Finite Group Databasebeta

← #11756379

Subgroups — #11756379

Order 960.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#121C211yesmaximal, characteristic, complemented
2#91829C211yesmaximal, characteristic, complemented
3#91828C211yesmaximal, characteristic, complemented
4#91828C211yesmaximal, characteristic, complemented
5#91827C211yesmaximal, characteristic, complemented
6#91826C211yesmaximal, characteristic, complemented
7#91826C211yesmaximal, characteristic, complemented
8#91819C211yesmaximal, characteristic, complemented
9#91818C211yesmaximal, characteristic, complemented
10#91787C211yesmaximal, characteristic, complemented
11#91783C211yesmaximal, characteristic, complemented
12#91775C211yesmaximal, characteristic, complemented
13#91773C211yesmaximal, characteristic, complemented
14#91771C211yesmaximal, characteristic, complemented
15#91768C211yesmaximal, characteristic, complemented
16#65954—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic
20C2×C3×C5×D4C2211yescharacteristic, complemented
21C22×C3×C4×C5C2211yescharacteristic, complemented
22C2×#1220C2211yescharacteristic
23C2×#1220C2211yescharacteristic
24C2×#1220C2211yescharacteristic
25C2×#1220C2211yescharacteristic
26C2×#1220C2211yescharacteristic
27C2×#1220C2211yescharacteristic, complemented
28C2×#1220C2211yescharacteristic, complemented
29C22×Dic15C2211yescharacteristic, complemented
30C2×D60C2211yescharacteristic
31C2×D60C2211yescharacteristic
32C2×C4×D15C2211yescharacteristic, complemented
33C3×C5×C4⋊C4C2211yescharacteristic, complemented
34C3×C5×C22⋊C4C2211yescharacteristic
35C3×C5×C22⋊C4C2211yescharacteristic, complemented
36#6719C2211yescharacteristic
37#6719C2211yescharacteristic
38#6719C2211yescharacteristic, complemented
39#6714C2211yescharacteristic
40#6714C2211yescharacteristic
41#6714C2211yescharacteristic
42#6714C2211yescharacteristic
43#6714C2211yescharacteristic
44#6714C2211yescharacteristic
45#6714C2211yescharacteristic, complemented
46C4⋊Dic15C2211yescharacteristic, complemented
47C4⋊Dic15C2211yescharacteristic, complemented
48#6712C2211yescharacteristic, complemented
49#6712C2211yescharacteristic, complemented
50#6712C2211yescharacteristic, complemented
51C4×Dic15C2211yescharacteristic, complemented
52#5620—51nomaximal, Hall
53C5×#121D311yescharacteristic, complemented
54#4086—31no—
55#4085—31no—
56#4085—31no—
57#4084—31no—
58#4083—31no—
59#4083—31no—
60#4076—31no—
61#4075—31no—
62#4044—31no—
63#4040—31no—
64#4032—31no—
65#4030—31no—
66#4028—31no—
67#4025—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C23×C3×C5C2311yescharacteristic
71C22×D15—41no—
72C22×D15—41no—
73C22×D15—41no—
74C22×D15C2311yescharacteristic
75C22×D15C2311yescharacteristic
76C22×D15C2311yescharacteristic
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2311yescharacteristic
82C2×C3×C4×C5C2311yescharacteristic
83C2×C3×C4×C5C2311yescharacteristic
84C2×C3×C4×C5C2311yescharacteristic
85#1220—41no—
86#1220—41no—
