Finite Group Databasebeta

← C23×D5×#41 #13013181

Subgroups — C23×D5×#41 #13013181

Order 1280.

65470 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×#41C211yesmaximal, characteristic, complemented
2C22×D5×#41C21112yesmaximal, direct product factor
3C23×Q8×D5C211yesmaximal, characteristic, complemented
4C23×#713C211yesmaximal, characteristic, complemented
5C23×D4×D5C213yesmaximal, complemented
6C23×#711C213yesmaximal, complemented
7C23×#709C213yesmaximal, complemented
8C24×C4×D5C213yesmaximal, complemented
9C25×D5C2213yes—
10C22×C5×#41C22156yescomplemented
11C23×C5×Q8C2211yescharacteristic, complemented
12C23×C5×D4C2213yescomplemented
13C24×C4×C5C2213yescomplemented
14C23×C22⋊D5C2216yescomplemented
15C24×Dic5C2213yescomplemented
16C2×D5×#41C2211792yesdirect product factor
17C22×#713C22156yescomplemented
18C22×Q8×D5C22156yescomplemented
19C22×#711C221168yescomplemented
20C22×D4×D5C221168yescomplemented
21C22×#709C221168yescomplemented
22C23×D20C2213yescomplemented
23C23×C4×D5C2211yescharacteristic
24C23×C4×D5C2213yes—
25C23×C4×D5C221168yescomplemented
26C23×C4×D5C2213yescomplemented
27C23×C4×D5C2213yescomplemented
28C23×Dic10C2213yescomplemented
29C24×#41—51nomaximal, Sylow
30C25×C5C2313yes—
31C24×D5—248no—
32C24×D5C2313yes—
33C24×D5C23184yes—
34C24×D5C2311yescharacteristic
35C2×C5×#41C231448yescomplemented
36C22×C5×Q8C23128yescomplemented
37C22×C5×D4C23184yescomplemented
38C23×C4×C5C2313yes—
39C23×C4×C5C2311yescharacteristic
40C23×C4×C5C23184yescomplemented
41C22×C22⋊D5C231168yescomplemented
42C23×Dic5C2313yes—
43C23×Dic5C2311yescharacteristic
44C23×Dic5C23184yescomplemented
45D5×#41C2314096yesdirect product factor
46C2×#713C231448yescomplemented
47C2×Q8×D5C231448yescomplemented
48C2×#711C2311344yescomplemented
49C2×D4×D5C2311344yescomplemented
50C2×#709C2311344yescomplemented
51C22×D20C23184yescomplemented
52C22×C4×D5C23128yes—
53C22×C4×D5C23184yes—
54C22×C4×D5C2311344yescomplemented
55C22×C4×D5C23184yescomplemented
56C22×C4×D5C23184yescomplemented
57C22×Dic10C23184yescomplemented
58C23×#41—5112no—
59C23×#41—51no—
60C23×#41—53no—
61C23×#41—53no—
62C23×#41D511yescharacteristic, direct product factor
63C24×Q8—51no—
64C24×D4—53no—
65C25×C4—53no—
66C24×C5—224no—
67C24×C5C24142yes—
68C24×C5C2411yescharacteristic
69C23×D5—224no—
70C23×D5—2672no—
71C23×D5#41116yesdirect product factor
72C23×D5C24142yes—
73C23×D5C241336yes—
74C23×D5C24114yes—
75C5×#41C241512yescomplemented
76C2×C5×Q8C241112yescomplemented
77C2×C5×D4C241336yescomplemented
78C22×C4×C5C24142yes—
79C22×C4×C5C24114yes—
80C22×C4×C5C241336yescomplemented
81C2×C22⋊D5C241672yescomplemented
82C22×Dic5C24142yes—
83C22×Dic5C24114yes—
84C22×Dic5C241336yescomplemented
85#713C241512yescomplemented
86Q8×D5C241512yescomplemented
87#711C2411536yescomplemented
88D4×D5C2411536yescomplemented
89#709C2411536yescomplemented
90C2×D20C241336yescomplemented
91C2×C4×D5C241112yes—
92C2×C4×D5C241336yes—
93C2×C4×D5C2411536yescomplemented
94C2×C4×D5C241336yescomplemented
95C2×C4×D5C241336yescomplemented
96C2×Dic10C241336yescomplemented
97C26—53no—
98C22×#41—51792no—
99C22×#41—556no—
100C22×#41—5168no—
101C22×#41—5168no—
