Finite Group Databasebeta

← D4×(C3⋊D3)⋊D5 #13089413

Subgroups — D4×(C3⋊D3)⋊D5 #13089413

Order 1440.

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

normal subgroups only

This group has 998 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×(C3⋊D3)⋊D5C212yesmaximal, complemented
2C5×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×D4×D15C212yesmaximal, complemented
4#10624236C212yesmaximal, complemented
5#10624235C214yesmaximal, complemented
6#10624227C211yesmaximal, characteristic, complemented
7#10624226C212yesmaximal, complemented
8C4×(C3⋊D3)⋊D5C211yesmaximal, characteristic, complemented
9D3×D4×D5—32nomaximal
10C22×C5×C3⋊D3C2212yescomplemented
11C22×C3×D15C2214yescomplemented
12C2×(C3⋊D3)⋊D5—28no—
13C2×(C3⋊D3)⋊D5C2211yescharacteristic
14C2×(C3⋊D3)⋊D5C2214yescomplemented
15C2×(C3⋊D3)⋊D5C2212yescomplemented
16C32×C5×D4C2211yescharacteristic, complemented
17C5×#638C2212yescomplemented
18C5×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C4×C5×C3⋊D3C2211yescharacteristic, complemented
20C3×#1220C2214yescomplemented
21C3×D60C2212yescomplemented
22C3×C4×D15C2212yescomplemented
23#67157C2212yescomplemented
24#67156C2214yescomplemented
25#67155C2211yescharacteristic, complemented
26#67154C2212yescomplemented
27D32×D4—51nomaximal, Hall
28C22×D3×D5—34no—
29D4×D15D312yescomplemented
30C5×D3×D4—32no—
31C5×D3×D4—61no—
32C3×D4×D5—32no—
33#6790—34no—
34D3×C22⋊D5—34no—
35D5×#67—34no—
36#6777—32no—
37D3×D20—32no—
38D5×D12—32no—
39C4×D3×D5—32no—
40C22×C32×C5C2312yescomplemented
41C2×C5×C3⋊D3—24no—
42C2×C5×C3⋊D3C2311yescharacteristic
43C2×C5×C3⋊D3C2312yescomplemented
44C2×C3×D15—28no—
45C2×C3×D15C2312yes—
46C2×C3×D15C2314yescomplemented
47(C3⋊D3)⋊D5—24no—
48(C3⋊D3)⋊D5—28no—
49(C3⋊D3)⋊D5D414yesdirect product factor
50C32×C4×C5C2311yescharacteristic, complemented
51C5×C3⋊Dic3C2311yescharacteristic, complemented
52C3×Dic15C2312yescomplemented
53C2×D4×D5—91noHall
54C22×D32—52no—
55D4×C3⋊D3D511yescharacteristic, complemented
56C3×D3×D4—52no—
57#3811—52no—
58D3×#67—54no—
59#3802—51no—
60D3×D12—52no—
61C4×D32—51no—
62C22×D15C2×D314yescomplemented
63C22×C5×D3—34no—
64C22×C5×D3—62no—
65C22×C3×D5—34no—
66C2×D3×D5—32no—
67C2×D3×D5—34no—
68C2×D3×D5—34no—
69C2×D3×D5—34no—
70C2×D3×D5—616no—
71C3×C5×D4—21no—
72C3×C5×D4C2×D312yescomplemented
73#1220C2×D314yescomplemented
74D60C2×D312yescomplemented
75C4×D15C2×D312yescomplemented
76C5×#67—34no—
77C5×#67—62no—
78C5×D12—32no—
79C5×D12—61no—
80C4×C5×D3—32no—
81C4×C5×D3—61no—
82C3×C22⋊D5—34no—
83C3×D20—32no—
84C3×C4×D5—32no—
85#1203—34no—
86#1202—34no—
87#1201—34no—
88#1200—32no—
89D3×Dic5—32no—
90D5×Dic3—32no—
91C2×D3×D4—152no—
92C2×C32×C5—22no—
93C2×C32×C5C2411yescharacteristic
94C5×C3⋊D3—22no—
95C5×C3⋊D3C2×D412yescomplemented
96C3×D15—24no—
97C3×D15C2×D414yescomplemented
98C23×D5—92no—
99C2×C5×D4—91no—
100C2×C22⋊D5—92no—
101D4×D5—32no—
102D4×D5—92no—
103D4×D5—94no—
104C2×D20—91no—
105C2×C4×D5—91no—
106C22×C3⋊D3C2×D512yescomplemented
107C22×C3×D3—54no—
108C2×D32—51no—
109C2×D32—52no—
110C2×D32—54no—
111C2×D32—108no—
112C32×D4C2×D511yescharacteristic, complemented
113#638C2×D512yescomplemented
114C4⋊(C3⋊D3)C2×D511yescharacteristic, complemented
115C4×C3⋊D3C2×D511yescharacteristic, complemented
116C3×#67—54no—
