Finite Group Databasebeta

← #11756413

Subgroups — #11756413

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D15C211yesmaximal, characteristic, complemented
2C2×#6817C211yesmaximal, characteristic, complemented
3C3×C5×#123C211yesmaximal, characteristic, complemented
4#91828C211yesmaximal, characteristic, complemented
5C2×#6714C211yesmaximal, characteristic, complemented
6#91785C211yesmaximal, characteristic, complemented
7#91784C211yesmaximal, characteristic, complemented
8#91783C211yesmaximal, characteristic, complemented
9#91782C211yesmaximal, characteristic, complemented
10#91774C211yesmaximal, characteristic, complemented
11#91773C211yesmaximal, characteristic, complemented
12#91771C211yesmaximal, characteristic, complemented
13#91771C211yesmaximal, characteristic, complemented
14#91770C211yesmaximal, characteristic, complemented
15C22⋊C4×D15C211yesmaximal, characteristic, complemented
16#65988—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C23×D15C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic
20C22×C3×C4×C5C2211yescharacteristic, complemented
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C2×#1220C2211yescharacteristic, complemented
24C2×#1220C2211yescharacteristic, complemented
25C22×Dic15C2211yescharacteristic, complemented
26D4×D15—24no—
27#6817—24no—
28C2×D60C2211yescharacteristic
29C2×D60C2211yescharacteristic
30C2×D60C2211yescharacteristic, complemented
31C2×D60C2211yescharacteristic, complemented
32C2×C4×D15C2211yescharacteristic
33C2×C4×D15C2211yescharacteristic, complemented
34C2×C4×D15C2211yescharacteristic, complemented
35C2×C4×D15C2211yescharacteristic, complemented
36C2×Dic30C2211yescharacteristic, complemented
37C3×C5×C4⋊C4C2211yescharacteristic, complemented
38C3×C5×C4⋊C4C2211yescharacteristic, complemented
39C3×C5×C22⋊C4C2211yescharacteristic, complemented
40C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C3×C5×C22⋊C4C2211yescharacteristic, complemented
42#6719C2211yescharacteristic, complemented
43#6714C2211yescharacteristic
44#6714C2211yescharacteristic
45#6714C2211yescharacteristic
46#6714C2211yescharacteristic, complemented
47#6714C2211yescharacteristic, complemented
48#6714C2211yescharacteristic, complemented
49#6714C2211yescharacteristic, complemented
50#6714C2211yescharacteristic, complemented
51#6712C2211yescharacteristic, complemented
52#6712C2211yescharacteristic, complemented
53C4×Dic15C2211yescharacteristic, complemented
54#5654—51nomaximal, Hall
55C2×D4×D5—31no—
56C2×#709—31no—
57C5×#123D311yescharacteristic, complemented
58#4085—31no—
59C2×#685—31no—
60#4042—31no—
61#4041—31no—
62#4040—31no—
63#4039—31no—
64#4031—31no—
65#4030—31no—
66#4028—31no—
67#4028—31no—
68#4027—31no—
69D5×C22⋊C4—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15—22no—
73C22×D15—22no—
74C22×D15—22no—
75C22×D15—22no—
76C22×D15—41no—
77C22×D15—41no—
78C22×D15C2311yescharacteristic
79C22×D15C2311yescharacteristic
80C22×D15C2311yescharacteristic
81C22×D15C2311yescharacteristic
82C3×C5×D4—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C2311yescharacteristic
85C2×C3×C4×C5C2311yescharacteristic
86C2×C3×C4×C5C2311yescharacteristic
87C2×C3×C4×C5C2311yescharacteristic
88C2×C3×C4×C5C2311yescharacteristic
89#1220—22no—
90#1220—22no—
91#1220—41no—
92#1220D414yescomplemented
93C2×Dic15—41no—
94C2×Dic15C2311yescharacteristic
