Finite Group Databasebeta

← #11755073

Subgroups — #11755073

Order 960.

692 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D15C211yesmaximal, characteristic, complemented
2C2×#6790C211yesmaximal, characteristic, complemented
3C5×#939C211yesmaximal, characteristic, complemented
4C3×#4085C211yesmaximal, characteristic, complemented
5#91577C211yesmaximal, characteristic, complemented
6#91573C211yesmaximal, characteristic, complemented
7#91572C211yesmaximal, characteristic, complemented
8#91569C211yesmaximal, characteristic, complemented
9#91566C211yesmaximal, characteristic, complemented
10#91562C211yesmaximal, characteristic, complemented
11C2×#6667C211yesmaximal, characteristic, complemented
12#91476C211yesmaximal, characteristic, complemented
13#91433C211yesmaximal, characteristic, complemented
14#91355C211yesmaximal, characteristic, complemented
15#91354C211yesmaximal, characteristic, complemented
16#65939—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C23×D15C2211yescharacteristic, complemented
19C22×D3×D5C2211yescharacteristic, complemented
20C2×C3×C5×D4C2211yescharacteristic, complemented
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic, complemented
23D4×D15—24no—
24C2×D60C2211yescharacteristic
25C2×C4×D15C2211yescharacteristic, complemented
26C2×C5×#67C2211yescharacteristic, complemented
27C2×C5×#67C2211yescharacteristic, complemented
28C22×C5×Dic3C2211yescharacteristic, complemented
29C2×C3×C22⋊D5C2211yescharacteristic, complemented
30C2×C3×C22⋊D5C2211yescharacteristic, complemented
31C22×C3×Dic5C2211yescharacteristic, complemented
32#6790—24no—
33C2×#1203C2211yescharacteristic
34C2×#1203C2211yescharacteristic, complemented
35C2×#1202C2211yescharacteristic
36C2×#1202C2211yescharacteristic, complemented
37C2×#1200C2211yescharacteristic, complemented
38C5×#217C2211yescharacteristic, complemented
39C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C5×Dic3⋊C4C2211yescharacteristic, complemented
41C3×C22⋊Dic5C2211yescharacteristic, complemented
42C3×#685C2211yescharacteristic, complemented
43C3×#683C2211yescharacteristic, complemented
44Dic3⋊Dic5C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic, complemented
47#6667C2211yescharacteristic, complemented
48#6667C2211yescharacteristic, complemented
49#6667C2211yescharacteristic, complemented
50#6667C2211yescharacteristic, complemented
51#6667C2211yescharacteristic, complemented
52(C2×D3)⋊Dic5C2211yescharacteristic, complemented
53#6665C2211yescharacteristic, complemented
54#5605—51nomaximal, Hall
55C2×D4×D5—31no—
56C2×D4×D5—31no—
57C5×#121—31no—
58#4085—31no—
59#4085D311yescharacteristic, complemented
60#4083—31no—
61#4083—31no—
62#4076—31no—
63C2×#685—31no—
64#4040—31no—
