Finite Group Databasebeta

← #11755029

Subgroups — #11755029

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×D5×#67C211yesmaximal, characteristic, complemented
2C2×#6779C211yesmaximal, characteristic, complemented
3#91829C211yesmaximal, characteristic, complemented
4C5×#939C211yesmaximal, characteristic, complemented
5C3×#4083C211yesmaximal, characteristic, complemented
6#91577C211yesmaximal, characteristic, complemented
7#91569C211yesmaximal, characteristic, complemented
8#91567C211yesmaximal, characteristic, complemented
9#91564C211yesmaximal, characteristic, complemented
10#91557C211yesmaximal, characteristic, complemented
11#91526C211yesmaximal, characteristic, complemented
12#91476C211yesmaximal, characteristic, complemented
13#91464C211yesmaximal, characteristic, complemented
14#91459C211yesmaximal, characteristic, complemented
15#91394C211yesmaximal, characteristic, complemented
16#65941—31nomaximal, Hall
17C23×C3×D5C2211yescharacteristic
18C22×D3×D5C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic, complemented
20C2×#1220C2211yescharacteristic
21C2×#1220C2211yescharacteristic, complemented
22C2×#1220C2211yescharacteristic, complemented
23C2×#1220C2211yescharacteristic, complemented
24C2×D60C2211yescharacteristic, complemented
25C2×C5×#67C2211yescharacteristic
26C2×C5×#67C2211yescharacteristic, complemented
27C22×C5×Dic3C2211yescharacteristic, complemented
28C2×C3×C22⋊D5C2211yescharacteristic
29C2×C3×C22⋊D5C2211yescharacteristic, complemented
30D5×#67—24no—
31C2×#1204C2211yescharacteristic, complemented
32C2×#1203C2211yescharacteristic, complemented
33C2×#1202C2211yescharacteristic
34C2×#1202C2211yescharacteristic
35C2×#1202C2211yescharacteristic, complemented
36C2×#1201C2211yescharacteristic
37C2×#1200C2211yescharacteristic, complemented
38#6779—24no—
39C2×D5×Dic3C2211yescharacteristic
40C4×Dic15C2211yescharacteristic, complemented
41C5×#217C2211yescharacteristic, complemented
42C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C5×Dic3⋊C4C2211yescharacteristic, complemented
44C3×C22⋊Dic5C2211yescharacteristic, complemented
45C3×#685C2211yescharacteristic
46C3×#685C2211yescharacteristic, complemented
47Dic3⋊Dic5C2211yescharacteristic, complemented
48#6667C2211yescharacteristic, complemented
49#6667C2211yescharacteristic, complemented
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51#6665C2211yescharacteristic
52#6665C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5592—51nomaximal, Hall
55C2×D4×D5—31no—
56C2×#709—31no—
57C5×#121—31no—
58#4086—31no—
59#4086—31no—
60#4084—31no—
61#4083—31no—
62#4083D311yescharacteristic, complemented
63#4076—31no—
64#4041—31no—
65#4038—31no—
66#4031—31no—
67#4031—31no—
68#4028—31no—
69#4028—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×D15C2311yescharacteristic
74C22×C5×D3C2311yescharacteristic
75C22×C3×D5—22no—
76C22×C3×D5—41no—
77C22×C3×D5—41no—
78C22×C3×D5C2311yescharacteristic
79C22×C3×D5C2311yescharacteristic
80C2×D3×D5—22no—
81C2×D3×D5—41no—
82C2×D3×D5—41no—
83C3×C5×D4—41no—
84C2×C3×C4×C5C2311yescharacteristic
85#1220—22no—
86#1220—22no—
87#1220—41no—
88#1220—41no—
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91D60—41no—
