Finite Group Databasebeta

← #12070497

Subgroups — #12070497

Order 1280.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611042C211yesmaximal, characteristic
2#10611027C211yesmaximal, characteristic
3#10610996C211yesmaximal, characteristic, complemented
4C5×#1450C211yesmaximal, characteristic, complemented
5#10601545C211yesmaximal, characteristic, complemented
6C2×#64676C211yesmaximal, characteristic, complemented
7#10600529C211yesmaximal, characteristic
8#10598881C211yesmaximal, characteristic, complemented
9#10598880C211yesmaximal, characteristic, complemented
10#10598880C211yesmaximal, characteristic, complemented
11#10598873C211yesmaximal, characteristic, complemented
12#10598849C211yesmaximal, characteristic, complemented
13#10598848C211yesmaximal, characteristic, complemented
14C8×Dic20C211yesmaximal, characteristic, complemented
15C8×#677C211yesmaximal, characteristic, complemented
16#65813C2211yescharacteristic
17C2×C4×Dic10C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C2×C4×C5×C8C2211yescharacteristic
21#65215C2211yescharacteristic
22C2×C4⋊#168C2211yescharacteristic
23#65134C411yescharacteristic
24#65134C411yescharacteristic
25#65129—21no—
26#65128—21no—
27#65118C411yescharacteristic
28#65118C411yescharacteristic
29#65117—21no—
30#65117—21no—
31#65028C411yescharacteristic
32#65027C411yescharacteristic
33#65025C411yescharacteristic
34#65019—21no—
35#65014—21no—
36#65010C411yescharacteristic
37#65008—21no—
38#65007—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×C82C2211yescharacteristic
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#18017—51nomaximal, Sylow
68C22×Dic10C2×C411yescharacteristic
69C22×C5×C8—21no—
70C2×C42×C5C2311yescharacteristic
71#4076C2×C411yescharacteristic
72#4075—21no—
73C4×C22⋊D5—21no—
74C2×C4⋊Dic5C2×C411yescharacteristic
75#4070C2×C411yescharacteristic
76C2×#683—21no—
77C2×C4×Dic5—21no—
78C22×#168—21no—
79C2×Dic20C2×C411yescharacteristic
80C2×Dic20C2×C411yescharacteristic
81C2×#677C2×C411yescharacteristic
82C2×#677C2×C411yescharacteristic
83C2×#676—21no—
84C2×C8×D5—21no—
85#4022—21no—
86#4021C2×C411yescharacteristic
87C4×D20C2311yescharacteristic
88#4018—21no—
89#4016C2×C411yescharacteristic
90C4×Dic10—21no—
91C4×Dic10—21no—
92C4×Dic10C2×C411yescharacteristic
93C4×Dic10C2×C411yescharacteristic
94C4×Dic10C2311yescharacteristic
95C4×Dic10C2311yescharacteristic
96C4×Dic10C2311yescharacteristic
97C5×C4⋊C8C2×C411yescharacteristic
98C5×C4⋊C8C2×C411yescharacteristic
99C5×C4⋊C8D411yescharacteristic
100C5×C4⋊C8D411yescharacteristic
101C5×C22⋊C8C2×C411yescharacteristic
102C5×C22⋊C8C2×C411yescharacteristic
103C5×C22⋊C8D411yescharacteristic
104C5×C22⋊C8D411yescharacteristic
105C4×C5×C8—21no—
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
144#3935—21no—
145#3108—51no—
146#2994—51no—
147#2984—51no—
148#1591—51no—
149#1590—51no—
150#1588—51no—
151#1587—51no—
152#1587—51no—
153#1585—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1573—51no—
157#1494—51no—
158C2×Q8⋊C8—51no—
159#1450D511yescharacteristic, 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
174C2×C5×C8—24no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8C22×C411yescharacteristic
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C2×C5×C8C2×D411yescharacteristic
184C2×C5×C8C2×D411yescharacteristic
185C42×C5C22×C411yescharacteristic
186C42×C5C2×D411yescharacteristic
187C42×C5#4111yescharacteristic
188C42×C5C2411yescharacteristic
189C22⋊Dic5—21no—
190#685—21no—
191#685—21no—
192#685—21no—