65#4040—31no—
66#4029—31no—
67#4029—31no—
68#4028—31no—
69#4028—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15—22no—
73C22×D15—41no—
74C22×D15—41no—
75C22×D15—41no—
76C22×D15—41no—
77C22×D15D414yescomplemented
78C22×D15C2311yescharacteristic
79C22×D15C2311yescharacteristic
80C22×D15C2311yescharacteristic
81C22×C5×D3C2311yescharacteristic
82C22×C3×D5C2311yescharacteristic
83C2×D3×D5—22no—
84C2×D3×D5—41no—
85C2×D3×D5—41no—
86C3×C5×D4—22no—
87C2×C3×C4×C5C2311yescharacteristic
88#1220—22no—
89#1220—22no—
90C2×Dic15C2311yescharacteristic
91D60—22no—
92C4×D15—22no—
93C5×#67—22no—
94C5×#67—41no—
95C2×C5×Dic3—41no—
96C2×C5×Dic3C2311yescharacteristic
97C2×C5×Dic3C2311yescharacteristic
98C2×C5×Dic3C2311yescharacteristic
99C3×C22⋊D5—22no—
100C3×C22⋊D5—41no—
101C2×C3×Dic5—41no—
102C2×C3×Dic5C2311yescharacteristic
103C2×C3×Dic5C2311yescharacteristic
104C2×C3×Dic5C2311yescharacteristic
105#1203—22no—
106#1203—41no—
107#1202—22no—
108#1202—41no—
109#1200—22no—
110C2×D3×D4—51no—
111C2×D3×D4—51no—
112C3×#121—51no—
113#939—51no—
114#939D511yescharacteristic, complemented
115#937—51no—
116#937—51no—
117#930—51no—
118C2×(C2×D3)⋊C4—51no—
119#894—51no—
120#894—51no—
121#883—51no—
122#883—51no—
123#882—51no—
124#882—51no—
125C23×D5—31no—
126C23×D5—31no—
127C23×D5—31no—
128C2×C5×D4—31no—
129C2×C5×D4—31no—
130C2×C5×D4C2×D311yescharacteristic, complemented
131C22×C4×C5—31no—
132C2×C22⋊D5—31no—
133C2×C22⋊D5—31no—
134C2×C22⋊D5—31no—
135C2×C22⋊D5—31no—
136C2×C22⋊D5C2×D311yescharacteristic, complemented
137C2×C22⋊D5C2×D311yescharacteristic, complemented
138C22×Dic5C2×D311yescharacteristic, complemented
139D4×D5—64no—
140D4×D5—64no—
141C2×D20—31no—
142C2×D20—31no—
143C2×D20—31no—
144C2×C4×D5—31no—
145C2×C4×D5—31no—
146C5×C4⋊C4—31no—
147C5×C22⋊C4—31no—
148C5×C22⋊C4—31no—
149C22⋊Dic5—31no—
150C22⋊Dic5C2×D311yescharacteristic, complemented
151#685—31no—
152#685—31no—
153#685—31no—
154#685—31no—
155#685—31no—
156#685—31no—
157#685—31no—
158#685C2×D311yescharacteristic, complemented
159C4⋊Dic5—31no—
160#683—31no—
161#683C2×D311yescharacteristic, complemented
162#534—151noSylow
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5C2×D412yes—
169C22×C3×C5C2411yescharacteristic
170C2×D15—21no—
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C2×D15—21no—
175C2×D15—21no—
176C2×D15—21no—
177C2×D15—44no—
178C2×D15—44no—
179C2×D15C2×D412yes—
180C2×D15C2×D412yes—
181C2×C5×D3—21no—
182C2×C5×D3—21no—
183C2×C5×D3—21no—
184C2×C3×D5—21no—
185C2×C3×D5—21no—
186C2×C3×D5—21no—
187D3×D5—44no—
188C3×C4×C5—21no—
189Dic15—21no—
190C3×Dic5—21no—
191C3×Dic5—21no—
192C3×Dic5—21no—
193C5×Dic3—21no—
194C5×Dic3—21no—
195C5×Dic3—21no—
196C23×D3—51no—
197C23×D3—51no—
198C23×D3—51no—
199C2×C3×D4—51no—
