Finite Group Databasebeta

← #14437945

Subgroups — #14437945

Order 1920.

976 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 164 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
1D15×#125C211yesmaximal, characteristic, complemented
2#11752750C211yesmaximal, characteristic
3C5×#5067C211yesmaximal, characteristic, complemented
4C3×#65356C211yesmaximal, characteristic, complemented
5#11747478C214yesmaximal, complemented
6#11747409C214yesmaximal, complemented
7#11746983C211yesmaximal, characteristic, complemented
8#11746908C211yesmaximal, characteristic, complemented
9#11746892C211yesmaximal, characteristic, complemented
10D5×#490—31nomaximal, Hall
11C2×#6777—22no—
12C2×#6777C2212yes—
13C3×C5×#125C2211yescharacteristic, complemented
14C4⋊C4×D15—22no—
15C4⋊C4×D15C2212yes—
16#91779C2212yescomplemented
17#91778—22no—
18C42×D15C2211yescharacteristic
19#91759C2211yescharacteristic, complemented
20C5×#874C2211yescharacteristic
21C3×#4020C2211yescharacteristic
22#91463—22no—
23#91463C2212yes—
24C2×#6648C2212yes—
25C5×#809C2214yescomplemented
26C5×#803C2211yescharacteristic, complemented
27C3×#3941C2214yescomplemented
28C3×#3935C2211yescharacteristic, complemented
29#90967C2214yescomplemented
30#90965C2214yescomplemented
31#90954C2212yescomplemented
32D3×#490—51nomaximal, Hall
33D5×#127—31no—
34D5×#125—31no—
35C5×#490—31no—
36#65360—31no—
37#65356D311yescharacteristic, complemented
38D5×#102—34no—
39#65053—34no—
40#65002—31no—
41D5×#97—31no—
42C22×D3×D5—22no—
43C2×C4×D15—22no—
44C2×C4×D15D412yes—
45C2×C4×D15C2311yescharacteristic
46C2×C5×D12—22no—
47C2×C5×D12C2312yes—
48C2×C3×D20—22no—
49C2×C3×D20C2312yes—
50C2×#1201—22no—
51C2×#1201—24no—
52#6777—28no—
53#6777—48no—
54C3×C5×C4⋊C4—22no—
55C3×C5×C4⋊C4C2312yes—
56C3×C42×C5C2311yescharacteristic
57C4⋊Dic15—22no—
58C4⋊Dic15C2312yes—
59#6712—22no—
60#6712—22no—
61#6712—22no—
62C4×Dic15D412yes—
63C4×Dic15C2311yescharacteristic
64C2×C5×C3⋊C8C2312yes—
65C2×C3×#168C2312yes—
66#6648—24no—
67D3×#127—51no—
68D3×#125—51no—
69C3×#490—51no—
70#5071—51no—
71#5067D511yescharacteristic, complemented
72D3×#102—54no—
73#4764—54no—
74#4713—51no—
75D3×#97—51no—
76C2×D4×D5—32no—
77C2×D4×D5—62no—
78C5×#127—31no—
79C5×#125C2×D311yescharacteristic, complemented
80#4086—32no—
81#4086—62no—
82C2×C8×D5—32no—
83D5×C4⋊C4—32no—
84D5×C4⋊C4—62no—
85#4036—32no—
86#4035—62no—
87#4020C2×D311yescharacteristic
88C42×D5—31no—
89#4016—31no—
90C5×#102—34no—
91C5×#97—31no—
92#3964—34no—
93#3953—34no—
94#3947—32no—
95#3941C2×D314yescomplemented
96#3935C2×D311yescharacteristic, complemented
97C2×#490—151noSylow
98C22×D15C2×D411yescharacteristic
99C22×C5×D3—22no—
100C22×C3×D5—22no—
101C2×D3×D5—44no—
102C2×D3×D5—48no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5C2×D412yes—
105C2×C3×C4×C5C2411yescharacteristic
106C2×Dic15—22no—
107C2×Dic15C2×D412yes—
108C2×Dic15C2×D411yescharacteristic
109C4×D15—24no—
110C4×D15—44no—
111C4×D15#4114yes—
112C5×D12—24no—
113C5×D12—44no—
114C3×D20—24no—
115C3×D20—44no—
116#1201—48no—
117#1201—44no—
118C3×#168—22no—
119C5×C3⋊C8—22no—
120C2×D3×D4—52no—
