Finite Group Databasebeta

← #11753302

Subgroups — #11753302

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
1#91773C211yesmaximal, characteristic, complemented
2C5×#886C211yesmaximal, characteristic, complemented
3C3×#4030C211yesmaximal, characteristic, complemented
4#91577C211yesmaximal, characteristic, complemented
5#91569C211yesmaximal, characteristic, complemented
6#91569C211yesmaximal, characteristic, complemented
7#91567C211yesmaximal, characteristic, complemented
8#91476C211yesmaximal, characteristic, complemented
9#91474C211yesmaximal, characteristic, complemented
10#91465C211yesmaximal, characteristic, complemented
11#91450C211yesmaximal, characteristic, complemented
12#91447C211yesmaximal, characteristic, complemented
13#91361C211yesmaximal, characteristic, complemented
14#91355C211yesmaximal, characteristic, complemented
15#91337C211yesmaximal, characteristic, complemented
16#66000—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic, complemented
20C2×D60C2211yescharacteristic
21C2×C4×D15C2211yescharacteristic, complemented
22C2×C5×#67C2211yescharacteristic
23C22×C5×Dic3C2211yescharacteristic, complemented
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×C22⋊D5C2211yescharacteristic, complemented
26C2×C3×D20C2211yescharacteristic
27C2×C3×C4×D5C2211yescharacteristic, complemented
28C2×#1203C2211yescharacteristic
29C2×#1202C2211yescharacteristic
30C2×#1202C2211yescharacteristic
31C2×#1202C2211yescharacteristic, complemented
32C2×#1201C2211yescharacteristic
33C3×C5×C22⋊C4C2211yescharacteristic, complemented
34#6714C2211yescharacteristic
35#6712C2211yescharacteristic, complemented
36C5×(C2×D3)⋊C4C2211yescharacteristic
37C5×(C2×D3)⋊C4C2211yescharacteristic
38C5×C4⋊Dic3C2211yescharacteristic, complemented
39C5×C4⋊Dic3C2211yescharacteristic, complemented
40C3×#685C2211yescharacteristic
41C3×#683C2211yescharacteristic, complemented
42Dic3⋊Dic5C2211yescharacteristic, complemented
43Dic3⋊Dic5C2211yescharacteristic, complemented
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic, complemented
47(C2×D3)⋊Dic5C2211yescharacteristic
48#6665C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5620—51nomaximal, Hall
53C5×#123—31no—
54#4086—31no—
55#4083—31no—
56#4076—31no—
57#4076—31no—
58#4044—31no—
59#4044—31no—
60#4041—31no—
61#4041—31no—
62#4030—31no—
63#4030D311yescharacteristic, complemented
64#4029—31no—
65#4029—31no—
66#4028—31no—
67#4028—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C5×D3C2311yescharacteristic
72C22×C3×D5C2311yescharacteristic
73C22×C3×D5C2311yescharacteristic
74C2×D3×D5—41no—
75C2×D3×D5—41no—
76C2×D3×D5—41no—
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79#1220—41no—
80#1220—41no—
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83D60—41no—
84C4×D15—41no—
85C5×#67—41no—
86C2×C5×Dic3—41no—
87C2×C5×Dic3C2311yescharacteristic
88C2×C5×Dic3C2311yescharacteristic
89C2×C5×Dic3C2311yescharacteristic
90C3×C22⋊D5—41no—
91C3×C22⋊D5—41no—
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94C3×D20—41no—
95C3×C4×D5—41no—
96#1203—41no—
97#1202—41no—
98#1202—41no—
99#1202—41no—
100#1201—41no—
101C3×#121—51no—
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#886D511yescharacteristic, complemented
113#884—51no—
114#882—51no—
115#879—51no—
116C23×D5—31no—
117C2×C5×D4—31no—
118C22×C4×C5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5C2×D311yescharacteristic
124C2×C22⋊D5C2×D311yescharacteristic, complemented
125C2×D20—31no—
126C2×D20—31no—
127C2×D20—31no—
128C2×D20—31no—
129C2×D20C2×D311yescharacteristic
130C2×C4×D5—31no—
131C2×C4×D5C2×D311yescharacteristic, complemented
132C5×C4⋊C4—31no—
133C5×C4⋊C4—31no—
134C5×C22⋊C4—31no—
135C5×C22⋊C4—31no—
136C5×C22⋊C4C2×D311yescharacteristic, complemented
