Finite Group Databasebeta

← #12963844

Subgroups — #12963844

Order 1280.

1962 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10618158C211yesmaximal, characteristic
2C5×#2961C211yesmaximal, characteristic, complemented
3#10615060C211yesmaximal, characteristic, complemented
4#10611674C218yesmaximal, complemented
5#10611672C218yesmaximal, complemented
6#10610804C212yesmaximal, complemented
7#10610802C212yesmaximal, complemented
8#10610773C211yesmaximal, characteristic, complemented
9#10610769C211yesmaximal, characteristic, complemented
10#10610284C212yesmaximal, complemented
11#10610281C212yesmaximal, complemented
12#10610222C211yesmaximal, characteristic, complemented
13C2×D5×#97C211yesmaximal, characteristic, complemented
14C5×#533C2211yescharacteristic
15C2×#4053C2212yes—
16C2×#4047C2212yes—
17C22×C8×D5C2211yescharacteristic
18C22×C8×D5C2211yescharacteristic
19#66062C412yes—
20#66059C412yes—
21#66025C414yes—
22#65961C414yes—
23#65958C414yes—
24#65914C2214yes—
25C4×#713C2214yes—
26#65858C2212yes—
27#65856C2212yes—
28#65811C2211yescharacteristic
29C2×C42×D5C2211yescharacteristic
30C5×#446C2218yescomplemented
31C5×#424C2212yes—
32C5×#423C2211yescharacteristic
33C5×#405C2212yes—
34C2×C5×#97C2211yescharacteristic
35#65418C2212yes—
36#65415C2212yes—
37M16×Dic5C2212yes—
38#65399C2212yes—
39C2×#3947C2211yescharacteristic
40C2×#3947C2211yescharacteristic
41#65313C2218yescomplemented
42#65288C2212yes—
43#65286C2212yes—
44#65213C2211yescharacteristic
45C2×#3935C2211yescharacteristic
46#65129C2218yescomplemented
47#65125C2218yes—
48#65125C2218yescomplemented
49#65124C2214yes—
50#65124C2218yescomplemented
51#65123C2218yes—
52#65122C2214yes—
53#64997C2214yescomplemented
54#64995C2218yes—
55#64995C2218yescomplemented
56D5×#97C2214yes—
57D5×#97C2214yes—
58D5×#97C2214yescomplemented
59#64978C2214yescomplemented
60C4×#676C2214yescomplemented
61C8×D20C2218yes—
62#60207—51nomaximal, Sylow
63C2×#713C2×C414yes—
64C2×#709C2312yes—
65C22×C4×D5C2×C412yes—
66C22×C4×D5C2311yescharacteristic
67C2×C5×M16C2312yes—
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C5×C4⋊Q8C2×C412yes—
71C5×#125C2×C412yes—
72C5×C22⋊Q8C2×C414yes—
73C4×C5×Q8C2314yes—
74C5×#117C2312yes—
75C2×C42×C5C2311yescharacteristic
76#4093C2×C414yes—
77#4092C2×C414yes—
78Q8×Dic5C2×C414yes—
79#4076C2×C414yes—
80C2×C4×Dic5C2×C412yes—
81C2×C4×Dic5C2311yescharacteristic
82C2×#681C2312yes—
83C22×#168C2311yescharacteristic
84C22×#168C2311yescharacteristic
85#4053—28no—
86#4047—28no—
87C2×#676C2314yes—
88C2×#676C2314yes—
89C2×C8×D5—24no—
90C2×C8×D5—24no—
91C2×C8×D5C2314yes—
92C2×C8×D5C2314yes—
93C2×C8×D5C2314yes—
94C2×C8×D5C2314yes—
95#4044C2×C418yes—
96#4043C2×C414yes—
97#4041C2×C414yes—
98#4041C2×C414yes—
99#4040C2×C418yes—
100#4039C2×C414yes—
101#4039C2×C414yes—
102#4039C2×C418yes—
103#4038C2×C414yes—
104#4038C2×C418yes—
105#4036C2×C414yes—
106#4033C2×C414yes—
107#4032C2×C414yes—
108#4028C2×C414yes—
109#4027C2×C418yes—
110#4021C2×C412yes—
111#4020C2×C411yescharacteristic
112C4×D20C2314yes—
113C4×D20C2318yes—
