Finite Group Databasebeta

← #12070439

Subgroups — #12070439

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#10611060C211yesmaximal, characteristic
2#10611033C211yesmaximal, characteristic
3#10610739C211yesmaximal, characteristic, complemented
4C5×#1573C211yesmaximal, characteristic, complemented
5#10601596C211yesmaximal, characteristic, complemented
6#10601536C211yesmaximal, characteristic, complemented
7#10601218C211yesmaximal, characteristic
8#10599358C211yesmaximal, characteristic, complemented
9#10599355C211yesmaximal, characteristic, complemented
10#10599353C211yesmaximal, characteristic, complemented
11#10599350C211yesmaximal, characteristic, complemented
12#10599316C211yesmaximal, characteristic, complemented
13#10599315C211yesmaximal, characteristic, complemented
14#10599313C211yesmaximal, characteristic, complemented
15#10599310C211yesmaximal, characteristic, complemented
16C4×#709C2211yescharacteristic
17#65804C2211yescharacteristic
18C5×#432C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C2×C5×C4⋊C8C2211yescharacteristic
21#65391—21no—
22#65390—21no—
23#65214C2211yescharacteristic
24C4×#681C2211yescharacteristic
25#65140C411yescharacteristic
26#65138C411yescharacteristic
27#65135C411yescharacteristic
28#65130C411yescharacteristic
29#65127C2211yescharacteristic
30#65127C2211yescharacteristic
31#65120C2211yescharacteristic
32#65120C2211yescharacteristic
33#65119C2211yescharacteristic
34#65119C2211yescharacteristic
35#65119C2211yescharacteristic
36#65119C2211yescharacteristic
37#65117—21no—
38#65117—21no—
39#65022C411yescharacteristic
40#65022C411yescharacteristic
41#65018—21no—
42#65018—21no—
43#65012C411yescharacteristic
44#65012C411yescharacteristic
45#64996—21no—
46#64994—21no—
47C4×Dic20C2211yescharacteristic
48C4×Dic20C2211yescharacteristic
49C4×#677C2211yescharacteristic
50C4×#677C2211yescharacteristic
51C5×#335C2211yescharacteristic
52C5×#335C2211yescharacteristic
53C5×#334C2211yescharacteristic
54C5×#334C2211yescharacteristic
55#64704C2211yescharacteristic
56#64704C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64704C2211yescharacteristic
60#64704C2211yescharacteristic
61#64703C2211yescharacteristic
62#64703C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18013—51nomaximal, Sylow
68C2×#709C2×C411yescharacteristic
69C22×C5×C8—21no—
70C2×C42×C5C2311yescharacteristic
71C4×C22⋊D5—21no—
72C4×C22⋊D5—21no—
73#4072—21no—
74#4072C2×C411yescharacteristic
75#4070—21no—
76#4070C2×C411yescharacteristic
77#4070C2×C411yescharacteristic
78C2×#681D411yescharacteristic
79C2×#681D411yescharacteristic
80C2×Dic20C2×C411yescharacteristic
81C2×Dic20C2×C411yescharacteristic
82C2×#677C2×C411yescharacteristic
83C2×#677C2×C411yescharacteristic
84C2×#676—21no—
85C2×#676—21no—
86C4×D20C2×C411yescharacteristic
87C4×D20C2311yescharacteristic
88#4018—21no—
89C42×D5—21no—
90#4016—21no—
91#4015C2×C411yescharacteristic
92#4015C2×C411yescharacteristic
93C4×Dic10—21no—
94C4×Dic10C2×C411yescharacteristic
95C4×Dic10C2311yescharacteristic
96C4×Dic10C2311yescharacteristic
97C4×Dic10C2311yescharacteristic
98C5×C4⋊C8—21no—
99C5×C4⋊C8C2×C411yescharacteristic
100C5×C4⋊C8C2×C411yescharacteristic
101C5×C4⋊C8C2311yescharacteristic
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×C22⋊C8—21no—
106C5×C22⋊C8C2×C411yescharacteristic
107C5×C22⋊C8C2×C411yescharacteristic
108C5×#97—21no—
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C22⋊#168—21no—
112#3953C2×C411yescharacteristic
113#3953C2×C411yescharacteristic
