Finite Group Databasebeta

← #11753160

Subgroups — #11753160

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#91771C211yesmaximal, characteristic, complemented
2C5×#879C211yesmaximal, characteristic, complemented
3C3×#4029C211yesmaximal, characteristic, complemented
4#91572C211yesmaximal, characteristic, complemented
5#91561C211yesmaximal, characteristic, complemented
6#91533C211yesmaximal, characteristic, complemented
7#91526C211yesmaximal, characteristic, complemented
8#91459C211yesmaximal, characteristic, complemented
9#91450C211yesmaximal, characteristic, complemented
10#91444C211yesmaximal, characteristic, complemented
11#91433C211yesmaximal, characteristic, complemented
12#91428C211yesmaximal, characteristic, complemented
13#91419C211yesmaximal, characteristic, complemented
14#91353C211yesmaximal, characteristic, complemented
15#91345C211yesmaximal, characteristic, complemented
16#66038—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×D60C2211yescharacteristic
20C2×D60C2211yescharacteristic
21C2×C3×C22⋊D5C2211yescharacteristic
22C2×C3×C4×D5C2211yescharacteristic, complemented
23C2×#1204C2211yescharacteristic, complemented
24C2×#1202C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1202C2211yescharacteristic, complemented
27C2×#1200C2211yescharacteristic
28C2×#1200C2211yescharacteristic
29C2×#1200C2211yescharacteristic, complemented
30C3×C5×C22⋊C4C2211yescharacteristic
31#6714C2211yescharacteristic
32#6714C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×#217C2211yescharacteristic
35C5×C4⋊Dic3C2211yescharacteristic, complemented
36C5×Dic3⋊C4C2211yescharacteristic, complemented
37C5×Dic3⋊C4C2211yescharacteristic, complemented
38C4×C5×Dic3C2211yescharacteristic, complemented
39C3×C22⋊Dic5C2211yescharacteristic
40C3×#685C2211yescharacteristic, complemented
41C3×C4⋊Dic5C2211yescharacteristic, complemented
42C3×#683C2211yescharacteristic, complemented
43#6668C2211yescharacteristic, complemented
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic, complemented
49#6667C2211yescharacteristic, complemented
50#6665C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5657—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#4029D311yescharacteristic, complemented
63#4028—31no—
64#4028—31no—
65D5×C22⋊C4—31no—
66#4021—31no—
67C4×D20—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15—22no—
70C22×D15—41no—
71C22×D15—41no—
72C22×D15C2311yescharacteristic
73C22×D15C2311yescharacteristic
74C22×D15C2311yescharacteristic
75C22×C3×D5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78#1220—41no—
79C2×Dic15C2311yescharacteristic
80D60—22no—
81D60—41no—
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C3×C22⋊D5—41no—
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C3×C4×D5—41no—
91#1204—41no—
92#1202—22no—
93#1202—41no—
94#1202—41no—
95#1200—41no—
96#1200—41no—
97#1200—41no—
98C3×#123—51no—
99#938—51no—
100#937—51no—
101#930—51no—
102C4×#67—51no—
103#898—51no—
104#897—51no—
105#894—51no—
106#893—51no—
107#885—51no—
108#885—51no—
109#884—51no—
110#882—51no—
111D3×C22⋊C4—51no—
112#879D511yescharacteristic, complemented
113C23×D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5C2×D311yescharacteristic
116C2×D20—31no—
117C2×D20—31no—
118C2×D20—31no—
119C2×D20—31no—
120C2×D20—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
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⋊C4C2×D311yescharacteristic
132C42×C5—31no—
133C22⋊Dic5C2×D311yescharacteristic
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#685—31no—
143#685C2×D311yescharacteristic, complemented
144C4⋊Dic5C2×D311yescharacteristic, complemented
145#683—31no—
146#683C2×D311yescharacteristic, complemented
147C4×Dic5—31no—
148#538—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—44no—
162C2×D15#4112yes—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×Dic5—21no—
172C5×Dic3—21no—
173C5×Dic3—21no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C23×D3—51no—
177C2×C3×D4—51no—
178C22×C3×C4—51no—
179C2×#67—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×D12—51no—
184C2×D12—51no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×Dic6—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C22⋊C4—51no—
193C3×C22⋊C4C2×D511yescharacteristic
194#217—51no—
195#217C2×D511yescharacteristic
196#217C2×D511yescharacteristic
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)⋊C4—51no—
203(C2×D3)⋊C4—51no—
204(C2×D3)⋊C4—51no—
205C4⋊Dic3—51no—
206C4⋊Dic3C2×D511yescharacteristic, complemented
207Dic3⋊C4C2×D511yescharacteristic, complemented
208Dic3⋊C4C2×D511yescharacteristic, complemented
209C4×Dic3—51no—
210C4×Dic3C2×D511yescharacteristic, complemented
211C23×C5C22×D311yescharacteristic
212C22×D5—31no—
213C22×D5—31no—
214C22×D5—31no—
215C22×D5—62no—
216C22×D5—121no—
217C22×D5—121no—
218C22×D5C22×D311yescharacteristic
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5C22×D311yescharacteristic
224C2×C4×C5C22×D311yescharacteristic
225C22⋊D5—41no—
226C22⋊D5—121no—
227C2×Dic5—31no—
228C2×Dic5C22×D311yescharacteristic
229C2×Dic5C22×D311yescharacteristic
230C2×Dic5C22×D311yescharacteristic
231D20—62no—