92C5×#67—22no—
93C5×#67—41no—
94C2×C5×Dic3—22no—
95C2×C5×Dic3C2311yescharacteristic
96C2×C5×Dic3C2311yescharacteristic
97C2×C5×Dic3C2311yescharacteristic
98C3×C22⋊D5—22no—
99C3×C22⋊D5—41no—
100C2×C3×Dic5C2311yescharacteristic
101C2×C3×Dic5C2311yescharacteristic
102#1204—22no—
103#1203—41no—
104#1202—22no—
105#1202—22no—
106#1202—41no—
107#1201—22no—
108#1200—22no—
109D5×Dic3D414yescomplemented
110C22×#67—51no—
111C2×#237—51no—
112C3×#120—51no—
113#953—51no—
114#940—51no—
115#940—51no—
116#939—51no—
117#939D511yescharacteristic, complemented
118#937—51no—
119#885—51no—
120#885—51no—
121#884—51no—
122#884—51no—
123#882—51no—
124#877—51no—
125C23×D5—31no—
126C23×D5C2×D311yescharacteristic
127C2×C5×D4—31no—
128C2×C5×D4—31no—
129C2×C5×D4C2×D311yescharacteristic, complemented
130C22×C4×C5—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⋊D5C2×D311yescharacteristic
138C2×C22⋊D5C2×D311yescharacteristic, complemented
139D4×D5—64no—
140#709—64no—
141C2×D20—31no—
142C2×D20—31no—
143C2×D20—31no—
144C2×D20—31no—
145C2×C4×D5—31no—
146C2×C4×D5—31no—
147C2×Dic10—31no—
148C5×C4⋊C4—31no—
149C5×C22⋊C4—31no—
150C5×C22⋊C4—31no—
151C22⋊Dic5—31no—
152C22⋊Dic5C2×D311yescharacteristic, complemented
153#685—31no—
154#685—31no—
155#685—31no—
156#685—31no—
157#685C2×D311yescharacteristic
158#685C2×D311yescharacteristic, complemented
159C4⋊Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162#535—151noSylow
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5C2411yescharacteristic
170C2×D15—21no—
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C2×D15—21no—
175C2×D15—21no—
176C2×C5×D3—21no—
177C2×C5×D3—21no—
178C2×C5×D3—21no—
179C2×C3×D5—21no—
180C2×C3×D5—21no—
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C2×C3×D5—21no—
184C2×C3×D5—44no—
185C2×C3×D5C2×D412yes—
186D3×D5—44no—
187C3×C4×C5—21no—
188Dic15—21no—
189Dic15C2×D412yes—
190C3×Dic5—21no—
191C3×Dic5—21no—
192C5×Dic3—21no—
193C5×Dic3—21no—
194C5×Dic3C2×D412yes—
195C24×C3—51no—
196C23×D3—51no—
197C2×C3×D4—51no—
198C2×C3×D4—51no—
199C2×C3×D4C2×D511yescharacteristic, complemented
200C2×#67—51no—
201C2×#67—51no—
202C2×#67—51no—
203C2×#67—51no—
204C2×#67—51no—
205C2×#67—51no—
206C2×#67—51no—
207C2×#67—51no—
208C2×#67—104no—
209C2×#67C2×D511yescharacteristic
210C2×#67C2×D511yescharacteristic, complemented
211C22×Dic3—51no—
212C22×Dic3C2×D511yescharacteristic, complemented
213#237—104no—
214C2×D12—51no—
215C2×D12—51no—
216C2×C4×D3—51no—
217C2×Dic6—51no—
218C3×C22⋊C4—51no—
219C3×C22⋊C4—51no—
220C3×C22⋊C4—51no—
221#217—51no—
222#217—51no—
223#217C2×D511yescharacteristic, complemented
224(C2×D3)⋊C4—51no—
225(C2×D3)⋊C4—51no—
226(C2×D3)⋊C4—51no—
227(C2×D3)⋊C4C2×D511yescharacteristic, complemented
228Dic3⋊C4—51no—
229Dic3⋊C4C2×D511yescharacteristic, complemented
230C4×Dic3—51no—
231C4×Dic3—51no—
232C23×C5—31no—
233C23×C5C22×D311yescharacteristic
234C23×C5C22×D311yescharacteristic
235C22×D5—22no—
236C22×D5—31no—
237C22×D5—31no—
238C22×D5—41no—
239C22×D5—41no—
240C22×D5—62no—
241C22×D5—121no—
242C22×D5—121no—
243C22×D5C22×D311yescharacteristic
244C22×D5C22×D311yescharacteristic
245C5×D4—41no—
246C5×D4—62no—
247C5×D4—121no—
248C2×C4×C5—31no—
