Finite Group Databasebeta

← #11753299

Subgroups — #11753299

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×#885C211yesmaximal, characteristic, complemented
3C3×#4028C211yesmaximal, characteristic, complemented
4#91577C211yesmaximal, characteristic, complemented
5#91564C211yesmaximal, characteristic, complemented
6#91563C211yesmaximal, characteristic, complemented
7#91534C211yesmaximal, characteristic, complemented
8#91474C211yesmaximal, characteristic, complemented
9#91474C211yesmaximal, characteristic, complemented
10#91464C211yesmaximal, characteristic, complemented
11#91462C211yesmaximal, characteristic, complemented
12#91455C211yesmaximal, characteristic, complemented
13#91368C211yesmaximal, characteristic, complemented
14#91364C211yesmaximal, characteristic, complemented
15#91353C211yesmaximal, characteristic, complemented
16#66017—31nomaximal, Hall
17C23×C3×D5C2211yescharacteristic, complemented
18C22×D3×D5C2211yescharacteristic, complemented
19C2×#1220C2211yescharacteristic
20C2×Dic30C2211yescharacteristic, complemented
21C2×C5×#67C2211yescharacteristic
22C2×C5×Dic6C2211yescharacteristic, complemented
23C2×C3×C22⋊D5C2211yescharacteristic
24C2×C3×D20C2211yescharacteristic
25C2×C3×D20C2211yescharacteristic
26C2×#1204C2211yescharacteristic, complemented
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic
29C2×#1201C2211yescharacteristic
30C2×#1201C2211yescharacteristic
31C3×C5×C22⋊C4C2211yescharacteristic, complemented
32#6719C2211yescharacteristic, complemented
33#6714C2211yescharacteristic, complemented
34#6714C2211yescharacteristic, complemented
35C4×Dic15C2211yescharacteristic, complemented
36C5×#217C2211yescharacteristic, complemented
37C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C4×C5×Dic3C2211yescharacteristic, complemented
40C3×#685C2211yescharacteristic, complemented
41C3×#685C2211yescharacteristic, complemented
42#6667C2211yescharacteristic, complemented
43(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44#6665C2211yescharacteristic, complemented
45#6665C2211yescharacteristic, complemented
46#6665C2211yescharacteristic, complemented
47#6665C2211yescharacteristic, complemented
48#6665C2211yescharacteristic, complemented
49#6665C2211yescharacteristic, complemented
50#6665C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5594—51nomaximal, Hall
53C5×#124—31no—
54#4093—31no—
55#4093—31no—
56#4083—31no—
57#4083—31no—
58#4031—31no—
59#4031—31no—
60#4031—31no—
61#4031—31no—
62#4028—31no—
63#4028—31no—
64#4028—31no—
65#4028D311yescharacteristic, complemented
66#4021—31no—
67#4021—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5—41no—
72C22×C3×D5—41no—
73C22×C3×D5—41no—
74C22×C3×D5C2311yescharacteristic
75C22×C3×D5C2311yescharacteristic
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
89C2×C5×Dic3C2311yescharacteristic
90C2×C5×Dic3C2311yescharacteristic
91C5×Dic6—41no—
92C3×C22⋊D5—41no—
93C2×C3×Dic5C2311yescharacteristic
94C3×D20—41no—
95C3×D20—41no—
96#1204—41no—
97#1202—41no—
98#1202—41no—
99#1201—41no—
100#1201—41no—
101C3×#120—51no—
102#953—51no—
103#953—51no—
104#937—51no—
105#937—51no—
106#937—51no—
107#936—51no—
108#936—51no—
109#936—51no—
110#885—51no—
111#885—51no—
112#885—51no—
113#885—51no—
114#885—51no—
115#885D511yescharacteristic, complemented
116C23×D5—31no—
117C23×D5C2×D311yescharacteristic, complemented
118C2×C5×Q8—31no—
119C2×C5×D4—31no—
120C2×C22⋊D5—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5C2×D311yescharacteristic
124C2×D20—31no—
125C2×D20—31no—
126C2×D20C2×D311yescharacteristic
127C2×D20C2×D311yescharacteristic
128C2×Dic10—31no—
129C2×Dic10—31no—
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C5×C22⋊C4—31no—
