Finite Group Databasebeta

← #12068939

Subgroups — #12068939

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611675C211yesmaximal, characteristic
2#10611651C211yesmaximal, characteristic, complemented
3C4×#4064C211yesmaximal, characteristic
4C5×#1587C211yesmaximal, characteristic, complemented
5#10601749C211yesmaximal, characteristic, complemented
6#10601726C211yesmaximal, characteristic, complemented
7#10601696C211yesmaximal, characteristic, complemented
8#10599321C211yesmaximal, characteristic, complemented
9#10599313C211yesmaximal, characteristic, complemented
10#10599022C211yesmaximal, characteristic
11D5×Q8⋊C8C211yesmaximal, characteristic, complemented
12#10599016C211yesmaximal, characteristic, complemented
13#10599015C211yesmaximal, characteristic, complemented
14#10598881C211yesmaximal, characteristic, complemented
15#10598862C211yesmaximal, characteristic, complemented
16C2×#4064C411yescharacteristic
17C4×#713C2211yescharacteristic
18C4×Q8×D5C2211yescharacteristic
19C5×#446C2211yescharacteristic
20C5×C8×Q8C2211yescharacteristic
21C4×C5×Q16C2211yescharacteristic
22#65473C411yescharacteristic
23C4×#689C2211yescharacteristic
24C4×#688C2211yescharacteristic
25#65313C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27#65178C411yescharacteristic
28#65170C411yescharacteristic
29#65127C2211yescharacteristic
30#65126—21no—
31#65125—21no—
32#65122—21no—
33#65122C2211yescharacteristic
34D5×C4⋊C8C2211yescharacteristic
35#65119—21no—
36#65119C2211yescharacteristic
37#65106C411yescharacteristic
38#65092C411yescharacteristic
39#65091C411yescharacteristic
40#65078C411yescharacteristic
41#64995—21no—
42#64994—21no—
43C4×#677C2211yescharacteristic
44#64977C2211yescharacteristic
45C4×#676C2211yescharacteristic
46#64974—21no—
47#64974C2211yescharacteristic
48C4×C8×D5C2211yescharacteristic
49C8×Dic10—21no—
50C8×Dic10C2211yescharacteristic
51C5×#334C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64703C2211yescharacteristic
59#64700C2211yescharacteristic
60#64699C2211yescharacteristic
61#64679C2211yescharacteristic
62#64678C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64675C2211yescharacteristic
66#64674C2211yescharacteristic
67#17874—51nomaximal, Sylow
68C2×#713C2×C411yescharacteristic
69C2×Q8×D5C2×C411yescharacteristic
70C2×C5×Q16C2×C411yescharacteristic
71C4×C5×Q8C2311yescharacteristic
72C4×C5×Q8C2311yescharacteristic
73Q8×Dic5C2×C411yescharacteristic
74Q8×Dic5C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77#4064—24no—
78C2×#677C2×C411yescharacteristic
79C2×#676—21no—
80C2×#676—21no—
81C2×#676C2×C411yescharacteristic
82C2×#676C2×C411yescharacteristic
83C2×C8×D5—21no—
84C2×C8×D5—21no—
85#4039—21no—
86#4039C2×C411yescharacteristic
87#4038—21no—
88#4038C2×C411yescharacteristic
89D5×C4⋊C4—21no—
90D5×C4⋊C4C2×C411yescharacteristic
91#4033—21no—
92#4033C2×C411yescharacteristic
93C4×D20—21no—
94C4×D20C2311yescharacteristic
95C42×D5—21no—
96C42×D5—21no—
97C42×D5C2311yescharacteristic
98C4×Dic10—21no—
99C4×Dic10C2311yescharacteristic
100C5×#107C2×C411yescharacteristic
101C5×C4⋊C8—21no—
102C5×C4⋊C8—21no—
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#103C2×C411yescharacteristic
