Finite Group Databasebeta

← C3×D143⋊D15 #38788205

Subgroups — C3×D143⋊D15 #38788205

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×C5×D143C211yesmaximal, characteristic, complemented
2C3×C11×D195C211yesmaximal, characteristic, complemented
3C3×C13×D165C211yesmaximal, characteristic, complemented
4D143⋊D15C311yesmaximal, characteristic, direct product factor
5C3×D55⋊D13—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D33⋊D13—51nomaximal, Hall
8C13×D165C2×C311yescharacteristic, complemented
9C11×D195C2×C311yescharacteristic, complemented
10C3×C13×D55—31no—
11C3×C11×D65—31no—
12C3×C5×D143—21no—
13C3×C5×D143D311yescharacteristic, complemented
14C3×C5×D143C2×C311yescharacteristic, complemented
15D55⋊D13—31noHall
16C3×C13×D33—51no—
17C3×C11×D39—51no—
18C32×D143D511yescharacteristic, complemented
19C3×D13×D15—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D11×D15—131nomaximal, Hall
24D33⋊D13—51no—
25C3×D11×D13—151no—
26C13×D55—31no—
27C11×D65—31no—
28C5×D143C3×D311yescharacteristic, complemented
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×D195D1111yescharacteristic, complemented
31C3×C13×D15—111no—
32C32×C5×D13—111no—
33C3×D165D1311yescharacteristic, complemented
34C3×C11×D15—131no—
35C32×C5×D11—131no—
36C13×D33—51no—
37C11×D39—51no—
38C3×D143—21no—
39C3×D143C3×D511yescharacteristic, complemented
40C3×D143D1511yescharacteristic, complemented
41C3×C13×D11—151no—
42C3×C11×D13—151no—
43D13×D15—111no—
44C3×D5×D13—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
51C3×D3×D13—551noHall
52C3×C11×C13—21no—
53C3×C11×C13C2×C3×D511yescharacteristic, complemented
54C3×C11×C13C2×D1511yescharacteristic, complemented
55C3×D3×D11—651noHall
56D195C3×D1111yescharacteristic, complemented
57C13×D15—111no—
58C3×D65—31no—
59C3×D5×C13—331no—
60C3×C5×D13—111no—
61C3×C5×D13—111no—
62C3×C5×D13—221no—
63D165C3×D1311yescharacteristic, complemented
64C11×D15—131no—
65C3×D55—31no—
66C3×D5×C11—391no—
67C3×C5×D11—131no—
68C3×C5×D11—131no—
69C3×C5×D11—261no—
70D143C3×D1511yescharacteristic, complemented
71C11×D13—151no—
72C13×D11—151no—
73D5×D13—331noHall
74C3×D39—51no—
75C3×D3×C13—551no—
76C32×D13—111no—
77D5×D11—391noHall
78C3×D33—51no—
79C3×D3×C11—651no—
80C32×D11—131no—
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×C11D3×D1311yescharacteristic, complemented
87C3×C5×C11C2×C3×D1311yescharacteristic, complemented
88C2×C3×D13—1651no—
89D3×D13—551no—
90C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
91C2×C3×D11—1951no—
92D3×D11—651no—
93D65—31no—
94C5×D13—111no—
95D5×C13—331no—
96C32×C13D5×D1111yescharacteristic, complemented, Hall
97D55—31no—
98C5×D11—131no—
99D5×C11—391no—
100C32×C11D5×D1311yescharacteristic, complemented, Hall
101C2×C32×C5—1431no—
102C3×D15—111no—
103C3×D15—131no—
104C2×C3×C13—1651no—
105D39—51no—
106C3×D13—111no—
107C3×D13—111no—
108C3×D13—151no—
109C3×D13—221no—
110D3×C13—551no—
111C2×C3×C11—1951no—
112D33—51no—
113C3×D11—131no—
114C3×D11—131no—
115C3×D11—151no—
116C3×D11—261no—
117D3×C11—651no—
118C5×C13C3×D3×D1111yescharacteristic, complemented, Hall
119C2×D15—1431no—
120C2×C3×D5—4291no—
121C5×C11C3×D3×D1311yescharacteristic, 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×C11C3×D5×D1311yescharacteristic, complemented
131C3×C11D13×D1511yescharacteristic, complemented
132C2×C3×C5—2861no—
133C2×C3×C5—1431no—
134C2×C3×C5—1431no—
135D15—111no—
136D15—131no—
137C3×D5—331no—
138C3×D5—391no—
139C2×C13—1651no—
140D13—111no—
141D13—151no—
142C2×C11—1951no—
143D11—131no—
144D11—151no—
145C2×D5—4291noHall
146C2×C32—1431no—
147C3×D3—551no—
148C3×D3—651no—
149C3×C5—21no—
150C3×C5C3×D11×D1311yescharacteristic, complemented
151C3×C5D33⋊D1311yescharacteristic, complemented
152C13C3×D11×D1511yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11C3×D13×D1511yescharacteristic, complemented, Sylow
156C2×C5—1431no—
157D5—331no—
158D5—391no—
159C32D55⋊D1311yescharacteristic, complemented, Sylow
160C2×C3—2861no—
161C2×C3—1431no—
162C2×C3—1431no—
163C2×C3—1651no—
164C2×C3—1951no—
165D3—551no—
166D3—651no—
167C5C3×D33⋊D1311yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—21no—
170C3C3×D55⋊D1311yescharacteristic, complemented
171C3D143⋊D1511yescharacteristic, direct product factor
172C2—1431no—
173C2—1651no—
174C2—1951no—
subgroupG/H
center, hypercenterC3D143⋊D15
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×D143C2semidirect
2. C3×C11×D195C2semidirect
3. C3×C13×D165C2semidirect
4. D143⋊D15C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. C13×D165C2×C3semidirect
9. C11×D195C2×C3semidirect
13. C3×C5×D143D3semidirect
14. C3×C5×D143C2×C3semidirect
18. C32×D143D5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
28. C5×D143C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
30. C3×D195D11semidirect
33. C3×D165D13semidirect
39. C3×D143C3×D5semidirect
40. C3×D143D15semidirect
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
56. D195C3×D11semidirect
63. D165C3×D13semidirect
70. D143C3×D15semidirect
82. C3×C5×C13D3×D11semidirect
83. C3×C5×C13C2×C3×D11semidirect
86. C3×C5×C11D3×D13semidirect
87. C3×C5×C11C2×C3×D13semidirect
90. C11×C13C2×C3×D15semidirect
96. C32×C13D5×D11semidirect
100. C32×C11D5×D13semidirect
118. C5×C13C3×D3×D11semidirect
121. C5×C11C3×D3×D13semidirect
123. C32×C5D11×D13semidirect
126. C3×C13C3×D5×D11semidirect
127. C3×C13D11×D15semidirect
130. C3×C11C3×D5×D13semidirect
131. C3×C11D13×D15semidirect
150. C3×C5C3×D11×D13semidirect
151. C3×C5D33⋊D13semidirect
152. C13C3×D11×D15semidirect
155. C11C3×D13×D15semidirect
159. C32D55⋊D13semidirect
167. C5C3×D33⋊D13semidirect
170. C3C3×D55⋊D13semidirect
171. C3D143⋊D15direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D1432
C3×C11×D1952
C3×C13×D1652
D143⋊D153
C3×D55⋊D133
C3×D33⋊D135
C3×D13×D1511
C3×D11×D1513