Finite Group Databasebeta

← C3×C5×D5×D39 #26043749

Subgroups — C3×C5×D5×D39 #26043749

Order 11700.

212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C3×C5×D195C211yesmaximal, characteristic, complemented
2C3×C52×D39C211yesmaximal, characteristic, complemented
3C32×C5×D5×C13C211yesmaximal, characteristic, complemented
4C5×D5×D39C311yesmaximal, characteristic, direct product factor
5C3×C5×D5×D13—31nomaximal
6C32×C52×C13C2211yescharacteristic, complemented, Hall
7C2×C3×C5×D39—51nomaximal
8C3×D5×D39C511yesmaximal, characteristic, direct product factor
9C5×D195C2×C311yescharacteristic, complemented
10C52×D39C2×C311yescharacteristic, complemented
11C3×C5×D65—31no—
12C3×C5×D5×C13—21no—
13C3×C5×D5×C13D311yescharacteristic, complemented
14C3×C5×D5×C13C2×C311yescharacteristic, complemented
15C3×C52×D13—31no—
16C5×D5×D13—31noHall
17C2×C32×C5×C13—51no—
18C3×D195C2×C511yescharacteristic, complemented
19C3×C5×D39—22no—
20C3×C5×D39—51no—
21C3×C5×D39D511yescharacteristic, direct product factor
22C3×C5×D39C2×C511yescharacteristic, complemented
23C32×D5×C13C2×C511yescharacteristic, complemented
24C3×C52×C13—21no—
25C3×C52×C13C2×D311yescharacteristic, complemented
26C3×C52×C13C22×C311yescharacteristic, complemented
27C3×C5×D3×D5—131nomaximal, Hall
28C2×C5×D39—51no—
29C2×C3×C5×D13—151no—
30D5×D39C3×C511yescharacteristic, direct product factor
31C3×D5×D13—31no—
32C5×D65—31no—
33C5×D5×C13C3×D311yescharacteristic, complemented
34C52×D13—31no—
35C32×C5×C13—22no—
36C32×C5×C13C2×D511yescharacteristic, complemented
37C32×C5×C13C22×C511yescharacteristic, complemented
38C2×C3×D39—51noHall
39C3×C5×D15—131no—
40C3×C52×D3—131no—
41C32×C5×D5D1311yescharacteristic, complemented
42C2×C3×C5×C13—51no—
43C2×C3×C5×C13—51no—
44C2×C3×C5×C13—101no—
45D195C2×C3×C511yescharacteristic, complemented
46C5×D39—22no—
47C5×D39—51no—
48C5×D39C3×D511yescharacteristic, direct product factor
49C5×D39C2×C3×C511yescharacteristic, complemented
50C3×D65—31no—
51C3×D5×C13—21no—
52C3×D5×C13C5×D311yescharacteristic, complemented
53C3×D5×C13C2×C3×C511yescharacteristic, complemented
54C3×C5×D13—31no—
55C3×C5×D13—31no—
56C3×C5×D13—62no—
57C3×C5×D13—151no—
58C52×C13C2×C3×D311yescharacteristic, complemented, Hall
59C2×C3×C5×D5—391no—
60C5×D3×D5—131no—
61C2×C5×D13—151no—
62D5×D13—31no—
63C2×C32×C13—51no—
64C3×D39—51no—
65C3×D39C5×D511yescharacteristic, direct product factor
66C32×C52C2×D1311yescharacteristic, complemented, Hall
67C3×C5×C13—22no—
68C3×C5×C13—22no—
69C3×C5×C13—21no—
70C3×C5×C13—21no—
71C3×C5×C13—42no—
72C3×C5×C13D3×D511yescharacteristic, complemented
73C3×C5×C13C2×C3×D511yescharacteristic, complemented
