Finite Group Databasebeta

← #12963998

Subgroups — #12963998

Order 1280.

1950 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617743C211yesmaximal, characteristic
2C5×#2971C211yesmaximal, characteristic, complemented
3#41×#168C211yesmaximal, characteristic, complemented
4Q8×#676C211yesmaximal, characteristic, complemented
5C8×Q8×D5C211yesmaximal, characteristic, complemented
6#10611636C211yesmaximal, characteristic, complemented
7C8×#713C211yesmaximal, characteristic, complemented
8#10611272C213yesmaximal, complemented
9#10611269C213yesmaximal, complemented
10#10611252C213yesmaximal, complemented
11#10611249C213yesmaximal, complemented
12#10611065C213yesmaximal, complemented
13#10611056C213yesmaximal, complemented
14C4×#4053C213yesmaximal, complemented
15#10610242C213yesmaximal, complemented
16C4×C5×#41C2211yescharacteristic
17#66168C411yescharacteristic
18#66165C411yescharacteristic
19C2×#4053C2213yes—
20C2×#4053C2213yes—
21#65910C411yescharacteristic
22C4×#713C2211yescharacteristic
23C4×Q8×D5C2211yescharacteristic
24#65903C411yescharacteristic
25#65893C413yes—
26#65892C413yes—
27#65891C2213yes—
28#65882C2213yes—
29#65867C413yes—
30#65864C413yes—
31#65813C2213yes—
32C4×#709C2213yes—
33C5×C8×Q8C2211yescharacteristic
34C5×C8×Q8C2211yescharacteristic
35C5×#436C2213yes—
36C5×#436C2213yes—
37C5×#432C2213yes—
38C4×C5×M16C2213yes—
39#65417C2216yes—
40#65416C2216yes—
41#65411C2213yes—
42#65411C2213yes—
43Q8×#168C2211yescharacteristic
44Q8×#168C2211yescharacteristic
45D4×#168C2213yes—
46D4×#168C2213yes—
47#65214C2213yes—
48C2×C4×#168C2213yes—
49#65127C2213yes—
50#65126C2213yes—
51#65124C2213yes—
52#65123C2213yes—
53#65122C2213yes—
54D5×C4⋊C8C2213yes—
55#65120C2213yes—
56#65119C2213yes—
57#65019C2216yes—
58#65016C2216yes—
59#65014C2216yes—
60#65009C2216yes—
61#64998C2216yes—
62#64997C2213yes—
63#64997C2211yescharacteristic
64#64997C2213yes—
65#64997C2213yes—
66#64977C2213yes—
67C4×#676C2213yes—
68C4×#676C2213yes—
69C8×D20C2213yes—
70C4×C8×D5C2213yes—
71C4×C8×D5C2213yes—
72#64968C2213yes—
73C8×Dic10C2213yes—
74#60218—51nomaximal, Sylow
75C2×C5×#41C2×C411yescharacteristic
76C2×#713C2×C411yescharacteristic
77C2×Q8×D5C2×C411yescharacteristic
78C2×#709C2313yes—
79C2×C5×M16C2313yes—
80C2×C5×M16C2313yes—
81C4×C5×Q8C2×C411yescharacteristic
82C4×C5×Q8C2311yescharacteristic
83C4×C5×D4C2×C413yes—
84C4×C5×D4C2313yes—
85C5×#117C2×C413yes—
86C2×C42×C5C2313yes—
87Q8×Dic5C2×C411yescharacteristic
88Q8×Dic5C2×C411yescharacteristic
89#4086C2×C413yes—
90#4084C2×C413yes—
91#4084C2×C413yes—
92#4082C2×C413yes—
93#4076C2×C413yes—
94#4075C2×C416yes—
95C4×C22⋊D5C2×C413yes—
96C4×C22⋊D5C2×C413yes—
97C4×C22⋊D5C2×C413yes—
98C4×C22⋊D5C2×C413yes—
99C4×C22⋊D5C2316yes—
100#4072C2313yes—
