Finite Group Databasebeta

← #12069994

Subgroups — #12069994

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614865C211yesmaximal, characteristic
2#10614862C211yesmaximal, characteristic, complemented
3#10610784C211yesmaximal, characteristic, complemented
4C5×#1495C211yesmaximal, characteristic, complemented
5#10601557C211yesmaximal, characteristic, complemented
6#10601533C211yesmaximal, characteristic, complemented
7#10601283C211yesmaximal, characteristic, complemented
8#10599020C211yesmaximal, characteristic, complemented
9#10599017C211yesmaximal, characteristic, complemented
10#10599008C211yesmaximal, characteristic, complemented
11#10599005C211yesmaximal, characteristic, complemented
12#10598956C211yesmaximal, characteristic, complemented
13#10598954C211yesmaximal, characteristic, complemented
14#10598944C211yesmaximal, characteristic, complemented
15#10598942C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17#65813C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#423C2211yescharacteristic
20#65417—21no—
21#65416—21no—
22#65357C411yescharacteristic
23#65353C411yescharacteristic
24#65348C411yescharacteristic
25#65345C411yescharacteristic
26#65340C411yescharacteristic
27#65337C411yescharacteristic
28#65330C411yescharacteristic
29#65327C411yescharacteristic
30C4×#689C2211yescharacteristic
31C4×#688C2211yescharacteristic
32#65313C2211yescharacteristic
33Q8×#168C2211yescharacteristic
34C4×#687C2211yescharacteristic
35C4×#686C2211yescharacteristic
36#65301—21no—
37#65301C2211yescharacteristic
38#65300—21no—
39D4×#168C2211yescharacteristic
40#65289—21no—
41#65288—21no—
42#65214C2211yescharacteristic
43#65213C2211yescharacteristic
44C2×C4×#168C2211yescharacteristic
45#65129—21no—
46#65128—21no—
47#65127C2211yescharacteristic
48#65123C2211yescharacteristic
49#65120C2211yescharacteristic
50#65119C2211yescharacteristic
51C5×Q8⋊C8C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×D4⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic
56#64700C2211yescharacteristic
57#64700C2211yescharacteristic
58#64700C2211yescharacteristic
59#64679C2211yescharacteristic
60#64679C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64674C2211yescharacteristic
64#64674C2211yescharacteristic
65C8×#168C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#17974—51nomaximal, Sylow
68C2×C5×M16—21no—
69C5×#126—21no—
70C5×#125C2×C411yescharacteristic
71C5×#124C2×C411yescharacteristic
72C5×#123—21no—
73C5×C22⋊Q8C2×C411yescharacteristic
74C5×#121C2×C411yescharacteristic
75C4×C5×Q8C2311yescharacteristic
76C4×C5×D4—21no—
77C4×C5×D4C2311yescharacteristic
78C5×#117—21no—
79C2×C42×C5C2311yescharacteristic
80C2×#689C2×C411yescharacteristic
81C2×#688C2×C411yescharacteristic
82C2×#687C2×C411yescharacteristic
83C2×#686C2×C411yescharacteristic
84#4076C2×C411yescharacteristic
85#4075—21no—
86C4×C22⋊D5—21no—
87#4070C2×C411yescharacteristic
88C2×#681—21no—
89C2×#681—21no—
90C22×#168—21no—
91C22×#168C2×C411yescharacteristic
92C22×#168C2×C411yescharacteristic
93C2×#676—21no—
94C2×C8×D5—21no—
95#4022—21no—
96#4021C2×C411yescharacteristic
97C4×D20C2311yescharacteristic
98#4018—21no—
99#4016C2×C411yescharacteristic
100C4×Dic10C2311yescharacteristic
101C5×C4⋊C8—21no—
102C5×C4⋊C8—21no—
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×C22⋊C8—21no—
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2311yescharacteristic
108#3967C2×C411yescharacteristic
109#3967C2×C411yescharacteristic
110#3964C2×C411yescharacteristic
111#3964C2×C411yescharacteristic
112C22⋊#168—21no—
113C22⋊#168—21no—
114C22⋊#168D411yescharacteristic
115C22⋊#168D411yescharacteristic
116#3952—21no—
117#3952—21no—
118#3947—21no—
119#3946—21no—
120#3946—21no—
121C8×Dic5—21no—
122#3942C2×C411yescharacteristic
123#3942C2×C411yescharacteristic
124#3941C2×C411yescharacteristic
125#3941C2×C411yescharacteristic
126#3940C2×C411yescharacteristic
127#3940C2×C411yescharacteristic
128#3939C2×C411yescharacteristic
129#3939C2×C411yescharacteristic
130C4⋊#168—21no—
131C4⋊#168—21no—
132C4⋊#168—21no—
133C4⋊#168D411yescharacteristic
134C4⋊#168D411yescharacteristic
135C4⋊#168C2311yescharacteristic
136C4⋊#168C2311yescharacteristic
137#3935—21no—
138C4×#168—21no—