114#3952—21no—
115#3952—21no—
116#3950C2×C411yescharacteristic
117#3950C2×C411yescharacteristic
118#3949C2×C411yescharacteristic
119#3949C2×C411yescharacteristic
120#3948C2×C411yescharacteristic
121#3948C2×C411yescharacteristic
122#3948C2×C411yescharacteristic
123#3948C2×C411yescharacteristic
124#3948C2×C411yescharacteristic
125#3948C2×C411yescharacteristic
126#3947—21no—
127#3947—21no—
128#3946—21no—
129#3946—21no—
130#3946—21no—
131#3946—21no—
132#3946—21no—
133#3946—21no—
134C8×Dic5—21no—
135C8×Dic5—21no—
136C8×Dic5—21no—
137C8×Dic5—21no—
138C4⋊#168—21no—
139#3935D411yescharacteristic
140#3935D411yescharacteristic
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3107—51no—
146#2971—51no—
147#2962—51no—
148#1592—51no—
149#1590—51no—
150#1588—51no—
151#1587—51no—
152#1584—51no—
153#1583—51no—
154#1579—51no—
155C8×Q16—51no—
156#1573D511yescharacteristic, complemented
157#1497—51no—
158#1477—51no—
159#1453—51no—
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C2×C22⋊D5—21no—
164#709—22no—
165#709—41no—
166C2×D20C22×C411yescharacteristic
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×Dic10—21no—
171C2×Dic10C22×C411yescharacteristic
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—42no—
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C22×C411yescharacteristic
182C2×C5×C8C22×C411yescharacteristic
183C42×C5C22×C411yescharacteristic
184C42×C5C2×D411yescharacteristic
185C42×C5#4111yescharacteristic
186C42×C5C2411yescharacteristic
187C22⋊Dic5—21no—
188C22⋊Dic5—21no—
189C22⋊Dic5—21no—
190#685—21no—
191#685—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—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—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210#681—22no—
211#681—41no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168C2×D411yescharacteristic
215C2×#168C2×D411yescharacteristic
216C2×#168C2×D411yescharacteristic
217C2×#168C2×D411yescharacteristic
218Dic20—22no—
219Dic20—22no—
220#677—41no—
221#677—41no—
222#676—42no—
223#676—42no—
224#533—51no—
225C4×#41—51no—
226#485—51no—
227#485—51no—
228#475—51no—
229#474—51no—
230#462—51no—
231#461—51no—
232#452—51no—
233#452—51no—
234#446—51no—
235#446—51no—
236#446—101no—
237#446—101no—
238C8×Q8—51no—
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—51no—
248#436—101no—
249#436—101no—
250#432—101no—
251#432C2×D511yescharacteristic
252#431—51no—
253#431C2×D511yescharacteristic
254#424—101no—
255C2×C4⋊C8C2×D511yescharacteristic
256#405—101no—
257C4×M16—51no—
258C4×M16—101no—
259#335C2×D511yescharacteristic
260#335C2×D511yescharacteristic
261#334C2×D511yescharacteristic
262#334C2×D511yescharacteristic
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#322—51no—
272#322—51no—
273#322—51no—
274C82—51no—
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—42no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296D20—21no—
297D20—21no—
298C4×D5—42no—
299C4×D5—41no—
300C4×D5—41no—
301C4×D5—81no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10—21no—
306Dic10—21no—
307Dic10—81no—
308Dic10#13112yes—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8—41no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—41no—
321#168—41no—
322#168#13712yes—
323C2×#41—51no—
324C2×Q16—51no—
325C2×Q16—51no—
326C2×SD16—51no—
327C2×SD16—51no—
328C2×M16—51no—
329C2×M16—51no—
330C2×M16—101no—
331C2×M16—101no—
332C22×C8—21no—
333C4⋊Q8—51no—
334C4⋊Q8—51no—
335#125—101no—
336C22⋊Q8—51no—
337C22⋊Q8—51no—
338C22⋊Q8—101no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8—51no—
