Finite Group Databasebeta

← #12070530

Subgroups — #12070530

Order 1280.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2974C211yesmaximal, characteristic, complemented
2#10614040C211yesmaximal, characteristic
3#10611027C211yesmaximal, characteristic, complemented
4C2×D4⋊#168C211yesmaximal, characteristic, complemented
5#10601657C211yesmaximal, characteristic, complemented
6#10601655C211yesmaximal, characteristic, complemented
7#10601654C211yesmaximal, characteristic, complemented
8#10601653C211yesmaximal, characteristic, complemented
9#10601635C211yesmaximal, characteristic, complemented
10#10601634C211yesmaximal, characteristic, complemented
11#10601633C211yesmaximal, characteristic, complemented
12#10601632C211yesmaximal, characteristic, complemented
13#10601593C211yesmaximal, characteristic, complemented
14#10601590C211yesmaximal, characteristic, complemented
15#10601535C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17#65813C2211yescharacteristic
18C5×#436C2211yescharacteristic
19C5×#436C2211yescharacteristic
20C5×#435—21no—
21C5×#435—21no—
22C5×C8×D4C2211yescharacteristic
23C5×C8×D4C2211yescharacteristic
24C5×#432C2211yescharacteristic
25C5×#431C2211yescharacteristic
26C5×#407—21no—
27C2×C5×C22⋊C8—21no—
28#65507C411yescharacteristic
29#65506C411yescharacteristic
30C4×#687C2211yescharacteristic
31C4×#687C2211yescharacteristic
32#65305C411yescharacteristic
33#65305C411yescharacteristic
34C4×#686C2211yescharacteristic
35C4×#686C2211yescharacteristic
36#65298C411yescharacteristic
37#65298C411yescharacteristic
38#65259C411yescharacteristic
39#65257C411yescharacteristic
40#65214C2211yescharacteristic
41C2×C4⋊#168C2211yescharacteristic
42C2×C4×#168C2211yescharacteristic
43#65129—21no—
44#65128—21no—
45#65019—21no—
46#65014—21no—
47#64977C2211yescharacteristic, complemented
48C8×D20C2211yescharacteristic, complemented
49#64968C2211yescharacteristic, complemented
50C8×Dic10C2211yescharacteristic, complemented
51D4⋊#168C2211yescharacteristic
52D4⋊#168C2211yescharacteristic
53D4⋊#168C2211yescharacteristic
54D4⋊#168C2211yescharacteristic
55#64704C2211yescharacteristic, complemented
56#64704C2211yescharacteristic, complemented
57#64703C2211yescharacteristic, complemented
58#64703C2211yescharacteristic, complemented
59#64700C2211yescharacteristic, complemented
60#64700C2211yescharacteristic, complemented
61#64699C2211yescharacteristic, complemented
62#64699C2211yescharacteristic, complemented
63#64675C2211yescharacteristic, complemented
64#64675C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#18020—51nomaximal, Sylow
68C22×C5×D4C2×C411yescharacteristic
69C23×C4×C5—21no—
70C2×C5×M16—21no—
71C2×C5×M16—21no—
72C22×C5×C8—21no—
73C22×C5×C8—21no—
74C4×C5×D4—21no—
75C4×C5×D4—21no—
76C4×C5×D4C2×C411yescharacteristic
77C4×C5×D4C2×C411yescharacteristic
78C4×C5×D4C2311yescharacteristic
79C4×C5×D4C2311yescharacteristic
80C2×C5×C4⋊C4C2×C411yescharacteristic
81C2×C5×C22⋊C4—21no—
82C2×C42×C5C2311yescharacteristic
83C2×#687C2×C411yescharacteristic
84C2×#687C2×C411yescharacteristic
85C2×#686C2×C411yescharacteristic
86C2×#686C2×C411yescharacteristic
87#4076C2×C411yescharacteristic
88#4075—21no—
89C4×C22⋊D5—21no—
90#4070C2×C411yescharacteristic
91C22×#168—21no—
92C22×#168—21no—
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⋊C8D411yescharacteristic