114#4018C2314yes—
115C42×D5C2×C412yes—
116C42×D5C2×C412yes—
117C42×D5C2312yes—
118C42×D5C2312yes—
119C42×D5C2314yes—
120#4015C2×C411yescharacteristic
121C5×C4⋊C8C2314yes—
122C5×C4⋊C8C2318yes—
123C5×#97C2314yes—
124C5×#97C2314yes—
125C4×C5×C8C2314yes—
126#3952C2318yes—
127#3952C2318yes—
128#3952C2318yes—
129#3947C2314yes—
130#3947C2312yes—
131#3947C2312yes—
132#3947C2312yes—
133#3947C2312yes—
134C8×Dic5C2314yes—
135C4⋊#168C2318yes—
136C4⋊#168C2314yes—
137#3935C2314yes—
138#3935C2314yes—
139C4×#168C2314yes—
140#3444—51no—
141#2970—58no—
142#2968—58no—
143#2961—51no—
144#2961D511yescharacteristic, complemented
145#2932—51no—
146#2932—51no—
147#2929—52no—
148#2929—52no—
149#2923—52no—
150#2920—51no—
151#2875—52no—
152C22×#97—51no—
153C23×D5C22×C411yescharacteristic
154C2×C5×Q8C22×C414yes—
155C22×C4×C5C22×C412yes—
156C22×C4×C5C2411yescharacteristic
157C2×C22⋊D5C22×C414yes—
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C412yes—
160#713—48no—
161#709—24no—
162#709—24no—
163C2×D20C22×C412yes—
164C2×D20C22×C418yes—
165C2×D20C22×C414yes—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—44no—
169C2×C4×D5C22×C412yes—
170C2×C4×D5C22×C412yes—
171C2×C4×D5C22×C412yes—
172C2×C4×D5C22×C412yes—
173C2×C4×D5C22×C412yes—
174C2×C4×D5C22×C418yes—
175C2×C4×D5C2412yes—
176C2×C4×D5C2414yes—
177C2×Dic10C22×C412yes—
178C5×M16—24no—
179C2×C5×C8—22no—
180C2×C5×C8#4114yescomplemented
181C2×C5×C8C2412yes—
182C2×C5×C8C2414yes—
183C2×C5×C8C2412yes—
184C5×C4⋊C4C22×C414yes—
185C5×C4⋊C4C22×C418yes—
186C5×C4⋊C4C22×C414yes—
187C5×C22⋊C4C22×C414yes—
188C42×C5C22×C411yescharacteristic
189C42×C5C22×C411yescharacteristic
190C42×C5C2412yes—
191C42×C5C2414yes—
192#685C22×C418yes—
193#685C22×C418yes—
194#685C22×C418yes—
195#685C22×C418yes—
196C4⋊Dic5C22×C414yes—
197C4⋊Dic5C22×C418yes—
198#683C22×C418yes—
199C4×Dic5C22×C412yes—
200C4×Dic5C22×C412yes—
201C4×Dic5C22×C412yes—
202C4×Dic5C22×C412yes—
203C4×Dic5C22×C412yes—
204C4×Dic5C22×C418yes—
205C4×Dic5C2411yescharacteristic
206C4×Dic5C2411yescharacteristic
207#681—24no—
208C2×#168—22no—
209C2×#168#4114yescomplemented
210C2×#168C2414yes—
211C2×#168C2412yes—
212C2×#168C2412yes—
213#676—28no—
214#676—28no—
215C8×D5—28no—
216C8×D5—28no—
217C8×D5—28no—
218C8×D5—28no—
219C2×#131—52no—
220C2×#131—52no—
221C23×C8—51no—
222C23×C8—51no—
223#533—52no—
224#533C2×D511yescharacteristic
225#532—52no—
226#532—51no—
227#529—54no—
228#529—54no—
229#529—54no—
230#525—54no—
231#525—52no—
232C4×#41—54no—
233C4×#41—52no—
234C22×C42—51no—
235#446—58no—
236#446C2×D518yescomplemented
237#435—58no—
238#435—58no—
239#435—58no—
240#435—58no—
241C8×D4—58no—
242C8×D4—58no—
243#433—58no—
244#432—54no—
245#432—58no—
246#431—54no—
247#424—52no—
248#424C2×D512yes—
249#423—51no—
250#423C2×D511yescharacteristic
251#408—52no—
252#408—52no—
253#407—52no—
254#405—52no—
255#405—54no—
256#405—54no—
257#405C2×D512yes—
258C4×M16—52no—
259C4×M16—54no—
260C2×#97—51no—
261C2×#97—51no—
262C2×#97—51no—
263C2×#97—54no—
264C2×#97—54no—
265C2×#97—54no—
266C2×#97C2×D511yescharacteristic
