Finite Group Databasebeta

← #12070342

Subgroups — #12070342

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614872C211yesmaximal, characteristic
2#10614860C211yesmaximal, characteristic, complemented
3#10610774C211yesmaximal, characteristic, complemented
4C5×#1495C211yesmaximal, characteristic, complemented
5#10601550C211yesmaximal, characteristic, complemented
6#10601536C211yesmaximal, characteristic, complemented
7#10601288C211yesmaximal, characteristic, complemented
8#10599017C211yesmaximal, characteristic, complemented
9#10599016C211yesmaximal, characteristic, complemented
10#10599009C211yesmaximal, characteristic, complemented
11#10599007C211yesmaximal, characteristic, complemented
12#10598956C211yesmaximal, characteristic, complemented
13#10598951C211yesmaximal, characteristic, complemented
14#10598945C211yesmaximal, characteristic, complemented
15#10598941C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C2×D5×M16—21no—
18C2×C4×D20C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C5×#423C2211yescharacteristic
21#65415—21no—
22#65355C411yescharacteristic
23#65355C411yescharacteristic
24#65346C411yescharacteristic
25#65346C411yescharacteristic
26#65335C411yescharacteristic
27#65333C411yescharacteristic
28#65325C411yescharacteristic
29#65323C411yescharacteristic
30C4×#688C2211yescharacteristic
31C4×#688C2211yescharacteristic
32#65313C2211yescharacteristic, complemented
33Q8×#168C2211yescharacteristic, complemented
34C4×#686C2211yescharacteristic
35C4×#686C2211yescharacteristic
36#65301—21no—
37#65301C2211yescharacteristic, complemented
38#65300—21no—
39D4×#168C2211yescharacteristic, complemented
40#65289—21no—
41#65286—21no—
42#65214C2211yescharacteristic
43#65214C2211yescharacteristic
44C4×#681C2211yescharacteristic
45#65127C2211yescharacteristic
46#65127C2211yescharacteristic
47#65125—21no—
48#65125—21no—
49#65123C2211yescharacteristic
50#65123C2211yescharacteristic
51C5×Q8⋊C8C2211yescharacteristic, complemented
52C5×Q8⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic, complemented
54C5×D4⋊C8C2211yescharacteristic, complemented
55#64700C2211yescharacteristic, complemented
56#64700C2211yescharacteristic, complemented
57#64699C2211yescharacteristic, complemented
58#64699C2211yescharacteristic, complemented
59#64679C2211yescharacteristic
60#64679C2211yescharacteristic
61#64679C2211yescharacteristic
62#64679C2211yescharacteristic
63#64675C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#18006—51nomaximal, Sylow
68C22×D20C2×C411yescharacteristic
69C22×C4×D5—21no—
70C2×C5×M16—21no—
71C5×#126—21no—
72C5×#125C2×C411yescharacteristic
73C5×#124C2×C411yescharacteristic
74C5×#123—21no—
75C5×C22⋊Q8C2×C411yescharacteristic
76C5×#121C2×C411yescharacteristic
77C4×C5×Q8C2311yescharacteristic
78C4×C5×D4—21no—
79C4×C5×D4C2311yescharacteristic
80C5×#117—21no—
81C2×C42×C5C2311yescharacteristic
82C2×#688C2×C411yescharacteristic
83C2×#688C2×C411yescharacteristic
84C2×#686C2×C411yescharacteristic
85C2×#686C2×C411yescharacteristic
86C2×#685—21no—
87C2×C4⋊Dic5C2×C411yescharacteristic
88C2×#681—21no—
89C2×#681D411yescharacteristic
90C2×#681D411yescharacteristic
91C22×#168—21no—
92D5×M16—44no—
93C2×#676—21no—
94C2×#676—21no—
95C2×C8×D5—21no—
96C2×C8×D5—21no—
97C4×D20—21no—
98C4×D20—21no—
99C4×D20C2×C411yescharacteristic
100C4×D20C2×C411yescharacteristic
101C4×D20C2311yescharacteristic
102C4×D20C2311yescharacteristic
103C5×C4⋊C8—21no—
104C5×C4⋊C8—21no—
