Finite Group Databasebeta

← #11753248

Subgroups — #11753248

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×#6768C211yesmaximal, characteristic, complemented
3#91773C211yesmaximal, characteristic, complemented
4C5×#882C211yesmaximal, characteristic, complemented
5C3×#4031C211yesmaximal, characteristic, complemented
6#91570C211yesmaximal, characteristic, complemented
7#91567C211yesmaximal, characteristic, complemented
8#91558C211yesmaximal, characteristic, complemented
9#91476C211yesmaximal, characteristic, complemented
10#91475C211yesmaximal, characteristic, complemented
11#91461C211yesmaximal, characteristic, complemented
12#91453C211yesmaximal, characteristic, complemented
13#91451C211yesmaximal, characteristic, complemented
14#91398C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65926—31nomaximal, Hall
17C23×C5×D3C2211yescharacteristic
18C22×D3×D5C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×#1220C2211yescharacteristic, complemented
21C2×D60C2211yescharacteristic, complemented
22C2×C4×D15C2211yescharacteristic, complemented
23C2×C5×#67C2211yescharacteristic, complemented
24C2×C5×D12C2211yescharacteristic
25C2×C5×D12C2211yescharacteristic, complemented
26C2×C3×C22⋊D5C2211yescharacteristic
27C2×C3×Dic10C2211yescharacteristic, complemented
28D3×C22⋊D5—24no—
29C2×#1203C2211yescharacteristic
30C2×#1203C2211yescharacteristic
31C2×#1203C2211yescharacteristic, complemented
32C2×#1203C2211yescharacteristic, complemented
33C2×#1203C2211yescharacteristic, complemented
34C2×#1202C2211yescharacteristic, complemented
35C2×#1201C2211yescharacteristic
36C2×#1201C2211yescharacteristic, complemented
37C2×D3×Dic5C2211yescharacteristic
38C2×D3×Dic5C2211yescharacteristic, complemented
39#6768—24no—
40C3×C5×C22⋊C4C2211yescharacteristic, complemented
41#6714C2211yescharacteristic, complemented
42#6712C2211yescharacteristic, complemented
43C5×(C2×D3)⋊C4C2211yescharacteristic
44C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×C22⋊Dic5C2211yescharacteristic, complemented
46C3×#685C2211yescharacteristic, complemented
47C3×#685C2211yescharacteristic, complemented
48C3×C4×Dic5C2211yescharacteristic, complemented
49#6669C2211yescharacteristic, complemented
50#6667C2211yescharacteristic, complemented
51(C2×D3)⋊Dic5C2211yescharacteristic
52(C2×D3)⋊Dic5C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5674—51nomaximal, Hall
55C22×C22⋊D5—31no—
56C2×#711—31no—
57C5×#120—31no—
58#4099—31no—
59#4086—31no—
60#4086—31no—
61#4085—31no—
62#4085—31no—
63#4083—31no—
64#4031—31no—
65#4031D311yescharacteristic, complemented
66#4030—31no—
67#4030—31no—
68#4028—31no—
69#4023—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×C5×D3—22no—
74C22×C5×D3—41no—
75C22×C5×D3—41no—
76C22×C5×D3C2311yescharacteristic
77C22×C5×D3C2311yescharacteristic
78C22×C5×D3C2311yescharacteristic
79C22×C3×D5C2311yescharacteristic
80C2×D3×D5—22no—
81C2×D3×D5—41no—
82C2×D3×D5—41no—
83C2×C3×C4×C5C2311yescharacteristic
84C2×C3×C4×C5C2311yescharacteristic
85#1220—22no—
86#1220—41no—
87C2×Dic15C2311yescharacteristic
88C2×Dic15C2311yescharacteristic
89D60—41no—
90C4×D15—22no—
91C5×#67—41no—
92C2×C5×Dic3C2311yescharacteristic
93C5×D12—22no—
94C5×D12—41no—
95C3×C22⋊D5—22no—
96C2×C3×Dic5C2311yescharacteristic
97C2×C3×Dic5C2311yescharacteristic
98C2×C3×Dic5C2311yescharacteristic
