Finite Group Databasebeta

← C3×D15×D143 #38788204

Subgroups — C3×D15×D143 #38788204

Order 25740.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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×C13×D15C211yesmaximal, characteristic, complemented
3C3×D2145C211yesmaximal, characteristic, complemented
4D15×D143C311yesmaximal, characteristic, direct product factor
5C3×D5×D143—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D3×D143—51nomaximal, Hall
8D2145C2×C311yescharacteristic, complemented
9C11×C13×D15C2×C311yescharacteristic, complemented
10C3×D715—31no—
11C3×D5×C11×C13—31no—
12C3×C5×D143—21no—
13C3×C5×D143D311yescharacteristic, complemented
14C3×C5×D143C2×C311yescharacteristic, complemented
15D5×D143—31noHall
16C3×D429—51no—
17C3×D3×C11×C13—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
24C2×C3×D143—151no—
25D3×D143—51no—
26D715—31no—
27D5×C11×C13—31no—
28C5×D143C3×D311yescharacteristic, complemented
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×D195—111no—
31C3×C13×D15D1111yescharacteristic, complemented
32C32×C5×D13—111no—
33C3×D165—131no—
34C3×C11×D15D1311yescharacteristic, complemented
35C32×C5×D11—131no—
36C2×C3×C11×C13—151no—
37D429—51no—
38D3×C11×C13—51no—
39C3×D143—21no—
40C3×D143—151no—
41C3×D143C3×D511yescharacteristic, complemented
42C3×D143D1511yescharacteristic, direct product factor
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
49C2×D143—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
56D195—111no—
57C13×D15C3×D1111yescharacteristic, complemented
58C3×D65—331no—
59C3×D5×C13—31no—
60C3×C5×D13—111no—
61C3×C5×D13—111no—
62C3×C5×D13—221no—
63D165—131no—
64C11×D15C3×D1311yescharacteristic, complemented
65C3×D55—391no—
66C3×D5×C11—31no—
67C3×C5×D11—131no—
68C3×C5×D11—131no—
69C3×C5×D11—261no—
70C2×C11×C13—151no—
71D143—151no—
72D143C3×D1511yescharacteristic, direct product factor
73D5×D13—331noHall
74C3×D39—551no—
75C3×D3×C13—51no—
76C32×D13—111no—
77D5×D11—391noHall
78C3×D33—651no—
79C3×D3×C11—51no—
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—331no—
94C5×D13—111no—
95D5×C13—31no—
96C32×C13D5×D1111yescharacteristic, complemented, Hall
97D55—391no—
98C5×D11—131no—
99D5×C11—31no—
100C32×C11D5×D1311yescharacteristic, complemented, Hall
101C2×C32×C5—1431no—
102C3×D15—1431no—
103C3×D15D14311yescharacteristic, direct product factor
104C2×C3×C13—151no—
105D39—551no—
106C3×D13—111no—
107C3×D13—111no—
108C3×D13—221no—
109C3×D13—1651no—
110D3×C13—51no—
111C2×C3×C11—151no—
112D33—651no—
113C3×D11—131no—
114C3×D11—131no—
115C3×D11—261no—
116C3×D11—1951no—
117D3×C11—51no—
118C5×C13C3×D3×D1111yescharacteristic, complemented, Hall
119C2×D15—1431no—
120C2×C3×D5—4291no—
121C5×C11C3×D3×D1311yescharacteristic, complemented, Hall
122C2×D13—1651noHall
123C32×C5C2×D14311yescharacteristic, 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—1431no—
136D15C3×D14311yescharacteristic, direct product factor
137C3×D5—31no—
138C3×D5—4291no—
139C2×C13—151no—
140D13—111no—
141D13—1651no—
142C2×C11—151no—
143D11—131no—
144D11—1951no—
145C2×D5—4291noHall
146C2×C32—1431no—
147C3×D3—51no—
148C3×D3—7151no—
149C3×C5—21no—
150C3×C5D3×D14311yescharacteristic, complemented
151C3×C5C2×C3×D14311yescharacteristic, complemented
152C13C3×D11×D1511yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11C3×D13×D1511yescharacteristic, complemented, Sylow
156C2×C5—1431no—
157D5—31no—
158D5—4291no—
159C32D5×D14311yescharacteristic, complemented, Sylow
160C2×C3—151no—
161C2×C3—2861no—
162C2×C3—21451no—
163C2×C3—1431no—
164C2×C3—1431no—
165D3—51no—
166D3—7151no—
167C5C3×D3×D14311yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—21no—
170C3C3×D5×D14311yescharacteristic, complemented
171C3D15×D14311yescharacteristic, direct product factor
172C2—151no—
173C2—21451no—
174C2—1431no—
subgroupG/H
center, hypercenterC3D15×D143
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×C13×D15C2semidirect
3. C3×D2145C2semidirect
4. D15×D143C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. D2145C2×C3semidirect
9. C11×C13×D15C2×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
31. C3×C13×D15D11semidirect
34. C3×C11×D15D13semidirect
41. C3×D143C3×D5semidirect
42. C3×D143D15direct (N × H)
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
57. C13×D15C3×D11semidirect
64. C11×D15C3×D13semidirect
72. D143C3×D15direct (N × H)
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
103. C3×D15D143direct (N × H)
118. C5×C13C3×D3×D11semidirect
121. C5×C11C3×D3×D13semidirect
123. C32×C5C2×D143semidirect
126. C3×C13C3×D5×D11semidirect
127. C3×C13D11×D15semidirect
130. C3×C11C3×D5×D13semidirect
131. C3×C11D13×D15semidirect
136. D15C3×D143direct (N × H)
150. C3×C5D3×D143semidirect
151. C3×C5C2×C3×D143semidirect
152. C13C3×D11×D15semidirect
155. C11C3×D13×D15semidirect
159. C32D5×D143semidirect
167. C5C3×D3×D143semidirect
170. C3C3×D5×D143semidirect
171. C3D15×D143direct (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×C13×D152
C3×D21452
D15×D1433
C3×D5×D1433
C3×D3×D1435
C3×D13×D1511
C3×D11×D1513