Finite Group Databasebeta

← #12069337

Subgroups — #12069337

Order 1280.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611689C211yesmaximal, characteristic, complemented
2C8×#713C211yesmaximal, characteristic
3#10611478C211yesmaximal, characteristic
4C5×#1584C211yesmaximal, characteristic, complemented
5#10601746C211yesmaximal, characteristic, complemented
6#10601727C211yesmaximal, characteristic, complemented
7#10601695C211yesmaximal, characteristic, complemented
8#10599368C211yesmaximal, characteristic, complemented
9#10599351C211yesmaximal, characteristic, complemented
10#10599031C211yesmaximal, characteristic
11#10599028C211yesmaximal, characteristic, complemented
12#10599008C211yesmaximal, characteristic, complemented
13#10599007C211yesmaximal, characteristic, complemented
14#10598872C211yesmaximal, characteristic, complemented
15#10598862C211yesmaximal, characteristic, complemented
16#65912C2211yescharacteristic
17C4×#713C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic
20C4×C5×Q16C2211yescharacteristic
21#65476C411yescharacteristic
22#65471C411yescharacteristic
23C4×#689C2211yescharacteristic
24C4×#688C2211yescharacteristic
25Q8×#168C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27#65179C411yescharacteristic
28#65177C411yescharacteristic
29#65128—21no—
30#65126C2211yescharacteristic
31#65123—21no—
32#65123C2211yescharacteristic
33#65122—21no—
34#65122C2211yescharacteristic
35#65119—21no—
36#65119C2211yescharacteristic
37#65107C411yescharacteristic
38#65104C411yescharacteristic
39#65099C411yescharacteristic
40#65080C411yescharacteristic
41#64997—21no—
42#64990—21no—
43C4×#677C2211yescharacteristic
44C4×#676C2211yescharacteristic
45C8×D20—21no—
46C8×D20C2211yescharacteristic
47#64974C2211yescharacteristic
48C4×C8×D5—21no—
49C4×C8×D5C2211yescharacteristic
50#64968C2211yescharacteristic
51C5×#335C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64703C2211yescharacteristic
59#64700C2211yescharacteristic
60#64699C2211yescharacteristic
61#64679C2211yescharacteristic
62#64677C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64675C2211yescharacteristic
66#64674C2211yescharacteristic
67#17916—51nomaximal, Sylow
68C2×#713C2×C411yescharacteristic
69C2×C5×Q16C2×C411yescharacteristic
70C4×C5×Q8C2311yescharacteristic
71C4×C5×Q8C2311yescharacteristic
72#4092C2×C411yescharacteristic
73Q8×Dic5C2×C411yescharacteristic
74#4090C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77C2×#677C2×C411yescharacteristic
78C2×#676—21no—
79C2×#676—21no—
80C2×C8×D5—21no—
81C2×C8×D5—21no—
82C2×C8×D5D411yescharacteristic
83C2×C8×D5D411yescharacteristic
84#4043C2×C411yescharacteristic
85#4042—21no—
86#4039—21no—
87#4039C2×C411yescharacteristic
88#4038—21no—
89#4038C2×C411yescharacteristic
90#4035—21no—
91#4034C2×C411yescharacteristic
92C4×D20—21no—
93C4×D20C2311yescharacteristic
94#4018—21no—
95C42×D5—21no—
96C42×D5C2311yescharacteristic
97C4×Dic10—21no—
98C4×Dic10C2311yescharacteristic
99C5×#107C2×C411yescharacteristic
100C5×C4⋊C8—21no—
101C5×C4⋊C8—21no—
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×#103C2×C411yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#97—21no—
107C4×C5×C8—21no—
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111#3967C2×C411yescharacteristic
112#3967C2×C411yescharacteristic
113#3953C2×C411yescharacteristic
114#3952—21no—
115#3952—21no—
116#3952—21no—
117#3952C2×C411yescharacteristic
118#3952C2×C411yescharacteristic
119#3949C2×C411yescharacteristic
120#3948C2×C411yescharacteristic
121#3947—21no—
122#3947—21no—
123#3946—21no—
124#3946—21no—
125#3946—21no—
126#3946C2×C411yescharacteristic
127#3946C2×C411yescharacteristic
128C8×Dic5—21no—
129C8×Dic5—21no—
130C8×Dic5D411yescharacteristic
131C8×Dic5D411yescharacteristic
132#3942C2×C411yescharacteristic
133#3941C2×C411yescharacteristic
134#3940C2×C411yescharacteristic
135#3939C2×C411yescharacteristic
136C4⋊#168—21no—
137C4⋊#168—21no—
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140C4×#168—21no—
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3107—51no—
146C8×#41—51no—
