195C3×D1111yescharacteristic, complemented
57C5×D39—111no—
58C3×D65—31no—
59C3×D5×C13—111no—
60C3×D5×C13—111no—
61C3×D5×C13—221no—
62C3×C5×D13—331no—
63C11×D15—131no—
64C5×D33—131no—
65C3×D55—21no—
66C3×D55C3×D1311yescharacteristic, complemented
67C3×D55D3911yescharacteristic, complemented
68C3×D5×C11—391no—
69C3×C5×D11—391no—
70D143—31no—
71C11×D13—151no—
72C13×D11—51no—
73D5×D13—331noHall
74C2×C32×C13—551no—
75C3×D39—51no—
76C3×D39—111no—
77D5×D11—391noHall
78C3×D33—131no—
79C3×D3×C11—651no—
80C32×D11—51no—
81C3×C5×C13—21no—
82C3×C5×C13D3×D1111yescharacteristic, complemented
83C3×C5×C13C2×C3×D1111yescharacteristic, complemented
84C3×D3×D5—1431noHall
85C3×C5×C11—21no—
86C3×C5×C11C2×C3×D1311yescharacteristic, complemented
87C3×C5×C11C2×D3911yescharacteristic, complemented
88C2×D39—551no—
89C2×C3×D13—1651no—
90C11×C13C3×D3×D511yescharacteristic, complemented, Hall
91C2×C3×D11—1951no—
92D3×D11—651no—
93D65—31no—
94C5×D13—331no—
95D5×C13—111no—
96C32×C13D5×D1111yescharacteristic, complemented, Hall
97D55C3×D3911yescharacteristic, complemented
98C5×D11—391no—
99D5×C11—391no—
100C32×C11D5×D1311yescharacteristic, complemented, Hall
101C3×D15—131no—
102C3×C5×D3—1431no—
103C32×D5—111no—
104C2×C3×C13—551no—
105C2×C3×C13—551no—
106C2×C3×C13—1101no—
107D39—51no—
108D39—111no—
109C3×D13—151no—
110C3×D13—331no—
111C2×C3×C11—1951no—
112D33—131no—
113C3×D11—51no—
114C3×D11—51no—
115C3×D11—101no—
116C3×D11—391no—
117D3×C11—651no—
118C5×C13C3×D3×D1111yescharacteristic, complemented, Hall
119C2×C3×D5—4291no—
120D3×D5—1431no—
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×C13D15⋊D1111yescharacteristic, complemented
128C2×C3×D3—7151noHall
129C3×C11—21no—
130C3×C11C3×D5×D1311yescharacteristic, complemented
131C3×C11D5×D3911yescharacteristic, complemented
132C2×C3×C5—4291no—
133D15—131no—
134C3×D5—111no—
135C3×D5—111no—
136C3×D5—221no—
137C3×D5—391no—
138C5×D3—1431no—
139C2×C13—551no—
140D13—151no—
141D13—331no—
142C2×C11—1951no—
143D11—51no—
144D11—391no—
145C2×D5—4291noHall
146C2×C32—551no—
147C3×D3—651no—
148C3×D3—1431no—
149C3×C5—21no—
150C3×C5C3×D11×D1311yescharacteristic, complemented
151C3×C5D11×D3911yescharacteristic, complemented
152C13C3×D15⋊D1111yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11C3×D5×D3911yescharacteristic, complemented, Sylow
156C2×C5—4291no—
157D5—111no—
158D5—391no—
159C32D55⋊D1311yescharacteristic, complemented, Sylow
160C2×C3—551no—
161C2×C3—551no—
162C2×C3—1101no—
163C2×C3—4291no—
164C2×C3—1951no—
165D3—651no—
166D3—1431no—
167C5C3×D11×D3911yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—21no—
170C3C3×D55⋊D1311yescharacteristic, complemented
171C3D55⋊D3911yescharacteristic, direct product factor
172C2—551no—
173C2—4291no—
174C2—1951no—
subgroupG/H
center, hypercenterC3D55⋊D39
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×C13×D55C2semidirect
2. C3×C5×D429C2semidirect
3. C3×C11×D195C2semidirect
4. D55⋊D39C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. C11×D195C2×C3semidirect
9. C5×D429C2×C3semidirect
11. C3×C13×D55D3semidirect
12. C3×C13×D55C2×C3semidirect
16. C3×D429D5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
26. C13×D55C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
30. C3×D195D11semidirect
35. C32×D55D13semidirect
36. D429C3×D5semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13D3×D5semidirect
54. C3×C11×C13C2×C3×D5semidirect
56. D195C3×D11semidirect
66. C3×D55C3×D13semidirect
67. C3×D55D39semidirect
82. C3×C5×C13D3×D11semidirect
83. C3×C5×C13C2×C3×D11semidirect
86. C3×C5×C11C2×C3×D13semidirect
87. C3×C5×C11C2×D39semidirect
90. C11×C13C3×D3×D5semidirect
96. C32×C13D5×D11semidirect
97. D55C3×D39semidirect
100. C32×C11D5×D13semidirect
118. C5×C13C3×D3×D11semidirect
121. C5×C11C2×C3×D39semidirect
123. C32×C5D11×D13semidirect
126. C3×C13C3×D5×D11semidirect
127. C3×C13D15⋊D11semidirect
130. C3×C11C3×D5×D13semidirect
131. C3×C11D5×D39semidirect
150. C3×C5C3×D11×D13semidirect
151. C3×C5D11×D39semidirect
152. C13C3×D15⋊D11semidirect
155. C11C3×D5×D39semidirect
159. C32D55⋊D13semidirect
167. C5C3×D11×D39semidirect
170. C3C3×D55⋊D13semidirect
171. C3D55⋊D39direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C13×D552
C3×C5×D4292
C3×C11×D1952
D55⋊D393
C3×D55⋊D133
C3×D11×D395
C3×D5×D3911
C3×D15⋊D1113