Finite Group Databasebeta

← #12070430

Subgroups — #12070430

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611042C211yesmaximal, characteristic
2#10610242C211yesmaximal, characteristic
3M16×Dic10C211yesmaximal, characteristic, complemented
4C5×#1453C211yesmaximal, characteristic, complemented
5#10601560C211yesmaximal, characteristic, complemented
6#10601557C211yesmaximal, characteristic
7#10601546C211yesmaximal, characteristic, complemented
8#10598882C211yesmaximal, characteristic, complemented
9#10598880C211yesmaximal, characteristic, complemented
10#10598879C211yesmaximal, characteristic, complemented
11#10598878C211yesmaximal, characteristic, complemented
12#10598873C211yesmaximal, characteristic, complemented
13#10598869C211yesmaximal, characteristic, complemented
14#10598848C211yesmaximal, characteristic, complemented
15C8×Dic20C211yesmaximal, characteristic, complemented
16#65813C2211yescharacteristic
17C2×C4×Dic10C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C4×C5×M16C2211yescharacteristic
21#65417—21no—
22#65416—21no—
23#65407—21no—
24M16×Dic5—21no—
25#65214C2211yescharacteristic
26#65213C2211yescharacteristic
27#65134C411yescharacteristic
28#65134C411yescharacteristic
29#65118C411yescharacteristic
30#65118C411yescharacteristic
31#65028C411yescharacteristic
32#65027C411yescharacteristic
33#65025C411yescharacteristic
34#65010C411yescharacteristic
35#64998—21no—
36#64997—21no—
37#64990—21no—
38#64990—21no—
39C4×Dic20C2211yescharacteristic
40C4×Dic20C2211yescharacteristic
41C4×#677C2211yescharacteristic
42C4×#677C2211yescharacteristic
43#64977C2211yescharacteristic
44C8×D20C2211yescharacteristic
45#64968C2211yescharacteristic
46#64968C2211yescharacteristic
47#64968C2211yescharacteristic
48C8×Dic10C2211yescharacteristic
49C8×Dic10C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51C5×#322C2211yescharacteristic
52C5×#322C2211yescharacteristic
53C5×#322C2211yescharacteristic
54C5×C82C2211yescharacteristic
55#64679C2211yescharacteristic
56#64679C2211yescharacteristic
57#64678C2211yescharacteristic
58#64678C2211yescharacteristic
59#64677C2211yescharacteristic
60#64677C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64676C2211yescharacteristic
65#64676C2211yescharacteristic
66#64676C2211yescharacteristic
67#18012—51nomaximal, Sylow
68C22×Dic10C2×C411yescharacteristic
69C2×C5×M16D411yescharacteristic
70C2×C5×M16D411yescharacteristic
71C2×C42×C5C2311yescharacteristic
72#4076C2×C411yescharacteristic
73#4075—21no—
74C4×C22⋊D5—21no—
75C2×C4⋊Dic5C2×C411yescharacteristic
76#4070C2×C411yescharacteristic
77C2×#683—21no—
78C2×C4×Dic5—21no—
79C2×#681—21no—
80C2×Dic20C2×C411yescharacteristic
81C2×Dic20C2×C411yescharacteristic
82C2×#677C2×C411yescharacteristic
83C2×#677C2×C411yescharacteristic
84C2×#676—21no—
85C2×C8×D5—21no—
86#4022—21no—
87#4021C2×C411yescharacteristic
88C4×D20C2311yescharacteristic
89#4018—21no—
90#4016C2×C411yescharacteristic
91C4×Dic10—21no—
92C4×Dic10—21no—
93C4×Dic10C2×C411yescharacteristic
94C4×Dic10C2×C411yescharacteristic
95C4×Dic10C2311yescharacteristic
96C4×Dic10C2311yescharacteristic
97C4×Dic10C2311yescharacteristic
98C5×C4⋊C8—21no—
99C5×C4⋊C8C2×C411yescharacteristic
100C5×C4⋊C8C2×C411yescharacteristic
101C5×C22⋊C8—21no—
102C5×C22⋊C8C2×C411yescharacteristic
103C5×C22⋊C8C2×C411yescharacteristic
104C5×#97D411yescharacteristic
105C5×#97D411yescharacteristic
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2311yescharacteristic
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112C22⋊#168—21no—
113#3953C2×C411yescharacteristic
114#3953C2×C411yescharacteristic
115#3952—21no—
116#3952—21no—
117#3950C2×C411yescharacteristic
118#3950C2×C411yescharacteristic
119#3949C2×C411yescharacteristic
120#3949C2×C411yescharacteristic
121#3948C2×C411yescharacteristic
122#3948C2×C411yescharacteristic
123#3948C2×C411yescharacteristic
124#3948C2×C411yescharacteristic
125#3948C2×C411yescharacteristic
126#3948C2×C411yescharacteristic
127#3947—21no—
128#3947—21no—
129#3947—21no—
130#3946—21no—
131#3946—21no—
132#3946—21no—
133#3946—21no—
134#3946—21no—
135#3946—21no—
136C8×Dic5—21no—
137C8×Dic5—21no—
138C8×Dic5—21no—
