Finite Group Databasebeta

← D4×D15⋊D5 #72230731

Subgroups — D4×D15⋊D5 #72230731

Order 2400.

1052 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C22×D15⋊D5C212yesmaximal, complemented
2C5×D4×D15C212yesmaximal, complemented
3C3×D4×C5⋊D5C211yesmaximal, characteristic, complemented
4#11925664C212yesmaximal, complemented
5#11925663C214yesmaximal, complemented
6#11925655C211yesmaximal, characteristic, complemented
7#11925654C212yesmaximal, complemented
8C4×D15⋊D5C211yesmaximal, characteristic, complemented
9D4×D52—31nomaximal, Hall
10C22×C5×D15C2214yescomplemented
11C22×C3×C5⋊D5C2212yescomplemented
12C2×D15⋊D5—28no—
13C2×D15⋊D5C2211yescharacteristic
14C2×D15⋊D5C2212yescomplemented
15C2×D15⋊D5C2214yescomplemented
16C3×C52×D4C2211yescharacteristic, complemented
17C5×#1220C2214yescomplemented
18C5×D60C2212yescomplemented
19C4×C5×D15C2212yescomplemented
20C3×C22⋊(C5⋊D5)C2212yescomplemented
21C3×C4⋊(C5⋊D5)C2211yescharacteristic, complemented
22C3×C4×C5⋊D5C2211yescharacteristic, complemented
23#10597128C2212yescomplemented
24#10597127C2214yescomplemented
25#10597126C2211yescharacteristic, complemented
26#10597125C2212yescomplemented
27D3×D4×D5—52nomaximal
28C22×D52—32no—
29D4×C5⋊D5D311yescharacteristic, complemented
30C5×D4×D5—32no—
31#87886—32no—
32D5×C22⋊D5—34no—
33#87877—31no—
34D5×D20—32no—
35C4×D52—31no—
36C22×C3×C52C2312yescomplemented
37C2×C5×D15—28no—
38C2×C5×D15C2312yes—
39C2×C5×D15C2314yescomplemented
40C2×C3×C5⋊D5—24no—
41C2×C3×C5⋊D5C2311yescharacteristic
42C2×C3×C5⋊D5C2312yescomplemented
43D15⋊D5—28no—
44D15⋊D5—24no—
45D15⋊D5D414yesdirect product factor
46C3×C4×C52C2311yescharacteristic, complemented
47C5×Dic15C2312yescomplemented
48C3×#1039C2311yescharacteristic, complemented
49C22×D3×D5—54no—
50D4×D15D512yescomplemented
51C5×D3×D4—52no—
52C3×D4×D5—52no—
53C3×D4×D5—102no—
54#6790—54no—
55D3×C22⋊D5—54no—
56D5×#67—54no—
57#6777—52no—
58D3×D20—52no—
59D5×D12—52no—
60C4×D3×D5—52no—
61C22×C5⋊D5C2×D312yescomplemented
62C22×C5×D5—34no—
63C2×D52—31no—
64C2×D52—32no—
65C2×D52—34no—
66C2×D52—68no—
67C52×D4C2×D311yescharacteristic, complemented
68C22⋊(C5⋊D5)C2×D312yescomplemented
69C4⋊(C5⋊D5)C2×D311yescharacteristic, complemented
70C4×C5⋊D5C2×D311yescharacteristic, complemented
71C5×C22⋊D5—34no—
72C5×D20—32no—
73C4×C5×D5—32no—
74#6038—34no—
75#6037—32no—
76#6036—31no—
77D5×Dic5—32no—
78C2×D4×D5—152no—
79C2×C3×C52—22no—
80C2×C3×C52C2411yescharacteristic
81C5×D15—24no—
82C5×D15C2×D414yescomplemented
83C3×C5⋊D5—22no—
84C3×C5⋊D5C2×D412yescomplemented
85C22×D15C2×D514yescomplemented
86C22×C5×D3—54no—
87C22×C3×D5—54no—
88C22×C3×D5—104no—
89C2×D3×D5—52no—
90C2×D3×D5—54no—
91C2×D3×D5—54no—
92C2×D3×D5—54no—
93C2×D3×D5—1016no—
94C3×C5×D4—22no—
95C3×C5×D4C2×D512yescomplemented
96#1220C2×D514yescomplemented
97D60C2×D512yescomplemented
98C4×D15C2×D512yescomplemented
99C5×#67—54no—
100C5×D12—52no—
101C4×C5×D3—52no—
102C3×C22⋊D5—54no—
103C3×C22⋊D5—104no—
104C3×D20—52no—
105C3×D20—102no—
106C3×C4×D5—52no—
107C3×C4×D5—102no—
108#1203—54no—
109#1202—54no—
110#1201—54no—
111#1200—52no—
112D3×Dic5—52no—
113D5×Dic3—52no—
114C22×C52C22×D312yescomplemented
115C2×C5⋊D5—24no—
116C2×C5⋊D5C22×D311yescharacteristic
117C2×C5⋊D5C22×D312yescomplemented
