Finite Group Databasebeta

← C11×D15×D13⋊C3 #38788092

Subgroups — C11×D15×D13⋊C3 #38788092

Order 25740.

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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
2C11×C3⋊(C5⋊(D13⋊C3))C211yesmaximal, characteristic, complemented
3C3×C5×C11×D13⋊C3C211yesmaximal, characteristic, complemented
4C11×D13×D15C311yesmaximal, characteristic, complemented
5D5×C11×D13⋊C3—31nomaximal
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7D3×C11×D13⋊C3—51nomaximal, Hall
8C11×C5⋊(D13⋊C3)—31no—
9D5×C11×C13⋊C3—31no—
10C5×C11×D13⋊C3—21no—
11C5×C11×D13⋊C3D311yescharacteristic, complemented
12C11×D195C2×C311yescharacteristic, complemented
13C11×C13×D15C2×C311yescharacteristic, complemented
14C3×C5×C11×D13C2×C311yescharacteristic, complemented
15D5×C11×D13—31noHall
16D3×C11×C13⋊C3—51no—
17C11×C3⋊(D13⋊C3)—51no—
18C3×C11×D13⋊C3D511yescharacteristic, complemented
19D15×D13⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
20C5×C11×C13⋊C3—21no—
21C5×C11×C13⋊C3C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C2×C3×C11×D15—131nomaximal, Hall
24D3×C11×D13—51no—
25C2×C11×D13⋊C3—151no—
26C11×D65—31no—
27D5×C11×C13—31no—
28C5×C11×D13C3×D311yescharacteristic, complemented
29C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
30C3⋊(C5⋊(D13⋊C3))C2×C1111yescharacteristic, complemented
31D15×C13⋊C3C2×C1111yescharacteristic, complemented
32C3×C5×D13⋊C3C2×C1111yescharacteristic, complemented
33C2×C32×C5×C11—131no—
34C3×C11×D15—131no—
35C3×C11×D15—131no—
36C11×D39—51no—
37D3×C11×C13—51no—
38C3×C11×D13C3×D511yescharacteristic, complemented
39C2×C11×C13⋊C3—151no—
40C11×D13⋊C3—21no—
41C11×D13⋊C3—151no—
42C11×D13⋊C3D1511yescharacteristic, direct product factor
43D13×D15C3×C1111yescharacteristic, complemented
44D5×D13⋊C3—31no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×C11×D15—131no—
47C2×C3×D5×C11—391no—
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⋊C3C2×D1511yescharacteristic, complemented
55C2×C3×D3×C11—651noHall
56D195C2×C3×C1111yescharacteristic, complemented
57C13×D15C2×C3×C1111yescharacteristic, complemented
58C3×C5×D13C2×C3×C1111yescharacteristic, complemented
59C5⋊(D13⋊C3)—31no—
60D5×C13⋊C3—31no—
61C5×D13⋊C3—21no—
62C5×D13⋊C3D3×C1111yescharacteristic, complemented
63C2×C3×C5×C11—131no—
64C2×C3×C5×C11—131no—
65C2×C3×C5×C11—261no—
66C11×D15—131no—
67C11×D15D13⋊C311yescharacteristic, direct product factor
68C3×D5×C11—391no—
69C3×D5×C11—391no—
70C2×C11×C13—151no—
71C11×D13—151no—
72C11×D13C3×D1511yescharacteristic, complemented
73D5×D13—31noHall
74C3⋊(D13⋊C3)—51no—
75D3×C13⋊C3—51no—
76C3×D13⋊C3D5×C1111yescharacteristic, complemented
77C2×D5×C11—391noHall
78C2×C32×C11—131no—
79C3×D3×C11—651no—
80C3×D3×C11—651no—
81C3×C5×C13C22×C3×C1111yescharacteristic, complemented
82C5×C13⋊C3—21no—
83C5×C13⋊C3C2×D3×C1111yescharacteristic, complemented
84C2×C3×D15—131noHall
85C3×C5×C11—131no—
86C3×C5×C11—261no—
87C3×C5×C11C2×D13⋊C311yescharacteristic, complemented
88D3×D13—51no—
89C2×D13⋊C3—151no—
90C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
91C22×C3×C11—1951no—
92C2×D3×C11—651no—
93D65—31no—
94C5×D13C3×D3×C1111yescharacteristic, complemented
95D5×C13—31no—
96C3×C13⋊C3C2×D5×C1111yescharacteristic, complemented, Hall
97C2×C5×C11—131no—
98D5×C11—31no—
99D5×C11—391no—
100C32×C11—131noHall
101C2×C32×C5—131no—
102C3×D15—131no—
103C3×D15—131no—
104D39—51no—
