Finite Group Databasebeta

← C11×D15⋊(D13⋊C3) #38788101

Subgroups — C11×D15⋊(D13⋊C3) #38788101

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
1C11×D15×C13⋊C3C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C11×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
4C11×D15⋊D13C311yesmaximal, characteristic, complemented
5D5×C11×D13⋊C3—31nomaximal
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7D3×C11×D13⋊C3—51nomaximal, Hall
8C11×C5⋊(D13⋊C3)—21no—
9C11×C5⋊(D13⋊C3)D311yescharacteristic, complemented
10D5×C11×C13⋊C3—31no—
11C5×C11×D13⋊C3—31no—
12C11×C13×D15C2×C311yescharacteristic, complemented
13C5×C11×D39C2×C311yescharacteristic, complemented
14C3×C11×D65C2×C311yescharacteristic, complemented
15D5×C11×D13—31noHall
16D3×C11×C13⋊C3—51no—
17C11×C3⋊(D13⋊C3)D511yescharacteristic, complemented
18C3×C11×D13⋊C3—51no—
19D15⋊(D13⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
20C5×C11×C13⋊C3—21no—
21C5×C11×C13⋊C3C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D3×D5×C11—131nomaximal, Hall
24D3×C11×D13—51no—
25C2×C11×D13⋊C3—151no—
26C11×D65C3×D311yescharacteristic, complemented
27D5×C11×C13—31no—
28C5×C11×D13—31no—
29C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
30D15×C13⋊C3C2×C1111yescharacteristic, complemented
31C5×C3⋊(D13⋊C3)C2×C1111yescharacteristic, complemented
32C3×C5⋊(D13⋊C3)C2×C1111yescharacteristic, complemented
33C3×C11×D15—131no—
34C3×C5×D3×C11—131no—
35C32×D5×C11—131no—
36C11×D39C3×D511yescharacteristic, complemented
37D3×C11×C13—51no—
38C3×C11×D13—51no—
39C2×C11×C13⋊C3—151no—
40C11×D13⋊C3—31no—
41C11×D13⋊C3—51no—
42C11×D13⋊C3—101no—
43D15⋊D13C3×C1111yescharacteristic, complemented
44D5×D13⋊C3—31no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×C3×D5×C11—391no—
47D3×D5×C11—131no—
48C3×C5×C13⋊C3C22×C1111yescharacteristic, complemented, Hall
49C2×C11×D13—151noHall
50C32×C5×C11—131noHall
51D3×D13⋊C3—51noHall
52C3×C11×C13C2×C3×D511yescharacteristic, complemented
53C11×C13⋊C3—21no—
54C11×C13⋊C3D3×D511yescharacteristic, complemented
55C2×C3×D3×C11—651noHall
56C13×D15C2×C3×C1111yescharacteristic, complemented
57C5×D39C2×C3×C1111yescharacteristic, complemented
58C3×D65C2×C3×C1111yescharacteristic, complemented
59C5⋊(D13⋊C3)—21no—
60C5⋊(D13⋊C3)D3×C1111yescharacteristic, complemented
61D5×C13⋊C3—31no—
62C5×D13⋊C3—31no—
63C2×C3×C5×C11—391no—
64C11×D15D13⋊C311yescharacteristic, complemented
65C5×D3×C11—131no—
66C3×D5×C11—131no—
67C3×D5×C11—131no—
68C3×D5×C11—261no—
69C3×D5×C11—391no—
70C2×C11×C13—151no—
71C11×D13—31no—
72C11×D13—51no—
73D5×D13—31noHall
74C3⋊(D13⋊C3)D5×C1111yescharacteristic, complemented
75D3×C13⋊C3—51no—
76C3×D13⋊C3—51no—
77C2×D5×C11—391noHall
78C2×C32×C11—651no—
79C3×D3×C11—131no—
80C3×D3×C11—651no—
81C3×C5×C13C22×C3×C1111yescharacteristic, complemented
82C5×C13⋊C3—21no—
83C5×C13⋊C3C2×D3×C1111yescharacteristic, complemented
84C3×D3×D5—131noHall
85C3×C5×C11—131no—
86C3×C5×C11—261no—
87C3×C5×C11C2×D13⋊C311yescharacteristic, complemented
88D3×D13—51no—
89C2×D13⋊C3—151no—
90C11×C13C3×D3×D511yescharacteristic, complemented, Hall
91C22×C3×C11—1951no—
92C2×D3×C11—651no—
93D65C3×D3×C1111yescharacteristic, complemented
94C5×D13—31no—
95D5×C13—31no—
96C3×C13⋊C3C2×D5×C1111yescharacteristic, complemented, Hall
97C2×C5×C11—391no—
98D5×C11—31no—
99D5×C11—131no—
100C32×C11—131noHall
101C3×D15—131no—
102C3×C5×D3—131no—
103C32×D5—131no—
104D39C3×D5×C1111yescharacteristic, complemented
