Finite Group Databasebeta

← #11752756

Subgroups — #11752756

Order 960.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91764C211yesmaximal, characteristic, complemented
2C5×#876C211yesmaximal, characteristic, complemented
3C3×C4×D20C211yesmaximal, characteristic, complemented
4#91476C211yesmaximal, characteristic, complemented
5#91474C211yesmaximal, characteristic, complemented
6D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#91462C211yesmaximal, characteristic, complemented
8#91459C211yesmaximal, characteristic, complemented
9#91448C211yesmaximal, characteristic, complemented
10#91444C211yesmaximal, characteristic, complemented
11#91438C211yesmaximal, characteristic, complemented
12#91431C211yesmaximal, characteristic, complemented
13#91409C211yesmaximal, characteristic, complemented
14#91348C211yesmaximal, characteristic, complemented
15#91345C211yesmaximal, characteristic, complemented
16#66038—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×D60C2211yescharacteristic
19C2×Dic30C2211yescharacteristic, complemented
20C2×C3×D20C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×C3×C4×D5C2211yescharacteristic, complemented
23C2×#1203C2211yescharacteristic
24C2×#1202C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1202C2211yescharacteristic, complemented
27C2×#1201C2211yescharacteristic
28C2×#1200C2211yescharacteristic, complemented
29C2×D5×Dic3C2211yescharacteristic
30C3×C42×C5C2211yescharacteristic, complemented
31#6714C2211yescharacteristic
32#6714C2211yescharacteristic
33#6714C2211yescharacteristic, complemented
34#6714C2211yescharacteristic, complemented
35C5×(C2×D3)⋊C4C2211yescharacteristic
36C5×(C2×D3)⋊C4C2211yescharacteristic
37C5×(C2×D3)⋊C4C2211yescharacteristic
38C5×Dic3⋊C4C2211yescharacteristic, complemented
39C5×Dic3⋊C4C2211yescharacteristic, complemented
40C5×Dic3⋊C4C2211yescharacteristic, complemented
41C3×#685C2211yescharacteristic
42C3×#685C2211yescharacteristic, complemented
43C3×C4⋊Dic5C2211yescharacteristic, complemented
44#6669C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5560—51nomaximal, Hall
53C5×#126—31no—
54#4044—31no—
55#4042—31no—
56#4041—31no—
57#4041—31no—
58#4040—31no—
59#4039—31no—
60#4031—31no—
61#4030—31no—
62#4029—31no—
63#4028—31no—
64#4028—31no—
65D5×C22⋊C4—31no—
66#4021—31no—
67C4×D20D311yescharacteristic, complemented
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C22×C3×D5C2311yescharacteristic
73C2×D3×D5—22no—
74C2×D3×D5—41no—
75C2×D3×D5—41no—
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81D60—41no—
82Dic30—41no—
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C3×D20—22no—
89C3×C4×D5—41no—
90C3×C4×D5—41no—
91#1203—41no—
92#1202—22no—
93#1202—41no—
94#1202—41no—
95#1201—41no—
96#1200—41no—
97D5×Dic3—41no—
98C3×C4×D4—51no—
99#939—51no—
100#937—51no—
101#930—51no—
102#929—51no—
103C4×#67—51no—
104C2×(C2×D3)⋊C4—51no—
105#898—51no—
106#894—51no—
107#885—51no—
108#884—51no—
109#882—51no—
110#878—51no—
111#876D511yescharacteristic, complemented
112#875—51no—
113C23×D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5—31no—
116C2×D20—31no—
117C2×D20—31no—
118C2×D20—31no—
119C2×D20—31no—
120C2×D20C2×D311yescharacteristic
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5C2×D311yescharacteristic
124C2×C4×D5C2×D311yescharacteristic, complemented
125C2×Dic10—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—31no—
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C42×C5C2×D311yescharacteristic, complemented
133C22⋊Dic5—31no—
134#685—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685—31no—
142#685C2×D311yescharacteristic
143#685C2×D311yescharacteristic, complemented
