Finite Group Databasebeta

← #11755439

Subgroups — #11755439

Order 960.

692 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 144 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×C5×#67C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊D5C211yesmaximal, characteristic, complemented
3#91842C211yesmaximal, characteristic, complemented
4C3×#4099C211yesmaximal, characteristic, complemented
5#91577C212yesmaximal, complemented
6#91565C212yesmaximal, complemented
7#91558C212yesmaximal, complemented
8#91555C212yesmaximal, complemented
9D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
10#91542C211yesmaximal, characteristic, complemented
11#91536C211yesmaximal, characteristic, complemented
12#66138—31nomaximal, Hall
13C24×C3×C5C2211yescharacteristic, complemented
14C23×C5×D3C2211yescharacteristic
15C22×D3×D5C2211yescharacteristic, complemented
16C2×#1220C2211yescharacteristic
17C2×#1220C2212yescomplemented
18C2×C5×#67—24no—
19C2×C5×#67C2212yes—
20C2×C5×#67C2212yescomplemented
21C22×C5×Dic3C2211yescharacteristic, complemented
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2212yescomplemented
24D3×C22⋊D5—24no—
25C2×#1203C2211yescharacteristic, complemented
26C2×#1201C2211yescharacteristic, complemented
27C2×D3×Dic5C2211yescharacteristic, complemented
28C2×D3×Dic5C2212yescomplemented
29#6719C2211yescharacteristic, complemented
30#6719C2212yescomplemented
31C3×C22⋊Dic5C2211yescharacteristic, complemented
32C3×C22⋊Dic5C2212yescomplemented
33#6669C2212yescomplemented
34#6668C2212yescomplemented
35#6667C2212yescomplemented
36(C2×D3)⋊Dic5C2212yescomplemented
37#6665C2212yescomplemented
38#5589—51nomaximal, Hall
39C22×C5×D4—31no—
40C22×C22⋊D5—31no—
41#4099—31no—
42#4099D311yescharacteristic, complemented
43C2×C22⋊Dic5—31no—
44#4085—32no—
45#4085—32no—
46#4083—32no—
47#4081—32no—
48#4075—31no—
49#4075—31no—
50C23×C3×C5—22no—
51C23×C3×C5—42no—
52C23×C3×C5C2312yes—
53C23×C3×C5C2311yescharacteristic
54C22×D15C2311yescharacteristic
55C22×C5×D3—42no—
56C22×C5×D3D414yescomplemented
57C22×C5×D3C2311yescharacteristic
58C22×C5×D3C2311yescharacteristic
59C22×C3×D5C2311yescharacteristic
60C2×D3×D5—22no—
61C2×D3×D5—42no—
62#1220—22no—
63#1220—42no—
64C2×Dic15C2312yes—
65C2×Dic15C2311yescharacteristic
66C5×#67—24no—
67C5×#67—24no—
68C2×C5×Dic3—22no—
69C2×C5×Dic3C2312yes—
70C3×C22⋊D5—22no—
71C3×C22⋊D5—42no—
72C2×C3×Dic5C2312yes—
73C2×C3×Dic5C2311yescharacteristic
74#1203—22no—
75#1201—22no—
76D3×Dic5—22no—
77D3×Dic5—42no—
78C22×#67D511yescharacteristic, complemented
79C2×D3×D4—51no—
80C3×#120—51no—
81#953—51no—
82#938—52no—
83#937—52no—
84#935—51no—
85#886—51no—
86#884—52no—
87#883—52no—
88D3×C22⋊C4—51no—
89C24×C5—31no—
90C24×C5C2×D311yescharacteristic, complemented
91C23×D5—31no—
92C2×C5×D4—32no—
93C2×C5×D4—32no—
94C2×C5×D4—64no—
95C22×C4×C5—31no—
96C2×C22⋊D5—31no—
97C2×C22⋊D5—31no—
98C2×C22⋊D5—32no—
99C2×C22⋊D5—31no—
100C2×C22⋊D5—64no—
101C2×C22⋊D5C2×D311yescharacteristic
102C2×C22⋊D5C2×D312yescomplemented
103C22×Dic5—31no—
104C22×Dic5—32no—
105C22⋊Dic5—31no—
106C22⋊Dic5—32no—
107C22⋊Dic5—32no—
108C22⋊Dic5C2×D311yescharacteristic, complemented
109C22⋊Dic5C2×D312yescomplemented
110#685—32no—