343C4×Q8—101no—
344C4×D4—51no—
345C4×D4—51no—
346C4×D4—101no—
347C4×D4—101no—
348#117—51no—
349#117—101no—
350#117—101no—
351C2×C42—101no—
352C2×C42C22×D511yescharacteristic
353#107—51no—
354#107—51no—
355#106—51no—
356#106—51no—
357C4⋊C8—21no—
358C4⋊C8—101no—
359C4⋊C8—101no—
360C4⋊C8—101no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8C4×D511yescharacteristic
366C4⋊C8C4×D511yescharacteristic
367C4⋊C8C22×D511yescharacteristic
368C4⋊C8C22×D511yescharacteristic
369C4⋊C8C22×D511yescharacteristic
370C4⋊C8C22×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—21no—
386#97—51no—
387#97—51no—
388#97—101no—
389#97—101no—
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
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—
422#41—102no—
423#41—201no—
424C2×Q8—51no—
425C2×Q8—51no—
426C2×Q8—51no—
427C2×Q8—101no—
428C2×D4—51no—
429C2×D4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4C2×C4×D511yescharacteristic
434C22×C4D4×D511yescharacteristic
435C22×C4#71311yescharacteristic
436Q16—102no—
437Q16—102no—
438SD16—201no—
439SD16—201no—
440M16—102no—
441M16—202no—
442M16—202no—
443M16—201no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8C2×C4×D511yescharacteristic
456C2×C8C2×C4×D511yescharacteristic
457C2×C8C2×C4×D511yescharacteristic
458C2×C8C2×C4×D511yescharacteristic
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
483C42D4×D511yescharacteristic
484C42#71311yescharacteristic
485C42C23×D511yescharacteristic
486C2×C5—41no—
487C2×C5#293311yescharacteristic
488C2×C5C4×#13711yescharacteristic
489C2×C5#295711yescharacteristic
490D5—81no—
491C23—101no—
492C23#403911yescharacteristic
493Q8—52no—
494Q8—101no—
495Q8—101no—
496Q8—101no—
497Q8—101no—
498Q8—101no—
499Q8—401no—
500D4—101no—
501D4—101no—
502D4—202no—
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×C4#403911yescharacteristic
520C2×C4#403911yescharacteristic
521C2×C4#403911yescharacteristic
522C2×C4C22×C4×D511yescharacteristic
523C2×C4C2×D4×D511yescharacteristic
524C2×C4C2×#71311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—52no—
534C8—101no—
535C8—101no—
536C8—101no—
537C8—201no—
538C8—201no—
539C5#1801311yescharacteristic, complemented, Sylow
540C22—21no—
541C22—21no—
542C22—21no—
543C22—201no—
544C22—201no—
545C22—201no—
546C22C2×#403911yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—102no—
552C4—201no—
553C4—201no—
554C4—201no—
555C4—201no—
556C4—201no—
557C4—201no—
558C4D5×#13111yescharacteristic
559C4#6608411yescharacteristic
560C4#6610711yescharacteristic
561C4D5×#13711yescharacteristic
562C2—41no—
563C2—401no—
564C2#1061080611yescharacteristic
565C2#1061093111yescharacteristic
566C2#1061098011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1573C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenter#1573D5
hypocenterC5#18013
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #10610739C2semidirect
4. C5×#1573C2semidirect
5. #10601596C2semidirect
6. #10601536C2semidirect
8. #10599358C2semidirect
9. #10599355C2semidirect
10. #10599353C2semidirect
11. #10599350C2semidirect
12. #10599316C2semidirect
13. #10599315C2semidirect
14. #10599313C2semidirect
15. #10599310C2semidirect
156. #1573D5semidirect
539. C5#18013semidirect

Maximal subgroups

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

subgroupindex
#106110602
#106110332
#106107392
C5×#15732
#106015962
#106015362
#106012182
#105993582
#105993552
#105993532
#105993502
#105993162
#105993152
#105993132
#105993102
#180135