121C2×D3×D4—102no—
122C3×#127—51no—
123C3×#125C2×D511yescharacteristic, complemented
124#940—52no—
125#940—102no—
126C2×D3×C8—52no—
127D3×C4⋊C4—52no—
128D3×C4⋊C4—102no—
129#890—52no—
130#889—102no—
131#874C2×D511yescharacteristic
132C42×D3—51no—
133#870—51no—
134C3×#102—54no—
135C3×#97—51no—
136#832—54no—
137#821—54no—
138#815—52no—
139#809C2×D514yescomplemented
140#803C2×D511yescharacteristic, complemented
141C23×D5—62no—
142C2×C5×D4—32no—
143C2×C5×D4—62no—
144C2×C22⋊D5—62no—
145C2×C22⋊D5—64no—
146D4×D5—68no—
147D4×D5—128no—
148C2×D20—22no—
149C2×D20C22×D312yes—
150C2×C4×D5—31no—
151C2×C4×D5—32no—
152C2×C4×D5—62no—
153C2×C5×C8—32no—
154C5×C4⋊C4—22no—
155C5×C4⋊C4C22×D312yes—
156C42×C5C22×D311yescharacteristic
157C4⋊Dic5—32no—
158C4⋊Dic5—62no—
159#683—62no—
160#683—62no—
161#683—62no—
162C4×Dic5—32no—
163C4×Dic5—31no—
164C2×#168C22×D312yes—
165C8×D5—64no—
166C2×#127—151no—
167C2×#125—151no—
168#490—31no—
169#490—51no—
170#490—151no—
171#490—151no—
172#490—154no—
173C2×#102—154no—
174C2×#97—151no—
175C22×C3×C5C22×D411yescharacteristic
176C2×D15#12412yes—
177C2×D15AGL(1,ℤ/8)14yes—
178C2×C5×D3—42no—
179C2×C5×D3—44no—
180C2×C3×D5—42no—
181C2×C3×D5—44no—
182D3×D5—88no—
183C3×C4×C5—22no—
184C3×C4×C5—42no—
185C3×C4×C5C2×#4112yes—
186Dic15—22no—
187Dic15—42no—
188Dic15#12412yes—
189C23×D3—102no—
190C2×C3×D4—52no—
191C2×C3×D4—102no—
192C2×#67—104no—
193C2×#67—102no—
194D3×D4—108no—
195D3×D4—208no—
196C2×D12—22no—
197C2×D12C22×D512yes—
198C2×C4×D3—51no—
199C2×C4×D3—52no—
200C2×C4×D3—102no—
201C2×C3×C8—52no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4C22×D512yes—
204C3×C42C22×D511yescharacteristic
205C4⋊Dic3—52no—
206C4⋊Dic3—102no—
207Dic3⋊C4—102no—
208Dic3⋊C4—102no—
209Dic3⋊C4—102no—
210C4×Dic3—52no—
211C4×Dic3—51no—
212C2×C3⋊C8C22×D512yes—
213D3×C8—104no—
214C23×C5—62no—
215C22×D5—22no—
216C22×D5—31no—
217C22×D5—124no—
218C22×D5—128no—
219C5×D4—64no—
220C5×D4—124no—
221C2×C4×C5—22no—
222C2×C4×C5D3×D412yes—
223C2×C4×C5C23×D311yescharacteristic
224C22⋊D5—124no—
225C22⋊D5—128no—
226C2×Dic5—31no—
227C2×Dic5—32no—
228C2×Dic5—62no—
229D20—24no—
230D20—44no—
231C4×D5—34no—
232C4×D5—64no—
233C4×D5—124no—
234C5×C8—62no—
235#168—22no—
236C22×D4—152no—
237C22×D4—302no—
238C22×C8—152no—
239#127—31no—
240#127—51no—
241#127—152no—
242#127—302no—
243#125—152no—
244#125—151no—
245#125—302no—
246#125D3×D511yescharacteristic, complemented
247C2×C4⋊C4—152no—
248C2×C4⋊C4—302no—
249C2×C42—151no—
250#102—34no—
251#102—54no—
252#102—154no—
253#102—154no—
254#97—31no—
255#97—51no—
256#97—152no—
257C2×C3×C5C2×#12411yescharacteristic
258C2×C3×C5C2×AGL(1,ℤ/8)12yes—
259D15#49014yescomplemented
260C3×D5—82no—
261C5×D3—82no—
262C23×C3—102no—
263C22×D3—22no—
264C22×D3—51no—
265C22×D3—204no—
266C22×D3—208no—
267C3×D4—104no—
268C3×D4—204no—
269C2×C3×C4—22no—
270C2×C3×C4D4×D512yes—
271C2×C3×C4C23×D511yescharacteristic
272#67—204no—
273#67—208no—
274C2×Dic3—51no—
275C2×Dic3—52no—
276C2×Dic3—102no—
277D12—24no—
278D12—44no—
279C4×D3—54no—
280C4×D3—104no—
281C4×D3—204no—
282C3×C8—102no—
283C3⋊C8—22no—
284C22×C5—122no—