139C4⋊#168—21no—
140C4⋊#168C2311yescharacteristic
141C4⋊#168C2311yescharacteristic
142C4⋊#168C2311yescharacteristic
143C4⋊#168C2311yescharacteristic
144C4×#168—21no—
145#3108—51no—
146#2969—51no—
147Q8×M16—51no—
148#1593—51no—
149#1590—51no—
150#1587—51no—
151#1585—51no—
152#1584—51no—
153#1583—51no—
154SD16⋊C8—51no—
155C8×Q16—51no—
156#1574—51no—
157#1495—51no—
158#1479—51no—
159#1453D511yescharacteristic, complemented
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C2×C22⋊D5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C2×D20C22×C411yescharacteristic
167C2×C4×D5—21no—
168C2×Dic10—22no—
169C2×Dic10—21no—
170C2×Dic10—41no—
171C2×Dic10C22×C411yescharacteristic
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C5×M16—22no—
175C5×M16—41no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C22×C411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C2×C5×C8C2×D411yescharacteristic
184C2×C5×C8C2×D411yescharacteristic
185C2×C5×C8C2×D411yescharacteristic
186C42×C5C22×C411yescharacteristic
187C42×C5C2×D411yescharacteristic
188C42×C5#4111yescharacteristic
189C42×C5C2411yescharacteristic
190C22⋊Dic5—21no—
191#685—21no—
192#685—21no—
193#685—21no—
194#685—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5C22×C411yescharacteristic
197C4⋊Dic5C22×C411yescharacteristic
198C4⋊Dic5C22×C411yescharacteristic
199C4⋊Dic5C22×C411yescharacteristic
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205#683—21no—
206#683—21no—
207#683—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213#681—42no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218Dic20—22no—
219Dic20—41no—
220#677—22no—
221#677—41no—
222#676—42no—
223C8×D5—42no—
224#529—51no—
225C2×C4×Q8—51no—
226#483—51no—
227#480—51no—
228#479—51no—
229#479—51no—
230#464—51no—
231#464—51no—
232#451—51no—
233#448—51no—
234#446—51no—
235#446—51no—
236#446—51no—
237#446—101no—
238#446—101no—
239C8×Q8—51no—
240C8×Q8—51no—
241C8×Q8—51no—
242C4×Q16—51no—
243C4×Q16—51no—
244C4×SD16—51no—
245C4×SD16—51no—
246#436—51no—
247#436—101no—
248#435—101no—
249C8×D4—51no—
250#433—101no—
251#431—51no—
252#431C2×D511yescharacteristic
253#431C2×D511yescharacteristic
254#423—51no—
255#423—101no—
256#405—101no—
257C4×M16—101no—
258C4×M16C2×D511yescharacteristic
259#335—51no—
260#335—51no—
261#334—51no—
262#334—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269D4⋊C8—51no—
270D4⋊C8—51no—
271#322C2×D511yescharacteristic
272#322C2×D511yescharacteristic
273#322C2×D511yescharacteristic
274C82C2×D511yescharacteristic
275C23×C5C4×D411yescharacteristic
276C22×D5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—41no—
282C2×C4×C5C4×D411yescharacteristic
283C2×C4×C5C4×D411yescharacteristic
284C2×C4×C5C4×D411yescharacteristic
285C2×C4×C5C23×C411yescharacteristic
286C2×C4×C5C22×D411yescharacteristic
287C2×C4×C5C2×#4111yescharacteristic
288C22⋊D5—81no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—42no—
297C2×Dic5—81no—
298D20—21no—
299D20—21no—
300C4×D5—41no—
301C4×D5—41no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10—21no—
306Dic10—21no—
307Dic10—42no—
308Dic10#13112yes—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—21no—
314C5×C8—21no—
315C5×C8—21no—
316C5×C8—41no—
317C5×C8—41no—
318C5×C8#13712yes—
319#168—41no—
320#168—41no—
321#168—41no—
322#168—41no—
323C22×Q8—51no—
324C2×Q16—51no—
325C2×Q16—51no—
326C2×SD16—51no—
327C2×SD16—51no—
328C2×M16—101no—
329C2×M16—101no—
330C2×M16D2011yescharacteristic
331C2×M16D2011yescharacteristic
332C22×C8—101no—
333#126—101no—
334#125—51no—
335#124—51no—
336#123—101no—
337C22⋊Q8—51no—
338#121—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8—51no—
343C4×Q8—51no—
344C4×Q8—101no—
345C4×Q8—101no—
346C4×D4—51no—
347C4×D4—101no—
348#117—101no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—101no—
351C2×C42—101no—
352C2×C42C22×D511yescharacteristic
353#107—51no—
354#107—51no—
355#106—51no—
356#106—51no—
357C4⋊C8—21no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—51no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8C4×D511yescharacteristic
370C4⋊C8C4×D511yescharacteristic
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#103—51no—