232D20—62no—
233D20—121no—
234D20—121no—
235D20—121no—
236C4×D5—41no—
237C4×D5—121no—
238C4×D5—121no—
239C4×D5—121no—
240Dic10—121no—
241#126—31no—
242#126—151no—
243#124—151no—
244#124—151no—
245#123—51no—
246#123—151no—
247C22⋊Q8—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#120—151no—
252#120—151no—
253C4×D4—151no—
254C4×D4—151no—
255C2×C22⋊C4—151no—
256C2×C3×C5—41no—
257C2×C3×C5C2×#4111yescharacteristic
258C2×C3×C5H(5,𝔽2)11yescharacteristic
259C2×C3×C5H(5,𝔽2)11yescharacteristic
260D15—22no—
261D15—41no—
262D15—41no—
263C3×D5—41no—
264C23×C3—51no—
265C23×C3C22×D511yescharacteristic
266C22×D3—51no—
267C22×D3—51no—
268C22×D3—51no—
269C22×D3—102no—
270C22×D3—201no—
271C22×D3—201no—
272C3×D4—201no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—201no—
277C2×C3×C4C22×D511yescharacteristic
278C2×C3×C4C22×D511yescharacteristic
279#67—102no—
280#67—201no—
281#67—201no—
282#67—201no—
283C2×Dic3—51no—
284C2×Dic3C22×D511yescharacteristic
285C2×Dic3C22×D511yescharacteristic
286C2×Dic3C22×D511yescharacteristic
287C2×Dic3C22×D511yescharacteristic
288D12—102no—
289D12—201no—
290C4×D3—201no—
291C4×D3—201no—
292C4×D3—201no—
293Dic6—201no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5C23×D311yescharacteristic
298C2×D5—21no—
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—32no—
302C2×D5—61no—
303C2×D5—61no—
304C2×D5—61no—
305C2×D5—61no—
306C2×D5—61no—
307C2×D5—61no—
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—124no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—61no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317Dic5—21no—
318Dic5—21no—
319Dic5—21no—
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—151no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—31no—
337C4⋊C4—51no—
338C4⋊C4—51no—
339C4⋊C4—151no—
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—51no—
343C22⋊C4—51no—
344C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic
354C42—31no—
355C42—151no—
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—101no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3C23×D511yescharacteristic
364C2×D3—52no—
365C2×D3—101no—
366C2×D3—101no—
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—101no—
377C3×C4—101no—
378C3×C4—101no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—21no—
383Dic3—101no—
384C2×C5—41no—
385C2×C5#100411yescharacteristic
386C2×C5D3×#4111yescharacteristic
387C2×C5#100911yescharacteristic
388D5—41no—
389D5—62no—
390D5—121no—
391D5—121no—
392C23—51no—
393C23—151no—
394C23—151no—
395C23—151no—
396C23—302no—
397C23—601no—
398C23—601no—
399C23C2×D3×D511yescharacteristic
400Q8—601no—
401D4—201no—
402D4—302no—
403D4—302no—
404D4—601no—
405D4—601no—
406D4—601no—
407D4—601no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—51no—
413C2×C4—51no—
414C2×C4—51no—
415C2×C4—151no—
416C2×C4—201no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4—601no—
420C2×C4C2×D3×D511yescharacteristic
421C2×C4C2×D3×D511yescharacteristic
422C2×C3—41no—
423C2×C3—201no—
424C2×C3D5×#4111yescharacteristic
425C2×C3#414911yescharacteristic
426C2×C3#414911yescharacteristic
427D3—102no—
428D3—201no—
429D3—201no—
430C5#565711yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—101no—
435C22—101no—
436C22—101no—
437C22—152no—
438C22—301no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22—301no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22—604no—
447C22C22×D3×D511yescharacteristic
448C4—21no—
449C4—21no—
450C4—61no—
451C4—61no—
452C4—61no—
453C4—61no—
454C4—101no—
455C4—101no—
456C4—101no—
457C4—301no—
458C3#6603811yescharacteristic, complemented, Sylow
459C2—41no—
460C2—201no—
461C2—302no—
462C2—601no—
463C2—601no—
464C2#9201911yescharacteristic
465C2#9202411yescharacteristic
466C2#9202611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #91771C2semidirect
2. C5×#879C2semidirect
3. C3×#4029C2semidirect
4. #91572C2semidirect
5. #91561C2semidirect
6. #91533C2semidirect
7. #91526C2semidirect
8. #91459C2semidirect
9. #91450C2semidirect
10. #91444C2semidirect
11. #91433C2semidirect
12. #91428C2semidirect
13. #91419C2semidirect
14. #91353C2semidirect
15. #91345C2semidirect
22. C2×C3×C4×D5C22semidirect
23. C2×#1204C22semidirect
26. C2×#1202C22semidirect
29. C2×#1200C22semidirect
35. C5×C4⋊Dic3C22semidirect
36. C5×Dic3⋊C4C22semidirect
37. C5×Dic3⋊C4C22semidirect
38. C4×C5×Dic3C22semidirect
40. C3×#685C22semidirect
41. C3×C4⋊Dic5C22semidirect
42. C3×#683C22semidirect
43. #6668C22semidirect
48. #6667C22semidirect
49. #6667C22semidirect
50. #6665C22semidirect
51. Dic3×Dic5C22semidirect
62. #4029D3semidirect
112. #879D5semidirect
124. C2×C4×D5C2×D3semidirect
143. #685C2×D3semidirect
144. C4⋊Dic5C2×D3semidirect
146. #683C2×D3semidirect
206. C4⋊Dic3C2×D5semidirect
207. Dic3⋊C4C2×D5semidirect
208. Dic3⋊C4C2×D5semidirect
210. C4×Dic3C2×D5semidirect
356. C3×C5#538semidirect
430. C5#5657semidirect
458. C3#66038semidirect

Maximal subgroups

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

subgroupindex
#917712
C5×#8792
C3×#40292
#915722
#915612
#915332
#915262
#914592
#914502
#914442
#914332
#914282
#914192
#913532
#913452
#660383
#56575