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—62no—
252C2×C4×C5C22×D311yescharacteristic
253C22⋊D5—22no—
254C22⋊D5—41no—
255C22⋊D5—62no—
256C22⋊D5—62no—
257C22⋊D5—62no—
258C22⋊D5—121no—
259C22⋊D5—121no—
260C22⋊D5—121no—
261C2×Dic5—31no—
262C2×Dic5—31no—
263C2×Dic5C22×D311yescharacteristic
264C2×Dic5C22×D311yescharacteristic
265D20—62no—
266D20—62no—
267D20—121no—
268D20—121no—
269C4×D5—34no—
270C4×D5—62no—
271Dic10—62no—
272C2×#41—151no—
273C22×D4—151no—
274#127—151no—
275#127—151no—
276#124—151no—
277#124—151no—
278#121—31no—
279#121—151no—
280#121—151no—
281#121—151no—
282#120—51no—
283#120—151no—
284#120—151no—
285#120—151no—
286#117—151no—
287C2×C3×C5—41no—
288C2×C3×C5—41no—
289C2×C3×C5C22×D411yescharacteristic
290C2×C3×C5H(5,𝔽2)11yescharacteristic
291C2×C3×C5H(5,𝔽2)11yescharacteristic
292D15—41no—
293D15—41no—
294C3×D5—22no—
295C3×D5—41no—
296C5×D3—41no—
297C23×C3—51no—
298C23×C3—51no—
299C23×C3—102no—
300C23×C3—201no—
301C23×C3—201no—
302C23×C3C22×D511yescharacteristic
303C23×C3C22×D511yescharacteristic
304C22×D3—51no—
305C22×D3—51no—
306C22×D3—102no—
307C22×D3—201no—
308C22×D3—201no—
309C22×D3C22×D511yescharacteristic
310C3×D4—41no—
311C3×D4—102no—
312C3×D4—201no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4C22×D511yescharacteristic
316#67—22no—
317#67—41no—
318#67—102no—
319#67—102no—
320#67—102no—
321#67—102no—
322#67—102no—
323#67—201no—
324#67—201no—
325#67—201no—
326C2×Dic3—22no—
327C2×Dic3—51no—
328C2×Dic3—54no—
329C2×Dic3—51no—
330C2×Dic3C22×D511yescharacteristic
331C2×Dic3C22×D511yescharacteristic
332C2×Dic3C22×D511yescharacteristic
333D12—201no—
334D12—201no—
335C4×D3—102no—
336Dic6—102no—
337C22×C5—21no—
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×C5C23×D311yescharacteristic
347C2×D5—21no—
348C2×D5—21no—
349C2×D5—21no—
350C2×D5—21no—
351C2×D5—21no—
352C2×D5—44no—
353C2×D5—61no—
354C2×D5—61no—
355C2×D5—61no—
356C2×D5—61no—
357C2×D5—61no—
358C2×D5—61no—
359C2×D5—124no—
360C2×D5D3×D412yes—
361C4×C5—21no—
362C4×C5—32no—
363C4×C5—61no—
364C4×C5—61no—
365Dic5—21no—
366Dic5—21no—
367Dic5—32no—
368Dic5—61no—
369C24—51no—
370C24—151no—
371#41—304no—
372C2×Q8—151no—
373C2×D4—31no—
374C2×D4—31no—
375C2×D4—51no—
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—304no—
388C2×D4D3×D511yescharacteristic, complemented
389C22×C4—31no—
390C22×C4—151no—
391C22×C4—151no—
392C4⋊C4—31no—
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⋊C4—151no—
404C42—151no—
405C42—151no—
406C3×C5#53511yescharacteristic, complemented, Hall
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—52no—
414C22×C3—101no—
415C22×C3—101no—
416C22×C3—101no—
417C22×C3—101no—
418C22×C3—101no—
419C22×C3—204no—
420C22×C3C23×D511yescharacteristic
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3—101no—
425C2×D3—101no—
426C2×D3—101no—
427C2×D3—101no—
428C2×D3—101no—
429C2×D3—101no—
430C2×D3—204no—
431C3×C4—21no—
432C3×C4—101no—
433C3×C4—101no—
434Dic3—21no—
435Dic3—21no—
436Dic3—52no—
437Dic3—101no—
438Dic3D4×D512yes—
439C2×C5—41no—
440C2×C5—41no—
441C2×C5—121no—
442C2×C5C2×D3×D411yescharacteristic
443C2×C5#100411yescharacteristic
444C2×C5#100411yescharacteristic
445D5—22no—
446D5—41no—
447D5—121no—
448D5—121no—