74C3×C5×C13C2×C5×D311yescharacteristic, complemented
75C3×C5×C13C22×C3×C511yescharacteristic, complemented
76C2×C3×C5×D3—651no—
77C3×D3×D5—131no—
78C2×D39—51no—
79C2×C3×D13—151no—
80C2×C3×C52—391no—
81C5×D15—131no—
82C52×D3—131no—
83C3×C5×D5—21no—
84C3×C5×D5—391no—
85C3×C5×D5C3×D1311yescharacteristic, complemented
86C3×C5×D5D3911yescharacteristic, direct product factor
87C2×C5×C13—51no—
88D65—31no—
89C5×D13—31no—
90C5×D13—31no—
91C5×D13—62no—
92C5×D13—151no—
93D5×C13C3×C5×D311yescharacteristic, complemented
94C32×C13C2×C5×D511yescharacteristic, complemented, Hall
95C2×C5×D5—391noHall
96C2×C32×C5—51no—
97C3×D15—131no—
98C3×C5×D3—131no—
99C3×C5×D3—131no—
100C3×C5×D3—262no—
101C3×C5×D3—651no—
102C32×D5C5×D1311yescharacteristic, complemented
103C2×C3×C13—51no—
104C2×C3×C13—51no—
105C2×C3×C13—101no—
106D39—51no—
107D39C3×C5×D511yescharacteristic, direct product factor
108C3×D13—31no—
109C3×D13—151no—
110C3×C52—21no—
111C3×C52C2×C3×D1311yescharacteristic, complemented
112C3×C52C2×D3911yescharacteristic, complemented
113C5×C13—22no—
114C5×C13C3×D3×D511yescharacteristic, complemented
115C5×C13C2×C3×C5×D311yescharacteristic, complemented
116C22×C3×C5—1951no—
117C2×C5×D3—651no—
118C2×C3×D5—391no—
119D3×D5—131no—
120C2×D13—151noHall
121C2×C52—391no—
122C5×D5—391no—
123C5×D5C3×D3911yescharacteristic, direct product factor
124C32×C5—22no—
125C32×C5D5×D1311yescharacteristic, complemented
126C32×C5C2×C5×D1311yescharacteristic, complemented
127C3×C13—21no—
128C3×C13C5×D3×D511yescharacteristic, complemented
129C3×C13C2×C3×C5×D511yescharacteristic, complemented
130C2×C3×D3—651noHall
131C2×C3×C5—51no—
132C2×C3×C5—51no—
133C2×C3×C5—101no—
134C2×C3×C5—391no—
135C2×C3×C5—391no—
136C2×C3×C5—782no—
137C2×C3×C5—1951no—
138D15—131no—
139C3×D5—21no—
140C3×D5—391no—
141C3×D5C3×C5×D1311yescharacteristic, complemented
142C3×D5C5×D3911yescharacteristic, direct product factor
143C5×D3—131no—
144C5×D3—131no—
145C5×D3—262no—
146C5×D3—651no—
147C2×C13—51no—
148D13—31no—
149D13—151no—
150C52C2×C3×D3911yescharacteristic, complemented, Sylow
151C22×C5—1951no—
152C2×D5—391no—
153C2×C32—51no—
154C3×D3—131no—
155C3×D3—651no—
156C3×C5—21no—
157C3×C5—21no—
158C3×C5—22no—
159C3×C5—22no—
160C3×C5—42no—
161C3×C5C3×D5×D1311yescharacteristic, complemented
162C3×C5D5×D3911yescharacteristic, direct product factor
163C3×C5C2×C3×C5×D1311yescharacteristic, complemented
164C3×C5C2×C5×D3911yescharacteristic, complemented
165C13C3×C5×D3×D511yescharacteristic, complemented, Sylow
166C22×C3—1951no—
167C2×D3—651no—
168C2×C5—51no—
169C2×C5—391no—
170C2×C5—391no—
171C2×C5—782no—
172C2×C5—1951no—