95C2×Dic15C2311yescharacteristic
96C2×Dic15C2311yescharacteristic
97C2×Dic15C2311yescharacteristic
98D60—22no—
99D60—22no—
100D60—22no—
101D60—41no—
102C4×D15—22no—
103C4×D15—22no—
104C4×D15—22no—
105C4×D15—41no—
106Dic30—22no—
107C2×D3×D4—51no—
108C2×#235—51no—
109C3×#123D511yescharacteristic, complemented
110#939—51no—
111C2×(C2×D3)⋊C4—51no—
112#896—51no—
113#895—51no—
114#894—51no—
115#893—51no—
116#885—51no—
117#884—51no—
118#882—51no—
119#882—51no—
120#67⋊C4—51no—
121D3×C22⋊C4—51no—
122C23×D5—31no—
123C23×D5—31no—
124C2×C5×D4C2×D311yescharacteristic
125C22×C4×C5C2×D311yescharacteristic, complemented
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C2×C22⋊D5—31no—
129C2×C22⋊D5—31no—
130C22×Dic5—31no—
131D4×D5—64no—
132#709—64no—
133C2×D20—31no—
134C2×D20—31no—
135C2×D20—31no—
136C2×D20—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×Dic10—31no—
142C5×C4⋊C4C2×D311yescharacteristic, complemented
143C5×C4⋊C4C2×D311yescharacteristic, complemented
144C5×C22⋊C4C2×D311yescharacteristic, complemented
145C5×C22⋊C4C2×D311yescharacteristic, complemented
146C5×C22⋊C4C2×D311yescharacteristic, complemented
147C22⋊Dic5—31no—
148#685—31no—
149#685—31no—
150#685—31no—
151#685—31no—
152#685—31no—
153#685—31no—
154#685—31no—
155#685—31no—
156#683—31no—
157#683—31no—
158C4×Dic5—31no—
159#546—151noSylow
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5C2×D412yes—
166C22×C3×C5C2411yescharacteristic
167C2×D15—21no—
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C2×D15—21no—
175C2×D15—21no—
176C2×D15—21no—
177C2×D15—44no—
178C2×D15—44no—
179C2×D15C2×D412yes—
180C2×D15#4112yescomplemented
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186Dic15—21no—
187Dic15—21no—
188Dic15—21no—
189Dic15C2×D412yes—
190C23×D3—51no—
191C23×D3—51no—
192C2×C3×D4C2×D511yescharacteristic
193C22×C3×C4C2×D511yescharacteristic, complemented
194C2×#67—51no—
195C2×#67—51no—
196C2×#67—51no—
197C2×#67—51no—
198C22×Dic3—51no—
199D3×D4—104no—
200#235—104no—
201C2×D12—51no—
202C2×D12—51no—
203C2×D12—51no—
204C2×D12—51no—
205C2×C4×D3—51no—
206C2×C4×D3—51no—
207C2×C4×D3—51no—
208C2×C4×D3—51no—
209C2×Dic6—51no—
210C3×C4⋊C4C2×D511yescharacteristic, complemented
211C3×C4⋊C4C2×D511yescharacteristic, complemented
212C3×C22⋊C4C2×D511yescharacteristic, complemented
213C3×C22⋊C4C2×D511yescharacteristic, complemented
214C3×C22⋊C4C2×D511yescharacteristic, complemented
215#217—51no—
216(C2×D3)⋊C4—51no—
217(C2×D3)⋊C4—51no—
218(C2×D3)⋊C4—51no—
219(C2×D3)⋊C4—51no—
220(C2×D3)⋊C4—51no—
221(C2×D3)⋊C4—51no—
222(C2×D3)⋊C4—51no—
223(C2×D3)⋊C4—51no—
224Dic3⋊C4—51no—
225Dic3⋊C4—51no—
226C4×Dic3—51no—
227C23×C5C22×D311yescharacteristic
228C23×C5C22×D311yescharacteristic
229C22×D5—31no—
230C22×D5—31no—
231C22×D5—31no—
232C22×D5—31no—
233C22×D5—62no—
234C22×D5—62no—
235C22×D5—62no—
236C22×D5—62no—
237C22×D5—121no—
238C22×D5—121no—
239C5×D4—22no—
240C2×C4×C5—22no—
241C2×C4×C5C22×D311yescharacteristic
242C2×C4×C5C22×D311yescharacteristic
243C2×C4×C5C22×D311yescharacteristic
244C2×C4×C5C22×D311yescharacteristic
245C2×C4×C5C22×D311yescharacteristic
246C22⋊D5—34no—
247C22⋊D5—62no—
248C22⋊D5—62no—
249C22⋊D5—121no—
250C2×Dic5—31no—
251C2×Dic5—31no—
252C2×Dic5—31no—
253C2×Dic5—31no—
254C2×Dic5—121no—
255D20—62no—
256D20—62no—
257D20—62no—
258D20—121no—
259C4×D5—62no—
260C4×D5—62no—
261C4×D5—62no—