137C22⋊Dic5—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685—31no—
144#685—31no—
145#685C2×D311yescharacteristic
146C4⋊Dic5—31no—
147C4⋊Dic5—31no—
148#683—31no—
149#683C2×D311yescharacteristic, complemented
150C4×Dic5—31no—
151#560—151noSylow
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5C2411yescharacteristic
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×C5×D3—21no—
163C2×C5×D3—21no—
164C2×C5×D3—21no—
165C2×C3×D5—21no—
166C2×C3×D5—21no—
167C2×C3×D5—21no—
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171D3×D5—44no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174Dic15—21no—
175Dic15—21no—
176C3×Dic5—21no—
177C3×Dic5—21no—
178C5×Dic3—21no—
179C5×Dic3—21no—
180C5×Dic3—21no—
181C23×D3—51no—
182C2×C3×D4—51no—
183C2×C3×D4—51no—
184C2×C3×D4—51no—
185C22×C3×C4—51no—
186C2×#67—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67—51no—
190C2×#67—51no—
191C2×#67—51no—
192C2×#67C2×D511yescharacteristic
193C22×Dic3C2×D511yescharacteristic, complemented
194C2×D12—51no—
195C2×D12—51no—
196C2×C4×D3—51no—
197C3×C4⋊C4—51no—
198C3×C22⋊C4—51no—
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)⋊C4C2×D511yescharacteristic
209(C2×D3)⋊C4C2×D511yescharacteristic
210C4⋊Dic3C2×D511yescharacteristic, complemented
211C4⋊Dic3C2×D511yescharacteristic, complemented
212Dic3⋊C4—51no—
213Dic3⋊C4—51no—
214Dic3⋊C4—51no—
215C4×Dic3—51no—
216C23×C5—31no—
217C23×C5C22×D311yescharacteristic
218C22×D5—31no—
219C22×D5—31no—
220C22×D5—121no—
221C22×D5—121no—
222C22×D5—121no—
223C22×D5C22×D311yescharacteristic
224C22×D5C22×D311yescharacteristic
225C5×D4—121no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—121no—
230C2×C4×C5C22×D311yescharacteristic
231C2×C4×C5C22×D311yescharacteristic
232C22⋊D5—41no—
233C22⋊D5—41no—
234C22⋊D5—121no—
235C22⋊D5—121no—
236C22⋊D5—121no—
237C22⋊D5—121no—
238C2×Dic5—31no—
239C2×Dic5—31no—
240C2×Dic5C22×D311yescharacteristic
241C2×Dic5C22×D311yescharacteristic
242D20—41no—
243D20—121no—
244D20—121no—
245D20—121no—
246D20—121no—
247C4×D5—41no—
248C4×D5—121no—
249#127—151no—
250#126—151no—
251#126—151no—
252#123—31no—
253#123—151no—
254#123—151no—
255#121—51no—
256#121—151no—
257#121—151no—
258#121—151no—
259#121—151no—
260#121—151no—
261#120—151no—
262#120—151no—
263#120—151no—
264C2×C3×C5—41no—
265C2×C3×C5H(5,𝔽2)11yescharacteristic
266C2×C3×C5H(5,𝔽2)11yescharacteristic
267C2×C3×C5H(5,𝔽2)11yescharacteristic
268D15—41no—
269D15—41no—
270C3×D5—41no—
271C3×D5—41no—
272C5×D3—41no—
273C23×C3—51no—
274C23×C3—51no—
275C23×C3C22×D511yescharacteristic
276C22×D3—51no—
277C22×D3—51no—
278C22×D3—201no—
279C22×D3—201no—
280C22×D3—201no—
281C22×D3C22×D511yescharacteristic
282C3×D4—201no—
283C3×D4—201no—
284C3×D4—201no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4—201no—
288C2×C3×C4C22×D511yescharacteristic
289C2×C3×C4C22×D511yescharacteristic
290#67—41no—
291#67—201no—
292#67—201no—
293#67—201no—
294#67—201no—
295#67—201no—
296#67—201no—
297C2×Dic3—41no—
298C2×Dic3—51no—
299C2×Dic3—51no—
300C2×Dic3C22×D511yescharacteristic
301C2×Dic3C22×D511yescharacteristic
302C2×Dic3C22×D511yescharacteristic
303D12—201no—
304D12—201no—
305C4×D3—201no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—61no—
310C22×C5—61no—
311C22×C5—61no—
312C22×C5C23×D311yescharacteristic
313C2×D5—21no—
314C2×D5—21no—
315C2×D5—21no—
316C2×D5—21no—
317C2×D5—21no—
318C2×D5—21no—
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—61no—
329C4×C5—61no—
330C4×C5—61no—
331Dic5—21no—
332Dic5—21no—
333Dic5—61no—
334Dic5—61no—
335C24—151no—
336C2×D4—31no—
337C2×D4—51no—
338C2×D4—51no—
339C2×D4—51no—
340C2×D4—151no—
341C2×D4—151no—
342C2×D4—151no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4—151no—
348C22×C4—31no—
349C22×C4—51no—