139C4×#168C2×C411yescharacteristic
140C4×#168C2×C411yescharacteristic
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3168—51no—
146#2993—51no—
147#2993—51no—
148#1594—51no—
149#1593—51no—
150#1590—51no—
151#1590—51no—
152#1580—51no—
153#1579—51no—
154C8×SD16—51no—
155C8×SD16—51no—
156#1566—51no—
157#1495—51no—
158#1495D511yescharacteristic, complemented
159#1450—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C22×C411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5C22×C411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5#4111yescharacteristic
167C2×C22⋊D5—21no—
168C2×D20C22×C411yescharacteristic
169C2×C4×D5—21no—
170C2×Dic10C22×C411yescharacteristic
171C5×M16—81no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4C22×C411yescharacteristic
181C5×C4⋊C4C22×C411yescharacteristic
182C5×C22⋊C4—21no—
183C5×C22⋊C4—21no—
184C5×C22⋊C4—21no—
185C5×C22⋊C4—21no—
186C5×C22⋊C4—21no—
187C42×C5—21no—
188C42×C5C22×C411yescharacteristic
189C42×C5C2×D411yescharacteristic
190C42×C5#4111yescharacteristic
191C42×C5C2411yescharacteristic
192C22⋊Dic5—21no—
193#689—22no—
194#688—22no—
195#687—22no—
196#686—22no—
197#685—21no—
198#685—21no—
199#685—21no—
200#685—21no—
201C4⋊Dic5C22×C411yescharacteristic
202C4⋊Dic5C22×C411yescharacteristic
203#683—21no—
204#683—21no—
205#683—21no—
206#683—21no—
207C4×Dic5—21no—
208#681—81no—
209#681—81no—
210C2×#168—22no—
211C2×#168—22no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—81no—
215C2×#168C22×C411yescharacteristic
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C22×C411yescharacteristic
219C2×#168C2×D411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223#676—81no—
224C8×D5—81no—
225#529—51no—
226#529C2×D511yescharacteristic
227#499—51no—
228#495—51no—
229#488—51no—
230#488—51no—
231#467—51no—
232#466—51no—
233#465—51no—
234#465—51no—
235#446—51no—
236#446—51no—
237C8×Q8—51no—
238C8×Q8—51no—
239C4×Q16—51no—
240C4×SD16—51no—
241C4×SD16—51no—
242C4×D8—51no—
243#436—51no—
244#436—51no—
245#436—101no—
246#436—101no—
247#435—101no—
248#435—101no—
249C8×D4—51no—
250C8×D4—51no—
251#433—101no—
252#433—101no—
253#431—51no—
254#431C2×D511yescharacteristic
255#424—101no—
256#424—101no—
257#423—51no—
258#423C2×D511yescharacteristic
259C2×C4×C8—51no—
260#334—51no—
261#334—51no—
262#334—51no—
263#334—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8C2×D511yescharacteristic
267Q8⋊C8C2×D511yescharacteristic
268D4⋊C8—51no—
269D4⋊C8—51no—
270D4⋊C8C2×D511yescharacteristic
271D4⋊C8C2×D511yescharacteristic
272#322—51no—
273#322—51no—
274C82—51no—
275C82—51no—
276C23×C5—21no—
277C23×C5C4×D411yescharacteristic
278C22×D5—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×D4—21no—
282C5×D4—21no—
283C5×D4—81no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5C4×D411yescharacteristic
295C2×C4×C5C4×D411yescharacteristic
296C2×C4×C5C4×D411yescharacteristic
297C2×C4×C5C23×C411yescharacteristic
298C2×C4×C5C22×D411yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C22⋊D5—81no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304D20—21no—
305D20—21no—
306C4×D5—41no—
307C4×D5—41no—
308Dic10—21no—
309Dic10—21no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314#168—21no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—41no—
321#168—41no—
322#168#13112yes—
323#168#13112yes—
324C2×Q16—51no—
325C2×SD16—51no—
326C2×SD16—51no—
327C2×D8—51no—
328C2×M16—21no—
329C2×M16—101no—
330C2×M16—101no—
331C2×M16—101no—
332C22×C8—51no—
333C22×C8—51no—
334C22×C8—101no—
335C22×C8—101no—
336#126—21no—
337#126—101no—
338#125—51no—
339#125C4×D511yescharacteristic
340#124—51no—
341#124C4×D511yescharacteristic
342#123—21no—
343#123—101no—
344C22⋊Q8—51no—
345C22⋊Q8C4×D511yescharacteristic
346#121—51no—
347#121C4×D511yescharacteristic
348C4×Q8—51no—
349C4×Q8C22×D511yescharacteristic
350C4×D4—21no—
351C4×D4—51no—
352C4×D4—101no—
353C4×D4C22×D511yescharacteristic
354#117—21no—
355#117—101no—
356C2×C42C22×D511yescharacteristic
357#107—51no—
358#107—51no—
359#106—51no—
360#106—51no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—51no—
364C4⋊C8—51no—
365C4⋊C8—51no—
366C4⋊C8—51no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8—101no—
370C4⋊C8—101no—
