Finite Group Databasebeta

← #11753300

Subgroups — #11753300

Order 960.

520 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91774C211yesmaximal, characteristic, complemented
2C5×#882C211yesmaximal, characteristic, complemented
3C3×#4031C211yesmaximal, characteristic, complemented
4#91577C211yesmaximal, characteristic, complemented
5#91570C211yesmaximal, characteristic, complemented
6#91568C211yesmaximal, characteristic, complemented
7#91525C211yesmaximal, characteristic, complemented
8#91475C211yesmaximal, characteristic, complemented
9#91475C211yesmaximal, characteristic, complemented
10#91464C211yesmaximal, characteristic, complemented
11#91462C211yesmaximal, characteristic, complemented
12#91373C211yesmaximal, characteristic, complemented
13#91370C211yesmaximal, characteristic, complemented
14#91350C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65928—31nomaximal, Hall
17C23×C5×D3C2211yescharacteristic, complemented
18C22×D3×D5C2211yescharacteristic, complemented
19C2×#1220C2211yescharacteristic
20C2×Dic30C2211yescharacteristic, complemented
21C2×C5×#67C2211yescharacteristic
22C2×C5×D12C2211yescharacteristic
23C2×C5×D12C2211yescharacteristic
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×Dic10C2211yescharacteristic, complemented
26C2×#1204C2211yescharacteristic, complemented
27C2×#1203C2211yescharacteristic
28C2×#1203C2211yescharacteristic
29C2×#1201C2211yescharacteristic
30C2×#1201C2211yescharacteristic
31C3×C5×C22⋊C4C2211yescharacteristic, complemented
32#6719C2211yescharacteristic, complemented
33#6714C2211yescharacteristic, complemented
34#6714C2211yescharacteristic, complemented
35C4×Dic15C2211yescharacteristic, complemented
36C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C3×C22⋊Dic5C2211yescharacteristic, complemented
39C3×#685C2211yescharacteristic, complemented
40C3×#685C2211yescharacteristic, complemented
41C3×C4×Dic5C2211yescharacteristic, complemented
42#6667C2211yescharacteristic, complemented
43(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44(C2×D3)⋊Dic5C2211yescharacteristic, complemented
45(C2×D3)⋊Dic5C2211yescharacteristic, complemented
46(C2×D3)⋊Dic5C2211yescharacteristic, complemented
47(C2×D3)⋊Dic5C2211yescharacteristic, complemented
48(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49(C2×D3)⋊Dic5C2211yescharacteristic, complemented
50#6665C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5683—51nomaximal, Hall
53C5×#120—31no—
54#4099—31no—
55#4099—31no—
56#4083—31no—
57#4083—31no—
58#4083—31no—
59#4082—31no—
60#4082—31no—
61#4082—31no—
62#4031—31no—
63#4031—31no—
64#4031—31no—
65#4031—31no—
66#4031—31no—
67#4031D311yescharacteristic, complemented
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C5×D3—41no—
71C22×C5×D3—41no—
72C22×C5×D3—41no—
73C22×C5×D3C2311yescharacteristic
74C22×C5×D3C2311yescharacteristic
75C22×C5×D3C2311yescharacteristic
76C22×C3×D5C2311yescharacteristic
77C2×D3×D5—41no—
78C2×D3×D5—41no—
79C2×D3×D5—41no—
80C2×C3×C4×C5C2311yescharacteristic
81C2×C3×C4×C5C2311yescharacteristic
82#1220—41no—
83C2×Dic15C2311yescharacteristic