105C3×D13—51no—
106D3×C13—51no—
107C2×C13⋊C3—151no—
108D13⋊C3—31no—
109D13⋊C3—51no—
110D13⋊C3—101no—
111C2×C3×C11—391no—
112C2×C3×C11—651no—
113C2×C3×C11—651no—
114C2×C3×C11—1301no—
115C2×C3×C11—1951no—
116D3×C11—51no—
117D3×C11—131no—
118C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
119C2×C3×D5—391no—
120D3×D5—131no—
121C5×C11D3×D13⋊C311yescharacteristic, complemented, Hall
122C2×D13—151noHall
123C32×C5—131noHall
124C22×C11—1951noHall
125C3×C13C2×C3×D5×C1111yescharacteristic, complemented
126C13⋊C3—21no—
127C13⋊C3D3×D5×C1111yescharacteristic, complemented
128C2×C3×D3—651noHall
129C3×C11—131no—
130C3×C11—261no—
131C3×C11D5×D13⋊C311yescharacteristic, complemented
132C2×C3×C5—391no—
133D15C11×D13⋊C311yescharacteristic, complemented
134C3×D5—131no—
135C3×D5—131no—
136C3×D5—261no—
137C3×D5—391no—
138C5×D3—131no—
139C2×C13—151no—
140D13—31no—
141D13—51no—
142C2×C11—151no—
143C2×C11—391no—
144C2×C11—651no—
145C2×D5—391noHall
146C2×C32—651no—
147C3×D3—131no—
148C3×D3—651no—
149C3×C5—131no—
150C3×C5—261no—
151C3×C5C2×C11×D13⋊C311yescharacteristic, complemented
152C13C3×D3×D5×C1111yescharacteristic, complemented, Sylow
153C22×C3—1951no—
154C2×D3—651no—
155C11D15⋊(D13⋊C3)11yescharacteristic, direct product factor, Sylow
156C2×C5—391no—
157D5—31no—
158D5—131no—
159C32—131noSylow
160C2×C3—391no—
161C2×C3—651no—
162C2×C3—651no—
163C2×C3—1301no—
164C2×C3—1951no—
165D3—51no—
166D3—131no—
167C5D3×C11×D13⋊C311yescharacteristic, complemented, Sylow
168C22—1951noSylow
169C3—131no—
170C3—261no—
171C3D5×C11×D13⋊C311yescharacteristic, complemented
172C2—151no—
173C2—391no—
174C2—651no—
subgroupG/H
center, hypercenterC11D15⋊(D13⋊C3)
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D15×C13⋊C3C2semidirect
2. C5×C11×C3⋊(D13⋊C3)C2semidirect
3. C3×C11×C5⋊(D13⋊C3)C2semidirect
4. C11×D15⋊D13C3semidirect
6. C3×C5×C11×C13⋊C3C22semidirect
9. C11×C5⋊(D13⋊C3)D3semidirect
12. C11×C13×D15C2×C3semidirect
13. C5×C11×D39C2×C3semidirect
14. C3×C11×D65C2×C3semidirect
17. C11×C3⋊(D13⋊C3)D5semidirect
19. D15⋊(D13⋊C3)C11direct (N × H)
21. C5×C11×C13⋊C3C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
26. C11×D65C3×D3semidirect
29. C3×C11×C13⋊C3C2×D5semidirect
30. D15×C13⋊C3C2×C11semidirect
31. C5×C3⋊(D13⋊C3)C2×C11semidirect
32. C3×C5⋊(D13⋊C3)C2×C11semidirect
36. C11×D39C3×D5semidirect
43. D15⋊D13C3×C11semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C3×C5×C13⋊C3C22×C11semidirect
52. C3×C11×C13C2×C3×D5semidirect
54. C11×C13⋊C3D3×D5semidirect
56. C13×D15C2×C3×C11semidirect
57. C5×D39C2×C3×C11semidirect
58. C3×D65C2×C3×C11semidirect
60. C5⋊(D13⋊C3)D3×C11semidirect
64. C11×D15D13⋊C3semidirect
74. C3⋊(D13⋊C3)D5×C11semidirect
81. C3×C5×C13C22×C3×C11semidirect
83. C5×C13⋊C3C2×D3×C11semidirect
87. C3×C5×C11C2×D13⋊C3semidirect
90. C11×C13C3×D3×D5semidirect
93. D65C3×D3×C11semidirect
96. C3×C13⋊C3C2×D5×C11semidirect
104. D39C3×D5×C11semidirect
118. C5×C13C2×C3×D3×C11semidirect
121. C5×C11D3×D13⋊C3semidirect
125. C3×C13C2×C3×D5×C11semidirect
127. C13⋊C3D3×D5×C11semidirect
131. C3×C11D5×D13⋊C3semidirect
133. D15C11×D13⋊C3semidirect
151. C3×C5C2×C11×D13⋊C3semidirect
152. C13C3×D3×D5×C11semidirect
155. C11D15⋊(D13⋊C3)direct (N × H)
167. C5D3×C11×D13⋊C3semidirect
171. C3D5×C11×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11×D15×C13⋊C32
C5×C11×C3⋊(D13⋊C3)2
C3×C11×C5⋊(D13⋊C3)2
C11×D15⋊D133
D5×C11×D13⋊C33
D3×C11×D13⋊C35
D15⋊(D13⋊C3)11
C3×D3×D5×C1113