144C4⋊Dic5C2×D311yescharacteristic, complemented
145#683—31no—
146#683—31no—
147C4×Dic5—31no—
148#538—151noSylow
149C22×C3×C5C2411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×C5×D3—21no—
157C2×C5×D3—21no—
158C2×C5×D3—21no—
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C2×C3×D5—21no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5#4112yes—
165D3×D5—44no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169Dic15—21no—
170Dic15—21no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C5×Dic3—21no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C23×D3—51no—
177C2×C3×D4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67—51no—
184C22×Dic3—51no—
185C2×D12—51no—
186C2×D12—51no—
187C2×C4×D3—51no—
188C2×Dic6—51no—
189C3×C4⋊C4—51no—
190C3×C22⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C42C2×D511yescharacteristic, complemented
193#217—51no—
194#217—51no—
195(C2×D3)⋊C4—51no—
196(C2×D3)⋊C4—51no—
197(C2×D3)⋊C4—51no—
198(C2×D3)⋊C4—51no—
199(C2×D3)⋊C4—51no—
200(C2×D3)⋊C4—51no—
201(C2×D3)⋊C4—51no—
202(C2×D3)⋊C4C2×D511yescharacteristic
203(C2×D3)⋊C4C2×D511yescharacteristic
204(C2×D3)⋊C4C2×D511yescharacteristic
205C4⋊Dic3—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4C2×D511yescharacteristic, complemented
208Dic3⋊C4C2×D511yescharacteristic, complemented
209Dic3⋊C4C2×D511yescharacteristic, complemented
210C4×Dic3—51no—
211C23×C5—31no—
212C22×D5—31no—
213C22×D5—31no—
214C22×D5—62no—
215C22×D5—121no—
216C22×D5—121no—
217C22×D5C22×D311yescharacteristic
218C22×D5C22×D311yescharacteristic
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5C22×D311yescharacteristic
223C2×C4×C5C22×D311yescharacteristic
224C2×C4×C5C22×D311yescharacteristic
225C22⋊D5—121no—
226C22⋊D5—121no—
227C2×Dic5—31no—
228C2×Dic5—31no—
229C2×Dic5C22×D311yescharacteristic
230C2×Dic5C22×D311yescharacteristic
231D20—22no—
232D20—62no—
233D20—121no—
234D20—121no—
235D20—121no—
236C4×D5—41no—
237C4×D5—41no—
238C4×D5—121no—
239C4×D5—121no—
240Dic10—121no—
241#126—31no—
242#126—151no—
243#124—151no—
244#124—151no—
245#123—151no—
246#123—151no—
247C22⋊Q8—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#120—151no—
252#120—151no—
253C4×D4—51no—
254C4×D4—151no—
255C2×C22⋊C4—151no—
256C2×C3×C5C2×#4111yescharacteristic
257C2×C3×C5H(5,𝔽2)11yescharacteristic
258C2×C3×C5H(5,𝔽2)11yescharacteristic
259D15—41no—
260D15—41no—
261C3×D5—22no—
262C3×D5—41no—
263C5×D3—41no—
264C23×C3—51no—
265C23×C3—51no—
266C22×D3—51no—
267C22×D3—51no—
268C22×D3—102no—
269C22×D3—201no—
270C22×D3—201no—
271C22×D3C22×D511yescharacteristic
272C3×D4—102no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—201no—
276C2×C3×C4—201no—
277C2×C3×C4C22×D511yescharacteristic
278C2×C3×C4C22×D511yescharacteristic
279C2×C3×C4C22×D511yescharacteristic
280#67—102no—
281#67—201no—
282#67—201no—
283#67—201no—
284C2×Dic3—51no—
285C2×Dic3—51no—
286C2×Dic3—201no—
287C2×Dic3C22×D511yescharacteristic
288C2×Dic3C22×D511yescharacteristic
289C2×Dic3C22×D511yescharacteristic
290D12—201no—
291D12—201no—
292C4×D3—201no—
293Dic6—201no—
294C22×C5—61no—
295C22×C5—61no—
296C22×C5—61no—
297C22×C5C23×D311yescharacteristic
298C2×D5—21no—
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—61no—
304C2×D5—61no—
305C2×D5—61no—
306C2×D5—61no—
307C2×D5—61no—
308C2×D5—61no—
309C2×D5—124no—
310C2×D5#23512yes—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317Dic5—21no—
318Dic5—21no—
319Dic5—61no—
320Dic5—61no—
321C24—151no—
322C2×Q8—151no—
323C2×D4—51no—
324C2×D4—151no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C2×D4—151no—
330C22×C4—51no—
331C22×C4—51no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—31no—