133C5×C22⋊C4C2×D311yescharacteristic, complemented
134C42×C5—31no—
135C22⋊Dic5—31no—
136C22⋊Dic5—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685—31no—
144#685—31no—
145#685—31no—
146#685—31no—
147#685C2×D311yescharacteristic, complemented
148#685C2×D311yescharacteristic, complemented
149C4×Dic5—31no—
150C4×Dic5—31no—
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×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—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—
171C2×C3×D5—44no—
172D3×D5—44no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175Dic15—21no—
176Dic15—21no—
177Dic15—21no—
178C3×Dic5—21no—
179C5×Dic3—21no—
180C5×Dic3—21no—
181C5×Dic3—21no—
182C24×C3—51no—
183C23×D3—51no—
184C2×C3×D4—51no—
185C2×C3×D4—51no—
186C2×C3×D4—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67—51no—
190C2×#67—51no—
191C2×#67—51no—
192C2×#67C2×D511yescharacteristic
193C2×Dic6—51no—
194C2×Dic6—51no—
195C2×Dic6C2×D511yescharacteristic, complemented
196C3×C22⋊C4—51no—
197C3×C22⋊C4—51no—
198C3×C22⋊C4C2×D511yescharacteristic, complemented
199#217—51no—
200#217—51no—
201#217—51no—
202#217—51no—
203#217—51no—
204#217—51no—
205#217—51no—
206#217—51no—
207#217C2×D511yescharacteristic, complemented
208(C2×D3)⋊C4—51no—
209(C2×D3)⋊C4—51no—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4—51no—
212(C2×D3)⋊C4C2×D511yescharacteristic, complemented
213(C2×D3)⋊C4C2×D511yescharacteristic, complemented
214C4×Dic3—51no—
215C4×Dic3—51no—
216C4×Dic3C2×D511yescharacteristic, complemented
217C23×C5—31no—
218C23×C5C22×D311yescharacteristic
219C22×D5—31no—
220C22×D5—41no—
221C22×D5—41no—
222C22×D5—41no—
223C22×D5—121no—
224C22×D5—121no—
225C22×D5—121no—
226C22×D5C22×D311yescharacteristic
227C22×D5C22×D311yescharacteristic
228C22×D5C22×D311yescharacteristic
229C5×Q8—121no—
230C5×D4—121no—
231C2×C4×C5—31no—
232C2×C4×C5—31no—
233C2×C4×C5—31no—
234C2×C4×C5C22×D311yescharacteristic
235C2×C4×C5C22×D311yescharacteristic
236C22⋊D5—41no—
237C22⋊D5—121no—
238C22⋊D5—121no—
239C22⋊D5—121no—
240C2×Dic5—31no—
241C2×Dic5—31no—
242C2×Dic5—31no—
243C2×Dic5C22×D311yescharacteristic
244D20—41no—
245D20—41no—
246D20—121no—
247D20—121no—
248Dic10—121no—
249Dic10—121no—
250#124—31no—
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—51no—
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—
271C3×D5—41no—
272C3×D5—41no—
273C5×D3—41no—
274C23×C3—51no—
275C23×C3—51no—
276C23×C3—51no—
277C23×C3—201no—
278C23×C3—201no—
279C23×C3—201no—
280C23×C3C22×D511yescharacteristic
281C22×D3—51no—
282C22×D3—201no—
283C22×D3—201no—
284C22×D3—201no—
285C22×D3C22×D511yescharacteristic
286C3×D4—201no—
287C3×D4—201no—
288C3×D4—201no—
289C2×C3×C4—51no—
290C2×C3×C4C22×D511yescharacteristic
291C2×C3×C4C22×D511yescharacteristic
292#67—41no—
293#67—201no—
294#67—201no—
295#67—201no—
296#67—201no—
297#67—201no—
298C2×Dic3—51no—
299C2×Dic3—51no—
300C2×Dic3—51no—
301C2×Dic3C22×D511yescharacteristic
302C2×Dic3C22×D511yescharacteristic
303C2×Dic3C22×D511yescharacteristic
304Dic6—41no—
305Dic6—201no—
306Dic6—201no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—61no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5C23×D311yescharacteristic
314C2×D5—21no—
315C2×D5—21no—
316C2×D5—21no—
317C2×D5—21no—
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—21no—
322C2×D5—21no—
323C2×D5—44no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5—61no—
327C2×D5—124no—
328C4×C5—21no—
329C4×C5—21no—
330C4×C5—61no—
331C4×C5—61no—
332C4×C5—61no—
333Dic5—21no—
334Dic5—61no—
335Dic5—61no—
336Dic5—61no—
337C24—51no—
338C24—151no—
339C2×Q8—31no—
340C2×Q8—151no—
341C2×Q8—151no—
342C2×D4—31no—
343C2×D4—51no—
344C2×D4—51no—