200C2×C3×D4—51no—
201C2×C3×D4C2×D511yescharacteristic, complemented
202C22×C3×C4—51no—
203C2×#67—51no—
204C2×#67—51no—
205C2×#67—51no—
206C2×#67—51no—
207C2×#67C2×D511yescharacteristic, complemented
208C2×#67C2×D511yescharacteristic, complemented
209C22×Dic3C2×D511yescharacteristic, complemented
210D3×D4—104no—
211D3×D4—104no—
212C2×D12—51no—
213C2×D12—51no—
214C2×D12—51no—
215C2×C4×D3—51no—
216C2×C4×D3—51no—
217C3×C4⋊C4—51no—
218C3×C22⋊C4—51no—
219C3×C22⋊C4—51no—
220#217—51no—
221#217C2×D511yescharacteristic, complemented
222(C2×D3)⋊C4—51no—
223(C2×D3)⋊C4—51no—
224(C2×D3)⋊C4—51no—
225(C2×D3)⋊C4—51no—
226(C2×D3)⋊C4—51no—
227(C2×D3)⋊C4—51no—
228(C2×D3)⋊C4—51no—
229(C2×D3)⋊C4C2×D511yescharacteristic, complemented
230C4⋊Dic3—51no—
231Dic3⋊C4—51no—
232Dic3⋊C4C2×D511yescharacteristic, complemented
233C23×C5—31no—
234C23×C5C22×D311yescharacteristic
235C23×C5C22×D311yescharacteristic
236C22×D5—31no—
237C22×D5—31no—
238C22×D5—34no—
239C22×D5—31no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—121no—
243C22×D5—121no—
244C22×D5—121no—
245C22×D5—121no—
246C22×D5—121no—
247C22×D5—121no—
248C22×D5C22×D311yescharacteristic
249C5×D4—22no—
250C5×D4—62no—
251C5×D4—121no—
252C2×C4×C5—31no—
253C2×C4×C5—31no—
254C2×C4×C5—31no—
255C2×C4×C5—121no—
256C2×C4×C5C22×D311yescharacteristic
257C22⋊D5—22no—
258C22⋊D5—41no—
259C22⋊D5—62no—
260C22⋊D5—62no—
261C22⋊D5—62no—
262C22⋊D5—121no—
263C2×Dic5—31no—
264C2×Dic5—41no—
265C2×Dic5C22×D311yescharacteristic
266C2×Dic5C22×D311yescharacteristic
267C2×Dic5C22×D311yescharacteristic
268D20—62no—
269D20—62no—
270D20—121no—
271C4×D5—62no—
272C4×D5—62no—
273C22×D4—151no—
274C22×D4—151no—
275#123—151no—
276#123—151no—
277#123—151no—
278#123—151no—
279#121—31no—
280#121—51no—
281#121—151no—
282#121—151no—
283#120—151no—
284#120—151no—
285#120—151no—
286#120—151no—
287C2×C22⋊C4—151no—
288C2×C3×C5—22no—
289C2×C3×C5—41no—
290C2×C3×C5C22×D411yescharacteristic
291C2×C3×C5H(5,𝔽2)11yescharacteristic
292C2×C3×C5H(5,𝔽2)11yescharacteristic
293D15—22no—
294D15—22no—
295D15—41no—
296C3×D5—41no—
297C5×D3—41no—
298C23×C3—51no—
299C23×C3C22×D511yescharacteristic
300C23×C3C22×D511yescharacteristic
301C22×D3—51no—
302C22×D3—51no—
303C22×D3—54no—
304C22×D3—51no—
305C22×D3—102no—
306C22×D3—102no—
307C22×D3—201no—
308C22×D3—201no—
309C22×D3—201no—
310C22×D3—201no—
311C22×D3—201no—
312C22×D3—201no—
313C22×D3C22×D511yescharacteristic
314C3×D4—22no—
315C3×D4—102no—
316C3×D4—201no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—51no—
320C2×C3×C4—201no—
321C2×C3×C4C22×D511yescharacteristic
322#67—22no—
323#67—41no—
324#67—102no—
325#67—102no—
326#67—102no—
327#67—201no—
328C2×Dic3—41no—
329C2×Dic3—51no—
330C2×Dic3C22×D511yescharacteristic