285C22×C5—124no—
286C22×C5C2×D3×D411yescharacteristic
287C2×D5—32no—
288C2×D5—34no—
289C2×D5—42no—
290C2×D5—44no—
291C2×D5—248no—
292C4×C5—22no—
293C4×C5—42no—
294C4×C5D3×#4112yes—
295Dic5—32no—
296Dic5—62no—
297Dic5—122no—
298C24—302no—
299C2×D4—32no—
300C2×D4—52no—
301C2×D4—62no—
302C2×D4—102no—
303C2×D4—308no—
304C2×D4—304no—
305C2×D4—302no—
306C2×D4—608no—
307C22×C4—151no—
308C22×C4—152no—
309C22×C4—302no—
310C2×C8—32no—
311C2×C8—52no—
312C2×C8—304no—
313C4⋊C4—22no—
314C4⋊C4—152no—
315C4⋊C4—302no—
316C4⋊C4—302no—
317C4⋊C4—302no—
318C4⋊C4—302no—
319C4⋊C4C2×D3×D512yes—
320C42—152no—
321C42—151no—
322C42C2×D3×D511yescharacteristic
323C3×C5C2×#49011yescharacteristic, complemented, Hall
324C22×C3—204no—
325C22×C3—202no—
326C22×C3C2×D4×D511yescharacteristic
327C2×D3—44no—
328C2×D3—42no—
329C2×D3—54no—
330C2×D3—52no—
331C2×D3—408no—
332C3×C4—22no—
333C3×C4—42no—
334C3×C4D5×#4112yes—
335Dic3—52no—
336Dic3—102no—
337Dic3—202no—
338C2×C5—242no—
339C2×C5D3×#12411yescharacteristic
340C2×C5D3×AGL(1,ℤ/8)12yes—
341D5—34no—
342D5—82no—
343C23—62no—
344C23—102no—
345C23—151no—
346C23—604no—
347C23—608no—
348D4—64no—
349D4—104no—
350D4—124no—
351D4—204no—
352D4—604no—
353D4—608no—
354C2×C4—22no—
355C2×C4—151no—
356C2×C4—154no—
357C2×C4—152no—
358C2×C4—304no—
359C2×C4—302no—
360C2×C4—604no—
361C2×C4#679012yes—
362C2×C4C22×D3×D511yescharacteristic
363C8—62no—
364C8—102no—
365C2×C3—402no—
366C2×C3D5×#12411yescharacteristic
367C2×C3D5×AGL(1,ℤ/8)12yes—
368D3—54no—
369D3—82no—
370C5D3×#49011yescharacteristic, complemented, Sylow
371C22—122no—
372C22—124no—
373C22—152no—
374C22—154no—
375C22—202no—
376C22—204no—
377C22—1208no—
378C22C2×#679011yescharacteristic
379C4—22no—
380C4—42no—
381C4—152no—
382C4—302no—
383C4—602no—
384C4#9203412yes—
385C3D5×#49011yescharacteristic, complemented, Sylow
386C2—154no—
387C2—242no—
388C2—402no—
389C2#1175528511yescharacteristic
390C2#1175532712yes—
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radical#11752750C2
hypercenter#125D3×D5
hypocenterC3×C5C2×#490
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. D15×#125C2semidirect
3. C5×#5067C2semidirect
4. C3×#65356C2semidirect
5. #11747478C2semidirect
6. #11747409C2semidirect
7. #11746983C2semidirect
8. #11746908C2semidirect
9. #11746892C2semidirect
13. C3×C5×#125C22semidirect
16. #91779C22semidirect
19. #91759C22semidirect
25. C5×#809C22semidirect
26. C5×#803C22semidirect
27. C3×#3941C22semidirect
28. C3×#3935C22semidirect
29. #90967C22semidirect
30. #90965C22semidirect
31. #90954C22semidirect
37. #65356D3semidirect
71. #5067D5semidirect
79. C5×#125C2×D3semidirect
95. #3941C2×D3semidirect
96. #3935C2×D3semidirect
123. C3×#125C2×D5semidirect
139. #809C2×D5semidirect
140. #803C2×D5semidirect
246. #125D3×D5semidirect
259. D15#490semidirect
323. C3×C5C2×#490semidirect
370. C5D3×#490semidirect
385. C3D5×#490semidirect

Maximal subgroups

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

subgroupindex
D15×#1252
#117527502
C5×#50672
C3×#653562
#117474782
#117474092
#117469832
#117469082
#117468922
D5×#4903
D3×#4905