Finite Group Databasebeta

← D5×C13⋊C3×D33 #38788106

Subgroups — D5×C13⋊C3×D33 #38788106

Order 25740.

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C13⋊C3×D165C211yesmaximal, characteristic, complemented
2C5×C13⋊C3×D33C211yesmaximal, characteristic, complemented
3C3×D5×C11×C13⋊C3C211yesmaximal, characteristic, complemented
4D5×C13×D33C311yesmaximal, characteristic, complemented
5D5×D11×C13⋊C3—31nomaximal
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C13⋊C3×D33—51nomaximal, Hall
8C13⋊C3×D55—31no—
9D5×C11×C13⋊C3—21no—
10D5×C11×C13⋊C3D311yescharacteristic, complemented
11C5×D11×C13⋊C3—31no—
12C13×D165C2×C311yescharacteristic, complemented
13C5×C13×D33C2×C311yescharacteristic, complemented
14C3×D5×C11×C13C2×C311yescharacteristic, complemented
15D5×C13×D11—31noHall
16C2×C3×C11×C13⋊C3—51no—
17C13⋊C3×D33—51no—
18C13⋊C3×D33D511yescharacteristic, direct product factor
19D3×D5×C13⋊C3—111nomaximal, Hall
20C5×C11×C13⋊C3—21no—
21C5×C11×C13⋊C3C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D5×D33—131nomaximal, Hall
24C2×C13×D33—51no—
25C2×D11×C13⋊C3—151no—
26C13×D55—31no—
27D5×C11×C13C3×D311yescharacteristic, complemented
28C5×C13×D11—31no—
29C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
30D15×C13⋊C3—111no—
31C5×D3×C13⋊C3—111no—
32C3×D5×C13⋊C3D1111yescharacteristic, complemented
33C3×D165—131no—
34C3×C5×D33—131no—
35C32×D5×C11—131no—
36C2×C3×C11×C13—51no—
37C13×D33—51no—
38C13×D33C3×D511yescharacteristic, complemented
39C2×C11×C13⋊C3—51no—
40C2×C11×C13⋊C3—101no—
41D11×C13⋊C3—31no—
42D11×C13⋊C3—151no—
43D3×D5×C13—111no—
44C2×D5×C13⋊C3—331no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46D5×D33C13⋊C311yescharacteristic, direct product factor
47C3×D5×D11—391no—
48C3×C5×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
49C2×C13×D11—151noHall
50C32×C5×C11—131noHall
51C2×D3×C13⋊C3—551noHall
52C3×C11×C13C2×C3×D511yescharacteristic, complemented
53C11×C13⋊C3—21no—
54C11×C13⋊C3D3×D511yescharacteristic, complemented
55C2×C3×D33—651noHall
56C13×D15—111no—
57C5×D3×C13—111no—
58C3×D5×C13C3×D1111yescharacteristic, complemented
59C2×C5×C13⋊C3—331no—
60D5×C13⋊C3—21no—
61D5×C13⋊C3—331no—
62D5×C13⋊C3D3311yescharacteristic, direct product factor
63D165C2×C13⋊C311yescharacteristic, complemented
64C5×D33C2×C13⋊C311yescharacteristic, complemented
65C3×D55—391no—
66C3×D5×C11—131no—
67C3×D5×C11—261no—
68C3×D5×C11C2×C13⋊C311yescharacteristic, complemented
69C3×C5×D11—391no—
70C2×C11×C13—51no—
71C13×D11—31no—
72C13×D11—151no—
73C2×D5×C13—331noHall
74C2×C3×C13⋊C3—51no—
75D3×C13⋊C3—111no—
76D3×C13⋊C3—551no—
77D5×D11—31noHall
78C2×C32×C11—651no—
79C3×D33—131no—
80C3×D33—651no—
81C3×C5×C13C2×C3×D1111yescharacteristic, complemented
82C5×C13⋊C3—21no—
83C5×C13⋊C3C2×D3311yescharacteristic, complemented
84C3×D3×D5—1431noHall
85C3×C5×C11—131no—
86C3×C5×C11—261no—
87C3×C5×C11C22×C13⋊C311yescharacteristic, complemented
88C2×D3×C13—551no—
89C22×C13⋊C3—1651no—
90C11×C13C3×D3×D511yescharacteristic, complemented, Hall
91C2×D33—51no—
92C2×C3×D11—1951no—
93C2×C5×C13—331no—
94D5×C13—331no—
95D5×C13C3×D3311yescharacteristic, complemented
96C3×C13⋊C3D5×D1111yescharacteristic, complemented, Hall
97D55—31no—
98C5×D11—31no—
99D5×C11D3×C13⋊C311yescharacteristic, complemented
100C32×C11—131noHall
101C3×D15—1431no—
102C3×C5×D3—1431no—
103C32×D5—131no—
104C2×C3×C13—51no—
105D3×C13—111no—
106D3×C13—551no—