102C5×C4⋊C8D411yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×C22⋊C8—21no—
106C5×C22⋊C8—21no—
107C5×C22⋊C8—21no—
108C5×C22⋊C8—21no—
109C5×C22⋊C8—21no—
110C5×C22⋊C8D411yescharacteristic
111C5×C22⋊C8D411yescharacteristic
112C5×#97—21no—
113C4×C5×C8C2311yescharacteristic
114C4×C5×C8C2311yescharacteristic
115#3964C2×C411yescharacteristic
116#3964C2×C411yescharacteristic
117#3964C2×C411yescharacteristic
118#3964C2×C411yescharacteristic
119C22⋊#168C2×C411yescharacteristic
120C22⋊#168C2×C411yescharacteristic
121#3952—21no—
122#3952—21no—
123#3947—21no—
124#3946—21no—
125#3946—21no—
126C8×Dic5—21no—
127#3942C2×C411yescharacteristic
128#3942C2×C411yescharacteristic
129#3941C2×C411yescharacteristic
130#3941C2×C411yescharacteristic
131#3940C2×C411yescharacteristic
132#3940C2×C411yescharacteristic
133#3939C2×C411yescharacteristic
134#3939C2×C411yescharacteristic
135C4⋊#168—21no—
136C4⋊#168C2×C411yescharacteristic
137C4⋊#168C2×C411yescharacteristic
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3105—51no—
146#2994—51no—
147#2974D511yescharacteristic, complemented
148#1594—51no—
149#1592—51no—
150#1583—51no—
151#1582—51no—
152#1581—51no—
153#1581—51no—
154#1580—51no—
155SD16⋊C8—51no—
156#1573—51no—
157#1494—51no—
158C2×D4⋊C8—51no—
159#1452—51no—
160C24×C5—21no—
161C2×C5×D4—22no—
162C2×C5×D4—21no—
163C2×C5×D4—41no—
164C2×C5×D4C22×C411yescharacteristic
165C2×C5×D4C22×C411yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—81no—
172C22×C4×C5—81no—
173C22×C4×C5C22×C411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C2×C22⋊D5—21no—
177C2×D20C22×C411yescharacteristic
178C2×C4×D5—21no—
179C2×Dic10C22×C411yescharacteristic
180C5×M16—81no—
181C5×M16—81no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—81no—
185C2×C5×C8—81no—
186C2×C5×C8C2×D411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C5×C4⋊C4—21no—
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C4⋊C4C22×C411yescharacteristic
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C42×C5C22×C411yescharacteristic
198C42×C5C2×D411yescharacteristic
199C42×C5#4111yescharacteristic
200C42×C5C2411yescharacteristic
201C22⋊Dic5—21no—
202#687—22no—
203#687—41no—
204#686—22no—
205#686—41no—
206#685—21no—
207#685—21no—
208#685—21no—
209#685—21no—
210C4⋊Dic5C22×C411yescharacteristic
211C4⋊Dic5C22×C411yescharacteristic
212#683—21no—
213#683—21no—
214#683—21no—
215#683—21no—
216C4×Dic5—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—21no—
221C2×#168—42no—
222C2×#168—81no—
223C2×#168C22×C411yescharacteristic
224C2×#168C22×C411yescharacteristic
225C2×#168C22×C411yescharacteristic
226C2×#168C22×C411yescharacteristic
227#676—81no—
228C8×D5—81no—
229#529—51no—
230C2×C4×D4C2×D511yescharacteristic
231#484—51no—
232#481—51no—
233#478—51no—
234#478—51no—
235#463—51no—
236#463—51no—
237#450—51no—
238#447—51no—
239#446—51no—
240C8×Q8—51no—
241C4×SD16—51no—
242C4×SD16—51no—
243C4×D8—51no—
244C4×D8—51no—
245#436—51no—
246#436C2×D511yescharacteristic
247#436C2×D511yescharacteristic
248#435—21no—
249#435—21no—
250#435—101no—
251C8×D4—51no—
252C8×D4—101no—
253C8×D4C2×D511yescharacteristic
254C8×D4C2×D511yescharacteristic
255#433—101no—
256#432C2×D511yescharacteristic
257#431—51no—
258#431C2×D511yescharacteristic
259#424—101no—
260C2×C4⋊C8—51no—
261#407—21no—
262C2×C22⋊C8—21no—
263C2×C4×C8—51no—
264#335—51no—
265#335—51no—
266#334—51no—