331C2×Dic3C22×D511yescharacteristic
332C2×Dic3C22×D511yescharacteristic
333D12—102no—
334D12—102no—
335D12—201no—
336C4×D3—102no—
337C4×D3—102no—
338C22×C5—21no—
339C22×C5—21no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—61no—
344C22×C5—61no—
345C22×C5—61no—
346C22×C5D3×D412yes—
347C22×C5C23×D311yescharacteristic
348C2×D5—21no—
349C2×D5—21no—
350C2×D5—21no—
351C2×D5—32no—
352C2×D5—32no—
353C2×D5—61no—
354C2×D5—61no—
355C2×D5—61no—
356C2×D5—61no—
357C2×D5—61no—
358C2×D5—61no—
359C2×D5—61no—
360C2×D5—124no—
361C2×D5—124no—
362C2×D5—124no—
363C4×C5—21no—
364C4×C5—61no—
365C4×C5—61no—
366C4×C5—61no—
367Dic5—21no—
368Dic5—21no—
369Dic5—21no—
370Dic5—61no—
371C24—151no—
372C24—151no—
373C24—151no—
374C2×D4—31no—
375C2×D4—31no—
376C2×D4—51no—
377C2×D4—51no—
378C2×D4—151no—
379C2×D4—151no—
380C2×D4—151no—
381C2×D4—151no—
382C2×D4—151no—
383C2×D4—151no—
384C2×D4—151no—
385C2×D4—304no—
386C2×D4—304no—
387C2×D4D3×D511yescharacteristic, complemented
388C22×C4—31no—
389C22×C4—51no—
390C22×C4—151no—
391C22×C4—151no—
392C4⋊C4—31no—
393C4⋊C4—51no—
394C4⋊C4—151no—
395C4⋊C4—151no—
396C22⋊C4—31no—
397C22⋊C4—31no—
398C22⋊C4—51no—
399C22⋊C4—51no—
400C22⋊C4—151no—
401C22⋊C4—151no—
402C22⋊C4—151no—
403C22⋊C4—151no—
404C22⋊C4—151no—
405C22⋊C4—151no—
406C22⋊C4—151no—
407C22⋊C4—151no—
408C3×C5#53411yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—101no—
415C22×C3—101no—
416C22×C3—101no—
417C22×C3D4×D512yes—
418C22×C3C23×D511yescharacteristic
419C2×D3—21no—
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—52no—
423C2×D3—52no—
424C2×D3—101no—
425C2×D3—101no—
426C2×D3—101no—
427C2×D3—101no—
428C2×D3—101no—
429C2×D3—101no—
430C2×D3—101no—
431C2×D3—204no—
432C2×D3—204no—
433C2×D3—204no—
434C3×C4—21no—
435C3×C4—101no—
436C3×C4—101no—
437C3×C4—101no—
438Dic3—21no—
439Dic3—21no—
440Dic3—21no—
441Dic3—101no—
442C2×C5—22no—
443C2×C5—41no—
444C2×C5—121no—
445C2×C5C2×D3×D411yescharacteristic
446C2×C5#100411yescharacteristic
447C2×C5#100911yescharacteristic
448D5—41no—
449D5—62no—
450D5—62no—
451D5—121no—
452C23—31no—
453C23—51no—
454C23—151no—
455C23—151no—
456C23—154no—
457C23—151no—
458C23—302no—
459C23—302no—
460C23—601no—
461C23—601no—
462C23—601no—
463C23—601no—
464C23—601no—
465C23—601no—
466C23C2×D3×D511yescharacteristic
467C23C2×D3×D511yescharacteristic
468D4—22no—
469D4—62no—
470D4—102no—
471D4—121no—
472D4—201no—
473D4—302no—
474D4—302no—
475D4—302no—
476D4—302no—
477D4—302no—
478D4—601no—
479D4—601no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—121no—
487C2×C4—151no—
488C2×C4—201no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4C2×D3×D511yescharacteristic
492C2×C3—22no—
493C2×C3—41no—
494C2×C3—201no—
495C2×C3C2×D4×D511yescharacteristic