193#685—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5C22×C411yescharacteristic
196C4⋊Dic5C22×C411yescharacteristic
197C4⋊Dic5C22×C411yescharacteristic
198C4⋊Dic5C22×C411yescharacteristic
199#683—21no—
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205#683—21no—
206#683—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—81no—
217Dic20—22no—
218Dic20—41no—
219#677—22no—
220#677—41no—
221#676—81no—
222C8×D5—81no—
223#529—51no—
224C2×C4×Q8—51no—
225#483—51no—
226#480—51no—
227#479—51no—
228#479—51no—
229#464—51no—
230#464—51no—
231#451—51no—
232#448—51no—
233#446—51no—
234#446—51no—
235#446—51no—
236#446—101no—
237#446—101no—
238C8×Q8—51no—
239C8×Q8—51no—
240C8×Q8—51no—
241C4×Q16—51no—
242C4×Q16—51no—
243C4×SD16—51no—
244C4×SD16—51no—
245#436—51no—
246#435—101no—
247C8×D4—51no—
248C8×D4—101no—
249#433—101no—
250#432—51no—
251#432—101no—
252#431—101no—
253#431C2×D511yescharacteristic
254#431C2×D511yescharacteristic
255#424—101no—
256C2×C4⋊C8—51no—
257C2×C4×C8C2×D511yescharacteristic
258#335—51no—
259#335—51no—
260#334—51no—
261#334—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268D4⋊C8—51no—
269D4⋊C8—51no—
270#322C2×D511yescharacteristic
271#322C2×D511yescharacteristic
272C82C2×D511yescharacteristic
273C82C2×D511yescharacteristic
274C23×C5C4×D411yescharacteristic
275C22×D5—21no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5C4×D411yescharacteristic
282C2×C4×C5C4×D411yescharacteristic
283C2×C4×C5C4×D411yescharacteristic
284C2×C4×C5C23×C411yescharacteristic
285C2×C4×C5C22×D411yescharacteristic
286C2×C4×C5C2×#4111yescharacteristic
287C22⋊D5—42no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297D20—21no—
298D20—21no—
299C4×D5—41no—
300C4×D5—41no—
301Dic10—21no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10—21no—
306Dic10—42no—
307Dic10#13112yes—
308C5×C8—22no—
309C5×C8—22no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—21no—
314C5×C8—21no—
315C5×C8—21no—
316C5×C8—21no—
317C5×C8—21no—
318#168—41no—
319#168—41no—
320#168—41no—
321#168—41no—
322C22×Q8—51no—
323C2×Q16—51no—
324C2×Q16—51no—
325C2×SD16—51no—
326C2×SD16—51no—
327C2×M16—101no—
328C22×C8—21no—
329C22×C8—101no—
330C22×C8—101no—
331#126—101no—
332#125—51no—
333#124—51no—
334#123—101no—
335C22⋊Q8—51no—
336#121—51no—
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8—101no—
343C4×Q8—101no—
344C4×D4—51no—
345C4×D4—101no—
346#117—101no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—101no—
349C2×C42—101no—
350C2×C42C22×D511yescharacteristic
351#107—51no—
352#107—51no—
353#106—51no—
354#106—51no—
355C4⋊C8—51no—
356C4⋊C8—51no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—101no—
360C4⋊C8—101no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8C4×D511yescharacteristic
367C4⋊C8C4×D511yescharacteristic
368C4⋊C8D2011yescharacteristic
369C4⋊C8D2011yescharacteristic
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#102—51no—
377#102—51no—
378C22⋊C8—101no—
379C22⋊C8—101no—
380C22⋊C8—101no—
381C22⋊C8C4×D511yescharacteristic
382C22⋊C8C4×D511yescharacteristic
383C22⋊C8D2011yescharacteristic
384C22⋊C8D2011yescharacteristic
385#97—101no—
386#97—101no—
387#97—101no—
388#97—101no—
389C4×C8—21no—
390C4×C8—101no—
391C4×C8—101no—
392C4×C8—101no—
393C4×C8C22×D511yescharacteristic
394C4×C8C22×D511yescharacteristic
395C4×C8C22×D511yescharacteristic
396C4×C8C22×D511yescharacteristic
397C4×C8C22×D511yescharacteristic
398C4×C8C22×D511yescharacteristic
399C22×C5—21no—
400C22×C5—21no—
401C22×C5#44312yes—
402C22×C5C2×C4×D411yescharacteristic
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—41no—