101#4070C2×C413yes—
102C22×#168C2313yes—
103C22×#168C2313yes—
104#4053—212no—
105#4053—212no—
106C2×#676C2313yes—
107C2×#676C2313yes—
108C2×#676C2313yes—
109C2×#676C2311yescharacteristic
110C2×C8×D5C2313yes—
111C2×C8×D5C2313yes—
112C2×C8×D5C2313yes—
113C2×C8×D5C2311yescharacteristic
114#4043C2×C413yes—
115#4041C2×C413yes—
116#4039C2×C413yes—
117#4038C2×C413yes—
118D5×C4⋊C4C2×C413yes—
119#4036C2×C413yes—
120#4034C2×C413yes—
121#4033C2×C413yes—
122#4031C2×C416yes—
123#4030C2×C416yes—
124#4029C2×C416yes—
125#4025C2×C416yes—
126#4022C2×C416yes—
127#4021C2×C413yes—
128C4×D20C2×C413yes—
129C4×D20C2×C413yes—
130C4×D20C2313yes—
131#4018C2311yescharacteristic
132#4018C2313yes—
133C42×D5C2313yes—
134C42×D5C2313yes—
135#4016C2×C413yes—
136C4×Dic10C2×C413yes—
137C4×Dic10C2×C413yes—
138C4×Dic10C2313yes—
139C5×C4⋊C8C2313yes—
140C5×C4⋊C8C2313yes—
141C5×C22⋊C8C2316yes—
142C5×#97C2311yescharacteristic
143C5×#97C2313yes—
144C4×C5×C8C2313yes—
145C4×C5×C8C2313yes—
146C22⋊#168C2316yes—
147#3952C2316yes—
148#3952C2316yes—
149#3947C2313yes—
150#3947C2313yes—
151#3947C2311yescharacteristic
152#3947C2313yes—
153#3946C2316yes—
154#3946C2316yes—
155C8×Dic5C2313yes—
156C8×Dic5C2313yes—
157C8×Dic5C2311yescharacteristic
158C8×Dic5C2313yes—
159C4⋊#168C2313yes—
160C4⋊#168C2313yes—
161C4×#168C2313yes—
162C4×#168C2313yes—
163C4×#168C2311yescharacteristic
164C4×#168C2313yes—
165#3480—51no—
166#2971—51no—
167#2971D511yescharacteristic, complemented
168#2969—53no—
169#2969—53no—
170#2966—53no—
171#2966—53no—
172C8×#41—51no—
173C8×#41—51no—
174Q8×M16—51no—
175C2×C8×Q8—51no—
176#2935—53no—
177#2931—53no—
178#2925—53no—
179C4×#131—53no—
180C5×#41—24no—
181C2×C5×Q8C22×C411yescharacteristic
182C2×C5×D4C22×C413yes—
183C22×C4×C5C22×C413yes—
184C22×C4×C5C22×C413yes—
185C22×C4×C5C2413yes—
186C2×C22⋊D5C22×C413yes—
187C2×C22⋊D5C22×C413yes—
188C2×C22⋊D5C22×C416yes—
189#713—24no—
190Q8×D5—24no—
191#709—26no—
192#709—26no—
193C2×D20C22×C413yes—
194C2×D20C22×C413yes—
195C2×C4×D5C22×C413yes—
196C2×C4×D5C22×C413yes—
197C2×C4×D5C22×C413yes—
198C2×C4×D5C22×C413yes—
199C2×C4×D5C2413yes—
200C2×C4×D5C2411yescharacteristic
201C2×Dic10C22×C413yes—
202C2×Dic10C22×C413yes—
203C5×M16—26no—
204C5×M16—26no—
205C2×C5×C8C2413yes—
206C2×C5×C8C2413yes—
207C2×C5×C8C2411yescharacteristic
208C2×C5×C8C2411yescharacteristic
209C5×C4⋊C4C22×C413yes—
210C5×C4⋊C4C22×C413yes—
211C5×C22⋊C4C22×C416yes—
212C42×C5C22×C413yes—
213C42×C5C22×C413yes—
214C42×C5C2411yescharacteristic
215C42×C5C2413yes—
216C22⋊Dic5C22×C413yes—
217C22⋊Dic5C22×C416yes—
218C22⋊Dic5C22×C413yes—
219#685C22×C411yescharacteristic
220#685C22×C411yescharacteristic
221#685C22×C413yes—
222#685C22×C413yes—
223#685C22×C416yes—
224#685C22×C416yes—
225C4⋊Dic5C22×C413yes—
226C4⋊Dic5C22×C413yes—