371C4⋊C8—101no—
372C4⋊C8C22×D511yescharacteristic
373C4⋊C8C22×D511yescharacteristic
374#103—51no—
375#103—51no—
376#103—51no—
377#103—51no—
378#102—51no—
379#102—51no—
380#102—51no—
381#102—51no—
382C22⋊C8—21no—
383C22⋊C8—51no—
384C22⋊C8—51no—
385C22⋊C8—101no—
386C22⋊C8—101no—
387C22⋊C8—101no—
388C22⋊C8—101no—
389#97—101no—
390#97—101no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—51no—
394C4×C8—51no—
395C4×C8—51no—
396C4×C8—51no—
397C4×C8—101no—
398C4×C8—101no—
399C4×C8C22×D511yescharacteristic
400C4×C8C22×D511yescharacteristic
401C22×C5—21no—
402C22×C5—21no—
403C22×C5—21no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5C2×C4×D411yescharacteristic
408C2×D5—41no—
409C2×D5—41no—
410C2×D5—41no—
411C4×C5—21no—
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—21no—
415C4×C5—41no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5C2×#13111yescharacteristic
419C4×C5C2×#13111yescharacteristic
420C4×C5#57711yescharacteristic
421C4×C5#57711yescharacteristic
422Dic5—41no—
423Dic5—41no—
424Dic5—41no—
425C2×Q8—51no—
426C2×Q8C2×C4×D511yescharacteristic
427C2×D4—21no—
428C2×D4—51no—
429C2×D4—101no—
430C2×D4C2×C4×D511yescharacteristic
431C22×C4—21no—
432C22×C4—101no—
433C22×C4C2×C4×D511yescharacteristic
434C22×C4D4×D511yescharacteristic
435C22×C4#71111yescharacteristic
436Q16—102no—
437SD16—102no—
438SD16—102no—
439D8—102no—
440M16—81no—
441M16—401no—
442M16—401no—
443M16—401no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—51no—
454C2×C8—51no—
455C2×C8—51no—
456C2×C8—102no—
457C2×C8—102no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—401no—
461C2×C8—401no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—51no—
467C4⋊C4—51no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4C2×C4×D511yescharacteristic
473C4⋊C4C2×C4×D511yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—101no—
480C22⋊C4—101no—
481C22⋊C4—101no—
482C22⋊C4—101no—
483C22⋊C4—101no—
484C42—21no—
485C42—101no—
486C42C2×C4×D511yescharacteristic
487C42D4×D511yescharacteristic
488C42#71111yescharacteristic
489C42C23×D511yescharacteristic
490C2×C5—41no—
491C2×C5—81no—
492C2×C5#293111yescharacteristic
493C2×C5#295211yescharacteristic
494C2×C5#295711yescharacteristic
495D5—81no—
496C23—21no—
497C23—101no—
498C23#402711yescharacteristic
499Q8—21no—
500Q8—21no—
501Q8—101no—
502Q8—101no—
503D4—21no—
504D4—21no—
505D4—81no—
506D4—101no—
507D4—101no—
508D4—401no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4#402711yescharacteristic
525C2×C4#402711yescharacteristic
526C2×C4#402711yescharacteristic
527C2×C4C22×C4×D511yescharacteristic
528C2×C4C2×D4×D511yescharacteristic
529C2×C4C2×#71111yescharacteristic
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—52no—
535C8—52no—
536C8—101no—
537C8—101no—
538C8—101no—
539C8—101no—
540C8—101no—
541C8—101no—
542C8—201no—
543C8—201no—
544C5#1797411yescharacteristic, complemented, Sylow
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—201no—
552C22—201no—
553C22—201no—
554C22C2×#402711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—201no—
563C4—201no—
564C4—201no—
565C4D5×#13111yescharacteristic
566C4D5×#13111yescharacteristic
567C4#6610911yescharacteristic
568C4#6611211yescharacteristic
569C2—41no—
570C2—81no—
571C2—401no—
572C2#1061038811yescharacteristic
573C2#1061060011yescharacteristic
574C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1495C2
socleC22×C5C2×C4×D4
prime radical#65327C4
cosocleC42×C5C24
hypercenter#1495D5
hypocenterC5#17974
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #10614862C2semidirect
3. #10610784C2semidirect
4. C5×#1495C2semidirect
5. #10601557C2semidirect
6. #10601533C2semidirect
7. #10601283C2semidirect
8. #10599020C2semidirect
9. #10599017C2semidirect
10. #10599008C2semidirect
11. #10599005C2semidirect
12. #10598956C2semidirect
13. #10598954C2semidirect
14. #10598944C2semidirect
15. #10598942C2semidirect
158. #1495D5semidirect
544. C5#17974semidirect

Maximal subgroups

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

subgroupindex
#106148652
#106148622
#106107842
C5×#14952
#106015572
#106015332
#106012832
#105990202
#105990172
#105990082
#105990052
#105989562
#105989542
#105989442
#105989422
#179745