107C5×#97—21no—
108C4×C5×C8—21no—
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112#3967C2×C411yescharacteristic
113#3967C2×C411yescharacteristic
114#3953C2×C411yescharacteristic
115#3952—21no—
116#3952—21no—
117#3952—21no—
118#3952D411yescharacteristic
119#3952D411yescharacteristic
120#3949C2×C411yescharacteristic
121#3948C2×C411yescharacteristic
122#3947C2×C411yescharacteristic
123#3947C2×C411yescharacteristic
124#3946—21no—
125#3946—21no—
126#3946—21no—
127#3946D411yescharacteristic
128#3946D411yescharacteristic
129C8×Dic5—21no—
130C8×Dic5—21no—
131C8×Dic5—21no—
132C8×Dic5—21no—
133#3942C2×C411yescharacteristic
134#3941C2×C411yescharacteristic
135#3940C2×C411yescharacteristic
136#3939C2×C411yescharacteristic
137C4⋊#168—21no—
138C4⋊#168—21no—
139C4⋊#168C2311yescharacteristic
140C4⋊#168C2311yescharacteristic
141#3935—21no—
142C4×#168—21no—
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146#2989—51no—
147#2982—51no—
148C4×#137—51no—
149#1588—51no—
150#1588—51no—
151#1587—51no—
152#1587D511yescharacteristic, complemented
153#1584—51no—
154#1584—51no—
155#1583—51no—
156#1583—51no—
157#1565—51no—
158#1476—51no—
159C2×Q8⋊C8—51no—
160#1451—51no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×Q8C22×C411yescharacteristic
163#713—22no—
164#713—22no—
165Q8×D5—22no—
166Q8×D5M1614yescomplemented
167C2×D20—21no—
168C2×D20C22×C411yescharacteristic
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×C4×D5C22×C411yescharacteristic
175C2×C4×D5C2×D411yescharacteristic
176C2×C4×D5#4111yescharacteristic
177C2×Dic10—21no—
178C2×Dic10C22×C411yescharacteristic
179C5×Q16—22no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8C22×C411yescharacteristic
184C2×C5×C8C22×C411yescharacteristic
185C2×C5×C8C2×D411yescharacteristic
186C2×C5×C8C2×D411yescharacteristic
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4C22×C411yescharacteristic
190C5×C4⋊C4C22×C411yescharacteristic
191C42×C5—21no—
192C42×C5—21no—
193C42×C5C2411yescharacteristic
194#689—22no—
195#688—22no—
196#685—21no—
197#685—21no—
198#685—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5C22×C411yescharacteristic
202C4⋊Dic5C22×C411yescharacteristic
203#683—21no—
204#683—21no—
205#683—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5C22×C411yescharacteristic
212C4×Dic5C2×D411yescharacteristic
213C4×Dic5#4111yescharacteristic
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168C22×C411yescharacteristic
218C2×#168C22×C411yescharacteristic
219C2×#168C2×D411yescharacteristic
220C2×#168C2×D411yescharacteristic
221#677—22no—
222#676—22no—
223#676—22no—
224#676—81no—
225#676—81no—
226C8×D5—42no—
227C8×D5—81no—
228C2×#137—51no—
229C4×#41—51no—
230C2×C4×Q8—51no—
231#446—51no—
232#446C2×D511yescharacteristic
233C8×Q8—51no—
234C8×Q8—51no—
235C8×Q8—51no—
236C8×Q8—101no—
237C8×Q8—101no—
238C8×Q8C2×D511yescharacteristic
239#441—51no—
240#441—51no—
241#440—51no—
242#440—51no—
243C4×Q16—51no—
244C4×Q16C2×D511yescharacteristic
245C4×SD16—51no—
246C4×SD16—51no—
247#436—51no—
248#436—51no—
249#435—101no—
250#435—101no—
251#432—101no—
252#431—51no—
253#431—51no—
254#431—101no—
255#431—101no—
256#428—51no—
257#423—101no—
258C2×C4⋊C8—51no—