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—31no—
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—31no—
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×C3—101no—
380C22×C3—101no—
381C22×C3—101no—
382C22×C3—101no—
383C22×C3—101no—
384C22×C3—101no—
385C22×C3—204no—
386C22×C3C23×D511yescharacteristic
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—21no—
390C2×D3—101no—
391C2×D3—101no—
392C2×D3—101no—
393C2×D3—204no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—101no—
397Dic3—21no—
398Dic3—21no—
399Dic3—21no—
400Dic3—101no—
401Dic3—101no—
402Dic3—101no—
403C2×C5—41no—
404C2×C5—121no—
405C2×C5#100411yescharacteristic
406C2×C5#100411yescharacteristic
407C2×C5#100411yescharacteristic
408D5—41no—
409D5—41no—
410D5—41no—
411D5—121no—
412C23—31no—
413C23—51no—
414C23—51no—
415C23—51no—
416C23—151no—
417C23—201no—
418C23—201no—
419C23—201no—
420C23—601no—
421C23—601no—
422C23—601no—
423C23C2×D3×D511yescharacteristic
424Q8—121no—
425Q8—601no—
426Q8—601no—
427D4—121no—
428D4—201no—
429D4—201no—
430D4—201no—
431D4—601no—
432D4—601no—
433D4—601no—
434D4—601no—
435D4—601no—
436C2×C4—31no—
437C2×C4—31no—
438C2×C4—31no—
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—201no—
448C2×C3—201no—
449C2×C3#414411yescharacteristic
450C2×C3#414911yescharacteristic
451C2×C3#414911yescharacteristic
452D3—41no—
453D3—201no—
454C5#559411yescharacteristic, complemented, Sylow
455C22—21no—
456C22—21no—
457C22—21no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—101no—
465C22—101no—
466C22—101no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—204no—
471C22—301no—
472C22—301no—
473C22—301no—
474C22—604no—
475C22C22×D3×D511yescharacteristic
476C4—21no—
477C4—21no—
478C4—61no—
479C4—61no—
480C4—61no—
481C4—101no—
482C4—301no—
483C4—301no—
484C4—301no—
485C3#6601711yescharacteristic, complemented, Sylow
486C2—41no—
487C2—121no—
488C2—201no—
489C2—201no—
490C2—201no—
491C2—601no—
492C2#9201711yescharacteristic
493C2#9202511yescharacteristic
494C2#9202611yescharacteristic
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×#885C2semidirect
3. C3×#4028C2semidirect
4. #91577C2semidirect
5. #91564C2semidirect
6. #91563C2semidirect
7. #91534C2semidirect
8. #91474C2semidirect
9. #91474C2semidirect
10. #91464C2semidirect
11. #91462C2semidirect
12. #91455C2semidirect
13. #91368C2semidirect
14. #91364C2semidirect
15. #91353C2semidirect
17. C23×C3×D5C22semidirect
18. C22×D3×D5C22semidirect
20. C2×Dic30C22semidirect
22. C2×C5×Dic6C22semidirect
26. C2×#1204C22semidirect
31. C3×C5×C22⋊C4C22semidirect
32. #6719C22semidirect
33. #6714C22semidirect
34. #6714C22semidirect
35. C4×Dic15C22semidirect
36. C5×#217C22semidirect
37. C5×(C2×D3)⋊C4C22semidirect
38. C5×(C2×D3)⋊C4C22semidirect
39. C4×C5×Dic3C22semidirect
40. C3×#685C22semidirect
41. C3×#685C22semidirect
42. #6667C22semidirect
43. (C2×D3)⋊Dic5C22semidirect
44. #6665C22semidirect
45. #6665C22semidirect
46. #6665C22semidirect
47. #6665C22semidirect
48. #6665C22semidirect
49. #6665C22semidirect
50. #6665C22semidirect
51. Dic3×Dic5C22semidirect
65. #4028D3semidirect
115. #885D5semidirect
117. C23×D5C2×D3semidirect
133. C5×C22⋊C4C2×D3semidirect
147. #685C2×D3semidirect
148. #685C2×D3semidirect
195. C2×Dic6C2×D5semidirect
198. C3×C22⋊C4C2×D5semidirect
207. #217C2×D5semidirect
212. (C2×D3)⋊C4C2×D5semidirect
213. (C2×D3)⋊C4C2×D5semidirect
216. C4×Dic3C2×D5semidirect
368. C22⋊C4D3×D5semidirect
372. C3×C5H(3,𝔽4)semidirect
454. C5#5594semidirect
485. C3#66017semidirect

Maximal subgroups

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

subgroupindex
#917742
C5×#8852
C3×#40282
#915772
#915642
#915632
#915342
#914742
#914642
#914622
#914552
#913682
#913642
#913532
#660173
#55945