102C22×#41C2×D5156yesdirect product factor
103C23×Q8—556no—
104C23×Q8—53no—
105C23×Q8C2×D511yescharacteristic, complemented
106C23×D4—56no—
107C23×D4—5168no—
108C23×D4—53no—
109C23×D4C2×D513yescomplemented
110C24×C4—53no—
111C24×C4—53no—
112C24×C4—53no—
113C24×C4—51no—
114C24×C4—53no—
115C24×C4—5168no—
116C24×C4C2×D513yescomplemented
117C23×C5—2168no—
118C23×C5C2×#4118yescomplemented
119C23×C5C25184yes—
120C23×C5C2517yes—
121C22×D5—2168no—
122C22×D5—21344no—
123C22×D5C2×#411112yesdirect product factor
124C22×D5C25184yes—
125C22×D5C251192yes—
126C22×D5C25128yes—
127C5×Q8C25164yescomplemented
128C5×D4C251192yescomplemented
129C2×C4×C5C25184yes—
130C2×C4×C5C25128yes—
131C2×C4×C5C251192yescomplemented
132C22⋊D5C251384yescomplemented
133C2×Dic5C25184yes—
134C2×Dic5C25128yes—
135C2×Dic5C251192yescomplemented
136D20C251192yescomplemented
137C4×D5C25164yes—
138C4×D5C251192yes—
139C4×D5C251192yescomplemented
140C4×D5C251192yescomplemented
141Dic10C251192yescomplemented
142C25—51no—
143C25—584no—
144C25—53no—
145C25—1048no—
146C25C22×D513yes—
147C2×#41—54096no—
148C2×#41—5448no—
149C2×#41—51344no—
150C2×#41—51344no—
151C2×#41C22×D51448yesdirect product factor
152C22×Q8—5448no—
153C22×Q8—584no—
154C22×Q8C22×D5128yescomplemented
155C22×D4—5168no—
156C22×D4—51344no—
157C22×D4—584no—
158C22×D4C22×D5184yescomplemented
159C23×C4—51no—
160C23×C4—53no—
161C23×C4—584no—
162C23×C4—528no—
163C23×C4—584no—
164C23×C4—584no—
165C23×C4—584no—
166C23×C4—51344no—
167C23×C4C22×D513yes—
168C23×C4C22×D511yescharacteristic
169C23×C4C22×D5184yescomplemented
170C22×C5—2168no—
171C22×C5C22×#41128yescomplemented
172C22×C5C26124yes—
173C22×C5C2617yes—
174C2×D5—2168no—
175C2×D5—2384no—
176C2×D5C22×#411112yesdirect product factor
177C2×D5C26124yes—
178C2×D5C2618yes—
179C4×C5C26124yes—
180C4×C5C2618yes—
181Dic5C26124yes—
182Dic5C2618yes—
183C24—224no—
184C24—516no—
185C24—514no—
186C24—5336no—
187C24—542no—
188C24—10672no—
189C24—1024no—
190C24C23×D5142yes—
191C24C23×D511yescharacteristic
192#41—5512no—
193#41—51536no—
194#41—51536no—
195#41C23×D51512yesdirect product factor
196C2×Q8—5512no—
197C2×Q8—5336no—
198C2×Q8C23×D51112yescomplemented
199C2×D4—5672no—
200C2×D4—51536no—
201C2×D4—5336no—
202C2×D4C23×D51336yescomplemented
203C22×C4—514no—
204C22×C4—542no—
205C22×C4—5336no—
206C22×C4—5112no—
207C22×C4—5336no—
208C22×C4—5336no—
209C22×C4—5336no—
210C22×C4—51536no—
211C22×C4C23×D5114yes—
212C22×C4C23×D5142yes—
213C22×C4C23×D51336yescomplemented
214C2×C5—224no—
215C2×C5C23×#41114yescomplemented
216C2×C5C2711yescharacteristic
217D5—224no—
218D5C23×#41116yesdirect product factor
219C23—2168no—
220C23—5112no—
221C23—528no—
222C23—5192no—
223C23—584no—
224C23—101344no—
225C23—10168no—
226C23D5×#4118yesdirect product factor
227C23C24×D5184yes—
228C23C24×D517yes—
229Q8—5192no—
230Q8C24×D5164yescomplemented
231D4—5384no—
232D4—5192no—
233D4C24×D51192yescomplemented
234C2×C4—528no—
235C2×C4—584no—
236C2×C4—5192no—
237C2×C4—564no—
238C2×C4—5192no—
239C2×C4—5192no—
240C2×C4—5192no—
241C2×C4C24×D5128yes—
242C2×C4C24×D5184yes—
243C2×C4C24×D51192yescomplemented
244C5C24×#4111yescharacteristic, complemented, Sylow
245C22—2168no—
246C22—5112no—