337C4⋊C4—51no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—31no—
343C22⋊C4—51no—
344C22⋊C4—51no—
345C22⋊C4—151no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C22⋊C4—151no—
353C22⋊C4—151no—
354C42—151no—
355C42D3×D511yescharacteristic, complemented
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—52no—
358C22×C3—101no—
359C22×C3—101no—
360C22×C3—101no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3C23×D511yescharacteristic
364C2×D3—21no—
365C2×D3—21no—
366C2×D3—21no—
367C2×D3—101no—
368C2×D3—101no—
369C2×D3—101no—
370C2×D3—101no—
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—204no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—101no—
378C3×C4—101no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—101no—
383Dic3—101no—
384C2×C5—121no—
385C2×C5C2×#23511yescharacteristic
386C2×C5#100411yescharacteristic
387C2×C5#100911yescharacteristic
388D5—22no—
389D5—41no—
390D5—121no—
391D5—121no—
392C23—31no—
393C23—51no—
394C23—51no—
395C23—151no—
396C23—151no—
397C23—302no—
398C23—601no—
399C23—601no—
400Q8—601no—
401D4—102no—
402D4—302no—
403D4—601no—
404D4—601no—
405D4—601no—
406D4—601no—
407D4—601no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—51no—
412C2×C4—51no—
413C2×C4—151no—
414C2×C4—151no—
415C2×C4—201no—
416C2×C4—201no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4C2×D3×D511yescharacteristic
420C2×C4C2×D3×D511yescharacteristic
421C2×C4C2×D3×D511yescharacteristic
422C2×C3—102no—
423C2×C3—201no—
424C2×C3D5×#4111yescharacteristic
425C2×C3#414911yescharacteristic
426C2×C3#414911yescharacteristic
427D3—41no—
428D3—201no—
429D3—201no—
430C5#556011yescharacteristic, complemented, Sylow
431C22—52no—
432C22—61no—
433C22—61no—
434C22—61no—
435C22—101no—
436C22—101no—
437C22—101no—
438C22—101no—
439C22—101no—
440C22—301no—
441C22—301no—
442C22—301no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22—604no—
447C22C22×D3×D511yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—61no—
452C4—61no—
453C4—61no—
454C4—101no—
455C4—101no—
456C4—301no—
457C4—301no—
458C3#6603811yescharacteristic, complemented, Sylow
459C2—102no—
460C2—121no—
461C2—201no—
462C2—601no—
463C2—601no—
464C2D5×#23511yescharacteristic
465C2#9201711yescharacteristic
466C2#9201911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #91764C2semidirect
2. C5×#876C2semidirect
3. C3×C4×D20C2semidirect
4. #91476C2semidirect
5. #91474C2semidirect
6. D5×(C2×D3)⋊C4C2semidirect
7. #91462C2semidirect
8. #91459C2semidirect
9. #91448C2semidirect
10. #91444C2semidirect
11. #91438C2semidirect
12. #91431C2semidirect
13. #91409C2semidirect
14. #91348C2semidirect
15. #91345C2semidirect
19. C2×Dic30C22semidirect
22. C2×C3×C4×D5C22semidirect
26. C2×#1202C22semidirect
28. C2×#1200C22semidirect
30. C3×C42×C5C22semidirect
33. #6714C22semidirect
34. #6714C22semidirect
38. C5×Dic3⋊C4C22semidirect
39. C5×Dic3⋊C4C22semidirect
40. C5×Dic3⋊C4C22semidirect
42. C3×#685C22semidirect
43. C3×C4⋊Dic5C22semidirect
44. #6669C22semidirect
45. #6668C22semidirect
50. #6665C22semidirect
51. Dic3×Dic5C22semidirect
67. C4×D20D3semidirect
111. #876D5semidirect
124. C2×C4×D5C2×D3semidirect
132. C42×C5C2×D3semidirect
143. #685C2×D3semidirect
144. C4⋊Dic5C2×D3semidirect
192. C3×C42C2×D5semidirect
207. Dic3⋊C4C2×D5semidirect
208. Dic3⋊C4C2×D5semidirect
209. Dic3⋊C4C2×D5semidirect
355. C42D3×D5semidirect
356. C3×C5#538semidirect
430. C5#5560semidirect
458. C3#66038semidirect

Maximal subgroups

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

subgroupindex
#917642
C5×#8762
C3×C4×D202
#914762
#914742
D5×(C2×D3)⋊C42
#914622
#914592
#914482
#914442
#914382
#914312
#914092
#913482
#913452
#660383
#55605