267#334—51no—
268Q8⋊C8—51no—
269Q8⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8—51no—
275D4⋊C8—51no—
276#322—51no—
277#322—51no—
278#322—51no—
279#322—51no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—42no—
283C23×C5—42no—
284C23×C5—81no—
285C23×C5C4×D411yescharacteristic
286C22×D5—21no—
287C5×D4—21no—
288C5×D4—21no—
289C5×D4—21no—
290C5×D4—42no—
291C5×D4#13112yes—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—81no—
304C2×C4×C5—81no—
305C2×C4×C5—81no—
306C2×C4×C5C4×D411yescharacteristic
307C2×C4×C5C4×D411yescharacteristic
308C2×C4×C5C4×D411yescharacteristic
309C2×C4×C5C23×C411yescharacteristic
310C2×C4×C5C22×D411yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C22⋊D5—42no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316D20—21no—
317D20—21no—
318C4×D5—41no—
319C4×D5—41no—
320Dic10—21no—
321Dic10—21no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—21no—
326C5×C8—41no—
327C5×C8—41no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—41no—
333#168—41no—
334#168—41no—
335#168—41no—
336C22×D4C4×D511yescharacteristic
337C23×C4—21no—
338C2×SD16—51no—
339C2×SD16—51no—
340C2×D8—51no—
341C2×D8—51no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—101no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—101no—
348C22×C8—101no—
349C22×C8—101no—
350#126—101no—
351#125—51no—
352#124—51no—
353#123—101no—
354C22⋊Q8—51no—
355#121—51no—
356C4×Q8—51no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—51no—
360C4×D4—101no—
361C4×D4C4×D511yescharacteristic
362C4×D4C4×D511yescharacteristic
363C4×D4C22×D511yescharacteristic
364C4×D4C22×D511yescharacteristic
365#117—101no—
366C2×C4⋊C4C4×D511yescharacteristic
367C2×C22⋊C4—21no—
368C2×C42C22×D511yescharacteristic
369#107—51no—
370#107—51no—
371#106—51no—
372#106—51no—
373C4⋊C8—51no—
374C4⋊C8—51no—
375C4⋊C8—51no—
376C4⋊C8—51no—
377C4⋊C8—101no—
378C4⋊C8—101no—
379C4⋊C8—101no—
380C4⋊C8C22⋊D511yescharacteristic
381C4⋊C8C22⋊D511yescharacteristic
382C4⋊C8C22×D511yescharacteristic
383C4⋊C8C22×D511yescharacteristic
384#103—51no—
385#103—51no—
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102—51no—
391#102—51no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—51no—
398C22⋊C8—51no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8C22⋊D511yescharacteristic
402C22⋊C8C22⋊D511yescharacteristic
403#97—21no—
404#97—101no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—51no—
409C4×C8—101no—
410C4×C8—101no—
411C4×C8C22×D511yescharacteristic
412C4×C8C22×D511yescharacteristic
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—22no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—84no—
422C22×C5#44412yes—
423C22×C5C2×C4×D411yescharacteristic
424C2×D5—41no—
425C2×D5—41no—
426C2×D5—41no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5C2×#13111yescharacteristic
434C4×C5#56811yescharacteristic
435C4×C5#57611yescharacteristic
436C4×C5#57711yescharacteristic
437Dic5—41no—
438Dic5—41no—
439Dic5—41no—
440C24—21no—
441C2×Q8—51no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—51no—
446C2×D4—101no—
447C2×D4C2×C4×D511yescharacteristic
448C2×D4C2×C4×D511yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—101no—
457C22×C4C2×C4×D511yescharacteristic
458C22×C4#70911yescharacteristic
459C22×C4C2×C22⋊D511yescharacteristic
460SD16—102no—
461SD16—201no—
462D8—102no—
463D8—201no—
464M16—81no—