377#102—51no—
378#102—51no—
379C22⋊C8—21no—
380C22⋊C8—101no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8C4×D511yescharacteristic
384C22⋊C8C4×D511yescharacteristic
385#97—101no—
386#97—101no—
387#97—101no—
388#97D2011yescharacteristic
389#97D2011yescharacteristic
390C4×C8—101no—
391C4×C8—101no—
392C4×C8—101no—
393C4×C8—101no—
394C4×C8C22×D511yescharacteristic
395C4×C8C22×D511yescharacteristic
396C4×C8C22×D511yescharacteristic
397C4×C8C22×D511yescharacteristic
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—21no—
403C22×C5C2×C4×D411yescharacteristic
404C2×D5—41no—
405C2×D5—41no—
406C2×D5—41no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5C2×#13111yescharacteristic
412C4×C5#56811yescharacteristic
413C4×C5C2×#13711yescharacteristic
414C4×C5#57511yescharacteristic
415Dic5—22no—
416Dic5—41no—
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420Dic5—41no—
421Dic5—41no—
422C2×Q8—51no—
423C2×Q8—51no—
424C2×Q8—51no—
425C2×Q8—102no—
426C2×Q8—101no—
427C2×Q8—201no—
428C2×D4—51no—
429C2×D4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4C2×C4×D511yescharacteristic
434C22×C4C2×D2011yescharacteristic
435C22×C4#70911yescharacteristic
436Q16—102no—
437Q16—201no—
438SD16—102no—
439SD16—201no—
440M16—22no—
441M16—41no—
442M16—202no—
443M16—202no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—202no—
451C2×C8C2×C4×D511yescharacteristic
452C2×C8C2×C4×D511yescharacteristic
453C2×C8C2×C4×D511yescharacteristic
454C2×C8C2×C4×D511yescharacteristic
455C2×C8C2×D2011yescharacteristic
456C2×C8C2×D2011yescharacteristic
457C2×C8C2×D2011yescharacteristic
458C2×C8C2×D2011yescharacteristic
459C4⋊C4—51no—
460C4⋊C4—51no—
461C4⋊C4—51no—
462C4⋊C4—51no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C22⋊C4—101no—
473C22⋊C4—101no—
474C22⋊C4—101no—
475C22⋊C4—101no—
476C22⋊C4—101no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42—101no—
482C42C2×C4×D511yescharacteristic
483C42C2×D2011yescharacteristic
484C42#70911yescharacteristic
485C42C23×D511yescharacteristic
486C2×C5—41no—
487C2×C5#293311yescharacteristic
488C2×C5C4×#13711yescharacteristic
489C2×C5#295711yescharacteristic
490D5—81no—
491C23—101no—
492C23C4×D2011yescharacteristic
493Q8—52no—
494Q8—101no—
495Q8—101no—
496Q8—101no—
497Q8—101no—
498Q8—101no—
499Q8—202no—
500D4—101no—
501D4—101no—
502D4—401no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—202no—
516C2×C4—201no—
517C2×C4—201no—
518C2×C4—401no—
519C2×C4C4×D2011yescharacteristic
520C2×C4C4×D2011yescharacteristic
521C2×C4C4×D2011yescharacteristic
522C2×C4C22×C4×D511yescharacteristic
523C2×C4C22×D2011yescharacteristic
524C2×C4C2×#70911yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—201no—
535C8—201no—
536C8—201no—
537C8—201no—
538C8#405512yes—
539C5#1801211yescharacteristic, complemented, Sylow
540C22—21no—
541C22—21no—
542C22—21no—
543C22—201no—
544C22—201no—
545C22—201no—
546C22C2×C4×D2011yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—102no—
552C4—201no—
553C4—201no—
554C4—201no—
555C4—201no—
556C4—201no—
557C4—201no—
558C4C2×#405511yescharacteristic
559C4#6608211yescharacteristic
560C4D5×#13111yescharacteristic
561C4#6608411yescharacteristic
562C2—41no—
563C2—401no—
564C2C4×#405511yescharacteristic
565C2#1061028611yescharacteristic
566C2#1061031111yescharacteristic
subgroupG/H
centerC2×C4C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1453C2
socleC22×C5C2×C4×D4
prime radical#4076C2×C4
cosocleC42×C5C24
hypercenter#1453D5
hypocenterC5#18012
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. M16×Dic10C2semidirect
4. C5×#1453C2semidirect
5. #10601560C2semidirect
7. #10601546C2semidirect
8. #10598882C2semidirect
9. #10598880C2semidirect
10. #10598879C2semidirect
11. #10598878C2semidirect
12. #10598873C2semidirect
13. #10598869C2semidirect
14. #10598848C2semidirect
15. C8×Dic20C2semidirect
159. #1453D5semidirect
539. C5#18012semidirect

Maximal subgroups

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

subgroupindex
#106110422
#106102422
M16×Dic102
C5×#14532
#106015602
#106015572
#106015462
#105988822
#105988802
#105988792
#105988782
#105988732
#105988692
#105988482
C8×Dic202
#180125