Finite Group Databasebeta

← #11755390

Subgroups — #11755390

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
1C22×C5×#67C211yesmaximal, characteristic, complemented
2C2×#6780C211yesmaximal, characteristic, complemented
3C2×#6719C211yesmaximal, characteristic, complemented
4C3×#4099C211yesmaximal, characteristic, complemented
5#91575C211yesmaximal, characteristic, complemented
6#91571C211yesmaximal, characteristic, complemented
7#91568C211yesmaximal, characteristic, complemented
8#91565C211yesmaximal, characteristic, complemented
9#67⋊Dic5C211yesmaximal, characteristic, complemented
10#91555C211yesmaximal, characteristic, complemented
11D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
12Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
13#91549C211yesmaximal, characteristic, complemented
14#91543C211yesmaximal, characteristic, complemented
15#91525C211yesmaximal, characteristic, complemented
16#66140—31nomaximal, Hall
17C24×C3×C5C2211yescharacteristic
18C23×C5×D3C2211yescharacteristic
19C22×Dic15C2211yescharacteristic, complemented
20C22×Dic15C2211yescharacteristic, complemented
21C2×C5×#67—24no—
22C2×C5×#67C2211yescharacteristic
23C2×C5×#67C2211yescharacteristic
24C2×C5×#67C2211yescharacteristic
25C2×C5×#67C2211yescharacteristic
26C22×C5×Dic3C2211yescharacteristic
27C2×C3×C22⋊D5C2211yescharacteristic
28C2×C3×C22⋊D5C2211yescharacteristic, complemented
29C2×C3×C22⋊D5C2211yescharacteristic, complemented
30C2×#1204C2211yescharacteristic, complemented
31C2×#1201C2211yescharacteristic, complemented
32C2×#1201C2211yescharacteristic, complemented
33C2×D3×Dic5C2211yescharacteristic, complemented
34C2×D3×Dic5C2211yescharacteristic, complemented
35#6780—24no—
36C2×D5×Dic3C2211yescharacteristic, complemented
37#6719C2211yescharacteristic
38#6719C2211yescharacteristic
39#6719C2211yescharacteristic, complemented
40#6719C2211yescharacteristic, complemented
41C3×C22⋊Dic5C2211yescharacteristic
42C3×C22⋊Dic5C2211yescharacteristic, complemented
43C3×C22⋊Dic5C2211yescharacteristic, complemented
44Dic3⋊Dic5C2211yescharacteristic, complemented
45#6669C2211yescharacteristic, complemented
46#6668C2211yescharacteristic, complemented
47#6668C2211yescharacteristic, complemented
48(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49(C2×D3)⋊Dic5C2211yescharacteristic, complemented
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51(C2×D3)⋊Dic5C2211yescharacteristic, complemented
52#6665C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5591—51nomaximal, Hall
55C22×C5×D4—31no—
56C2×#711—31no—
57#4099—31no—
58#4099D311yescharacteristic, complemented
59C2×C22⋊Dic5—31no—
60C2×C22⋊Dic5—31no—
61#4085—31no—
62#4085—31no—
63#4084—31no—
64#4082—31no—
65#4081—31no—
66#4081—31no—
67D4×Dic5—31no—
68C4×C22⋊D5—31no—
69#4070—31no—
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C2311yescharacteristic
74C23×C3×C5C2311yescharacteristic
75C23×C3×C5C2311yescharacteristic
76C22×C5×D3—22no—
77C22×C5×D3—22no—
78C22×C5×D3—41no—
79C22×C5×D3C2311yescharacteristic
80C22×C5×D3C2311yescharacteristic
81C22×C3×D5C2311yescharacteristic
82C2×Dic15—22no—
83C2×Dic15—41no—
84C2×Dic15C2311yescharacteristic
85C2×Dic15C2311yescharacteristic
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C5×#67—22no—