99C3×Dic10—22no—
100#1203—22no—
101#1203—22no—
102#1203—22no—
103#1203—41no—
104#1203—41no—
105#1202—41no—
106#1201—22no—
107#1201—41no—
108D3×Dic5—22no—
109D3×Dic5D414yescomplemented
110C2×#239—51no—
111C2×D3×D4—51no—
112C3×#124—51no—
113#947—51no—
114#940—51no—
115#884—51no—
116#884—51no—
117#884—51no—
118#884—51no—
119#882—51no—
120#882—51no—
121#882—51no—
122#882D511yescharacteristic, complemented
123#874—51no—
124#872—51no—
125C24×C5—31no—
126C23×D5—31no—
127C2×C5×D4—31no—
128C2×C5×D4—31no—
129C2×C5×D4—31no—
130C2×C22⋊D5—31no—
131C2×C22⋊D5—31no—
132C2×C22⋊D5—31no—
133C2×C22⋊D5—31no—
134C2×C22⋊D5—31no—
135C2×C22⋊D5—31no—
136C2×C22⋊D5—31no—
137C2×C22⋊D5—31no—
138C2×C22⋊D5—31no—
139C2×C22⋊D5—64no—
140C2×C22⋊D5C2×D311yescharacteristic
141C22×Dic5—31no—
142C22×Dic5—31no—
143#711—64no—
144C2×D20—31no—
145C2×D20—31no—
146C2×C4×D5—31no—
147C2×Dic10C2×D311yescharacteristic, complemented
148C5×C22⋊C4—31no—
149C5×C22⋊C4—31no—
150C5×C22⋊C4C2×D311yescharacteristic, complemented
151C22⋊Dic5—31no—
152C22⋊Dic5—31no—
153C22⋊Dic5C2×D311yescharacteristic, complemented
154#685—31no—
155#685—31no—
156#685C2×D311yescharacteristic, complemented
157#685C2×D311yescharacteristic, complemented
158#683—31no—
159#683—31no—
160C4×Dic5—31no—
161C4×Dic5C2×D311yescharacteristic, complemented
162#535—151noSylow
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5C2411yescharacteristic
167C2×D15—21no—
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C2×D15—21no—
172C2×D15—21no—
173C2×C5×D3—21no—
174C2×C5×D3—21no—
175C2×C5×D3—21no—
176C2×C5×D3—21no—
177C2×C5×D3—21no—
178C2×C5×D3—21no—
179C2×C5×D3—21no—
180C2×C5×D3—21no—
181C2×C5×D3—44no—
182C2×C5×D3C2×D412yes—
183C2×C3×D5—21no—
184C2×C3×D5—21no—
185C2×C3×D5—21no—
186D3×D5—44no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189Dic15—21no—
190Dic15C2×D412yes—
191C3×Dic5—21no—
192C3×Dic5—21no—
193C3×Dic5C2×D412yes—
194C5×Dic3—21no—
195C23×D3—51no—
196C23×D3C2×D511yescharacteristic
197C2×C3×Q8—51no—
198C2×C3×D4—51no—
199C2×#67—51no—
200C2×#67—51no—
201C2×#67—51no—
202C2×#67—51no—
203C2×#67—51no—
204C2×#67C2×D511yescharacteristic, complemented
205#239—104no—
206D3×D4—104no—
207C2×D12—51no—
208C2×D12—51no—
209C2×D12—51no—
210C2×D12—51no—
211C2×D12—51no—
212C2×D12—51no—
213C2×D12C2×D511yescharacteristic
214C2×D12C2×D511yescharacteristic, complemented
215C2×C4×D3—51no—
216C2×C4×D3—51no—
217C2×C4×D3—51no—
218C3×C22⋊C4—51no—
219C3×C22⋊C4—51no—
220C3×C22⋊C4—51no—
221C3×C22⋊C4C2×D511yescharacteristic, complemented
222C3×C42—51no—
223(C2×D3)⋊C4—51no—
224(C2×D3)⋊C4—51no—
225(C2×D3)⋊C4—51no—
226(C2×D3)⋊C4—51no—
227(C2×D3)⋊C4C2×D511yescharacteristic
228(C2×D3)⋊C4C2×D511yescharacteristic, complemented
229Dic3⋊C4—51no—
230Dic3⋊C4—51no—
231C4×Dic3—51no—
232C23×C5—31no—
233C23×C5—31no—
234C23×C5—31no—
235C23×C5—62no—
236C23×C5—121no—
237C23×C5—121no—
238C23×C5C22×D311yescharacteristic
239C22×D5—31no—
240C22×D5—31no—
241C22×D5—62no—
242C22×D5—121no—
243C22×D5—121no—
244C22×D5C22×D311yescharacteristic
245C5×D4—62no—
246C5×D4—121no—
247C5×D4—121no—
248C2×C4×C5—31no—
249C2×C4×C5C22×D311yescharacteristic
250C2×C4×C5C22×D311yescharacteristic
251C22⋊D5—22no—
252C22⋊D5—62no—
253C22⋊D5—62no—
254C22⋊D5—62no—
255C22⋊D5—62no—
256C22⋊D5—62no—
257C22⋊D5—121no—
258C22⋊D5—121no—
259C22⋊D5—121no—
260C22⋊D5—121no—