84C2×Dic15C2311yescharacteristic
85C2×Dic15C2311yescharacteristic
86Dic30—41no—
87C5×#67—41no—
88C2×C5×Dic3C2311yescharacteristic
89C5×D12—41no—
90C5×D12—41no—
91C3×C22⋊D5—41no—
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94C2×C3×Dic5C2311yescharacteristic
95C3×Dic10—41no—
96#1204—41no—
97#1203—41no—
98#1203—41no—
99#1201—41no—
100#1201—41no—
101C3×#124—51no—
102#947—51no—
103#947—51no—
104#937—51no—
105#937—51no—
106#885—51no—
107#885—51no—
108#885—51no—
109#885—51no—
110#882—51no—
111#882—51no—
112#882—51no—
113#882D511yescharacteristic, complemented
114#875—51no—
115#875—51no—
116C24×C5—31no—
117C23×D5—31no—
118C2×C5×D4—31no—
119C2×C5×D4—31no—
120C2×C5×D4—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5C2×D311yescharacteristic
127C2×Dic10—31no—
128C2×Dic10—31no—
129C2×Dic10C2×D311yescharacteristic, complemented
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C5×C22⋊C4C2×D311yescharacteristic, complemented
133C22⋊Dic5—31no—
134C22⋊Dic5—31no—
135C22⋊Dic5—31no—
136C22⋊Dic5—31no—
137C22⋊Dic5—31no—
138C22⋊Dic5—31no—
139C22⋊Dic5—31no—
140C22⋊Dic5—31no—
141C22⋊Dic5C2×D311yescharacteristic, complemented
142#685—31no—
143#685—31no—
144#685—31no—
145#685—31no—
146#685C2×D311yescharacteristic, complemented
147#685C2×D311yescharacteristic, complemented
148C4×Dic5—31no—
149C4×Dic5—31no—
150C4×Dic5C2×D311yescharacteristic, complemented
151H(3,𝔽4)—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×C5×D3—21no—
160C2×C5×D3—21no—
161C2×C5×D3—21no—
162C2×C5×D3—21no—
163C2×C5×D3—21no—
164C2×C5×D3—21no—
165C2×C5×D3—21no—
166C2×C5×D3—21no—
167C2×C5×D3—21no—
168C2×C5×D3—44no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172D3×D5—44no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175Dic15—21no—
176Dic15—21no—
177Dic15—21no—
178C3×Dic5—21no—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C5×Dic3—21no—
182C23×D3—51no—
183C23×D3C2×D511yescharacteristic, complemented
184C2×C3×Q8—51no—
185C2×C3×D4—51no—
186C2×#67—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67C2×D511yescharacteristic
190C2×D12—51no—
191C2×D12—51no—
192C2×D12C2×D511yescharacteristic
193C2×D12C2×D511yescharacteristic
194C2×Dic6—51no—
195C2×Dic6—51no—
196C3×C22⋊C4—51no—
197C3×C22⋊C4—51no—
198C3×C22⋊C4—51no—
199C3×C22⋊C4C2×D511yescharacteristic, complemented
200C3×C42—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—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4—51no—
212(C2×D3)⋊C4—51no—
213(C2×D3)⋊C4C2×D511yescharacteristic, complemented
214(C2×D3)⋊C4C2×D511yescharacteristic, complemented
215C4×Dic3—51no—
216C4×Dic3—51no—
217C23×C5—31no—
218C23×C5—31no—
219C23×C5—31no—
220C23×C5—121no—
221C23×C5—121no—
222C23×C5—121no—
223C23×C5C22×D311yescharacteristic
224C22×D5—31no—
225C22×D5—121no—
226C22×D5—121no—
227C22×D5—121no—
228C22×D5C22×D311yescharacteristic
229C5×D4—121no—
230C5×D4—121no—
231C5×D4—121no—
232C2×C4×C5—31no—
233C2×C4×C5C22×D311yescharacteristic
234C2×C4×C5C22×D311yescharacteristic
235C22⋊D5—41no—
236C22⋊D5—121no—
237C22⋊D5—121no—
238C22⋊D5—121no—
239C22⋊D5—121no—
240C22⋊D5—121no—
241C2×Dic5—31no—
242C2×Dic5—31no—
243C2×Dic5—31no—