247C22—58no—
248C22—524no—
249C22—10384no—
250C22—10168no—
251C22C2×D5×#41128yesdirect product factor
252C22C25×D5124yes—
253C22C25×D517yes—
254C4—58no—
255C4—524no—
256C4C25×D518yes—
257C4C25×D5124yes—
258C2—224no—
259C2—516no—
260C2—1024no—
261C2C22×D5×#41114yesdirect product factor
262C2C26×D511yescharacteristic
subgroupG/H
centerC23×C4C22×D5
commutator, cosocleC2×C5C27
FrattiniC2C26×D5
FittingC23×C5×#41C2
socleC24×C5C24
hypercenterC23×#41D5
hypocenterC5C24×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C23×C5×#41C2semidirect
2. C22×D5×#41C2direct (N × H)
3. C23×Q8×D5C2semidirect
4. C23×#713C2semidirect
5. C23×D4×D5C2semidirect
6. C23×#711C2semidirect
7. C23×#709C2semidirect
8. C24×C4×D5C2semidirect
10. C22×C5×#41C22semidirect
11. C23×C5×Q8C22semidirect
12. C23×C5×D4C22semidirect
13. C24×C4×C5C22semidirect
14. C23×C22⋊D5C22semidirect
15. C24×Dic5C22semidirect
16. C2×D5×#41C22direct (N × H)
17. C22×#713C22semidirect
18. C22×Q8×D5C22semidirect
19. C22×#711C22semidirect
20. C22×D4×D5C22semidirect
21. C22×#709C22semidirect
22. C23×D20C22semidirect
25. C23×C4×D5C22semidirect
26. C23×C4×D5C22semidirect
27. C23×C4×D5C22semidirect
28. C23×Dic10C22semidirect
35. C2×C5×#41C23semidirect
36. C22×C5×Q8C23semidirect
37. C22×C5×D4C23semidirect
40. C23×C4×C5C23semidirect
41. C22×C22⋊D5C23semidirect
44. C23×Dic5C23semidirect
45. D5×#41C23direct (N × H)
46. C2×#713C23semidirect
47. C2×Q8×D5C23semidirect
48. C2×#711C23semidirect
49. C2×D4×D5C23semidirect
50. C2×#709C23semidirect
51. C22×D20C23semidirect
54. C22×C4×D5C23semidirect
55. C22×C4×D5C23semidirect
56. C22×C4×D5C23semidirect
57. C22×Dic10C23semidirect
62. C23×#41D5direct (N × H)
71. C23×D5#41direct (N × H)
75. C5×#41C24semidirect
76. C2×C5×Q8C24semidirect
77. C2×C5×D4C24semidirect
80. C22×C4×C5C24semidirect
81. C2×C22⋊D5C24semidirect
84. C22×Dic5C24semidirect
85. #713C24semidirect
86. Q8×D5C24semidirect
87. #711C24semidirect
88. D4×D5C24semidirect
89. #709C24semidirect
90. C2×D20C24semidirect
93. C2×C4×D5C24semidirect
94. C2×C4×D5C24semidirect
95. C2×C4×D5C24semidirect
96. C2×Dic10C24semidirect
102. C22×#41C2×D5direct (N × H)
105. C23×Q8C2×D5semidirect
109. C23×D4C2×D5semidirect
116. C24×C4C2×D5semidirect
118. C23×C5C2×#41semidirect
123. C22×D5C2×#41direct (N × H)
127. C5×Q8C25semidirect
128. C5×D4C25semidirect
131. C2×C4×C5C25semidirect
132. C22⋊D5C25semidirect
135. C2×Dic5C25semidirect
136. D20C25semidirect
139. C4×D5C25semidirect
140. C4×D5C25semidirect
141. Dic10C25semidirect
151. C2×#41C22×D5direct (N × H)
154. C22×Q8C22×D5semidirect
158. C22×D4C22×D5semidirect
169. C23×C4C22×D5semidirect
171. C22×C5C22×#41semidirect
176. C2×D5C22×#41direct (N × H)
195. #41C23×D5direct (N × H)
198. C2×Q8C23×D5semidirect
202. C2×D4C23×D5semidirect
213. C22×C4C23×D5semidirect
215. C2×C5C23×#41semidirect
218. D5C23×#41direct (N × H)
226. C23D5×#41direct (N × H)
230. Q8C24×D5semidirect
233. D4C24×D5semidirect
243. C2×C4C24×D5semidirect
244. C5C24×#41semidirect
251. C22C2×D5×#41direct (N × H)
261. C2C22×D5×#41direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×#412
C22×D5×#412
C23×Q8×D52
C23×#7132
C23×D4×D52
C23×#7112
C23×#7092
C24×C4×D52
C24×#415