111#685—32no—
112#683—32no—
113#683—32no—
114#534—151noSylow
115C22×C3×C5—22no—
116C22×C3×C5—22no—
117C22×C3×C5—22no—
118C22×C3×C5—22no—
119C22×C3×C5—44no—
120C22×C3×C5C2×D412yes—
121C22×C3×C5C2411yescharacteristic
122C2×D15—21no—
123C2×D15—22no—
124C2×C5×D3—22no—
125C2×C5×D3—22no—
126C2×C5×D3—44no—
127C2×C5×D3C2×D412yes—
128C2×C5×D3C2×D412yes—
129C2×C3×D5—21no—
130C2×C3×D5—22no—
131D3×D5—44no—
132Dic15—21no—
133Dic15—22no—
134C3×Dic5—21no—
135C3×Dic5—22no—
136C5×Dic3—22no—
137C24×C3C2×D511yescharacteristic, complemented
138C23×D3—51no—
139C23×D3C2×D511yescharacteristic
140C2×C3×D4—51no—
141C2×C3×D4—52no—
142C2×#67—24no—
143C2×#67—51no—
144C2×#67—51no—
145C2×#67—52no—
146C2×#67C2×D512yes—
147C2×#67C2×D512yescomplemented
148C22×Dic3C2×D511yescharacteristic, complemented
149D3×D4—104no—
150C2×D12—51no—
151C2×C4×D3—51no—
152C2×C4×D3—52no—
153C3×C22⋊C4—51no—
154C3×C22⋊C4—52no—
155#217—51no—
156#217—52no—
157#217—52no—
158(C2×D3)⋊C4—52no—
159(C2×D3)⋊C4—52no—
160C4⋊Dic3—52no—
161Dic3⋊C4—52no—
162C23×C5—22no—
163C23×C5—31no—
164C23×C5—31no—
165C23×C5—34no—
166C23×C5—42no—
167C23×C5—122no—
168C23×C5C22×D312yes—
169C23×C5C22×D311yescharacteristic
170C22×D5—31no—
171C22×D5—62no—
172C22×D5—122no—
173C22×D5C22×D311yescharacteristic
174C5×D4—64no—
175C5×D4—64no—
176C2×C4×C5—32no—
177C2×C4×C5—62no—
178C22⋊D5—22no—
179C22⋊D5—42no—
180C22⋊D5—62no—
181C22⋊D5—62no—
182C22⋊D5—62no—
183C22⋊D5—122no—
184C2×Dic5—31no—
185C2×Dic5—32no—
186C2×Dic5—62no—
187C2×Dic5—122no—
188C2×Dic5C22×D311yescharacteristic
189C2×Dic5C22×D312yes—
190C22×D4—31no—
191C22×D4—151no—
192#123—151no—
193#123—152no—
194#123—151no—
195#121—152no—
196#121—152no—
197#120—51no—
198#120—152no—
199#120—151no—
200C2×C22⋊C4—151no—
201C2×C3×C5—22no—
202C2×C3×C5—42no—
203C2×C3×C5C22×D411yescharacteristic
204C2×C3×C5H(5,𝔽2)12yes—
205D15—41no—
206C3×D5—41no—
207C5×D3—22no—
208C5×D3—22no—
209C23×C3—22no—
210C23×C3—42no—
211C23×C3—51no—
212C23×C3C22×D512yes—
213C23×C3C22×D511yescharacteristic
214C22×D3—42no—
215C22×D3—51no—
216C22×D3—102no—
217C22×D3—202no—
218C22×D3C22⋊D514yescomplemented
219C22×D3C22×D511yescharacteristic
220C22×D3C22×D511yescharacteristic
221C3×D4—102no—
222C3×D4—202no—
223C2×C3×C4—51no—
224C2×C3×C4—52no—
225#67—24no—
226#67—24no—
227#67—102no—
228#67—102no—
229#67—202no—
230C2×Dic3—22no—
231C2×Dic3—52no—
232C2×Dic3—51no—
233C2×Dic3C22×D512yes—
234D12—102no—
235C4×D3—102no—
236C4×D3—202no—
237C22×C5—22no—
238C22×C5—22no—
239C22×C5—22no—
240C22×C5—22no—
241C22×C5—32no—
242C22×C5—32no—
243C22×C5—44no—
244C22×C5—62no—
245C22×C5—62no—
246C22×C5—124no—
247C22×C5D3×D412yes—
248C22×C5C23×D311yescharacteristic
249C2×D5—21no—
250C2×D5—22no—
251C2×D5—61no—
252C2×D5—62no—
253C2×D5—124no—
254C4×C5—62no—
255Dic5—21no—
256Dic5—22no—
257Dic5—61no—
258Dic5—62no—
259C24—31no—
260C24—151no—
261C24D3×D511yescharacteristic, complemented
262C2×D4—32no—
263C2×D4—32no—
264C2×D4—51no—
265C2×D4—52no—
266C2×D4—64no—
267C2×D4—151no—
268C2×D4—151no—
269C2×D4—151no—
270C2×D4—152no—
271C2×D4—304no—
272C22×C4—31no—
273C22×C4—151no—
274C22×C4—152no—
275C4⋊C4—152no—
276C4⋊C4—152no—
277C22⋊C4—51no—
278C22⋊C4—52no—
279C22⋊C4—152no—
280C22⋊C4—152no—
281C22⋊C4—152no—