350C22×C4—151no—
351C4⋊C4—31no—
352C4⋊C4—31no—
353C4⋊C4—51no—
354C4⋊C4—151no—
355C4⋊C4—151no—
356C4⋊C4—151no—
357C22⋊C4—31no—
358C22⋊C4—31no—
359C22⋊C4—51no—
360C22⋊C4—151no—
361C22⋊C4—151no—
362C22⋊C4—151no—
363C22⋊C4—151no—
364C22⋊C4—151no—
365C22⋊C4—151no—
366C22⋊C4—151no—
367C22⋊C4—151no—
368C22⋊C4D3×D511yescharacteristic, complemented
369C42—151no—
370C3×C5#56011yescharacteristic, complemented, Hall
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—101no—
375C22×C3—101no—
376C22×C3—101no—
377C22×C3—101no—
378C22×C3—101no—
379C22×C3—101no—
380C22×C3C23×D511yescharacteristic
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—21no—
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—101no—
394C3×C4—101no—
395Dic3—21no—
396Dic3—21no—
397Dic3—21no—
398Dic3—101no—
399Dic3—101no—
400C2×C5—41no—
401C2×C5—121no—
402C2×C5#100411yescharacteristic
403C2×C5#100411yescharacteristic
404C2×C5#100911yescharacteristic
405D5—41no—
406D5—41no—
407D5—121no—
408D5—121no—
409C23—31no—
410C23—51no—
411C23—51no—
412C23—151no—
413C23—151no—
414C23—601no—
415C23—601no—
416C23—601no—
417C23C2×D3×D511yescharacteristic
418D4—121no—
419D4—201no—
420D4—201no—
421D4—201no—
422D4—601no—
423D4—601no—
424D4—601no—
425D4—601no—
426D4—601no—
427D4—601no—
428D4—601no—
429D4—601no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—121no—
436C2×C4—151no—
437C2×C4—151no—
438C2×C4—201no—
439C2×C4—601no—
440C2×C4C2×D3×D511yescharacteristic
441C2×C4C2×D3×D511yescharacteristic
442C2×C3—41no—
443C2×C3—201no—
444C2×C3—201no—
445C2×C3#414411yescharacteristic
446C2×C3#414911yescharacteristic
447C2×C3#414911yescharacteristic
448D3—41no—
449D3—201no—
450D3—201no—
451C5#562011yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—61no—
456C22—61no—
457C22—61no—
458C22—101no—
459C22—101no—
460C22—101no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22—301no—
468C22—301no—
469C22—301no—
470C22—604no—
471C22C22×D3×D511yescharacteristic
472C4—21no—
473C4—21no—
474C4—61no—
475C4—61no—
476C4—61no—
477C4—101no—
478C4—101no—
479C4—301no—
480C4—301no—
481C3#6600011yescharacteristic, complemented, Sylow
482C2—41no—
483C2—121no—
484C2—201no—
485C2—201no—
486C2—601no—
487C2—601no—
488C2#9201811yescharacteristic
489C2#9202611yescharacteristic
490C2#9202611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#560
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. #91773C2semidirect
2. C5×#886C2semidirect
3. C3×#4030C2semidirect
4. #91577C2semidirect
5. #91569C2semidirect
6. #91569C2semidirect
7. #91567C2semidirect
8. #91476C2semidirect
9. #91474C2semidirect
10. #91465C2semidirect
11. #91450C2semidirect
12. #91447C2semidirect
13. #91361C2semidirect
14. #91355C2semidirect
15. #91337C2semidirect
19. C2×#1220C22semidirect
21. C2×C4×D15C22semidirect
23. C22×C5×Dic3C22semidirect
25. C2×C3×C22⋊D5C22semidirect
27. C2×C3×C4×D5C22semidirect
31. C2×#1202C22semidirect
33. C3×C5×C22⋊C4C22semidirect
35. #6712C22semidirect
38. C5×C4⋊Dic3C22semidirect
39. C5×C4⋊Dic3C22semidirect
41. C3×#683C22semidirect
42. Dic3⋊Dic5C22semidirect
43. Dic3⋊Dic5C22semidirect
46. #6667C22semidirect
50. #6665C22semidirect
51. Dic3×Dic5C22semidirect
63. #4030D3semidirect
112. #886D5semidirect
124. C2×C22⋊D5C2×D3semidirect
131. C2×C4×D5C2×D3semidirect
136. C5×C22⋊C4C2×D3semidirect
149. #683C2×D3semidirect
193. C22×Dic3C2×D5semidirect
199. C3×C22⋊C4C2×D5semidirect
210. C4⋊Dic3C2×D5semidirect
211. C4⋊Dic3C2×D5semidirect
368. C22⋊C4D3×D5semidirect
370. C3×C5#560semidirect
451. C5#5620semidirect
481. C3#66000semidirect

Maximal subgroups

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

subgroupindex
#917732
C5×#8862
C3×#40302
#915772
#915692
#915672
#914762
#914742
#914652
#914502
#914472
#913612
#913552
#913372
#660003
#56205