89C5×#67—22no—
90C5×#67—22no—
91C5×#67D414yescomplemented
92C2×C5×Dic3—22no—
93C2×C5×Dic3C2311yescharacteristic
94C2×C5×Dic3C2311yescharacteristic
95C3×C22⋊D5—22no—
96C3×C22⋊D5—22no—
97C3×C22⋊D5—41no—
98C2×C3×Dic5C2311yescharacteristic
99C2×C3×Dic5C2311yescharacteristic
100C2×C3×Dic5C2311yescharacteristic
101#1204—22no—
102#1201—22no—
103#1201—41no—
104D3×Dic5—22no—
105D3×Dic5—41no—
106D5×Dic3—22no—
107C22×#67D511yescharacteristic, complemented
108C2×#237—51no—
109C3×#120—51no—
110C2×#217—51no—
111#939—51no—
112#939—51no—
113#938—51no—
114#937—51no—
115D4×Dic3—51no—
116#886—51no—
117#885—51no—
118#883—51no—
119#67⋊C4—51no—
120D3×C22⋊C4—51no—
121#878—51no—
122C24×C5—31no—
123C24×C5C2×D311yescharacteristic
124C2×C5×D4—31no—
125C2×C5×D4—31no—
126C2×C5×D4—31no—
127C2×C5×D4—31no—
128C2×C5×D4—64no—
129C22×C4×C5—31no—
130C2×C22⋊D5—31no—
131C2×C22⋊D5—31no—
132C2×C22⋊D5C2×D311yescharacteristic
133C2×C22⋊D5C2×D311yescharacteristic, complemented
134C2×C22⋊D5C2×D311yescharacteristic, complemented
135C22×Dic5—31no—
136C22×Dic5—31no—
137C22×Dic5—31no—
138C22×Dic5—31no—
139#711—64no—
140C2×C4×D5—31no—
141C2×Dic10—31no—
142C22⋊Dic5—31no—
143C22⋊Dic5—31no—
144C22⋊Dic5—31no—
145C22⋊Dic5—31no—
146C22⋊Dic5—31no—
147C22⋊Dic5—31no—
148C22⋊Dic5—31no—
149C22⋊Dic5—31no—
150C22⋊Dic5C2×D311yescharacteristic
151C22⋊Dic5C2×D311yescharacteristic, complemented
152C22⋊Dic5C2×D311yescharacteristic, complemented
153#685—31no—
154C4⋊Dic5—31no—
155#683—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×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—44no—
168C22×C3×C5C2×D412yes—
169C22×C3×C5#4112yescomplemented
170C22×C3×C5C2411yescharacteristic
171C2×C5×D3—21no—
172C2×C5×D3—21no—
173C2×C5×D3—21no—
174C2×C5×D3—21no—
175C2×C5×D3—21no—
176C2×C5×D3—44no—
177C2×C5×D3C2×D412yes—
178C2×C3×D5—21no—
179C2×C3×D5—21no—
180C2×C3×D5—21no—
181Dic15—21no—
182Dic15—21no—
183Dic15—21no—
184Dic15—21no—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C5×Dic3—21no—
189C5×Dic3C2×D412yes—
190C24×C3C2×D511yescharacteristic
191C23×D3C2×D511yescharacteristic
192C2×C3×D4—51no—
193C2×C3×D4—51no—
194C2×C3×D4—51no—
195C2×#67—24no—
196C2×#67—51no—
197C2×#67—51no—
198C2×#67C2×D511yescharacteristic
199C2×#67C2×D511yescharacteristic
200C2×#67C2×D511yescharacteristic
201C2×#67C2×D511yescharacteristic
202C22×Dic3—51no—
203C22×Dic3—51no—
204C22×Dic3—51no—
205C22×Dic3C2×D511yescharacteristic
206#237—104no—
207C2×C4×D3—51no—
208C2×C4×D3—51no—
209C2×Dic6—51no—
210C3×C22⋊C4—51no—
211C3×C22⋊C4—51no—
212C3×C22⋊C4—51no—
213#217—51no—
214#217—51no—
215#217—51no—
216#217—51no—
217#217—51no—
218(C2×D3)⋊C4—51no—
219(C2×D3)⋊C4—51no—
220(C2×D3)⋊C4—51no—
221(C2×D3)⋊C4—51no—
222C4⋊Dic3—51no—
223C4⋊Dic3—51no—
224Dic3⋊C4—51no—
225Dic3⋊C4—51no—
226C4×Dic3—51no—
227C23×C5—22no—
228C23×C5—22no—
229C23×C5—31no—
230C23×C5—31no—
231C23×C5—41no—
232C23×C5—62no—
233C23×C5—62no—
234C23×C5—121no—
235C23×C5C22×D311yescharacteristic
236C23×C5C22×D311yescharacteristic
237C23×C5C22×D311yescharacteristic
238C22×D5C22×D311yescharacteristic
239C5×D4—34no—
240C5×D4—62no—
241C5×D4—62no—
242C5×D4—62no—
243C2×C4×C5—31no—
244C2×C4×C5—31no—
245C2×C4×C5—62no—
246C22⋊D5—22no—
247C22⋊D5—22no—
248C22⋊D5—41no—
249C22⋊D5—62no—