227C4⋊Dic5C22×C413yes—
228C4⋊Dic5C22×C413yes—
229#683C22×C411yescharacteristic
230#683C22×C411yescharacteristic
231#683C22×C413yes—
232#683C22×C413yes—
233#683C22×C416yes—
234#683C22×C416yes—
235C4×Dic5C22×C413yes—
236C4×Dic5C22×C413yes—
237C4×Dic5C22×C413yes—
238C4×Dic5C22×C413yes—
239C4×Dic5C2411yescharacteristic
240C4×Dic5C2413yes—
241C2×#168—26no—
242C2×#168—26no—
243C2×#168C2413yes—
244C2×#168C2413yes—
245C2×#168C2411yescharacteristic
246C2×#168C2411yescharacteristic
247#676—26no—
248#676—26no—
249#676—26no—
250#676#4114yescomplemented
251C8×D5—26no—
252C8×D5—26no—
253C8×D5—26no—
254C8×D5#4114yescomplemented
255C2×#131—53no—
256C2×#131—53no—
257#559—53no—
258#557—51no—
259#556—53no—
260#553—53no—
261#553—53no—
262#550—51no—
263#548—51no—
264#548—51no—
265#532—53no—
266#529—53no—
267#529—53no—
268C4×#41—51no—
269C4×#41—53no—
270C4×#41C2×D511yescharacteristic
271C2×C4×Q8—51no—
272#446—53no—
273#446—53no—
274C8×Q8—51no—
275C8×Q8—51no—
276C8×Q8—53no—
277C8×Q8—53no—
278C8×Q8C2×D511yescharacteristic
279C8×Q8C2×D511yescharacteristic
280#436—56no—
281#436—53no—
282#436—53no—
283#436C2×D513yes—
284#436C2×D513yes—
285#435—56no—
286#435—56no—
287C8×D4—53no—
288C8×D4—53no—
289C8×D4—53no—
290C8×D4—56no—
291C8×D4—53no—
292#433—56no—
293#433—56no—
294#432—53no—
295#432C2×D513yes—
296#431—53no—
297#431—53no—
298#423—53no—
299C2×C4⋊C8—53no—
300#408—56no—
301#405—53no—
302#405—53no—
303#405—51no—
304#405—53no—
305#405—53no—
306#405—53no—
307C4×M16—53no—
308C4×M16—53no—
309C4×M16C2×D513yes—
310C2×C4×C8—53no—
311C2×C4×C8—53no—
312C2×C4×C8—53no—
313C23×C5C23×C413yes—
314C22×D5C23×C413yes—
315C22×D5C23×C411yescharacteristic
316C5×Q8#13114yescomplemented
317C5×D4—26no—
318C2×C4×C5—26no—
319C2×C4×C5—23no—
320C2×C4×C5—23no—
321C2×C4×C5—43no—
322C2×C4×C5C23×C413yes—
323C2×C4×C5C23×C411yescharacteristic
324C2×C4×C5C23×C411yescharacteristic
325C2×C4×C5C23×C413yes—
326C2×C4×C5C23×C413yes—
327C2×C4×C5C2511yescharacteristic
328C22⋊D5—26no—
329C22⋊D5—26no—
330C22⋊D5—46no—
331C2×Dic5C23×C411yescharacteristic
332C2×Dic5C23×C411yescharacteristic
333C2×Dic5C23×C413yes—
334C2×Dic5C23×C413yes—
335C2×Dic5C23×C413yes—
336C2×Dic5C23×C411yescharacteristic
337D20—26no—
338D20—26no—
339C4×D5—26no—
340C4×D5—26no—
341C4×D5—23no—
342C4×D5—23no—
343C4×D5—43no—
344C4×D5—43no—
345C4×D5C2×#4112yes—
346C4×D5C2×#4112yes—
347Dic10—26no—
348Dic10—26no—
349C5×C8—23no—
350C5×C8—23no—
351C5×C8C2×#4112yes—
352C5×C8C2×#4112yes—
353#168—23no—
354#168—23no—
355#168C2×#4112yes—
356#168C2×#4112yes—
357C2×#41—51no—
358C2×#41—53no—
359C2×#41C4×D511yescharacteristic
360C22×Q8—51no—
361#131—1012no—
362#131—1012no—
363C2×M16—51no—
364C2×M16—53no—
365C2×M16—53no—
366C2×M16—53no—
367C2×M16C22×D513yes—