496C2×C3#414411yescharacteristic
497C2×C3#414911yescharacteristic
498D3—41no—
499D3—102no—
500D3—102no—
501D3—201no—
502C5#560511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—61no—
509C22—61no—
510C22—61no—
511C22—101no—
512C22—101no—
513C22—101no—
514C22—152no—
515C22—152no—
516C22—301no—
517C22—301no—
518C22—301no—
519C22—301no—
520C22—301no—
521C22—301no—
522C22—301no—
523C22—604no—
524C22—604no—
525C22—604no—
526C22#679012yes—
527C22C22×D3×D511yescharacteristic
528C4—21no—
529C4—61no—
530C4—61no—
531C4—61no—
532C4—101no—
533C4—101no—
534C4—101no—
535C4—301no—
536C3#6593911yescharacteristic, complemented, Sylow
537C2—22no—
538C2—41no—
539C2—121no—
540C2—201no—
541C2—302no—
542C2—302no—
543C2—601no—
544C2#9202611yescharacteristic
545C2#9202711yescharacteristic
546C2C2×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×D15C2semidirect
2. C2×#6790C2semidirect
3. C5×#939C2semidirect
4. C3×#4085C2semidirect
5. #91577C2semidirect
6. #91573C2semidirect
7. #91572C2semidirect
8. #91569C2semidirect
9. #91566C2semidirect
10. #91562C2semidirect
11. C2×#6667C2semidirect
12. #91476C2semidirect
13. #91433C2semidirect
14. #91355C2semidirect
15. #91354C2semidirect
18. C23×D15C22semidirect
19. C22×D3×D5C22semidirect
20. C2×C3×C5×D4C22semidirect
22. C2×#1220C22semidirect
25. C2×C4×D15C22semidirect
26. C2×C5×#67C22semidirect
27. C2×C5×#67C22semidirect
28. C22×C5×Dic3C22semidirect
29. C2×C3×C22⋊D5C22semidirect
30. C2×C3×C22⋊D5C22semidirect
31. C22×C3×Dic5C22semidirect
34. C2×#1203C22semidirect
36. C2×#1202C22semidirect
37. C2×#1200C22semidirect
38. C5×#217C22semidirect
39. C5×(C2×D3)⋊C4C22semidirect
40. C5×Dic3⋊C4C22semidirect
41. C3×C22⋊Dic5C22semidirect
42. C3×#685C22semidirect
43. C3×#683C22semidirect
44. Dic3⋊Dic5C22semidirect
45. #6668C22semidirect
46. #6667C22semidirect
47. #6667C22semidirect
48. #6667C22semidirect
49. #6667C22semidirect
50. #6667C22semidirect
51. #6667C22semidirect
52. (C2×D3)⋊Dic5C22semidirect
53. #6665C22semidirect
59. #4085D3semidirect
77. C22×D15D4semidirect
114. #939D5semidirect
130. C2×C5×D4C2×D3semidirect
136. C2×C22⋊D5C2×D3semidirect
137. C2×C22⋊D5C2×D3semidirect
138. C22×Dic5C2×D3semidirect
150. C22⋊Dic5C2×D3semidirect
158. #685C2×D3semidirect
161. #683C2×D3semidirect
201. C2×C3×D4C2×D5semidirect
207. C2×#67C2×D5semidirect
208. C2×#67C2×D5semidirect
209. C22×Dic3C2×D5semidirect
221. #217C2×D5semidirect
229. (C2×D3)⋊C4C2×D5semidirect
232. Dic3⋊C4C2×D5semidirect
387. C2×D4D3×D5semidirect
408. C3×C5#534semidirect
502. C5#5605semidirect
536. C3#65939semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D152
C2×#67902
C5×#9392
C3×#40852
#915772
#915732
#915722
#915692
#915662
#915622
C2×#66672
#914762
#914332
#913552
#913542
#659393
#56055