147#2960—51no—
148#1584—51no—
149#1584D511yescharacteristic, complemented
150#1582—51no—
151#1582—51no—
152#1579—51no—
153#1579—51no—
154SD16⋊C8—51no—
155SD16⋊C8—51no—
156#1574—51no—
157#1489—51no—
158#1485—51no—
159#1451—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×Q8C22×C411yescharacteristic
162#713—22no—
163#713—22no—
164C2×D20—21no—
165C2×D20C22×C411yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5C22×C411yescharacteristic
170C2×C4×D5C2×D411yescharacteristic
171C2×C4×D5#4111yescharacteristic
172C2×Dic10—21no—
173C2×Dic10C22×C411yescharacteristic
174C5×Q16—22no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C2×D411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C4⋊C4C22×C411yescharacteristic
186C42×C5—21no—
187C42×C5—21no—
188C42×C5C2411yescharacteristic
189#689—22no—
190#688—22no—
191#685—21no—
192#685—21no—
193#685—21no—
194#685—21no—
195#685—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5C22×C411yescharacteristic
199C4⋊Dic5C22×C411yescharacteristic
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5C22×C411yescharacteristic
209C4×Dic5C2×D411yescharacteristic
210C4×Dic5#4111yescharacteristic
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168C22×C411yescharacteristic
215C2×#168C22×C411yescharacteristic
216C2×#168C2×D411yescharacteristic
217C2×#168C2×D411yescharacteristic
218#677—22no—
219#676—42no—
220#676—42no—
221C8×D5—22no—
222C8×D5—41no—
223C8×D5—42no—
224C8×D5—42no—
225#533—51no—
226C4×#41—51no—
227#485—51no—
228#485—51no—
229#475—51no—
230#474—51no—
231#462—51no—
232#461—51no—
233#452—51no—
234#452—51no—
235#446—51no—
236#446—101no—
237#446C2×D511yescharacteristic
238C8×Q8—51no—
239C8×Q8—51no—
240C8×Q8—51no—
241C8×Q8—101no—
242C8×Q8C2×D511yescharacteristic
243C4×Q16—51no—
244C4×Q16C2×D511yescharacteristic
245C4×SD16—51no—
246C4×SD16—51no—
247C8×D4—51no—
248C8×D4—51no—
249C8×D4—101no—
250C8×D4—101no—
251#431—51no—
252#431—51no—
253#431—101no—
254#424—101no—
255#423—51no—
256#405—101no—
257C4×M16—51no—
258C2×C4×C8—51no—
259C2×C4×C8—101no—
260#335—51no—
261#335C2×D511yescharacteristic
262#334—51no—
263#334—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8C2×D511yescharacteristic
269Q8⋊C8C2×D511yescharacteristic
270D4⋊C8—51no—
271D4⋊C8—51no—
272#322—51no—
273#322—51no—
274#322—51no—
275#322C2×D511yescharacteristic
276C22×D5—21no—
277C22×D5C4×D411yescharacteristic
278C5×Q8—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8#13112yes—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5C23×C411yescharacteristic
287C2×C4×C5C22×D411yescharacteristic
288C2×C4×C5C2×#4111yescharacteristic
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5C4×D411yescharacteristic
293C2×Dic5C4×D411yescharacteristic
294C2×Dic5C4×D411yescharacteristic
295D20—24no—
296D20—21no—
297D20#13112yes—
298C4×D5—24no—
299C4×D5—21no—
300C4×D5—21no—
301C4×D5—21no—
302C4×D5—21no—
303C4×D5—22no—
304C4×D5—41no—
305C4×D5—41no—
306C4×D5—42no—
307Dic10—21no—
308Dic10—21no—
309Dic10—42no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8#13712yes—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—21no—
321#168—41no—
322#168—41no—
323#168—41no—
324C2×#41—51no—
325C2×Q16—51no—
326C2×Q16C4×D511yescharacteristic
327C2×SD16—51no—
328C2×SD16—51no—
329C2×M16—101no—
330C2×M16—101no—
331C22×C8—51no—
332C22×C8—51no—
333C22×C8—101no—
334C22×C8—101no—
335C4⋊Q8—51no—
336C4⋊Q8—51no—
337#125—101no—
338C22⋊Q8—51no—
339C22⋊Q8—51no—
340C22⋊Q8—101no—
341C4×Q8—51no—
342C4×Q8—51no—
343C4×Q8—101no—
344C4×Q8C22×D511yescharacteristic
345C4×Q8C22×D511yescharacteristic
346C4×D4—51no—
347C4×D4—51no—
348C4×D4—101no—
349C4×D4—101no—
350#117—51no—
351#117—101no—
352#117—101no—
353C2×C42—51no—
354C2×C42—101no—
355#107—51no—
356#107C4×D511yescharacteristic
357#106—51no—
358#106—51no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—51no—
362C4⋊C8—51no—
363C4⋊C8—51no—
364C4⋊C8—51no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8—101no—
370C4⋊C8C22×D511yescharacteristic
371C4⋊C8C22×D511yescharacteristic
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#103C4×D511yescharacteristic