368C2×M16C22×D513yes—
369C22×C8—51no—
370C22×C8—53no—
371C22×C8—53no—
372C22×C8—53no—
373C22×C8—53no—
374C22×C8—53no—
375C4⋊Q8—53no—
376#127—53no—
377#126—56no—
378#126—56no—
379#125—53no—
380#125—53no—
381#124—53no—
382#124—56no—
383#124—53no—
384#123—56no—
385#123—56no—
386C22⋊Q8—53no—
387C22⋊Q8—53no—
388#121—53no—
389#121—53no—
390#121—53no—
391#121—53no—
392#121—56no—
393C4×Q8—51no—
394C4×Q8—51no—
395C4×Q8—53no—
396C4×Q8—53no—
397C4×Q8—53no—
398C4×Q8—53no—
399C4×Q8C4×D511yescharacteristic
400C4×Q8C22×D511yescharacteristic
401C4×D4—53no—
402C4×D4—53no—
403C4×D4—53no—
404C4×D4—53no—
405C4×D4—56no—
406C4×D4—53no—
407C4×D4—53no—
408C4×D4—53no—
409C4×D4—53no—
410C4×D4C4×D513yes—
411C4×D4C22×D513yes—
412#117—53no—
413#117—53no—
414#117—51no—
415#117—53no—
416#117C4×D513yes—
417C2×C4⋊C4—53no—
418C2×C42—53no—
419C2×C42—53no—
420C2×C42C22×D513yes—
421C4⋊C8—56no—
422C4⋊C8—56no—
423C4⋊C8—53no—
424C4⋊C8—53no—
425C4⋊C8C22×D513yes—
426C4⋊C8C22×D513yes—
427C22⋊C8—56no—
428C22⋊C8—56no—
429C22⋊C8—56no—
430C22⋊C8C22×D516yes—
431#97—51no—
432#97—53no—
433#97—53no—
434#97—53no—
435#97C22×D511yescharacteristic
436#97C22×D513yes—
437C4×C8—51no—
438C4×C8—53no—
439C4×C8—53no—
440C4×C8—53no—
441C4×C8—51no—
442C4×C8—53no—
443C4×C8—53no—
444C4×C8—53no—
445C4×C8C22×D513yes—
446C4×C8C22×D513yes—
447C22×C5—23no—
448C22×C5—23no—
449C22×C5—23no—
450C22×C5C24×C411yescharacteristic
451C2×D5—21no—
452C2×D5—21no—
453C2×D5—23no—
454C2×D5—23no—
455C2×D5—23no—
456C2×D5C4×#4112yes—
457C4×C5—23no—
458C4×C5—21no—
459C4×C5—23no—
460C4×C5—21no—
461C4×C5C2×#13116yes—
462C4×C5C22×#4111yescharacteristic
463C4×C5C22×#4111yescharacteristic
464Dic5—23no—
465Dic5—23no—
466Dic5—21no—
467Dic5—21no—
468Dic5—23no—
469Dic5C4×#4112yes—
470#41—24no—
471#41—106no—
472#41—106no—
473#41—104no—
474C2×Q8—53no—
475C2×Q8—53no—
476C2×Q8—104no—
477C2×Q8C2×C4×D511yescharacteristic
478C2×D4—53no—
479C2×D4—53no—
480C2×D4—56no—
481C2×D4—53no—
482C2×D4—53no—
483C2×D4C2×C4×D513yes—
484C22×C4—51no—
485C22×C4—53no—
486C22×C4—53no—
487C22×C4—53no—
488C22×C4—53no—
489C22×C4—53no—
490C22×C4C2×C4×D513yes—
491C22×C4C2×C4×D513yes—
492C22×C4C23×D513yes—
493M16—26no—
494M16—26no—
495M16—54no—
496M16—106no—
497M16—106no—
498M16—106no—
499C2×C8—51no—
500C2×C8—51no—
501C2×C8—54no—
502C2×C8—53no—
503C2×C8—53no—
504C2×C8—106no—
505C2×C8—106no—
506C2×C8—106no—
507C2×C8—106no—
508C2×C8—106no—
509C2×C8C23×D513yes—
510C2×C8C23×D513yes—
511C2×C8C23×D511yescharacteristic
512C2×C8C23×D511yescharacteristic
513C4⋊C4—53no—
514C4⋊C4—56no—
515C4⋊C4—51no—
516C4⋊C4—51no—
517C4⋊C4—53no—
518C4⋊C4—53no—
519C4⋊C4—53no—
520C4⋊C4—53no—
521C4⋊C4—53no—
522C4⋊C4—56no—
523C4⋊C4C2×C4×D513yes—
524C4⋊C4C2×C4×D513yes—
525C22⋊C4—53no—
526C22⋊C4—53no—
527C22⋊C4—56no—
528C22⋊C4—51no—