259#419—51no—
260#417—51no—
261C4×M16—51no—
262C2×C4×C8—51no—
263#335—51no—
264#335—51no—
265#334—51no—
266#334C2×D511yescharacteristic
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269Q8⋊C8—51no—
270Q8⋊C8—51no—
271Q8⋊C8C2×D511yescharacteristic
272Q8⋊C8C2×D511yescharacteristic
273D4⋊C8—51no—
274D4⋊C8—51no—
275#322—51no—
276#322—51no—
277#322—51no—
278#322C2×D511yescharacteristic
279C22×D5—21no—
280C22×D5C4×D411yescharacteristic
281C5×Q8—21no—
282C5×Q8—21no—
283C5×Q8—21no—
284C5×Q8C2×M1612yes—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5C23×C411yescharacteristic
290C2×C4×C5C22×D411yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5C4×D411yescharacteristic
296C2×Dic5C4×D411yescharacteristic
297C2×Dic5C4×D411yescharacteristic
298D20—21no—
299D20—21no—
300D20—42no—
301C4×D5—24no—
302C4×D5—21no—
303C4×D5—21no—
304C4×D5—41no—
305C4×D5—41no—
306C4×D5—41no—
307C4×D5—42no—
308C4×D5—81no—
309C4×D5—81no—
310C4×D5C2×M1612yes—
311C4×D5#13112yes—
312Dic10—21no—
313Dic10—24no—
314Dic10C2×M1612yes—
315C5×C8—22no—
316C5×C8—21no—
317C5×C8—21no—
318C5×C8—21no—
319C5×C8—21no—
320C5×C8—41no—
321C5×C8—41no—
322#168—21no—
323#168—21no—
324#168—21no—
325#168—21no—
326#168—41no—
327#168—41no—
328#168—41no—
329C2×#41—51no—
330C22×Q8—51no—
331#137—104no—
332C2×Q16—51no—
333C2×Q16C4×D511yescharacteristic
334C2×SD16—51no—
335C2×SD16—51no—
336C2×M16—51no—
337C2×M16—51no—
338C2×M16—101no—
339C2×M16—101no—
340C22×C8—101no—
341C22×C8—101no—
342C4×Q8—51no—
343C4×Q8—51no—
344C4×Q8—51no—
345C4×Q8—51no—
346C4×Q8—101no—
347C4×Q8—101no—
348C4×Q8C22×D511yescharacteristic
349C4×Q8C22×D511yescharacteristic
350C4×D4—51no—
351C4×D4—51no—
352C4×D4—101no—
353C4×D4—101no—
354#117—51no—
355#117—101no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—101no—
358C2×C42—51no—
359C2×C42—101no—
360C2×C42—101no—
361#107—51no—
362#107C4×D511yescharacteristic
363#106—51no—
364#106—51no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—51no—
368C4⋊C8—51no—
369C4⋊C8—51no—
370C4⋊C8—51no—
371C4⋊C8—101no—
372C4⋊C8—101no—
373C4⋊C8—101no—
374C4⋊C8—101no—
375C4⋊C8—101no—
376C4⋊C8C22×D511yescharacteristic
377C4⋊C8C22×D511yescharacteristic
378#103—51no—
379#103—51no—
380#103—51no—
381#103—51no—
382#103C4×D511yescharacteristic
383#103C4×D511yescharacteristic
384#102—51no—
385#102—51no—
386C22⋊C8—51no—
387C22⋊C8—51no—
388C22⋊C8—101no—
389C22⋊C8—101no—
390C22⋊C8—101no—
391#97—21no—
392#97—51no—
393#97—51no—
394#97—101no—
395C4×C8—21no—
396C4×C8—51no—
397C4×C8—51no—
398C4×C8—51no—
399C4×C8—101no—
400C4×C8—101no—
401C4×C8—101no—
402C4×C8—101no—
403C4×C8—101no—
404C4×C8C22×D511yescharacteristic
405C4×C8C22×D511yescharacteristic
406C4×C8C22×D511yescharacteristic
407C22×C5C2×C4×D411yescharacteristic
408C2×D5—21no—
409C2×D5—21no—
410C2×D5—41no—
411C2×D5—41no—
412C2×D5—41no—
413C2×D5#43512yes—
414C4×C5—22no—
415C4×C5—21no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5C22×M1611yescharacteristic
420C4×C5C2×#13111yescharacteristic
421C4×C5#57711yescharacteristic
422C4×C5#57811yescharacteristic
423Dic5—22no—
424Dic5—21no—
425Dic5—21no—
426Dic5—41no—
427Dic5—41no—
428Dic5#43512yes—
429#41—102no—
430#41—102no—
431C2×Q8—54no—
432C2×Q8—51no—
433C2×Q8—101no—