105C3×D13C3×D5×C1111yescharacteristic, complemented
106D3×C13—51no—
107C2×C13⋊C3—151no—
108D13⋊C3—21no—
109D13⋊C3—151no—
110D13⋊C3C11×D1511yescharacteristic, direct product factor
111C2×C3×C11—131no—
112C2×C3×C11—131no—
113C2×C3×C11—261no—
114C2×C3×C11—1951no—
115C2×C3×C11—1951no—
116D3×C11—51no—
117D3×C11—651no—
118C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
119C2×D15—131no—
120C2×C3×D5—391no—
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⋊C3C2×C11×D1511yescharacteristic, complemented
128C2×C3×D3—651noHall
129C3×C11—131no—
130C3×C11—261no—
131C3×C11D5×D13⋊C311yescharacteristic, complemented
132C2×C3×C5—131no—
133C2×C3×C5—131no—
134C2×C3×C5—261no—
135D15—131no—
136D15C11×D13⋊C311yescharacteristic, direct product factor
137C3×D5—391no—
138C3×D5—391no—
139C2×C13—151no—
140D13—151no—
141D13C3×C11×D1511yescharacteristic, complemented
142C2×C11—131no—
143C2×C11—151no—
144C2×C11—1951no—
145C2×D5—391noHall
146C2×C32—131no—
147C3×D3—651no—
148C3×D3—651no—
149C3×C5—131no—
150C3×C5—261no—
151C3×C5C2×C11×D13⋊C311yescharacteristic, complemented
152C13C2×C3×C11×D1511yescharacteristic, complemented, Sylow
153C22×C3—1951no—
154C2×D3—651no—
155C11D15×D13⋊C311yescharacteristic, direct product factor, Sylow
156C2×C5—131no—
157D5—31no—
158D5—391no—
159C32—131noSylow
160C2×C3—131no—
161C2×C3—131no—
162C2×C3—261no—
163C2×C3—1951no—
164C2×C3—1951no—
165D3—51no—
166D3—651no—
167C5D3×C11×D13⋊C311yescharacteristic, complemented, Sylow
168C22—1951noSylow
169C3—131no—
170C3—261no—
171C3D5×C11×D13⋊C311yescharacteristic, complemented
172C2—131no—
173C2—151no—
174C2—1951no—
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. C11×C3⋊(C5⋊(D13⋊C3))C2semidirect
3. C3×C5×C11×D13⋊C3C2semidirect
4. C11×D13×D15C3semidirect
6. C3×C5×C11×C13⋊C3C22semidirect
11. C5×C11×D13⋊C3D3semidirect
12. C11×D195C2×C3semidirect
13. C11×C13×D15C2×C3semidirect
14. C3×C5×C11×D13C2×C3semidirect
18. C3×C11×D13⋊C3D5semidirect
19. D15×D13⋊C3C11direct (N × H)
21. C5×C11×C13⋊C3C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
28. C5×C11×D13C3×D3semidirect
29. C3×C11×C13⋊C3C2×D5semidirect
30. C3⋊(C5⋊(D13⋊C3))C2×C11semidirect
31. D15×C13⋊C3C2×C11semidirect
32. C3×C5×D13⋊C3C2×C11semidirect
38. C3×C11×D13C3×D5semidirect
42. C11×D13⋊C3D15direct (N × H)
43. D13×D15C3×C11semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C3×C5×C13⋊C3C22×C11semidirect
52. C3×C11×C13C2×C3×D5semidirect
54. C11×C13⋊C3C2×D15semidirect
56. D195C2×C3×C11semidirect
57. C13×D15C2×C3×C11semidirect
58. C3×C5×D13C2×C3×C11semidirect
62. C5×D13⋊C3D3×C11semidirect
67. C11×D15D13⋊C3direct (N × H)
72. C11×D13C3×D15semidirect
76. C3×D13⋊C3D5×C11semidirect
81. C3×C5×C13C22×C3×C11semidirect
83. C5×C13⋊C3C2×D3×C11semidirect
87. C3×C5×C11C2×D13⋊C3semidirect
90. C11×C13C2×C3×D15semidirect
94. C5×D13C3×D3×C11semidirect
96. C3×C13⋊C3C2×D5×C11semidirect
105. C3×D13C3×D5×C11semidirect
110. D13⋊C3C11×D15direct (N × H)
118. C5×C13C2×C3×D3×C11semidirect
121. C5×C11D3×D13⋊C3semidirect
125. C3×C13C2×C3×D5×C11semidirect
127. C13⋊C3C2×C11×D15semidirect
131. C3×C11D5×D13⋊C3semidirect
136. D15C11×D13⋊C3direct (N × H)
141. D13C3×C11×D15semidirect
151. C3×C5C2×C11×D13⋊C3semidirect
152. C13C2×C3×C11×D15semidirect
155. C11D15×D13⋊C3direct (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
C11×C3⋊(C5⋊(D13⋊C3))2
C3×C5×C11×D13⋊C32
C11×D13×D153
D5×C11×D13⋊C33
D3×C11×D13⋊C35
D15×D13⋊C311
C2×C3×C11×D1513