282C22⋊C4—151no—
283C22⋊C4—152no—
284C3×C5#53411yescharacteristic, complemented, Hall
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—44no—
290C22×C3—102no—
291C22×C3—101no—
292C22×C3C2×C22⋊D512yes—
293C22×C3C23×D511yescharacteristic
294C2×D3—22no—
295C2×D3—22no—
296C2×D3—44no—
297C2×D3—102no—
298C2×D3—101no—
299C2×D3—204no—
300C2×D3C2×C22⋊D512yes—
301C2×D3C2×C22⋊D512yes—
302C3×C4—102no—
303C3×C4—101no—
304Dic3—22no—
305Dic3—102no—
306Dic3—101no—
307C2×C5—22no—
308C2×C5—42no—
309C2×C5—62no—
310C2×C5—62no—
311C2×C5C2×D3×D411yescharacteristic
312C2×C5#100412yes—
313D5—41no—
314D5—121no—
315C23—22no—
316C23—31no—
317C23—31no—
318C23—34no—
319C23—42no—
320C23—51no—
321C23—122no—
322C23—151no—
323C23—302no—
324C23—602no—
325C23C2×D3×D512yes—
326C23C2×D3×D511yescharacteristic
327D4—64no—
328D4—64no—
329D4—102no—
330D4—202no—
331D4—302no—
332D4—302no—
333D4—302no—
334D4—602no—
335C2×C4—32no—
336C2×C4—52no—
337C2×C4—51no—
338C2×C4—62no—
339C2×C4—152no—
340C2×C4—151no—
341C2×C4—302no—
342C2×C4—602no—
343C2×C3—22no—
344C2×C3—42no—
345C2×C3—201no—
346C2×C3#414412yes—
347C2×C3C22×C22⋊D511yescharacteristic
348D3—22no—
349D3—22no—
350D3—201no—
351C5#558911yescharacteristic, complemented, Sylow
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—32no—
357C22—32no—
358C22—44no—
359C22—62no—
360C22—62no—
361C22—101no—
362C22—102no—
363C22—124no—
364C22—301no—
365C22—302no—
366C22—604no—
367C22D3×C22⋊D512yes—
368C22C22×D3×D511yescharacteristic
369C4—62no—
370C4—101no—
371C4—102no—
372C4—301no—
373C4—302no—
374C3#6613811yescharacteristic, complemented, Sylow
375C2—22no—
376C2—42no—
377C2—62no—
378C2—62no—
379C2—201no—
380C2—601no—
381C2C2×D3×C22⋊D511yescharacteristic
382C2#9204912yes—
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
hypercenterC24D3×D5
hypocenterC3×C5#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C5×#67C2semidirect
2. C2×D3×C22⋊D5C2semidirect
3. #91842C2semidirect
4. C3×#4099C2semidirect
5. #91577C2semidirect
6. #91565C2semidirect
7. #91558C2semidirect
8. #91555C2semidirect
9. D3×C22⋊Dic5C2semidirect
10. #91542C2semidirect
11. #91536C2semidirect
13. C24×C3×C5C22semidirect
15. C22×D3×D5C22semidirect
17. C2×#1220C22semidirect
20. C2×C5×#67C22semidirect
21. C22×C5×Dic3C22semidirect
23. C2×C3×C22⋊D5C22semidirect
25. C2×#1203C22semidirect
26. C2×#1201C22semidirect
27. C2×D3×Dic5C22semidirect
28. C2×D3×Dic5C22semidirect
29. #6719C22semidirect
30. #6719C22semidirect
31. C3×C22⋊Dic5C22semidirect
32. C3×C22⋊Dic5C22semidirect
33. #6669C22semidirect
34. #6668C22semidirect
35. #6667C22semidirect
36. (C2×D3)⋊Dic5C22semidirect
37. #6665C22semidirect
42. #4099D3semidirect
56. C22×C5×D3D4semidirect
78. C22×#67D5semidirect
90. C24×C5C2×D3semidirect
102. C2×C22⋊D5C2×D3semidirect
108. C22⋊Dic5C2×D3semidirect
109. C22⋊Dic5C2×D3semidirect
137. C24×C3C2×D5semidirect
147. C2×#67C2×D5semidirect
148. C22×Dic3C2×D5semidirect
218. C22×D3C22⋊D5semidirect
261. C24D3×D5semidirect
284. C3×C5#534semidirect
351. C5#5589semidirect
374. C3#66138semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#672
C2×D3×C22⋊D52
#918422
C3×#40992
#915772
#915652
#915582
#915552
D3×C22⋊Dic52
#915422
#915362
#661383
#55895