262C4×D5—121no—
263Dic10—62no—
264C2×#41—151no—
265C22×D4—151no—
266#124—151no—
267#123—151no—
268#123D1511yescharacteristic, complemented
269C22⋊Q8—151no—
270#121—151no—
271#121—151no—
272#121—151no—
273#120—151no—
274#120—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C22⋊C4—151no—
278C2×C22⋊C4—151no—
279C2×C3×C5—22no—
280C2×C3×C5—41no—
281C2×C3×C5C22×D411yescharacteristic
282C2×C3×C5C2×#4111yescharacteristic
283C2×C3×C5H(5,𝔽2)11yescharacteristic
284D15—22no—
285D15—22no—
286D15—41no—
287D15—41no—
288C23×C3C22×D511yescharacteristic
289C23×C3C22×D511yescharacteristic
290C22×D3—51no—
291C22×D3—51no—
292C22×D3—51no—
293C22×D3—51no—
294C22×D3—102no—
295C22×D3—102no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—201no—
299C22×D3—201no—
300C3×D4—22no—
301C2×C3×C4—22no—
302C2×C3×C4C22×D511yescharacteristic
303C2×C3×C4C22×D511yescharacteristic
304C2×C3×C4C22×D511yescharacteristic
305C2×C3×C4C22×D511yescharacteristic
306C2×C3×C4C22×D511yescharacteristic
307#67—54no—
308#67—102no—
309#67—102no—
310#67—201no—
311C2×Dic3—51no—
312C2×Dic3—51no—
313C2×Dic3—51no—
314C2×Dic3—51no—
315C2×Dic3—201no—
316D12—102no—
317D12—102no—
318D12—102no—
319D12—201no—
320C4×D3—102no—
321C4×D3—102no—
322C4×D3—102no—
323C4×D3—201no—
324Dic6—102no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5D3×D412yes—
331C22×C5C23×D311yescharacteristic
332C2×D5—32no—
333C2×D5—32no—
334C2×D5—61no—
335C2×D5—61no—
336C2×D5—61no—
337C2×D5—61no—
338C2×D5—61no—
339C2×D5—61no—
340C2×D5—61no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—61no—
344C2×D5—124no—
345C2×D5—124no—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—21no—
349C4×C5—21no—
350C4×C5—21no—
351Dic5—32no—
352Dic5—61no—
353Dic5—61no—
354Dic5—61no—
355C24—151no—
356C24—151no—
357#41—304no—
358C2×Q8—151no—
359C2×D4—151no—
360C2×D4—151no—
361C2×D4—151no—
362C2×D4—151no—
363C2×D4—151no—
364C2×D4—151no—
365C2×D4—151no—
366C2×D4—151no—
367C2×D4—304no—
368C2×D4C2×D1511yescharacteristic
369C22×C4—151no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4C2×D1511yescharacteristic, complemented
375C4⋊C4—151no—
376C4⋊C4—151no—
377C4⋊C4C2×D1511yescharacteristic, complemented
378C4⋊C4C2×D1511yescharacteristic, complemented
379C22⋊C4—151no—
380C22⋊C4—151no—
381C22⋊C4—151no—
382C22⋊C4—151no—
383C22⋊C4—151no—
384C22⋊C4—151no—
385C22⋊C4—151no—
386C22⋊C4—151no—
387C22⋊C4—151no—
388C22⋊C4C2×D1511yescharacteristic, complemented
389C22⋊C4C2×D1511yescharacteristic, complemented
390C22⋊C4C2×D1511yescharacteristic, complemented
391C42—151no—
392C3×C5#54611yescharacteristic, complemented, Hall
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3D4×D512yes—
399C22×C3C23×D511yescharacteristic
400C2×D3—52no—
401C2×D3—52no—
402C2×D3—101no—
403C2×D3—101no—
404C2×D3—101no—
405C2×D3—101no—
406C2×D3—101no—
407C2×D3—101no—
408C2×D3—101no—
409C2×D3—101no—
410C2×D3—101no—
411C2×D3—101no—
412C2×D3—204no—
413C2×D3—204no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419Dic3—52no—
420Dic3—101no—
421Dic3—101no—
422Dic3—101no—
423C2×C5—22no—
424C2×C5—41no—
425C2×C5C2×D3×D411yescharacteristic
426C2×C5D3×#4111yescharacteristic
427C2×C5#100911yescharacteristic
428D5—62no—
429D5—62no—
430D5—121no—
431D5—121no—
432C23—151no—
433C23—151no—
434C23—151no—
435C23—151no—
436C23—302no—
437C23—302no—
438C23—302no—
439C23—302no—
440C23—601no—
441C23—601no—