117C3×D12—52no—
118C3×C4×D3—52no—
119#626—54no—
120#625—52no—
121#624—51no—
122D3×Dic3—52no—
123C22×C3×C5—22no—
124C22×C3×C5C22×D314yescomplemented
125C2×D15—28no—
126C2×D15C22×D312yes—
127C2×D15C22×D314yescomplemented
128C2×C5×D3—32no—
129C2×C5×D3—34no—
130C2×C5×D3—61no—
131C2×C5×D3—62no—
132C2×C5×D3—68no—
133C2×C5×D3—124no—
134C2×C3×D5—32no—
135C2×C3×D5—34no—
136C2×C3×D5—68no—
137D3×D5—38no—
138D3×D5—68no—
139D3×D5—68no—
140D3×D5—68no—
141C3×C4×C5—21no—
142C3×C4×C5C22×D312yescomplemented
143Dic15C22×D312yescomplemented
144C3×Dic5—32no—
145C5×Dic3—32no—
146C5×Dic3—61no—
147C23×D3—154no—
148C2×C3×D4—152no—
149C2×#67—154no—
150D3×D4—32no—
151D3×D4—52no—
152D3×D4—61no—
153D3×D4—152no—
154D3×D4—152no—
155D3×D4—154no—
156D3×D4—154no—
157C2×D12—152no—
158C2×C4×D3—152no—
159C32×C5C22×D411yescharacteristic, complemented, Hall
160C23×C5—92no—
161C22×D5—34no—
162C22×D5—91no—
163C22×D5—92no—
164C22×D5—94no—
165C22×D5—188no—
166C5×D4—92no—
167C5×D4—91no—
168C5×D4D3211yescharacteristic, complemented
169C2×C4×C5—91no—
170C22⋊D5—34no—
171C22⋊D5—94no—
172C2×Dic5—91no—
173D20—32no—
174D20—92no—
175C4×D5—32no—
176C4×D5—92no—
177C22×C32C22×D512yescomplemented
178C2×C3⋊D3—24no—
179C2×C3⋊D3C22×D511yescharacteristic
180C2×C3⋊D3C22×D512yescomplemented
181C2×C3×D3—52no—
182C2×C3×D3—54no—
183C2×C3×D3—108no—
184D32—54no—
185D32—108no—
186D32—104no—
187C32×C4C22×D511yescharacteristic, complemented
188C3⋊Dic3C22×D511yescharacteristic, complemented
189C3×Dic3—52no—
190C22×D4—451noSylow
191C2×C3×C5—24no—
192C2×C3×C5—21no—
193C2×C3×C5—42no—
194C2×C3×C5C23×D312yes—
195D15—24no—
196D15D3×D414yescomplemented
197C3×D5—34no—
198C3×D5—64no—
199C5×D3—34no—
200C5×D3—62no—
201C5×D3—64no—
202C5×D3—122no—
203C23×C3—154no—
204C22×D3—34no—
205C22×D3—54no—
206C22×D3—62no—
207C22×D3—152no—
208C22×D3—154no—
209C22×D3—154no—
210C22×D3—154no—
211C22×D3—3016no—
212C3×D4—21no—
213C3×D4—154no—
214C3×D4—152no—
215C3×D4D3×D512yescomplemented
216C2×C3×C4—152no—
217#67—34no—
218#67—54no—
219#67—62no—
220#67—154no—
221#67—154no—
222C2×Dic3—152no—
223D12—32no—
224D12—52no—
225D12—61no—
226D12—154no—
227C4×D3—32no—
228C4×D3—52no—
229C4×D3—61no—
230C4×D3—152no—
231C4×D3—152no—
232C22×C5—91no—
233C22×C5—92no—
234C22×C5—184no—
235C22×C5C2×D3212yescomplemented
236C2×D5—32no—
237C2×D5—34no—
238C2×D5—68no—
239C2×D5—94no—
240C2×D5—188no—
241C2×D5—184no—
242C4×C5—91no—
243C4×C5C2×D3211yescharacteristic, complemented
244Dic5—32no—
245C2×C32—22no—
246C2×C32C23×D511yescharacteristic
247C3⋊D3—22no—
248C3⋊D3D4×D512yescomplemented
249C3×D3—54no—
250C3×D3—104no—
251C24—452no—
252C2×D4—91no—
253C2×D4—152no—
254C2×D4—451no—
255C2×D4—452no—
256C2×D4—454no—
257C2×D4—452no—
258C22×C4—451no—
259C3×C5—21no—
260C3×C5C2×D3×D412yescomplemented
261C22×C3—22no—
262C22×C3—152no—
263C22×C3—154no—
264C22×C3—308no—
265C22×C3C2×D3×D514yescomplemented
266C2×D3—32no—
267C2×D3—34no—
268C2×D3—52no—
269C2×D3—54no—
270C2×D3—61no—
271C2×D3—62no—
272C2×D3—68no—
273C2×D3—108no—
274C2×D3—124no—
275C2×D3—158no—
276C2×D3—308no—
277C2×D3—308no—
278C2×D3—308no—
279C3×C4—21no—
280C3×C4—152no—
281C3×C4C2×D3×D512yescomplemented
282Dic3—32no—
283Dic3—52no—
284Dic3—61no—
285C2×C5—22no—
286C2×C5—92no—
287C2×C5—182no—
288C2×C5C22×D3211yescharacteristic