173D5—391no—
174D5C3×C5×D3911yescharacteristic, direct product factor
175C32C5×D5×D1311yescharacteristic, complemented, Sylow
176C2×C3—51no—
177C2×C3—51no—
178C2×C3—101no—
179C2×C3—391no—
180C2×C3—1951no—
181D3—131no—
182D3—651no—
183C5—22no—
184C5C3×D5×D3911yescharacteristic, direct product factor
185C5C2×C3×C5×D3911yescharacteristic, complemented
186C22—1951noSylow
187C3—21no—
188C3C3×C5×D5×D1311yescharacteristic, complemented
189C3C5×D5×D3911yescharacteristic, direct product factor
190C2—51no—
191C2—391no—
192C2—1951no—
subgroupG/H
center, hypercenterC3×C5D5×D39
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D195C2semidirect
2. C3×C52×D39C2semidirect
3. C32×C5×D5×C13C2semidirect
4. C5×D5×D39C3direct (N × H)
6. C32×C52×C13C22semidirect
8. C3×D5×D39C5direct (N × H)
9. C5×D195C2×C3semidirect
10. C52×D39C2×C3semidirect
13. C3×C5×D5×C13D3semidirect
14. C3×C5×D5×C13C2×C3semidirect
18. C3×D195C2×C5semidirect
21. C3×C5×D39D5direct (N × H)
22. C3×C5×D39C2×C5semidirect
23. C32×D5×C13C2×C5semidirect
25. C3×C52×C13C2×D3semidirect
26. C3×C52×C13C22×C3semidirect
30. D5×D39C3×C5direct (N × H)
33. C5×D5×C13C3×D3semidirect
36. C32×C5×C13C2×D5semidirect
37. C32×C5×C13C22×C5semidirect
41. C32×C5×D5D13semidirect
45. D195C2×C3×C5semidirect
48. C5×D39C3×D5direct (N × H)
49. C5×D39C2×C3×C5semidirect
52. C3×D5×C13C5×D3semidirect
53. C3×D5×C13C2×C3×C5semidirect
58. C52×C13C2×C3×D3semidirect
65. C3×D39C5×D5direct (N × H)
66. C32×C52C2×D13semidirect
72. C3×C5×C13D3×D5semidirect
73. C3×C5×C13C2×C3×D5semidirect
74. C3×C5×C13C2×C5×D3semidirect
75. C3×C5×C13C22×C3×C5semidirect
85. C3×C5×D5C3×D13semidirect
86. C3×C5×D5D39direct (N × H)
93. D5×C13C3×C5×D3semidirect
94. C32×C13C2×C5×D5semidirect
102. C32×D5C5×D13semidirect
107. D39C3×C5×D5direct (N × H)
111. C3×C52C2×C3×D13semidirect
112. C3×C52C2×D39semidirect
114. C5×C13C3×D3×D5semidirect
115. C5×C13C2×C3×C5×D3semidirect
123. C5×D5C3×D39direct (N × H)
125. C32×C5D5×D13semidirect
126. C32×C5C2×C5×D13semidirect
128. C3×C13C5×D3×D5semidirect
129. C3×C13C2×C3×C5×D5semidirect
141. C3×D5C3×C5×D13semidirect
142. C3×D5C5×D39direct (N × H)
150. C52C2×C3×D39semidirect
161. C3×C5C3×D5×D13semidirect
162. C3×C5D5×D39direct (N × H)
163. C3×C5C2×C3×C5×D13semidirect
164. C3×C5C2×C5×D39semidirect
165. C13C3×C5×D3×D5semidirect
174. D5C3×C5×D39direct (N × H)
175. C32C5×D5×D13semidirect
184. C5C3×D5×D39direct (N × H)
185. C5C2×C3×C5×D39semidirect
188. C3C3×C5×D5×D13semidirect
189. C3C5×D5×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D1952
C3×C52×D392
C32×C5×D5×C132
C5×D5×D393
C3×C5×D5×D133
C2×C3×C5×D395
C3×D5×D395
C3×C5×D3×D513