449C23—31no—
450C23—51no—
451C23—51no—
452C23—102no—
453C23—151no—
454C23—151no—
455C23—201no—
456C23—201no—
457C23—302no—
458C23—601no—
459C23—601no—
460C23C2×D3×D511yescharacteristic
461C23C2×D3×D511yescharacteristic
462Q8—302no—
463D4—41no—
464D4—62no—
465D4—102no—
466D4—121no—
467D4—201no—
468D4—302no—
469D4—302no—
470D4—302no—
471D4—302no—
472D4—302no—
473D4—601no—
474D4—601no—
475D4—601no—
476D4—601no—
477D4—601no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—62no—
484C2×C4—154no—
485C2×C4—151no—
486C2×C4—151no—
487C2×C4—302no—
488C2×C4C2×D3×D511yescharacteristic
489C2×C3—41no—
490C2×C3—41no—
491C2×C3—102no—
492C2×C3—201no—
493C2×C3C2×D4×D511yescharacteristic
494C2×C3#414411yescharacteristic
495C2×C3#414911yescharacteristic
496D3—41no—
497D3—201no—
498D3—201no—
499C5#559211yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—52no—
507C22—61no—
508C22—61no—
509C22—61no—
510C22—101no—
511C22—101no—
512C22—101no—
513C22—101no—
514C22—101no—
515C22—204no—
516C22—301no—
517C22—301no—
518C22—301no—
519C22—301no—
520C22—301no—
521C22—301no—
522C22—604no—
523C22C22×D3×D511yescharacteristic
524C4—21no—
525C4—32no—
526C4—61no—
527C4—61no—
528C4—101no—
529C4—101no—
530C4—152no—
531C4—301no—
532C3#6594111yescharacteristic, complemented, Sylow
533C2—41no—
534C2—41no—
535C2—102no—
536C2—121no—
537C2—201no—
538C2—601no—
539C2—601no—
540C2D3×D4×D511yescharacteristic
541C2#9202611yescharacteristic
542C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#535
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×D5×#67C2semidirect
2. C2×#6779C2semidirect
3. #91829C2semidirect
4. C5×#939C2semidirect
5. C3×#4083C2semidirect
6. #91577C2semidirect
7. #91569C2semidirect
8. #91567C2semidirect
9. #91564C2semidirect
10. #91557C2semidirect
11. #91526C2semidirect
12. #91476C2semidirect
13. #91464C2semidirect
14. #91459C2semidirect
15. #91394C2semidirect
19. C2×C3×C5×D4C22semidirect
21. C2×#1220C22semidirect
22. C2×#1220C22semidirect
23. C2×#1220C22semidirect
24. C2×D60C22semidirect
26. C2×C5×#67C22semidirect
27. C22×C5×Dic3C22semidirect
29. C2×C3×C22⋊D5C22semidirect
31. C2×#1204C22semidirect
32. C2×#1203C22semidirect
35. C2×#1202C22semidirect
37. C2×#1200C22semidirect
40. C4×Dic15C22semidirect
41. C5×#217C22semidirect
42. C5×(C2×D3)⋊C4C22semidirect
43. C5×Dic3⋊C4C22semidirect
44. C3×C22⋊Dic5C22semidirect
46. C3×#685C22semidirect
47. Dic3⋊Dic5C22semidirect
48. #6667C22semidirect
49. #6667C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
52. #6665C22semidirect
53. Dic3×Dic5C22semidirect
62. #4083D3semidirect
109. D5×Dic3D4semidirect
117. #939D5semidirect
129. C2×C5×D4C2×D3semidirect
138. C2×C22⋊D5C2×D3semidirect
152. C22⋊Dic5C2×D3semidirect
158. #685C2×D3semidirect
199. C2×C3×D4C2×D5semidirect
210. C2×#67C2×D5semidirect
212. C22×Dic3C2×D5semidirect
223. #217C2×D5semidirect
227. (C2×D3)⋊C4C2×D5semidirect
229. Dic3⋊C4C2×D5semidirect
388. C2×D4D3×D5semidirect
406. C3×C5#535semidirect
499. C5#5592semidirect
532. C3#65941semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#672
C2×#67792
#918292
C5×#9392
C3×#40832
#915772
#915692
#915672
#915642
#915572
#915262
#914762
#914642
#914592
#913942
#659413
#55925