465M16—81no—
466M16—401no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—51no—
470C2×C8—51no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—81no—
474C2×C8—81no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C2×C8—202no—
480C2×C8—401no—
481C2×C8—401no—
482C2×C8C2×C22⋊D511yescharacteristic
483C2×C8C2×C22⋊D511yescharacteristic
484C2×C8C2×C22⋊D511yescharacteristic
485C2×C8C2×C22⋊D511yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—51no—
488C4⋊C4—51no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4C2×C4×D511yescharacteristic
494C4⋊C4C2×C4×D511yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C22⋊C4—101no—
504C42—101no—
505C42C2×C4×D511yescharacteristic
506C42#70911yescharacteristic
507C42C2×C22⋊D511yescharacteristic
508C42C23×D511yescharacteristic
509C2×C5—22no—
510C2×C5—42no—
511C2×C5—81no—
512C2×C5#293311yescharacteristic
513C2×C5#294611yescharacteristic
514C2×C5C2×#44411yescharacteristic
515D5—81no—
516C23—21no—
517C23—21no—
518C23—42no—
519C23—42no—
520C23—81no—
521C23—101no—
522C23C4×C22⋊D511yescharacteristic
523Q8—101no—
524Q8—101no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—101no—
530D4—101no—
531D4—202no—
532D4#405312yes—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4C4×C22⋊D511yescharacteristic
553C2×C4C4×C22⋊D511yescharacteristic
554C2×C4C4×C22⋊D511yescharacteristic
555C2×C4C22×C4×D511yescharacteristic
556C2×C4C2×#70911yescharacteristic
557C2×C4C22×C22⋊D511yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—101no—
565C8—101no—
566C8—101no—
567C8—101no—
568C8—201no—
569C8—201no—
570C8—201no—
571C8—201no—
572C5#1802011yescharacteristic, complemented, Sylow
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22#6543412yes—
586C22C2×C4×C22⋊D511yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—201no—
594C4—201no—
595C4—201no—
596C4C2×#405311yescharacteristic
597C4#6607911yescharacteristic
598C4#6616911yescharacteristic
599C4#6617011yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—401no—
604C2#1061426811yescharacteristic
605C2#1061548811yescharacteristic
606C2C2×#6543411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#2974C2
socleC22×C5C2×C4×D4
prime radical#65506C4
cosocleC42×C5C24
hypercenter#2974D5
hypocenterC5#18020
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
1. C5×#2974C2semidirect
3. #10611027C2semidirect
4. C2×D4⋊#168C2semidirect
5. #10601657C2semidirect
6. #10601655C2semidirect
7. #10601654C2semidirect
8. #10601653C2semidirect
9. #10601635C2semidirect
10. #10601634C2semidirect
11. #10601633C2semidirect
12. #10601632C2semidirect
13. #10601593C2semidirect
14. #10601590C2semidirect
15. #10601535C2semidirect
47. #64977C22semidirect
48. C8×D20C22semidirect
49. #64968C22semidirect
50. C8×Dic10C22semidirect
55. #64704C22semidirect
56. #64704C22semidirect
57. #64703C22semidirect
58. #64703C22semidirect
59. #64700C22semidirect
60. #64700C22semidirect
61. #64699C22semidirect
62. #64699C22semidirect
63. #64675C22semidirect
64. #64675C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
147. #2974D5semidirect
572. C5#18020semidirect

Maximal subgroups

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

subgroupindex
C5×#29742
#106140402
#106110272
C2×D4⋊#1682
#106016572
#106016552
#106016542
#106016532
#106016352
#106016342
#106016332
#106016322
#106015932
#106015902
#106015352
#180205