118C2×C5×D5—32no—
119C2×C5×D5—34no—
120C2×C5×D5—68no—
121D52—34no—
122D52—68no—
123D52—64no—
124C4×C52C22×D311yescharacteristic, complemented
125#1039C22×D311yescharacteristic, complemented
126C5×Dic5—32no—
127C2×D3×D4—251noHall
128C23×D5—154no—
129C2×C5×D4—152no—
130C2×C22⋊D5—154no—
131D4×D5—32no—
132D4×D5—52no—
133D4×D5—102no—
134D4×D5—152no—
135D4×D5—152no—
136D4×D5—154no—
137D4×D5—154no—
138C2×D20—152no—
139C2×C4×D5—152no—
140C3×C52C22×D411yescharacteristic, complemented, Hall
141C22×C3×C5—24no—
142C22×C3×C5C22×D514yescomplemented
143C2×D15—28no—
144C2×D15C22×D512yes—
145C2×D15C22×D514yescomplemented
146C2×C5×D3—52no—
147C2×C5×D3—54no—
148C2×C5×D3—108no—
149C2×C3×D5—52no—
150C2×C3×D5—54no—
151C2×C3×D5—102no—
152C2×C3×D5—104no—
153C2×C3×D5—108no—
154C2×C3×D5—208no—
155D3×D5—58no—
156D3×D5—108no—
157D3×D5—108no—
158D3×D5—108no—
159C3×C4×C5—22no—
160C3×C4×C5C22×D512yescomplemented
161Dic15C22×D512yescomplemented
162C3×Dic5—52no—
163C3×Dic5—102no—
164C5×Dic3—52no—
165C2×C52—22no—
166C2×C52C23×D311yescharacteristic
167C5⋊D5—22no—
168C5⋊D5D3×D412yescomplemented
169C5×D5—34no—
170C5×D5—64no—
171C23×D3—252no—
172C2×C3×D4—251no—
173C2×#67—252no—
174D3×D4—52no—
175D3×D4—252no—
176D3×D4—254no—
177C2×D12—251no—
178C2×C4×D3—251no—
179C23×C5—154no—
180C22×D5—34no—
181C22×D5—54no—
182C22×D5—104no—
183C22×D5—152no—
184C22×D5—154no—
185C22×D5—154no—
186C22×D5—154no—
187C22×D5—3016no—
188C5×D4—22no—
189C5×D4—154no—
190C5×D4—152no—
191C5×D4D3×D512yescomplemented
192C2×C4×C5—152no—
193C22⋊D5—34no—
194C22⋊D5—54no—
195C22⋊D5—104no—
196C22⋊D5—154no—
197C22⋊D5—154no—
198C2×Dic5—152no—
199D20—32no—
200D20—52no—
201D20—102no—
202D20—154no—
203C4×D5—32no—
204C4×D5—52no—
205C4×D5—102no—
206C4×D5—152no—
207C4×D5—152no—
208C22×D4—751noSylow
209C2×C3×C5—24no—
210C2×C3×C5—22no—
211C2×C3×C5—44no—
212C2×C3×C5C23×D512yes—
213D15—24no—
214D15D4×D514yescomplemented
215C3×D5—54no—
216C3×D5—104no—
217C3×D5—104no—
218C3×D5—204no—
219C5×D3—54no—
220C5×D3—104no—
221C52C2×D3×D411yescharacteristic, complemented, Sylow
222C23×C3—252no—
223C22×D3—54no—
224C22×D3—251no—
225C22×D3—252no—
226C22×D3—254no—
227C22×D3—508no—
228C3×D4—252no—
229C3×D4—251no—
230C3×D4D5211yescharacteristic, complemented
231C2×C3×C4—251no—
232#67—54no—
233#67—254no—
234C2×Dic3—251no—
235D12—52no—
236D12—252no—
237C4×D3—52no—
238C4×D3—252no—
239C22×C5—24no—
240C22×C5—152no—
241C22×C5—154no—
242C22×C5—308no—
243C22×C5C2×D3×D514yescomplemented
244C2×D5—32no—
245C2×D5—34no—
246C2×D5—52no—
247C2×D5—54no—
248C2×D5—68no—
249C2×D5—102no—
250C2×D5—104no—
251C2×D5—108no—
252C2×D5—158no—
253C2×D5—208no—
254C2×D5—308no—
255C2×D5—308no—
256C2×D5—308no—
257C4×C5—22no—
258C4×C5—152no—
259C4×C5C2×D3×D512yescomplemented
260Dic5—32no—
261Dic5—52no—
262Dic5—102no—
263C24—752no—
264C2×D4—152no—
265C2×D4—251no—
266C2×D4—752no—
267C2×D4—751no—
268C2×D4—752no—
269C2×D4—754no—
270C22×C4—751no—
271C3×C5—22no—
272C3×C5C2×D4×D512yescomplemented
273C22×C3—251no—
274C22×C3—252no—
275C22×C3—504no—
276C22×C3C2×D5212yescomplemented
277C2×D3—52no—
278C2×D3—54no—
279C2×D3—108no—
280C2×D3—254no—
281C2×D3—508no—
282C2×D3—504no—
283C3×C4—251no—
284C3×C4C2×D5211yescharacteristic, complemented
285Dic3—52no—
286C2×C5—24no—
287C2×C5—22no—