289D5—34no—
290D5—64no—
291C32C2×D4×D511yescharacteristic, complemented, Sylow
292C23—92no—
293C23—154no—
294C23—451no—
295C23—452no—
296C23—454no—
297C23—908no—
298D4—92no—
299D4—91no—
300D4—154no—
301D4—152no—
302D4—452no—
303D4—454no—
304D4(C3⋊D3)⋊D511yescharacteristic, direct product factor
305C2×C4—91no—
306C2×C4—152no—
307C2×C4—452no—
308C2×C4—451no—
309C2×C3—24no—
310C2×C3—21no—
311C2×C3—42no—
312C2×C3—154no—
313C2×C3—304no—
314C2×C3C22×D3×D512yes—
315D3—34no—
316D3—54no—
317D3—62no—
318D3—64no—
319D3—104no—
320D3—122no—
321C5D32×D411yescharacteristic, complemented, Sylow
322C22—91no—
323C22—92no—
324C22—152no—
325C22—154no—
326C22—184no—
327C22—308no—
328C22—454no—
329C22—904no—
330C22—908no—
331C22C2×(C3⋊D3)⋊D512yescomplemented
332C4—91no—
333C4—152no—
334C4C2×(C3⋊D3)⋊D511yescharacteristic, complemented
335C3—21no—
336C3D3×D4×D512yescomplemented
337C2—22no—
338C2—92no—
339C2—154no—
340C2—182no—
341C2—304no—
342C2C22×(C3⋊D3)⋊D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×(C3⋊D3)⋊D5
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C5×D4C22
hypercenterD4(C3⋊D3)⋊D5
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×(C3⋊D3)⋊D5C2semidirect
2. C5×D4×C3⋊D3C2semidirect
3. C3×D4×D15C2semidirect
4. #10624236C2semidirect
5. #10624235C2semidirect
6. #10624227C2semidirect
7. #10624226C2semidirect
8. C4×(C3⋊D3)⋊D5C2semidirect
10. C22×C5×C3⋊D3C22semidirect
11. C22×C3×D15C22semidirect
14. C2×(C3⋊D3)⋊D5C22semidirect
15. C2×(C3⋊D3)⋊D5C22semidirect
16. C32×C5×D4C22semidirect
17. C5×#638C22semidirect
18. C5×C4⋊(C3⋊D3)C22semidirect
19. C4×C5×C3⋊D3C22semidirect
20. C3×#1220C22semidirect
21. C3×D60C22semidirect
22. C3×C4×D15C22semidirect
23. #67157C22semidirect
24. #67156C22semidirect
25. #67155C22semidirect
26. #67154C22semidirect
29. D4×D15D3semidirect
40. C22×C32×C5C23semidirect
43. C2×C5×C3⋊D3C23semidirect
46. C2×C3×D15C23semidirect
49. (C3⋊D3)⋊D5D4direct (N × H)
50. C32×C4×C5C23semidirect
51. C5×C3⋊Dic3C23semidirect
52. C3×Dic15C23semidirect
55. D4×C3⋊D3D5semidirect
62. C22×D15C2×D3semidirect
72. C3×C5×D4C2×D3semidirect
73. #1220C2×D3semidirect
74. D60C2×D3semidirect
75. C4×D15C2×D3semidirect
95. C5×C3⋊D3C2×D4semidirect
97. C3×D15C2×D4semidirect
106. C22×C3⋊D3C2×D5semidirect
112. C32×D4C2×D5semidirect
113. #638C2×D5semidirect
114. C4⋊(C3⋊D3)C2×D5semidirect
115. C4×C3⋊D3C2×D5semidirect
124. C22×C3×C5C22×D3semidirect
127. C2×D15C22×D3semidirect
142. C3×C4×C5C22×D3semidirect
143. Dic15C22×D3semidirect
159. C32×C5C22×D4semidirect
168. C5×D4D32semidirect
177. C22×C32C22×D5semidirect
180. C2×C3⋊D3C22×D5semidirect
187. C32×C4C22×D5semidirect
188. C3⋊Dic3C22×D5semidirect
196. D15D3×D4semidirect
215. C3×D4D3×D5semidirect
235. C22×C5C2×D32semidirect
243. C4×C5C2×D32semidirect
248. C3⋊D3D4×D5semidirect
260. C3×C5C2×D3×D4semidirect
265. C22×C3C2×D3×D5semidirect
281. C3×C4C2×D3×D5semidirect
291. C32C2×D4×D5semidirect
304. D4(C3⋊D3)⋊D5direct (N × H)
321. C5D32×D4semidirect
331. C22C2×(C3⋊D3)⋊D5semidirect
334. C4C2×(C3⋊D3)⋊D5semidirect
336. C3D3×D4×D5semidirect

Maximal subgroups

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

subgroupindex
C22×(C3⋊D3)⋊D52
C5×D4×C3⋊D32
C3×D4×D152
#106242362
#106242352
#106242272
#106242262
C4×(C3⋊D3)⋊D52
D3×D4×D53
D32×D45