87#1220—41no—
88#1220—41no—
89#1220—41no—
90#1220—41no—
91#1220—41no—
92C2×Dic15—41no—
93C2×Dic15C2311yescharacteristic
94C2×Dic15C2311yescharacteristic
95C2×Dic15C2311yescharacteristic
96C2×Dic15C2311yescharacteristic
97C2×Dic15C2311yescharacteristic
98D60—41no—
99D60—41no—
100C4×D15—41no—
101C3×#121D511yescharacteristic, complemented
102#940—51no—
103#939—51no—
104#939—51no—
105#938—51no—
106#937—51no—
107#937—51no—
108#930—51no—
109#929—51no—
110#898—51no—
111#894—51no—
112#886—51no—
113#884—51no—
114#882—51no—
115#879—51no—
116C23×D5—31no—
117C2×C5×D4C2×D311yescharacteristic
118C2×C5×D4C2×D311yescharacteristic
119C2×C5×D4C2×D311yescharacteristic, complemented
120C22×C4×C5C2×D311yescharacteristic, complemented
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C22×Dic5—31no—
129C2×D20—31no—
130C2×D20—31no—
131C2×C4×D5—31no—
132C5×C4⋊C4C2×D311yescharacteristic, complemented
133C5×C22⋊C4C2×D311yescharacteristic
134C5×C22⋊C4C2×D311yescharacteristic, complemented
135C22⋊Dic5—31no—
136C22⋊Dic5—31no—
137C22⋊Dic5—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685—31no—
144#685—31no—
145C4⋊Dic5—31no—
146C4⋊Dic5—31no—
147#683—31no—
148#683—31no—
149#683—31no—
150C4×Dic5—31no—
151#560—151noSylow
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5C2411yescharacteristic
162C2×D15—21no—
163C2×D15—21no—
164C2×D15—21no—
165C2×D15—21no—
166C2×D15—21no—
167C2×D15—21no—
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C2×D15—44no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176Dic15—21no—
177Dic15—21no—
178Dic15—21no—
179Dic15—21no—
180Dic15—21no—
181C23×D3—51no—
182C2×C3×D4C2×D511yescharacteristic
183C2×C3×D4C2×D511yescharacteristic
184C2×C3×D4C2×D511yescharacteristic, complemented
185C22×C3×C4C2×D511yescharacteristic, complemented
186C2×#67—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67—51no—
190C2×#67—51no—
191C2×#67—51no—
192C2×#67—51no—
193C22×Dic3—51no—
194C2×D12—51no—
195C2×D12—51no—
196C2×C4×D3—51no—
197C3×C4⋊C4C2×D511yescharacteristic, complemented
198C3×C22⋊C4C2×D511yescharacteristic
199C3×C22⋊C4C2×D511yescharacteristic, complemented
200#217—51no—
201#217—51no—
202#217—51no—
203(C2×D3)⋊C4—51no—
204(C2×D3)⋊C4—51no—
205(C2×D3)⋊C4—51no—
206(C2×D3)⋊C4—51no—
207(C2×D3)⋊C4—51no—
208(C2×D3)⋊C4—51no—
209(C2×D3)⋊C4—51no—
210C4⋊Dic3—51no—
211C4⋊Dic3—51no—
212Dic3⋊C4—51no—
213Dic3⋊C4—51no—
214Dic3⋊C4—51no—
215C4×Dic3—51no—
216C23×C5C22×D311yescharacteristic
217C23×C5C22×D311yescharacteristic
218C23×C5C22×D311yescharacteristic
219C22×D5—31no—
220C22×D5—31no—
221C22×D5—31no—
222C22×D5—121no—
223C22×D5—121no—
224C22×D5—121no—
225C5×D4—41no—
226C5×D4—41no—
227C5×D4—41no—
228C2×C4×C5—41no—
229C2×C4×C5C22×D311yescharacteristic
230C2×C4×C5C22×D311yescharacteristic
231C2×C4×C5C22×D311yescharacteristic
232C2×C4×C5C22×D311yescharacteristic
233C22⋊D5—121no—
234C22⋊D5—121no—
235C22⋊D5—121no—
236C22⋊D5—121no—
237C22⋊D5—121no—
238C22⋊D5—121no—
239C22⋊D5—121no—
240C2×Dic5—31no—