377#103C4×D511yescharacteristic
378#102—51no—
379#102—51no—
380C22⋊C8—51no—
381C22⋊C8—51no—
382C22⋊C8—101no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—21no—
386#97—101no—
387#97—101no—
388C4×C8—21no—
389C4×C8—51no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—51no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C4×C8—101no—
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C4×C8C22×D511yescharacteristic
401C22×C5C2×C4×D411yescharacteristic
402C2×D5—21no—
403C2×D5—22no—
404C2×D5—21no—
405C2×D5—21no—
406C2×D5—41no—
407C2×D5—41no—
408C4×C5—22no—
409C4×C5—21no—
410C4×C5—41no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5C2×#13111yescharacteristic
414C4×C5C2×#13111yescharacteristic
415C4×C5C2×#13711yescharacteristic
416C4×C5#57511yescharacteristic
417Dic5—21no—
418Dic5—21no—
419Dic5—41no—
420Dic5—41no—
421Dic5—41no—
422Dic5#44412yes—
423#41—102no—
424#41—102no—
425C2×Q8—51no—
426C2×Q8—101no—
427C2×Q8C2×C4×D511yescharacteristic
428C2×Q8C2×C4×D511yescharacteristic
429C2×D4—51no—
430C2×D4—101no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437Q16—22no—
438Q16—102no—
439SD16—102no—
440SD16—102no—
441M16—202no—
442M16—202no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—51no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—102no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—201no—
455C2×C8—202no—
456C2×C8—202no—
457C2×C8C2×C4×D511yescharacteristic
458C2×C8C2×C4×D511yescharacteristic
459C2×C8D4×D511yescharacteristic
460C2×C8D4×D511yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—51no—
464C4⋊C4—51no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4C2×C4×D511yescharacteristic
473C4⋊C4C2×C4×D511yescharacteristic
474C22⋊C4—101no—
475C22⋊C4—101no—
476C22⋊C4—101no—
477C22⋊C4—101no—
478C22⋊C4—101no—
479C42—21no—
480C42—21no—
481C42—51no—
482C42—51no—
483C42—51no—
484C42—101no—
485C42—101no—
486C42—101no—
487C42C23×D511yescharacteristic
488C2×C5#292911yescharacteristic
489C2×C5C4×#13711yescharacteristic
490C2×C5C2×#44411yescharacteristic
491D5—41no—
492D5—42no—
493C23—51no—
494C23—101no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—101no—
499Q8—101no—
500Q8—202no—
501Q8#405312yes—
502D4—52no—
503D4—104no—
504D4—101no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—51no—
510C2×C4—51no—
511C2×C4—51no—
512C2×C4—102no—
513C2×C4—104no—
514C2×C4—101no—
515C2×C4—101no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—202no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4C22×C4×D511yescharacteristic
525C2×C4C2×D4×D511yescharacteristic
526C2×C4D5×#4111yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—101no—
534C8—101no—
535C8—101no—
536C8—101no—
537C8—201no—
538C8—201no—
539C8—201no—
540C8#406412yes—
541C5#1791611yescharacteristic, complemented, Sylow
542C22—102no—
543C22—101no—
544C22—101no—
545C22—101no—
546C22—201no—
547C22—201no—
548C22C4×D4×D511yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—52no—
555C4—101no—
556C4—101no—
557C4—201no—
558C4—201no—
559C4—201no—
560C4C2×#405311yescharacteristic
561C4D5×#13111yescharacteristic
562C4C2×#406411yescharacteristic
563C4#6610211yescharacteristic
564C2—201no—
565C2—202no—
566C2#1061120911yescharacteristic
567C2C4×#406411yescharacteristic
568C2D5×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1584C2
socleC22×C5C2×C4×D4
prime radicalC2×#713C2×C4
cosocleC42×C5C24
hypercenter#1584D5
hypocenterC5#17916
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
1. #10611689C2semidirect
4. C5×#1584C2semidirect
5. #10601746C2semidirect
6. #10601727C2semidirect
7. #10601695C2semidirect
8. #10599368C2semidirect
9. #10599351C2semidirect
11. #10599028C2semidirect
12. #10599008C2semidirect
13. #10599007C2semidirect
14. #10598872C2semidirect
15. #10598862C2semidirect
149. #1584D5semidirect
541. C5#17916semidirect

Maximal subgroups

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

subgroupindex
#106116892
C8×#7132
#106114782
C5×#15842
#106017462
#106017272
#106016952
#105993682
#105993512
#105990312
#105990282
#105990082
#105990072
#105988722
#105988622
#179165