288C2×C5—44no—
289C2×C5—154no—
290C2×C5—304no—
291C2×C5C22×D3×D512yes—
292D5—34no—
293D5—54no—
294D5—64no—
295D5—104no—
296D5—104no—
297D5—204no—
298C23—154no—
299C23—252no—
300C23—751no—
301C23—754no—
302C23—752no—
303C23—1508no—
304D4—154no—
305D4—152no—
306D4—252no—
307D4—251no—
308D4—754no—
309D4—752no—
310D4D15⋊D511yescharacteristic, direct product factor
311C2×C4—152no—
312C2×C4—251no—
313C2×C4—751no—
314C2×C4—752no—
315C2×C3—22no—
316C2×C3—252no—
317C2×C3—502no—
318C2×C3C22×D5211yescharacteristic
319D3—54no—
320D3—104no—
321C5—22no—
322C5D3×D4×D512yescomplemented
323C22—152no—
324C22—154no—
325C22—251no—
326C22—252no—
327C22—308no—
328C22—504no—
329C22—754no—
330C22—1508no—
331C22—1504no—
332C22C2×D15⋊D512yescomplemented
333C4—152no—
334C4—251no—
335C4C2×D15⋊D511yescharacteristic, complemented
336C3D4×D5211yescharacteristic, complemented, Sylow
337C2—22no—
338C2—154no—
339C2—252no—
340C2—304no—
341C2—502no—
342C2C22×D15⋊D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D15⋊D5
commutator, socle, cosocleC2×C3×C52C24
FittingC3×C52×D4C22
hypercenterD4D15⋊D5
hypocenterC3×C52C22×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×D15⋊D5C2semidirect
2. C5×D4×D15C2semidirect
3. C3×D4×C5⋊D5C2semidirect
4. #11925664C2semidirect
5. #11925663C2semidirect
6. #11925655C2semidirect
7. #11925654C2semidirect
8. C4×D15⋊D5C2semidirect
10. C22×C5×D15C22semidirect
11. C22×C3×C5⋊D5C22semidirect
14. C2×D15⋊D5C22semidirect
15. C2×D15⋊D5C22semidirect
16. C3×C52×D4C22semidirect
17. C5×#1220C22semidirect
18. C5×D60C22semidirect
19. C4×C5×D15C22semidirect
20. C3×C22⋊(C5⋊D5)C22semidirect
21. C3×C4⋊(C5⋊D5)C22semidirect
22. C3×C4×C5⋊D5C22semidirect
23. #10597128C22semidirect
24. #10597127C22semidirect
25. #10597126C22semidirect
26. #10597125C22semidirect
29. D4×C5⋊D5D3semidirect
36. C22×C3×C52C23semidirect
39. C2×C5×D15C23semidirect
42. C2×C3×C5⋊D5C23semidirect
45. D15⋊D5D4direct (N × H)
46. C3×C4×C52C23semidirect
47. C5×Dic15C23semidirect
48. C3×#1039C23semidirect
50. D4×D15D5semidirect
61. C22×C5⋊D5C2×D3semidirect
67. C52×D4C2×D3semidirect
68. C22⋊(C5⋊D5)C2×D3semidirect
69. C4⋊(C5⋊D5)C2×D3semidirect
70. C4×C5⋊D5C2×D3semidirect
82. C5×D15C2×D4semidirect
84. C3×C5⋊D5C2×D4semidirect
85. C22×D15C2×D5semidirect
95. C3×C5×D4C2×D5semidirect
96. #1220C2×D5semidirect
97. D60C2×D5semidirect
98. C4×D15C2×D5semidirect
114. C22×C52C22×D3semidirect
117. C2×C5⋊D5C22×D3semidirect
124. C4×C52C22×D3semidirect
125. #1039C22×D3semidirect
140. C3×C52C22×D4semidirect
142. C22×C3×C5C22×D5semidirect
145. C2×D15C22×D5semidirect
160. C3×C4×C5C22×D5semidirect
161. Dic15C22×D5semidirect
168. C5⋊D5D3×D4semidirect
191. C5×D4D3×D5semidirect
214. D15D4×D5semidirect
221. C52C2×D3×D4semidirect
230. C3×D4D52semidirect
243. C22×C5C2×D3×D5semidirect
259. C4×C5C2×D3×D5semidirect
272. C3×C5C2×D4×D5semidirect
276. C22×C3C2×D52semidirect
284. C3×C4C2×D52semidirect
310. D4D15⋊D5direct (N × H)
322. C5D3×D4×D5semidirect
332. C22C2×D15⋊D5semidirect
335. C4C2×D15⋊D5semidirect
336. C3D4×D52semidirect

Maximal subgroups

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

subgroupindex
C22×D15⋊D52
C5×D4×D152
C3×D4×C5⋊D52
#119256642
#119256632
#119256552
#119256542
C4×D15⋊D52
D4×D523
D3×D4×D55