261C2×Dic5—31no—
262C2×Dic5—34no—
263C2×Dic5—31no—
264C2×Dic5—62no—
265C2×Dic5C22×D311yescharacteristic
266C2×Dic5C22×D311yescharacteristic
267C2×Dic5C22×D311yescharacteristic
268D20—121no—
269D20—121no—
270C4×D5—62no—
271Dic10—22no—
272C2×#41—151no—
273C22×D4—151no—
274#127—151no—
275#127—151no—
276#124—51no—
277#124—151no—
278#121—151no—
279#121—151no—
280#121—151no—
281#121—151no—
282#120—31no—
283#120—151no—
284#120—151no—
285#120—151no—
286#117—151no—
287C2×C3×C5—41no—
288C2×C3×C5C22×D411yescharacteristic
289C2×C3×C5H(5,𝔽2)11yescharacteristic
290C2×C3×C5H(5,𝔽2)11yescharacteristic
291D15—41no—
292D15—41no—
293C3×D5—41no—
294C5×D3—22no—
295C5×D3—41no—
296C5×D3—41no—
297C23×C3—51no—
298C23×C3C22×D511yescharacteristic
299C22×D3—22no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—51no—
303C22×D3—51no—
304C22×D3—102no—
305C22×D3—201no—
306C22×D3—201no—
307C22×D3C22×D511yescharacteristic
308C22×D3C22×D511yescharacteristic
309C22×D3C22×D511yescharacteristic
310C3×Q8—102no—
311C3×D4—102no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4C22×D511yescharacteristic
316C2×C3×C4C22×D511yescharacteristic
317#67—41no—
318#67—102no—
319#67—102no—
320#67—201no—
321#67—201no—
322#67—201no—
323C2×Dic3—51no—
324C2×Dic3—51no—
325C2×Dic3C22×D511yescharacteristic
326D12—22no—
327D12—41no—
328D12—102no—
329D12—102no—
330D12—102no—
331D12—201no—
332D12—201no—
333D12—201no—
334C4×D3—54no—
335C4×D3—102no—
336C4×D3—102no—
337C22×C5—21no—
338C22×C5—21no—
339C22×C5—21no—
340C22×C5—32no—
341C22×C5—61no—
342C22×C5—61no—
343C22×C5—61no—
344C22×C5—61no—
345C22×C5—61no—
346C22×C5—61no—
347C22×C5—61no—
348C22×C5—61no—
349C22×C5—124no—
350C22×C5C23×D311yescharacteristic
351C2×D5—21no—
352C2×D5—21no—
353C2×D5—21no—
354C2×D5—61no—
355C2×D5—61no—
356C2×D5—61no—
357C2×D5—61no—
358C2×D5—61no—
359C2×D5—61no—
360C2×D5—124no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—61no—
364Dic5—21no—
365Dic5—21no—
366Dic5—32no—
367Dic5—61no—
368Dic5D3×D412yes—
369C24—31no—
370C24—151no—
371#41—304no—
372C2×Q8—51no—
373C2×D4—31no—
374C2×D4—31no—
375C2×D4—31no—
376C2×D4—51no—
377C2×D4—151no—
378C2×D4—151no—
379C2×D4—151no—
380C2×D4—151no—
381C2×D4—151no—
382C2×D4—151no—
383C2×D4—151no—
384C2×D4—151no—
385C2×D4—151no—
386C2×D4—151no—
387C2×D4—151no—
388C2×D4—304no—
389C22×C4—151no—
390C22×C4—151no—
391C22×C4—151no—
392C4⋊C4—151no—
393C4⋊C4—151no—
394C22⋊C4—31no—
395C22⋊C4—31no—
396C22⋊C4—51no—
397C22⋊C4—51no—
398C22⋊C4—51no—
399C22⋊C4—151no—
400C22⋊C4—151no—
401C22⋊C4—151no—
402C22⋊C4—151no—
403C22⋊C4D3×D511yescharacteristic, complemented
404C42—51no—
405C42—151no—
406C3×C5#53511yescharacteristic, complemented, Hall
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—101no—
411C22×C3—101no—
412C22×C3—101no—
413C22×C3C23×D511yescharacteristic
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—21no—
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—44no—
423C2×D3—101no—
424C2×D3—101no—
425C2×D3—101no—
426C2×D3—101no—
427C2×D3—101no—
428C2×D3—101no—
429C2×D3—204no—
430C2×D3D4×D512yes—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—52no—
434C3×C4—101no—
435C3×C4—101no—
436Dic3—21no—
437Dic3—52no—
438Dic3—101no—
439C2×C5—41no—
440C2×C5—62no—
441C2×C5—121no—
442C2×C5—121no—
443C2×C5C2×D3×D411yescharacteristic
444C2×C5#100911yescharacteristic