105C5×C4⋊C8C2311yescharacteristic
106C5×C4⋊C8C2311yescharacteristic
107C5×C22⋊C8—21no—
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110#3967C2×C411yescharacteristic
111#3967C2×C411yescharacteristic
112#3964C2×C411yescharacteristic
113#3964C2×C411yescharacteristic
114C22⋊#168—21no—
115C22⋊#168—21no—
116C22⋊#168—21no—
117C22⋊#168C2×C411yescharacteristic
118C22⋊#168C2×C411yescharacteristic
119#3952—21no—
120#3952—21no—
121#3952—21no—
122#3952—21no—
123#3941C2×C411yescharacteristic
124#3941C2×C411yescharacteristic
125#3941C2×C411yescharacteristic
126#3941C2×C411yescharacteristic
127#3940C2×C411yescharacteristic
128#3940C2×C411yescharacteristic
129#3939C2×C411yescharacteristic
130#3939C2×C411yescharacteristic
131C4⋊#168—21no—
132C4⋊#168—21no—
133C4⋊#168C2×C411yescharacteristic
134C4⋊#168C2×C411yescharacteristic
135C4⋊#168C2311yescharacteristic
136C4⋊#168C2311yescharacteristic
137#3935—21no—
138#3935D411yescharacteristic
139#3935D411yescharacteristic
140C4×#168—21no—
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146#3105—51no—
147#2969—51no—
148D4×M16—51no—
149#1594—51no—
150#1590—51no—
151#1588—51no—
152#1586—51no—
153#1582—51no—
154#1581—51no—
155SD16⋊C8—51no—
156C8×D8—51no—
157#1574—51no—
158#1495D511yescharacteristic, complemented
159#1478—51no—
160#1453—51no—
161C23×D5—21no—
162C2×C5×Q8C22×C411yescharacteristic
163C2×C5×D4—21no—
164C2×C5×D4C22×C411yescharacteristic
165C22×C4×C5—21no—
166C22×C4×C5C22×C411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5#4111yescharacteristic
169C22×Dic5—21no—
170C2×D20—22no—
171C2×D20—21no—
172C2×D20—41no—
173C2×D20C22×C411yescharacteristic
174C2×D20C22×C411yescharacteristic
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—42no—
180C2×C4×D5—42no—
181C5×M16—42no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C42×C5—21no—
198C42×C5C22×C411yescharacteristic
199C42×C5C2×D411yescharacteristic
200C42×C5#4111yescharacteristic
201C42×C5C2411yescharacteristic
202#688—22no—
203#688—41no—
204#686—22no—
205#686—41no—
206#685—21no—
207#685—21no—
208#685—21no—
209#685—21no—
210C4⋊Dic5—21no—
211C4⋊Dic5C22×C411yescharacteristic
212C4⋊Dic5C22×C411yescharacteristic
213#681—22no—
214#681—41no—
215#681—42no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—42no—
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222C2×#168C22×C411yescharacteristic
223C2×#168C2×D411yescharacteristic
224C2×#168C2×D411yescharacteristic
225C2×#168C2×D411yescharacteristic
226C2×#168C2×D411yescharacteristic
227#676—42no—
228#676—42no—
229C8×D5—42no—
230C8×D5—42no—
231C22×M16—101no—
232#529C2×D511yescharacteristic
233C2×C4×D4—51no—
234#484—51no—
235#481—51no—
236#478—51no—
237#478—51no—
238#463—51no—
239#463—51no—
240#450—51no—
241#447—51no—
242#446—51no—
243C8×Q8—51no—
244C4×SD16—51no—
245C4×SD16—51no—
246C4×D8—51no—
247C4×D8—51no—
248#436—51no—
249#436—51no—
250#436—51no—
251#436—101no—
252#435—101no—
253#435—101no—
254#435—101no—
255C8×D4—51no—
256C8×D4—51no—
257C8×D4—51no—
258#433—101no—
259#431—51no—
260#431—51no—
261#431C2×D511yescharacteristic
262#423C2×D511yescharacteristic
263#407—101no—
264#405—101no—
265C4×M16—51no—
266#335—51no—
267#335—51no—
268#334—51no—
269#334—51no—
270Q8⋊C8C2×D511yescharacteristic, complemented
271Q8⋊C8C2×D511yescharacteristic, complemented
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8—51no—
275D4⋊C8—51no—
276D4⋊C8C2×D511yescharacteristic, complemented
277D4⋊C8C2×D511yescharacteristic, complemented