267C23×C5C23×C411yescharacteristic
268C22×D5—22no—
269C22×D5—24no—
270C22×D5C23×C414yes—
271C22×D5C23×C412yes—
272C5×Q8—44no—
273C2×C4×C5—42no—
274C2×C4×C5C23×C412yes—
275C2×C4×C5C23×C412yes—
276C2×C4×C5C23×C418yes—
277C2×C4×C5C23×C411yescharacteristic
278C2×C4×C5C2×#4112yes—
279C2×C4×C5C2×#4112yes—
280C2×C4×C5C2511yescharacteristic
281C22⋊D5—28no—
282C2×Dic5—22no—
283C2×Dic5—42no—
284C2×Dic5C23×C412yes—
285C2×Dic5C23×C412yes—
286C2×Dic5C23×C412yes—
287C2×Dic5C23×C414yes—
288D20—216no—
289D20—24no—
290D20—44no—
291C4×D5—24no—
292C4×D5—24no—
293C4×D5—24no—
294C4×D5—22no—
295C4×D5—22no—
296C4×D5—24no—
297C4×D5—24no—
298C4×D5—42no—
299C4×D5—42no—
300C4×D5—48no—
301Dic10—24no—
302C5×C8—22no—
303C5×C8—24no—
304C5×C8C2×#4114yes—
305#168—22no—
306#168—24no—
307#168C2×#4114yes—
308C2×#41—54no—
309C2×#41—52no—
310C23×C4—51no—
311C23×C4—52no—
312#131—108no—
313#131—108no—
314C2×M16—52no—
315C2×M16—54no—
316C2×M16—54no—
317C2×M16C22×D512yes—
318C22×C8—51no—
319C22×C8—51no—
320C22×C8—54no—
321C22×C8—54no—
322C22×C8—54no—
323C22×C8—54no—
324C22×C8—104no—
325C22×C8—104no—
326C22×C8C22×D511yescharacteristic
327C22×C8C22×D511yescharacteristic
328C4⋊Q8—51no—
329C4⋊Q8C4×D512yes—
330#127—51no—
331#126—58no—
332#125—54no—
333#125C4×D512yes—
334#124—54no—
335#124—52no—
336#123—58no—
337#123—54no—
338C22⋊Q8—54no—
339C22⋊Q8—54no—
340C22⋊Q8C4×D514yes—
341#121—54no—
342#121—54no—
343#121—54no—
344#120—54no—
345C4×Q8—54no—
346C4×Q8—54no—
347C4×Q8C22×D514yes—
348C4×D4—58no—
349C4×D4—54no—
350C4×D4—54no—
351C4×D4—58no—
352C4×D4—58no—
353C4×D4—54no—
354#117—54no—
355#117—58no—
356#117—54no—
357#117C22×D512yes—
358C2×C42—52no—
359C2×C42—51no—
360C2×C42—52no—
361C2×C42—52no—
362C2×C42—54no—
363C2×C42—52no—
364C2×C42—52no—
365C2×C42C22×D511yescharacteristic
366C4⋊C8—54no—
367C4⋊C8—58no—
368C4⋊C8C22×D514yes—
369C4⋊C8C22×D518yes—
370C22⋊C8—58no—
371C22⋊C8—58no—
372C22⋊C8—58no—
373#97—52no—
374#97—52no—
375#97—52no—
376#97—52no—
377#97—54no—
378#97—54no—
379#97—54no—
380#97C22×D514yes—
381#97C22×D514yes—
382C4×C8—54no—
383C4×C8—54no—
384C4×C8C22×D514yes—
385C22×C5—22no—
386C22×C5C4×#4112yes—
387C22×C5C24×C411yescharacteristic
388C2×D5—28no—
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—24no—
392C2×D5—28no—
393C2×D5#56814yes—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—28no—
397C4×C5C4×#4112yes—
398C4×C5C22×#4111yescharacteristic
399C4×C5C22×#4111yescharacteristic
400Dic5—24no—
401Dic5—22no—
402Dic5—22no—
403Dic5—22no—
404C24—51no—
405#41—104no—
406#41—104no—
407#41—208no—
408C2×Q8—52no—
409C2×Q8C2×C4×D514yes—
410C2×D4—54no—
411C2×D4—58no—
412C2×D4—52no—
413C2×D4—54no—
414C22×C4—51no—
415C22×C4—52no—
416C22×C4—52no—
417C22×C4—52no—
418C22×C4—52no—
419C22×C4—52no—
420C22×C4—54no—
421C22×C4—52no—
422C22×C4—52no—
423C22×C4—58no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—204no—
427C22×C4C2×C4×D512yes—
428C22×C4C23×D511yescharacteristic
429M16—24no—
430M16—108no—
431M16—104no—
432M16—108no—
433C2×C8—22no—
434C2×C8—54no—
435C2×C8—52no—
436C2×C8—54no—
437C2×C8—52no—