241C2×Dic5—31no—
242C2×Dic5—31no—
243C2×Dic5—31no—
244C2×Dic5—31no—
245C2×Dic5—121no—
246D20—121no—
247D20—121no—
248C4×D5—121no—
249#127—151no—
250#126—151no—
251#126—151no—
252#123—151no—
253#123—151no—
254#123—151no—
255#121—151no—
256#121—151no—
257#121—151no—
258#121—151no—
259#121—151no—
260#121D1511yescharacteristic, complemented
261#120—151no—
262#120—151no—
263#120—151no—
264C2×C3×C5—41no—
265C2×C3×C5—41no—
266C2×C3×C5—41no—
267C2×C3×C5H(5,𝔽2)11yescharacteristic
268C2×C3×C5H(5,𝔽2)11yescharacteristic
269C2×C3×C5H(5,𝔽2)11yescharacteristic
270D15—41no—
271D15—41no—
272D15—41no—
273C23×C3C22×D511yescharacteristic
274C23×C3C22×D511yescharacteristic
275C23×C3C22×D511yescharacteristic
276C22×D3—51no—
277C22×D3—51no—
278C22×D3—51no—
279C22×D3—201no—
280C22×D3—201no—
281C22×D3—201no—
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—41no—
285C2×C3×C4—41no—
286C2×C3×C4C22×D511yescharacteristic
287C2×C3×C4C22×D511yescharacteristic
288C2×C3×C4C22×D511yescharacteristic
289C2×C3×C4C22×D511yescharacteristic
290#67—201no—
291#67—201no—
292#67—201no—
293#67—201no—
294#67—201no—
295#67—201no—
296#67—201no—
297C2×Dic3—51no—
298C2×Dic3—51no—
299C2×Dic3—51no—
300C2×Dic3—51no—
301C2×Dic3—51no—
302C2×Dic3—201no—
303D12—201no—
304D12—201no—
305C4×D3—201no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5C23×D311yescharacteristic
316C2×D5—61no—
317C2×D5—61no—
318C2×D5—61no—
319C2×D5—61no—
320C2×D5—61no—
321C2×D5—61no—
322C2×D5—61no—
323C2×D5—61no—
324C2×D5—61no—
325C2×D5—124no—
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—21no—
330Dic5—61no—
331Dic5—61no—
332Dic5—61no—
333Dic5—61no—
334Dic5—61no—
335C24—151no—
336C2×D4—151no—
337C2×D4—151no—
338C2×D4—151no—
339C2×D4—151no—
340C2×D4—151no—
341C2×D4—151no—
342C2×D4—151no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4C2×D1511yescharacteristic
346C2×D4C2×D1511yescharacteristic
347C2×D4C2×D1511yescharacteristic, complemented
348C22×C4—151no—
349C22×C4—151no—
350C22×C4C2×D1511yescharacteristic, complemented
351C4⋊C4—151no—
352C4⋊C4—151no—
353C4⋊C4—151no—
354C4⋊C4—151no—
355C4⋊C4—151no—
356C4⋊C4C2×D1511yescharacteristic, complemented
357C22⋊C4—151no—
358C22⋊C4—151no—
359C22⋊C4—151no—
360C22⋊C4—151no—
361C22⋊C4—151no—
362C22⋊C4—151no—
363C22⋊C4—151no—
364C22⋊C4—151no—
365C22⋊C4—151no—
366C22⋊C4—151no—
367C22⋊C4C2×D1511yescharacteristic
368C22⋊C4C2×D1511yescharacteristic, complemented
369C42—151no—
370C3×C5#56011yescharacteristic, complemented, Hall
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3C23×D511yescharacteristic
381C2×D3—101no—
382C2×D3—101no—
383C2×D3—101no—
384C2×D3—101no—
385C2×D3—101no—
386C2×D3—101no—
387C2×D3—101no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3—204no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395Dic3—101no—
396Dic3—101no—
397Dic3—101no—
398Dic3—101no—
399Dic3—101no—
400C2×C5—41no—
401C2×C5—41no—
402C2×C5—41no—
403C2×C5#100411yescharacteristic
404C2×C5#100411yescharacteristic