107C2×C13⋊C3—51no—
108C2×C13⋊C3—101no—
109C2×C13⋊C3—331no—
110C2×C13⋊C3—1651no—
111C2×C3×C11—51no—
112C2×C3×C11—651no—
113C2×C3×C11—1301no—
114D33—51no—
115D33D5×C13⋊C311yescharacteristic, direct product factor
116C3×D11—391no—
117C3×D11—1951no—
118C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
119C2×C3×D5—4291no—
120D3×D5—111no—
121C5×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
122C22×C13—1651noHall
123C32×C5—131noHall
124C2×D11—151noHall
125C3×C13C3×D5×D1111yescharacteristic, complemented
126C13⋊C3—21no—
127C13⋊C3D5×D3311yescharacteristic, direct product factor
128C2×C3×D3—7151noHall
129C3×C11—131no—
130C3×C11—261no—
131C3×C11C2×D5×C13⋊C311yescharacteristic, complemented
132C2×C3×C5—4291no—
133D15—111no—
134C3×D5—131no—
135C3×D5—261no—
136C3×D5—4291no—
137C3×D5D11×C13⋊C311yescharacteristic, complemented
138C5×D3—111no—
139C2×C13—51no—
140C2×C13—331no—
141C2×C13—1651no—
142C2×C11—51no—
143D11—31no—
144D11—151no—
145C2×D5—331noHall
146C2×C32—651no—
147C3×D3—1431no—
148C3×D3—7151no—
149C3×C5—131no—
150C3×C5—261no—
151C3×C5C2×D11×C13⋊C311yescharacteristic, complemented
152C13C3×D5×D3311yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—551no—
155C11D3×D5×C13⋊C311yescharacteristic, complemented, Sylow
156C2×C5—331no—
157D5—331no—
158D5C13⋊C3×D3311yescharacteristic, direct product factor
159C32—131noSylow
160C2×C3—51no—
161C2×C3—651no—
162C2×C3—21451no—
163C2×C3—1301no—
164C2×C3—4291no—
165D3—111no—
166D3—551no—
167C5C2×C13⋊C3×D3311yescharacteristic, complemented, Sylow
168C22—1651noSylow
169C3—131no—
170C3—261no—
171C3D5×D11×C13⋊C311yescharacteristic, complemented
172C2—51no—
173C2—331no—
174C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C13C22×C3
LCSG ▷ C3×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×D165C2semidirect
2. C5×C13⋊C3×D33C2semidirect
3. C3×D5×C11×C13⋊C3C2semidirect
4. D5×C13×D33C3semidirect
6. C3×C5×C11×C13⋊C3C22semidirect
10. D5×C11×C13⋊C3D3semidirect
12. C13×D165C2×C3semidirect
13. C5×C13×D33C2×C3semidirect
14. C3×D5×C11×C13C2×C3semidirect
18. C13⋊C3×D33D5direct (N × H)
21. C5×C11×C13⋊C3C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
27. D5×C11×C13C3×D3semidirect
29. C3×C11×C13⋊C3C2×D5semidirect
32. C3×D5×C13⋊C3D11semidirect
38. C13×D33C3×D5semidirect
45. C5×C11×C13C2×C3×D3semidirect
46. D5×D33C13⋊C3direct (N × H)
48. C3×C5×C13⋊C3C2×D11semidirect
52. C3×C11×C13C2×C3×D5semidirect
54. C11×C13⋊C3D3×D5semidirect
58. C3×D5×C13C3×D11semidirect
62. D5×C13⋊C3D33direct (N × H)
63. D165C2×C13⋊C3semidirect
64. C5×D33C2×C13⋊C3semidirect
68. C3×D5×C11C2×C13⋊C3semidirect
81. C3×C5×C13C2×C3×D11semidirect
83. C5×C13⋊C3C2×D33semidirect
87. C3×C5×C11C22×C13⋊C3semidirect
90. C11×C13C3×D3×D5semidirect
95. D5×C13C3×D33semidirect
96. C3×C13⋊C3D5×D11semidirect
99. D5×C11D3×C13⋊C3semidirect
115. D33D5×C13⋊C3direct (N × H)
118. C5×C13C2×C3×D33semidirect
121. C5×C11C2×D3×C13⋊C3semidirect
125. C3×C13C3×D5×D11semidirect
127. C13⋊C3D5×D33direct (N × H)
131. C3×C11C2×D5×C13⋊C3semidirect
137. C3×D5D11×C13⋊C3semidirect
151. C3×C5C2×D11×C13⋊C3semidirect
152. C13C3×D5×D33semidirect
155. C11D3×D5×C13⋊C3semidirect
158. D5C13⋊C3×D33direct (N × H)
167. C5C2×C13⋊C3×D33semidirect
171. C3D5×D11×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×D1652
C5×C13⋊C3×D332
C3×D5×C11×C13⋊C32
D5×C13×D333
D5×D11×C13⋊C33
C2×C13⋊C3×D335
D3×D5×C13⋊C311
C3×D5×D3313