529C22⋊C4—51no—
530C22⋊C4—53no—
531C22⋊C4—56no—
532C22⋊C4—53no—
533C22⋊C4—56no—
534C22⋊C4C2×C4×D516yes—
535C42—53no—
536C42—53no—
537C42—53no—
538C42—53no—
539C42—51no—
540C42—53no—
541C42C2×C4×D513yes—
542C42C2×C4×D513yes—
543C42C23×D511yescharacteristic
544C42C23×D513yes—
545C2×C5—43no—
546C2×C5C2×C4×#4111yescharacteristic
547C2×C5C22×#13111yescharacteristic
548C2×C5#357311yescharacteristic
549D5—22no—
550D5—43no—
551C23—51no—
552C23—53no—
553C23C22×C4×D513yes—
554Q8—106no—
555Q8—106no—
556Q8#405314yescomplemented
557D4—26no—
558D4—106no—
559D4—106no—
560D4—106no—
561D4—106no—
562D4—206no—
563C2×C4—26no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—43no—
567C2×C4—51no—
568C2×C4—52no—
569C2×C4—52no—
570C2×C4—51no—
571C2×C4—51no—
572C2×C4—53no—
573C2×C4—53no—
574C2×C4—53no—
575C2×C4—106no—
576C2×C4—106no—
577C2×C4—103no—
578C2×C4—103no—
579C2×C4—203no—
580C2×C4—203no—
581C2×C4C22×C4×D513yes—
582C2×C4C22×C4×D511yescharacteristic
583C2×C4C22×C4×D511yescharacteristic
584C2×C4C22×C4×D513yes—
585C2×C4C22×C4×D513yes—
586C2×C4C24×D511yescharacteristic
587C8—23no—
588C8—23no—
589C8—52no—
590C8—52no—
591C8—103no—
592C8—103no—
593C8D5×#4112yes—
594C8D5×#4112yes—
595C5#6021811yescharacteristic, complemented, Sylow
596C22—23no—
597C22—23no—
598C22—23no—
599C22—52no—
600C22—101no—
601C22—101no—
602C22—103no—
603C22—103no—
604C22—103no—
605C22C23×C4×D511yescharacteristic
606C4—23no—
607C4—21no—
608C4—21no—
609C4—23no—
610C4—52no—
611C4—103no—
612C4—101no—
613C4—103no—
614C4—101no—
615C4—103no—
616C4C2×#405316yes—
617C4C2×D5×#4111yescharacteristic
618C4C2×D5×#4111yescharacteristic
619C2—43no—
620C2—102no—
621C2—203no—
622C2C4×D5×#4111yescharacteristic
623C2C22×#405311yescharacteristic
624C2#1061906711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D5
commutator, socleC22×C5C24×C4
FittingC5×#2971C2
prime radical#10617743C2
cosocleC2×C4×C5C25
hypercenter#2971D5
hypocenterC5#60218
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. C5×#2971C2semidirect
3. #41×#168C2semidirect
4. Q8×#676C2semidirect
5. C8×Q8×D5C2semidirect
6. #10611636C2semidirect
7. C8×#713C2semidirect
8. #10611272C2semidirect
9. #10611269C2semidirect
10. #10611252C2semidirect
11. #10611249C2semidirect
12. #10611065C2semidirect
13. #10611056C2semidirect
14. C4×#4053C2semidirect
15. #10610242C2semidirect
167. #2971D5semidirect
250. #676#41semidirect
254. C8×D5#41semidirect
316. C5×Q8#131semidirect
556. Q8#4053semidirect
595. C5#60218semidirect

Maximal subgroups

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

subgroupindex
#106177432
C5×#29712
#41×#1682
Q8×#6762
C8×Q8×D52
#106116362
C8×#7132
#106112722
#106112692
#106112522
#106112492
#106110652
#106110562
C4×#40532
#106102422
#602185