405C2×C5#100911yescharacteristic
406D5—121no—
407D5—121no—
408D5—121no—
409C23—151no—
410C23—151no—
411C23—151no—
412C23—601no—
413C23—601no—
414C23—601no—
415C23C22×D1511yescharacteristic
416C23C22×D1511yescharacteristic
417C23C22×D1511yescharacteristic
418D4—41no—
419D4—41no—
420D4—41no—
421D4—601no—
422D4—601no—
423D4—601no—
424D4—601no—
425D4—601no—
426D4—601no—
427D4—601no—
428D4—601no—
429D4—601no—
430C2×C4—41no—
431C2×C4—151no—
432C2×C4—151no—
433C2×C4—151no—
434C2×C4—151no—
435C2×C4—151no—
436C2×C4—601no—
437C2×C4—601no—
438C2×C4C22×D1511yescharacteristic
439C2×C4C22×D1511yescharacteristic
440C2×C4C22×D1511yescharacteristic
441C2×C4C22×D1511yescharacteristic
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3#414411yescharacteristic
446C2×C3#414411yescharacteristic
447C2×C3#414911yescharacteristic
448D3—201no—
449D3—201no—
450D3—201no—
451C5#562011yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—301no—
462C22—301no—
463C22—301no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22—301no—
468C22—301no—
469C22—301no—
470C22—604no—
471C22C23×D1511yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—301no—
477C4—301no—
478C4—301no—
479C4—301no—
480C4—301no—
481C3#6595411yescharacteristic, complemented, Sylow
482C2—41no—
483C2—41no—
484C2—41no—
485C2—601no—
486C2—601no—
487C2—601no—
488C2#9209511yescharacteristic
489C2#9209511yescharacteristic
490C2#9210011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#121C2
hypercenter#121D15
hypocenterC3×C5#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×C5×#121C2semidirect
2. #91829C2semidirect
3. #91828C2semidirect
4. #91828C2semidirect
5. #91827C2semidirect
6. #91826C2semidirect
7. #91826C2semidirect
8. #91819C2semidirect
9. #91818C2semidirect
10. #91787C2semidirect
11. #91783C2semidirect
12. #91775C2semidirect
13. #91773C2semidirect
14. #91771C2semidirect
15. #91768C2semidirect
20. C2×C3×C5×D4C22semidirect
21. C22×C3×C4×C5C22semidirect
27. C2×#1220C22semidirect
28. C2×#1220C22semidirect
29. C22×Dic15C22semidirect
32. C2×C4×D15C22semidirect
33. C3×C5×C4⋊C4C22semidirect
35. C3×C5×C22⋊C4C22semidirect
38. #6719C22semidirect
45. #6714C22semidirect
46. C4⋊Dic15C22semidirect
47. C4⋊Dic15C22semidirect
48. #6712C22semidirect
49. #6712C22semidirect
50. #6712C22semidirect
51. C4×Dic15C22semidirect
53. C5×#121D3semidirect
101. C3×#121D5semidirect
119. C2×C5×D4C2×D3semidirect
120. C22×C4×C5C2×D3semidirect
132. C5×C4⋊C4C2×D3semidirect
134. C5×C22⋊C4C2×D3semidirect
184. C2×C3×D4C2×D5semidirect
185. C22×C3×C4C2×D5semidirect
197. C3×C4⋊C4C2×D5semidirect
199. C3×C22⋊C4C2×D5semidirect
260. #121D15semidirect
347. C2×D4C2×D15semidirect
350. C22×C4C2×D15semidirect
356. C4⋊C4C2×D15semidirect
368. C22⋊C4C2×D15semidirect
370. C3×C5#560semidirect
451. C5#5620semidirect
481. C3#65954semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1212
#918292
#918282
#918272
#918262
#918192
#918182
#917872
#917832
#917752
#917732
#917712
#917682
#659543
#56205