244C2×Dic5C22×D311yescharacteristic
245C2×Dic5C22×D311yescharacteristic
246C2×Dic5C22×D311yescharacteristic
247Dic10—41no—
248Dic10—121no—
249Dic10—121no—
250#124—51no—
251#124—151no—
252#124—151no—
253#124—151no—
254#124—151no—
255#124—151no—
256#124—151no—
257#124—151no—
258#124—151no—
259#120—31no—
260#120—151no—
261#120—151no—
262#120—151no—
263#120—151no—
264#120—151no—
265C2×C3×C5—41no—
266C2×C3×C5H(5,𝔽2)11yescharacteristic
267C2×C3×C5H(5,𝔽2)11yescharacteristic
268C2×C3×C5H(5,𝔽2)11yescharacteristic
269D15—41no—
270C3×D5—41no—
271C5×D3—41no—
272C5×D3—41no—
273C5×D3—41no—
274C23×C3—51no—
275C23×C3C22×D511yescharacteristic
276C22×D3—41no—
277C22×D3—41no—
278C22×D3—41no—
279C22×D3—51no—
280C22×D3—201no—
281C22×D3—201no—
282C22×D3—201no—
283C22×D3C22×D511yescharacteristic
284C22×D3C22×D511yescharacteristic
285C22×D3C22×D511yescharacteristic
286C3×Q8—201no—
287C3×D4—201no—
288C2×C3×C4—51no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4C22×D511yescharacteristic
292C2×C3×C4C22×D511yescharacteristic
293#67—41no—
294#67—201no—
295#67—201no—
296#67—201no—
297C2×Dic3—51no—
298C2×Dic3—51no—
299C2×Dic3—51no—
300C2×Dic3C22×D511yescharacteristic
301D12—41no—
302D12—41no—
303D12—201no—
304D12—201no—
305Dic6—201no—
306Dic6—201no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—61no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5—61no—
314C22×C5—61no—
315C22×C5—61no—
316C22×C5—61no—
317C22×C5—61no—
318C22×C5—61no—
319C22×C5—124no—
320C22×C5C23×D311yescharacteristic
321C2×D5—21no—
322C2×D5—21no—
323C2×D5—21no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5—61no—
327C2×D5—124no—
328C4×C5—21no—
329C4×C5—21no—
330C4×C5—61no—
331Dic5—21no—
332Dic5—21no—
333Dic5—21no—
334Dic5—61no—
335Dic5—61no—
336Dic5—61no—
337C24—31no—
338C24—151no—
339C2×Q8—51no—
340C2×Q8—151no—
341C2×Q8—151no—
342C2×D4—31no—
343C2×D4—31no—
344C2×D4—31no—
345C2×D4—51no—
346C2×D4—151no—
347C2×D4—151no—
348C2×D4—151no—
349C2×D4—151no—
350C2×D4—151no—
351C22⋊C4—31no—
352C22⋊C4—31no—
353C22⋊C4—51no—
354C22⋊C4—51no—
355C22⋊C4—51no—
356C22⋊C4—151no—
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⋊C4—151no—
368C22⋊C4D3×D511yescharacteristic, complemented
369C42—51no—
370C42—151no—
371C42—151no—
372C3×C5H(3,𝔽4)11yescharacteristic, complemented, Hall
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—101no—
377C22×C3—101no—
378C22×C3—101no—
379C22×C3C23×D511yescharacteristic
380C2×D3—21no—
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—21no—
385C2×D3—21no—
386C2×D3—21no—
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—44no—
390C2×D3—101no—
391C2×D3—101no—
392C2×D3—101no—
393C2×D3—204no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—101no—
397C3×C4—101no—
398C3×C4—101no—
399Dic3—21no—
400Dic3—101no—
401Dic3—101no—
402Dic3—101no—
403C2×C5—41no—
404C2×C5—121no—
405C2×C5—121no—
406C2×C5—121no—
407C2×C5#100411yescharacteristic
408C2×C5#100911yescharacteristic
409C2×C5#100911yescharacteristic
410D5—41no—
411D5—121no—
412C23—31no—
413C23—31no—
414C23—31no—
415C23—51no—
416C23—121no—
417C23—121no—
418C23—121no—
419C23—151no—