250C22⋊D5—121no—
251C2×Dic5—31no—
252C2×Dic5—31no—
253C2×Dic5—31no—
254C2×Dic5—31no—
255C2×Dic5—62no—
256C2×Dic5—62no—
257C2×Dic5—121no—
258C2×Dic5—121no—
259C2×Dic5C22×D311yescharacteristic
260C2×Dic5C22×D311yescharacteristic
261C2×Dic5C22×D311yescharacteristic
262C4×D5—62no—
263Dic10—62no—
264C2×#41—151no—
265C22×D4—31no—
266#124—151no—
267#123—151no—
268#123—151no—
269C22⋊Q8—151no—
270#121—151no—
271#121—151no—
272#121—151no—
273#120—51no—
274#120—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C22⋊C4—151no—
278C2×C22⋊C4—151no—
279C2×C3×C5—22no—
280C2×C3×C5—22no—
281C2×C3×C5—41no—
282C2×C3×C5C22×D411yescharacteristic
283C2×C3×C5C2×#4111yescharacteristic
284C2×C3×C5H(5,𝔽2)11yescharacteristic
285C3×D5—41no—
286C5×D3—22no—
287C5×D3—41no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—41no—
291C23×C3—51no—
292C23×C3C22×D511yescharacteristic
293C23×C3C22×D511yescharacteristic
294C23×C3C22×D511yescharacteristic
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—41no—
298C22×D3C22×D511yescharacteristic
299C22×D3C22×D511yescharacteristic
300C3×D4—102no—
301C3×D4—102no—
302C3×D4—201no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—51no—
306#67—22no—
307#67—22no—
308#67—22no—
309#67—102no—
310#67—201no—
311#67C22⋊D514yescomplemented
312C2×Dic3—22no—
313C2×Dic3—51no—
314C2×Dic3—51no—
315C2×Dic3—51no—
316C2×Dic3—51no—
317C2×Dic3—102no—
318C2×Dic3—102no—
319C2×Dic3—201no—
320C2×Dic3C22×D511yescharacteristic
321C2×Dic3C22×D511yescharacteristic
322C4×D3—102no—
323C4×D3—201no—
324Dic6—102no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—21no—
331C22×C5—21no—
332C22×C5—32no—
333C22×C5—44no—
334C22×C5—61no—
335C22×C5—61no—
336C22×C5—61no—
337C22×C5—61no—
338C22×C5—61no—
339C22×C5—124no—
340C22×C5D3×D412yes—
341C22×C5#23712yescomplemented
342C22×C5C23×D311yescharacteristic
343C2×D5—21no—
344C2×D5—21no—
345C2×D5—21no—
346C4×C5—32no—
347C4×C5—61no—
348Dic5—21no—
349Dic5—21no—
350Dic5—21no—
351Dic5—61no—
352Dic5—61no—
353Dic5—61no—
354Dic5—61no—
355C24—31no—
356C24D3×D511yescharacteristic
357#41—304no—
358C2×Q8—151no—
359C2×D4—31no—
360C2×D4—31no—
361C2×D4—31no—
362C2×D4—31no—
363C2×D4—51no—
364C2×D4—51no—
365C2×D4—51no—
366C2×D4—64no—
367C2×D4—151no—
368C2×D4—151no—
369C22×C4—31no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4—151no—
375C4⋊C4—151no—
376C4⋊C4—151no—
377C4⋊C4—151no—
378C4⋊C4—151no—
379C22⋊C4—51no—
380C22⋊C4—51no—
381C22⋊C4—51no—
382C22⋊C4—151no—
383C22⋊C4—151no—
384C22⋊C4—151no—
385C22⋊C4—151no—
386C22⋊C4—151no—
387C22⋊C4—151no—
388C22⋊C4—151no—
389C22⋊C4—151no—
390C22⋊C4—151no—
391C42—151no—
392C3×C5#54611yescharacteristic, complemented, Hall
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—44no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3—101no—
404C22×C3#71112yescomplemented
405C22×C3C2×C22⋊D512yes—
406C22×C3C23×D511yescharacteristic
407C2×D3—21no—
408C2×D3—21no—
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—44no—
413C2×D3C2×C22⋊D512yes—
414C3×C4—101no—
415C3×C4—101no—
416C3×C4—101no—
417Dic3—21no—
418Dic3—101no—
419Dic3—101no—
420Dic3—101no—
421Dic3—101no—
422Dic3C2×C22⋊D512yes—
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5—62no—
427C2×C5—121no—
428C2×C5C2×D3×D411yescharacteristic