278#322—51no—
279#322—51no—
280#322—51no—
281C82—51no—
282C23×C5—21no—
283C23×C5C4×D411yescharacteristic
284C22×D5—21no—
285C22×D5—21no—
286C22×D5—42no—
287C22×D5—42no—
288C22×D5—81no—
289C5×Q8—21no—
290C5×Q8—21no—
291C5×D4—21no—
292C5×D4—21no—
293C5×D4—81no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5C4×D411yescharacteristic
305C2×C4×C5C4×D411yescharacteristic
306C2×C4×C5C4×D411yescharacteristic
307C2×C4×C5C23×C411yescharacteristic
308C2×C4×C5C22×D411yescharacteristic
309C2×C4×C5C2×#4111yescharacteristic
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—42no—
313D20—21no—
314D20—21no—
315D20—21no—
316D20—42no—
317D20#13112yes—
318C4×D5—42no—
319C4×D5—42no—
320C4×D5—41no—
321C4×D5—41no—
322C4×D5—41no—
323C4×D5—41no—
324C5×C8—41no—
325C5×C8—41no—
326C5×C8—41no—
327C5×C8—41no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—21no—
334#168—21no—
335#168—41no—
336#168—41no—
337#168AGL(1,ℤ/8)12yes—
338C22×D4—51no—
339C23×C4—101no—
340C2×SD16—51no—
341C2×SD16—51no—
342C2×D8—51no—
343C2×D8—51no—
344C2×M16—21no—
345C2×M16—51no—
346C2×M16—51no—
347C2×M16—101no—
348C2×M16—101no—
349C2×M16—101no—
350C2×M16—204no—
351C22×C8—101no—
352C22×C8—101no—
353C22×C8—101no—
354#126—21no—
355#125C4×D511yescharacteristic
356#124C4×D511yescharacteristic
357#123—21no—
358C22⋊Q8C4×D511yescharacteristic
359#121C4×D511yescharacteristic
360C4×Q8C22×D511yescharacteristic
361C4×D4—21no—
362C4×D4—51no—
363C4×D4—51no—
364C4×D4—51no—
365C4×D4—51no—
366C4×D4—101no—
367C4×D4—101no—
368C4×D4C22×D511yescharacteristic
369#117—21no—
370C2×C4⋊C4—51no—
371C2×C22⋊C4—101no—
372C2×C42C22×D511yescharacteristic
373#107—51no—
374#107—51no—
375#106—51no—
376#106—51no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—51no—
380C4⋊C8—51no—
381C4⋊C8—51no—
382C4⋊C8—51no—
383C4⋊C8—101no—
384C4⋊C8—101no—
385C4⋊C8C22×D511yescharacteristic
386C4⋊C8C22×D511yescharacteristic
387#103—51no—
388#103—51no—
389#102—51no—
390#102—51no—
391#102—51no—
392#102—51no—
393#102—51no—
394#102—51no—
395C22⋊C8—21no—
396C22⋊C8—51no—
397C22⋊C8—51no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8—101no—
402C22⋊C8—101no—
403C22⋊C8—101no—
404C22⋊C8—101no—
405#97—51no—
406#97—51no—
407#97—101no—
408C4×C8—51no—
409C4×C8—51no—
410C4×C8—51no—
411C4×C8—51no—
412C4×C8—101no—
413C4×C8—101no—
414C4×C8C22×D511yescharacteristic
415C4×C8C22×D511yescharacteristic
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5C2×C4×D411yescharacteristic
423C2×D5—22no—
424C2×D5—41no—
425C2×D5—41no—
426C2×D5—41no—
427C2×D5—41no—
428C2×D5—41no—
429C2×D5—84no—
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—21no—
433C4×C5—21no—
434C4×C5—41no—
435C4×C5—41no—
436C4×C5—41no—
437C4×C5C2×#13111yescharacteristic
438C4×C5#56811yescharacteristic
439C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
440C4×C5#57511yescharacteristic
441Dic5—41no—
442Dic5—41no—
443C24—101no—
444C2×Q8C2×C4×D511yescharacteristic
445C2×D4—21no—
446C2×D4—51no—
447C2×D4—51no—
448C2×D4—102no—
449C2×D4—101no—
450C2×D4—201no—
451C2×D4C2×C4×D511yescharacteristic
452C22×C4—21no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—202no—
459C22×C4—202no—
460C22×C4C2×C4×D511yescharacteristic
461C22×C4D4×D511yescharacteristic
462C22×C4#71111yescharacteristic
463SD16—102no—
464SD16—201no—
465D8—102no—
466D8—201no—
467M16—42no—
468M16—102no—
469M16—202no—
470M16—202no—
471M16—201no—
472M16—202no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—51no—