420C23—601no—
421C23—601no—
422C23—601no—
423C23C2×D3×D511yescharacteristic
424Q8—201no—
425Q8—601no—
426Q8—601no—
427D4—121no—
428D4—121no—
429D4—121no—
430D4—201no—
431D4—601no—
432D4—601no—
433D4—601no—
434D4—601no—
435D4—601no—
436C2×C4—31no—
437C2×C4—51no—
438C2×C4—51no—
439C2×C4—51no—
440C2×C4—151no—
441C2×C4—151no—
442C2×C4—151no—
443C2×C4C2×D3×D511yescharacteristic
444C2×C4C2×D3×D511yescharacteristic
445C2×C3—41no—
446C2×C3—201no—
447C2×C3#414411yescharacteristic
448C2×C3#414411yescharacteristic
449C2×C3#414411yescharacteristic
450D3—41no—
451D3—41no—
452D3—41no—
453D3—201no—
454C5#568311yescharacteristic, complemented, Sylow
455C22—21no—
456C22—21no—
457C22—21no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—61no—
462C22—61no—
463C22—61no—
464C22—61no—
465C22—61no—
466C22—61no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—124no—
471C22—301no—
472C22—301no—
473C22—301no—
474C22—604no—
475C22C22×D3×D511yescharacteristic
476C4—21no—
477C4—21no—
478C4—61no—
479C4—101no—
480C4—101no—
481C4—101no—
482C4—301no—
483C4—301no—
484C4—301no—
485C3#6592811yescharacteristic, complemented, Sylow
486C2—41no—
487C2—121no—
488C2—121no—
489C2—121no—
490C2—201no—
491C2—601no—
492C2#9201811yescharacteristic
493C2#9202511yescharacteristic
494C2#9202711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5H(3,𝔽4)
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. #91774C2semidirect
2. C5×#882C2semidirect
3. C3×#4031C2semidirect
4. #91577C2semidirect
5. #91570C2semidirect
6. #91568C2semidirect
7. #91525C2semidirect
8. #91475C2semidirect
9. #91475C2semidirect
10. #91464C2semidirect
11. #91462C2semidirect
12. #91373C2semidirect
13. #91370C2semidirect
14. #91350C2semidirect
15. #91326C2semidirect
17. C23×C5×D3C22semidirect
18. C22×D3×D5C22semidirect
20. C2×Dic30C22semidirect
25. C2×C3×Dic10C22semidirect
26. C2×#1204C22semidirect
31. C3×C5×C22⋊C4C22semidirect
32. #6719C22semidirect
33. #6714C22semidirect
34. #6714C22semidirect
35. C4×Dic15C22semidirect
36. C5×(C2×D3)⋊C4C22semidirect
37. C5×(C2×D3)⋊C4C22semidirect
38. C3×C22⋊Dic5C22semidirect
39. C3×#685C22semidirect
40. C3×#685C22semidirect
41. C3×C4×Dic5C22semidirect
42. #6667C22semidirect
43. (C2×D3)⋊Dic5C22semidirect
44. (C2×D3)⋊Dic5C22semidirect
45. (C2×D3)⋊Dic5C22semidirect
46. (C2×D3)⋊Dic5C22semidirect
47. (C2×D3)⋊Dic5C22semidirect
48. (C2×D3)⋊Dic5C22semidirect
49. (C2×D3)⋊Dic5C22semidirect
50. #6665C22semidirect
51. Dic3×Dic5C22semidirect
67. #4031D3semidirect
113. #882D5semidirect
129. C2×Dic10C2×D3semidirect
132. C5×C22⋊C4C2×D3semidirect
141. C22⋊Dic5C2×D3semidirect
146. #685C2×D3semidirect
147. #685C2×D3semidirect
150. C4×Dic5C2×D3semidirect
183. C23×D3C2×D5semidirect
199. C3×C22⋊C4C2×D5semidirect
213. (C2×D3)⋊C4C2×D5semidirect
214. (C2×D3)⋊C4C2×D5semidirect
368. C22⋊C4D3×D5semidirect
372. C3×C5H(3,𝔽4)semidirect
454. C5#5683semidirect
485. C3#65928semidirect

Maximal subgroups

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

subgroupindex
#917742
C5×#8822
C3×#40312
#915772
#915702
#915682
#915252
#914752
#914642
#914622
#913732
#913702
#913502
#913262
#659283
#56835