429C2×C5C2×#23711yescharacteristic
430C2×C5#100411yescharacteristic
431D5—41no—
432C23—22no—
433C23—22no—
434C23—31no—
435C23—31no—
436C23—41no—
437C23—51no—
438C23—62no—
439C23—62no—
440C23—121no—
441C23C2×D3×D511yescharacteristic
442C23C2×D3×D511yescharacteristic
443C23C2×D3×D511yescharacteristic
444Q8—302no—
445D4—34no—
446D4—62no—
447D4—62no—
448D4—62no—
449D4—102no—
450D4—102no—
451D4—201no—
452D4—302no—
453D4—601no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—51no—
457C2×C4—51no—
458C2×C4—51no—
459C2×C4—62no—
460C2×C4—151no—
461C2×C4—151no—
462C2×C4—151no—
463C2×C4—151no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—601no—
468C2×C4—601no—
469C2×C3—22no—
470C2×C3—22no—
471C2×C3—41no—
472C2×C3—201no—
473C2×C3C2×#71111yescharacteristic
474C2×C3#414411yescharacteristic
475C2×C3C22×C22⋊D511yescharacteristic
476D3—22no—
477D3—41no—
478C5#559111yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—32no—
487C22—44no—
488C22—61no—
489C22—61no—
490C22—61no—
491C22—61no—
492C22—61no—
493C22—101no—
494C22—101no—
495C22—101no—
496C22—124no—
497C22#678012yescomplemented
498C22D3×C22⋊D512yes—
499C22C22×D3×D511yescharacteristic
500C4—32no—
501C4—61no—
502C4—101no—
503C4—101no—
504C4—101no—
505C4—301no—
506C4—301no—
507C4—301no—
508C4—301no—
509C3#6614011yescharacteristic, complemented, Sylow
510C2—22no—
511C2—22no—
512C2—41no—
513C2—62no—
514C2—121no—
515C2—201no—
516C2C2×#678011yescharacteristic
517C2C2×D3×C22⋊D511yescharacteristic
518C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
hypercenterC24D3×D5
hypocenterC3×C5#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C5×#67C2semidirect
2. C2×#6780C2semidirect
3. C2×#6719C2semidirect
4. C3×#4099C2semidirect
5. #91575C2semidirect
6. #91571C2semidirect
7. #91568C2semidirect
8. #91565C2semidirect
9. #67⋊Dic5C2semidirect
10. #91555C2semidirect
11. D3×C22⋊Dic5C2semidirect
12. Dic3×C22⋊D5C2semidirect
13. #91549C2semidirect
14. #91543C2semidirect
15. #91525C2semidirect
19. C22×Dic15C22semidirect
20. C22×Dic15C22semidirect
28. C2×C3×C22⋊D5C22semidirect
29. C2×C3×C22⋊D5C22semidirect
30. C2×#1204C22semidirect
31. C2×#1201C22semidirect
32. C2×#1201C22semidirect
33. C2×D3×Dic5C22semidirect
34. C2×D3×Dic5C22semidirect
36. C2×D5×Dic3C22semidirect
39. #6719C22semidirect
40. #6719C22semidirect
42. C3×C22⋊Dic5C22semidirect
43. C3×C22⋊Dic5C22semidirect
44. Dic3⋊Dic5C22semidirect
45. #6669C22semidirect
46. #6668C22semidirect
47. #6668C22semidirect
48. (C2×D3)⋊Dic5C22semidirect
49. (C2×D3)⋊Dic5C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
51. (C2×D3)⋊Dic5C22semidirect
52. #6665C22semidirect
53. Dic3×Dic5C22semidirect
58. #4099D3semidirect
91. C5×#67D4semidirect
107. C22×#67D5semidirect
133. C2×C22⋊D5C2×D3semidirect
134. C2×C22⋊D5C2×D3semidirect
151. C22⋊Dic5C2×D3semidirect
152. C22⋊Dic5C2×D3semidirect
169. C22×C3×C5#41semidirect
311. #67C22⋊D5semidirect
341. C22×C5#237semidirect
392. C3×C5#546semidirect
404. C22×C3#711semidirect
478. C5#5591semidirect
497. C22#6780semidirect
509. C3#66140semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#672
C2×#67802
C2×#67192
C3×#40992
#915752
#915712
#915682
#915652
#67⋊Dic52
#915552
D3×C22⋊Dic52
Dic3×C22⋊D52
#915492
#915432
#915252
#661403
#55915