438C2×C8—108no—
439C2×C8—108no—
440C2×C8—102no—
441C2×C8—108no—
442C2×C8—108no—
443C2×C8#71314yescomplemented
444C2×C8C23×D514yes—
445C2×C8C23×D512yes—
446C2×C8C23×D512yes—
447C4⋊C4—54no—
448C4⋊C4—58no—
449C4⋊C4—58no—
450C4⋊C4C2×C4×D514yes—
451C4⋊C4C2×C4×D518yes—
452C4⋊C4C2×C4×D514yes—
453C22⋊C4—58no—
454C22⋊C4—58no—
455C22⋊C4—58no—
456C22⋊C4—58no—
457C22⋊C4C2×C4×D514yes—
458C42—52no—
459C42—52no—
460C42—52no—
461C42—52no—
462C42—52no—
463C42—58no—
464C42—51no—
465C42—51no—
466C42C2×C4×D511yescharacteristic
467C42C2×C4×D511yescharacteristic
468C42C23×D514yes—
469C42C23×D512yes—
470C2×C5—22no—
471C2×C5C2×C4×#4111yescharacteristic
472C2×C5C2×#56812yes—
473D5—24no—
474D5—44no—
475C23—52no—
476C23—54no—
477C23—104no—
478C23—102no—
479C23C22×C4×D511yescharacteristic
480Q8—44no—
481Q8—104no—
482D4—1016no—
483D4—108no—
484D4—104no—
485D4—204no—
486C2×C4—42no—
487C2×C4—52no—
488C2×C4—52no—
489C2×C4—52no—
490C2×C4—54no—
491C2×C4—104no—
492C2×C4—104no—
493C2×C4—102no—
494C2×C4—104no—
495C2×C4—102no—
496C2×C4—104no—
497C2×C4—102no—
498C2×C4—104no—
499C2×C4—202no—
500C2×C4—202no—
501C2×C4—208no—
502C2×C4—202no—
503C2×C4C22×C4×D512yes—
504C2×C4C22×C4×D512yes—
505C2×C4C22×C4×D518yes—
506C2×C4C22×C4×D511yescharacteristic
507C2×C4C2×#71312yes—
508C2×C4D5×#4112yes—
509C2×C4C24×D511yescharacteristic
510C8—22no—
511C8—24no—
512C8—54no—
513C8—102no—
514C8—104no—
515C8C2×#71314yes—
516C5#6020711yescharacteristic, complemented, Sylow
517C22—22no—
518C22—54no—
519C22—108no—
520C22—102no—
521C22—102no—
522C22—104no—
523C22—108no—
524C22C4×#71312yes—
525C22C23×C4×D511yescharacteristic
526C4—22no—
527C4—22no—
528C4—28no—
529C4—102no—
530C4—104no—
531C4—102no—
532C4—102no—
533C4C4×#71312yes—
534C4C22×#71311yescharacteristic
535C4C2×D5×#4111yescharacteristic
536C2—22no—
537C2—104no—
538C2—204no—
539C2C2×C4×#71311yescharacteristic
540C2D5×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D5
commutator, socleC22×C5C24×C4
FittingC5×#2961C2
prime radical#10618158C2
cosocleC2×C4×C5C25
hypercenter#2961D5
hypocenterC5#60207
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. C5×#2961C2semidirect
3. #10615060C2semidirect
4. #10611674C2semidirect
5. #10611672C2semidirect
6. #10610804C2semidirect
7. #10610802C2semidirect
8. #10610773C2semidirect
9. #10610769C2semidirect
10. #10610284C2semidirect
11. #10610281C2semidirect
12. #10610222C2semidirect
13. C2×D5×#97C2semidirect
30. C5×#446C22semidirect
41. #65313C22semidirect
46. #65129C22semidirect
48. #65125C22semidirect
50. #65124C22semidirect
53. #64997C22semidirect
55. #64995C22semidirect
58. D5×#97C22semidirect
59. #64978C22semidirect
60. C4×#676C22semidirect
144. #2961D5semidirect
180. C2×C5×C8#41semidirect
209. C2×#168#41semidirect
236. #446C2×D5semidirect
443. C2×C8#713semidirect
516. C5#60207semidirect

Maximal subgroups

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

subgroupindex
#106181582
C5×#29612
#106150602
#106116742
#106116722
#106108042
#106108022
#106107732
#106107692
#106102842
#106102812
#106102222
C2×D5×#972
#602075