445C2×C5#100911yescharacteristic
446D5—41no—
447D5—121no—
448D5—121no—
449C23—31no—
450C23—31no—
451C23—31no—
452C23—51no—
453C23—62no—
454C23—121no—
455C23—121no—
456C23—151no—
457C23—151no—
458C23—302no—
459C23—601no—
460C23—601no—
461C23C2×D3×D511yescharacteristic
462Q8—102no—
463D4—62no—
464D4—102no—
465D4—121no—
466D4—121no—
467D4—302no—
468D4—302no—
469D4—302no—
470D4—302no—
471D4—302no—
472D4—601no—
473D4—601no—
474D4—601no—
475D4—601no—
476D4—601no—
477D4—601no—
478C2×C4—31no—
479C2×C4—51no—
480C2×C4—51no—
481C2×C4—51no—
482C2×C4—154no—
483C2×C4—151no—
484C2×C4—151no—
485C2×C4—302no—
486C2×C4—302no—
487C2×C4C2×D3×D511yescharacteristic
488C2×C4C2×D3×D511yescharacteristic
489C2×C3—41no—
490C2×C3—201no—
491C2×C3C2×D4×D511yescharacteristic
492C2×C3#414411yescharacteristic
493C2×C3#414411yescharacteristic
494D3—22no—
495D3—41no—
496D3—41no—
497D3—201no—
498D3—201no—
499C5#567411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—21no—
503C22—32no—
504C22—61no—
505C22—61no—
506C22—61no—
507C22—61no—
508C22—61no—
509C22—61no—
510C22—61no—
511C22—61no—
512C22—101no—
513C22—101no—
514C22—101no—
515C22—124no—
516C22—301no—
517C22—301no—
518C22—301no—
519C22—301no—
520C22—301no—
521C22—301no—
522C22—604no—
523C22C22×D3×D511yescharacteristic
524C4—21no—
525C4—21no—
526C4—52no—
527C4—61no—
528C4—101no—
529C4—101no—
530C4—152no—
531C4—301no—
532C3#6592611yescharacteristic, complemented, Sylow
533C2—41no—
534C2—62no—
535C2—121no—
536C2—121no—
537C2—201no—
538C2—601no—
539C2—601no—
540C2#9201811yescharacteristic
541C2D3×D4×D511yescharacteristic
542C2#9202711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#535
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. C2×D3×C22⋊D5C2semidirect
2. C2×#6768C2semidirect
3. #91773C2semidirect
4. C5×#882C2semidirect
5. C3×#4031C2semidirect
6. #91570C2semidirect
7. #91567C2semidirect
8. #91558C2semidirect
9. #91476C2semidirect
10. #91475C2semidirect
11. #91461C2semidirect
12. #91453C2semidirect
13. #91451C2semidirect
14. #91398C2semidirect
15. #91326C2semidirect
20. C2×#1220C22semidirect
21. C2×D60C22semidirect
22. C2×C4×D15C22semidirect
23. C2×C5×#67C22semidirect
25. C2×C5×D12C22semidirect
27. C2×C3×Dic10C22semidirect
31. C2×#1203C22semidirect
32. C2×#1203C22semidirect
33. C2×#1203C22semidirect
34. C2×#1202C22semidirect
36. C2×#1201C22semidirect
38. C2×D3×Dic5C22semidirect
40. C3×C5×C22⋊C4C22semidirect
41. #6714C22semidirect
42. #6712C22semidirect
44. C5×(C2×D3)⋊C4C22semidirect
45. C3×C22⋊Dic5C22semidirect
46. C3×#685C22semidirect
47. C3×#685C22semidirect
48. C3×C4×Dic5C22semidirect
49. #6669C22semidirect
50. #6667C22semidirect
52. (C2×D3)⋊Dic5C22semidirect
53. Dic3×Dic5C22semidirect
65. #4031D3semidirect
109. D3×Dic5D4semidirect
122. #882D5semidirect
147. C2×Dic10C2×D3semidirect
150. C5×C22⋊C4C2×D3semidirect
153. C22⋊Dic5C2×D3semidirect
156. #685C2×D3semidirect
157. #685C2×D3semidirect
161. C4×Dic5C2×D3semidirect
204. C2×#67C2×D5semidirect
214. C2×D12C2×D5semidirect
221. C3×C22⋊C4C2×D5semidirect
228. (C2×D3)⋊C4C2×D5semidirect
403. C22⋊C4D3×D5semidirect
406. C3×C5#535semidirect
499. C5#5674semidirect
532. C3#65926semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊D52
C2×#67682
#917732
C5×#8822
C3×#40312
#915702
#915672
#915582
#914762
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