478C2×C8—51no—
479C2×C8—51no—
480C2×C8—51no—
481C2×C8—51no—
482C2×C8—51no—
483C2×C8—51no—
484C2×C8—51no—
485C2×C8—101no—
486C2×C8—101no—
487C2×C8—202no—
488C2×C8—202no—
489C2×C8—202no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—51no—
495C4⋊C4—51no—
496C4⋊C4—101no—
497C4⋊C4C2×C4×D511yescharacteristic
498C4⋊C4C2×C4×D511yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—101no—
505C22⋊C4—101no—
506C22⋊C4—101no—
507C22⋊C4—101no—
508C42—21no—
509C42C2×C4×D511yescharacteristic
510C42D4×D511yescharacteristic
511C42#71111yescharacteristic
512C42C23×D511yescharacteristic
513C2×C5—41no—
514C2×C5—81no—
515C2×C5#293311yescharacteristic
516C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
517C2×C5#295711yescharacteristic
518D5—42no—
519D5—81no—
520C23—21no—
521C23—101no—
522C23—101no—
523C23—202no—
524C23—202no—
525C23—401no—
526C23#402711yescharacteristic
527Q8—21no—
528Q8—21no—
529D4—21no—
530D4—21no—
531D4—52no—
532D4—81no—
533D4—101no—
534D4—101no—
535D4—101no—
536D4—202no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—202no—
550C2×C4—202no—
551C2×C4—202no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4#402711yescharacteristic
557C2×C4#402711yescharacteristic
558C2×C4#402711yescharacteristic
559C2×C4C22×C4×D511yescharacteristic
560C2×C4C2×D4×D511yescharacteristic
561C2×C4C2×#71111yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—52no—
567C8—101no—
568C8—101no—
569C8—101no—
570C8—101no—
571C8—101no—
572C8—101no—
573C8—101no—
574C8—201no—
575C8—201no—
576C5#1800611yescharacteristic, complemented, Sylow
577C22—21no—
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—102no—
584C22—201no—
585C22—201no—
586C22—201no—
587C22—201no—
588C22—201no—
589C22—404no—
590C22C2×#402711yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—201no—
599C4—201no—
600C4D5×#13111yescharacteristic
601C4#6608411yescharacteristic
602C4D5×AGL(1,ℤ/8)11yescharacteristic
603C4#6611111yescharacteristic
604C2—41no—
605C2—81no—
606C2—202no—
607C2—401no—
608C2#1061039011yescharacteristic
609C2#1061059711yescharacteristic
610C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1495C2
socleC22×C5C2×C4×D4
prime radical#65325C4
cosocleC42×C5C24
hypercenter#1495D5
hypocenterC5#18006
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. #10614860C2semidirect
3. #10610774C2semidirect
4. C5×#1495C2semidirect
5. #10601550C2semidirect
6. #10601536C2semidirect
7. #10601288C2semidirect
8. #10599017C2semidirect
9. #10599016C2semidirect
10. #10599009C2semidirect
11. #10599007C2semidirect
12. #10598956C2semidirect
13. #10598951C2semidirect
14. #10598945C2semidirect
15. #10598941C2semidirect
32. #65313C22semidirect
33. Q8×#168C22semidirect
37. #65301C22semidirect
39. D4×#168C22semidirect
51. C5×Q8⋊C8C22semidirect
52. C5×Q8⋊C8C22semidirect
53. C5×D4⋊C8C22semidirect
54. C5×D4⋊C8C22semidirect
55. #64700C22semidirect
56. #64700C22semidirect
57. #64699C22semidirect
58. #64699C22semidirect
63. #64675C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. C8×#168C22semidirect
158. #1495D5semidirect
270. Q8⋊C8C2×D5semidirect
271. Q8⋊C8C2×D5semidirect
276. D4⋊C8C2×D5semidirect
277. D4⋊C8C2×D5semidirect
576. C5#18006semidirect

Maximal subgroups

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

subgroupindex
#106148722
#106148602
#106107742
C5×#14952
#106015502
#106015362
#106012882
#105990172
#105990162
#105990092
#105990072
#105989562
#105989512
#105989452
#105989412
#180065