406C4×C5—21no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5C2×#13111yescharacteristic
411C4×C5#56811yescharacteristic
412C4×C5#57711yescharacteristic
413C4×C5#57811yescharacteristic
414Dic5—22no—
415Dic5—41no—
416Dic5—41no—
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420Dic5—41no—
421C2×Q8—51no—
422C2×Q8—51no—
423C2×Q8—51no—
424C2×Q8—102no—
425C2×Q8—101no—
426C2×Q8—201no—
427C2×D4—51no—
428C2×D4—101no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4C2×C4×D511yescharacteristic
433C22×C4C2×D2011yescharacteristic
434C22×C4#70911yescharacteristic
435Q16—102no—
436Q16—201no—
437SD16—102no—
438SD16—201no—
439M16—401no—
440C2×C8—24no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—401no—
448C2×C8—401no—
449C2×C8C2×C4×D511yescharacteristic
450C2×C8C2×C4×D511yescharacteristic
451C2×C8C2×C4×D511yescharacteristic
452C2×C8C2×C4×D511yescharacteristic
453C2×C8C2×D2011yescharacteristic
454C2×C8C2×D2011yescharacteristic
455C2×C8C2×D2011yescharacteristic
456C2×C8C2×D2011yescharacteristic
457C4⋊C4—51no—
458C4⋊C4—51no—
459C4⋊C4—51no—
460C4⋊C4—51no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C22⋊C4—101no—
473C22⋊C4—101no—
474C22⋊C4—101no—
475C42—101no—
476C42—101no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42C2×C4×D511yescharacteristic
481C42C2×D2011yescharacteristic
482C42#70911yescharacteristic
483C42C23×D511yescharacteristic
484C2×C5—22no—
485C2×C5#293311yescharacteristic
486C2×C5#294711yescharacteristic
487C2×C5C2×#44311yescharacteristic
488D5—81no—
489C23—101no—
490C23C4×D2011yescharacteristic
491Q8—52no—
492Q8—101no—
493Q8—101no—
494Q8—101no—
495Q8—101no—
496Q8—101no—
497Q8—202no—
498D4—101no—
499D4—101no—
500D4—202no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—202no—
514C2×C4—202no—
515C2×C4—201no—
516C2×C4—201no—
517C2×C4C4×D2011yescharacteristic
518C2×C4C4×D2011yescharacteristic
519C2×C4C4×D2011yescharacteristic
520C2×C4C22×C4×D511yescharacteristic
521C2×C4C22×D2011yescharacteristic
522C2×C4C2×#70911yescharacteristic
523C8—22no—
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—201no—
534C8—201no—
535C8—201no—
536C8—201no—
537C5#1801711yescharacteristic, complemented, Sylow
538C22—21no—
539C22—21no—
540C22—201no—
541C22—201no—
542C22—201no—
543C22#6498912yes—
544C22C2×C4×D2011yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—102no—
550C4—201no—
551C4—201no—
552C4—201no—
553C4—201no—
554C4—201no—
555C4—201no—
556C4D5×#13111yescharacteristic
557C4#6608411yescharacteristic
558C4#6608511yescharacteristic
559C4#6608711yescharacteristic
560C2—22no—
561C2—401no—
562C2C2×#6498911yescharacteristic
563C2#1061028611yescharacteristic
564C2#1061030211yescharacteristic
subgroupG/H
centerC2×C4C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1450C2
socleC22×C5C2×C4×D4
prime radical#4076C2×C4
cosocleC42×C5C24
hypercenter#1450D5
hypocenterC5#18017
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
3. #10610996C2semidirect
4. C5×#1450C2semidirect
5. #10601545C2semidirect
6. C2×#64676C2semidirect
8. #10598881C2semidirect
9. #10598880C2semidirect
10. #10598880C2semidirect
11. #10598873C2semidirect
12. #10598849C2semidirect
13. #10598848C2semidirect
14. C8×Dic20C2semidirect
15. C8×#677C2semidirect
159. #1450D5semidirect
537. C5#18017semidirect

Maximal subgroups

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

subgroupindex
#106110422
#106110272
#106109962
C5×#14502
#106015452
C2×#646762
#106005292
#105988812
#105988802
#105988732
#105988492
#105988482
C8×Dic202
C8×#6772
#180175