442C23C22×D1511yescharacteristic
443C23C22×D1511yescharacteristic
444Q8—302no—
445D4—22no—
446D4—154no—
447D4—302no—
448D4—302no—
449D4—302no—
450D4—302no—
451D4—302no—
452D4—601no—
453D4—601no—
454C2×C4—22no—
455C2×C4—151no—
456C2×C4—151no—
457C2×C4—151no—
458C2×C4—151no—
459C2×C4—302no—
460C2×C4—302no—
461C2×C4—302no—
462C2×C4—601no—
463C2×C4—601no—
464C2×C4C22×D1511yescharacteristic
465C2×C4C22×D1511yescharacteristic
466C2×C4C22×D1511yescharacteristic
467C2×C4C22×D1511yescharacteristic
468C2×C4C22×D1511yescharacteristic
469C2×C3—22no—
470C2×C3—41no—
471C2×C3C2×D4×D511yescharacteristic
472C2×C3D5×#4111yescharacteristic
473C2×C3#414911yescharacteristic
474D3—102no—
475D3—102no—
476D3—201no—
477D3—201no—
478C5#565411yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—152no—
485C22—152no—
486C22—301no—
487C22—301no—
488C22—301no—
489C22—301no—
490C22—301no—
491C22—301no—
492C22—301no—
493C22—301no—
494C22—301no—
495C22—301no—
496C22—604no—
497C22—604no—
498C22D4×D1512yes—
499C22C23×D1511yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—152no—
506C4—301no—
507C4—301no—
508C4—301no—
509C3#6598811yescharacteristic, complemented, Sylow
510C2—22no—
511C2—41no—
512C2—302no—
513C2—302no—
514C2—601no—
515C2—601no—
516C2C2×D4×D1511yescharacteristic
517C2#41×D1511yescharacteristic
518C2#9210011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#123C2
hypercenter#123D15
hypocenterC3×C5#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×D4×D15C2semidirect
2. C2×#6817C2semidirect
3. C3×C5×#123C2semidirect
4. #91828C2semidirect
5. C2×#6714C2semidirect
6. #91785C2semidirect
7. #91784C2semidirect
8. #91783C2semidirect
9. #91782C2semidirect
10. #91774C2semidirect
11. #91773C2semidirect
12. #91771C2semidirect
13. #91771C2semidirect
14. #91770C2semidirect
15. C22⋊C4×D15C2semidirect
20. C22×C3×C4×C5C22semidirect
23. C2×#1220C22semidirect
24. C2×#1220C22semidirect
25. C22×Dic15C22semidirect
30. C2×D60C22semidirect
31. C2×D60C22semidirect
33. C2×C4×D15C22semidirect
34. C2×C4×D15C22semidirect
35. C2×C4×D15C22semidirect
36. C2×Dic30C22semidirect
37. C3×C5×C4⋊C4C22semidirect
38. C3×C5×C4⋊C4C22semidirect
39. C3×C5×C22⋊C4C22semidirect
40. C3×C5×C22⋊C4C22semidirect
41. C3×C5×C22⋊C4C22semidirect
42. #6719C22semidirect
46. #6714C22semidirect
47. #6714C22semidirect
48. #6714C22semidirect
49. #6714C22semidirect
50. #6714C22semidirect
51. #6712C22semidirect
52. #6712C22semidirect
53. C4×Dic15C22semidirect
57. C5×#123D3semidirect
92. #1220D4semidirect
109. C3×#123D5semidirect
125. C22×C4×C5C2×D3semidirect
142. C5×C4⋊C4C2×D3semidirect
143. C5×C4⋊C4C2×D3semidirect
144. C5×C22⋊C4C2×D3semidirect
145. C5×C22⋊C4C2×D3semidirect
146. C5×C22⋊C4C2×D3semidirect
180. C2×D15#41semidirect
193. C22×C3×C4C2×D5semidirect
210. C3×C4⋊C4C2×D5semidirect
211. C3×C4⋊C4C2×D5semidirect
212. C3×C22⋊C4C2×D5semidirect
213. C3×C22⋊C4C2×D5semidirect
214. C3×C22⋊C4C2×D5semidirect
268. #123D15semidirect
374. C22×C4C2×D15semidirect
377. C4⋊C4C2×D15semidirect
378. C4⋊C4C2×D15semidirect
388. C22⋊C4C2×D15semidirect
389. C22⋊C4C2×D15semidirect
390. C22⋊C4C2×D15semidirect
392. C3×C5#546semidirect
478. C5#5654semidirect
509. C3#65988semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D152
C2×#68172
C3×C5×#1232
#918282
C2×#67142
#917852
#917842
#917832
#917822
#917742
#917732
#917712
#917702
C22⋊C4×D152
#659883
#56545