434C2×Q8—102no—
435C2×Q8C2×C4×D511yescharacteristic
436C2×Q8C2×C4×D511yescharacteristic
437C2×D4—51no—
438C2×D4—101no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—101no—
447Q16—22no—
448Q16—102no—
449SD16—102no—
450SD16—102no—
451M16—102no—
452M16—102no—
453M16—401no—
454M16—401no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—51no—
459C2×C8—51no—
460C2×C8—51no—
461C2×C8—51no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—202no—
466C2×C8—401no—
467C2×C8C2×C4×D511yescharacteristic
468C2×C8C2×C4×D511yescharacteristic
469C2×C8D4×D511yescharacteristic
470C2×C8D4×D511yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—51no—
474C4⋊C4—51no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—101no—
480C4⋊C4C2×C4×D511yescharacteristic
481C4⋊C4C2×C4×D511yescharacteristic
482C22⋊C4—101no—
483C22⋊C4—101no—
484C22⋊C4—101no—
485C42—21no—
486C42—21no—
487C42—51no—
488C42—51no—
489C42—51no—
490C42—101no—
491C42—101no—
492C42—101no—
493C42—101no—
494C42—101no—
495C42C23×D511yescharacteristic
496C2×C5C2×#43511yescharacteristic
497C2×C5#294711yescharacteristic
498C2×C5#295611yescharacteristic
499D5—22no—
500D5—81no—
501C23—51no—
502C23—101no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—52no—
507Q8—104no—
508Q8—101no—
509Q8D5×M1612yes—
510D4—101no—
511D4—101no—
512D4—202no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—51no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—51no—
521C2×C4—51no—
522C2×C4—104no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—201no—
529C2×C4—202no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—401no—
533C2×C4—401no—
534C2×C4C22×C4×D511yescharacteristic
535C2×C4C2×D4×D511yescharacteristic
536C2×C4D5×#4111yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—101no—
545C8—101no—
546C8—101no—
547C8—101no—
548C8—201no—
549C8—201no—
550C8—201no—
551C5#1787411yescharacteristic, complemented, Sylow
552C22—52no—
553C22—101no—
554C22—101no—
555C22—201no—
556C22—201no—
557C22—201no—
558C22C4×D4×D511yescharacteristic
559C4—22no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—52no—
565C4—102no—
566C4—101no—
567C4—101no—
568C4—201no—
569C4—201no—
570C4C2×D5×M1611yescharacteristic
571C4D5×#13111yescharacteristic
572C4#6611211yescharacteristic
573C4#6611311yescharacteristic
574C2—102no—
575C2—401no—
576C2D5×#43511yescharacteristic
577C2#1061156111yescharacteristic
578C2#1061162011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1587C2
socleC22×C5C2×C4×D4
prime radicalC2×#713C2×C4
cosocleC42×C5C24
hypercenter#1587D5
hypocenterC5#17874
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
2. #10611651C2semidirect
4. C5×#1587C2semidirect
5. #10601749C2semidirect
6. #10601726C2semidirect
7. #10601696C2semidirect
8. #10599321C2semidirect
9. #10599313C2semidirect
11. D5×Q8⋊C8C2semidirect
12. #10599016C2semidirect
13. #10599015C2semidirect
14. #10598881C2semidirect
15. #10598862C2semidirect
152. #1587D5semidirect
166. Q8×D5M16semidirect
551. C5#17874semidirect

Maximal subgroups

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

subgroupindex
#106116752
#106116512
C4×#40642
C5×#15872
#106017492
#106017262
#106016962
#105993212
#105993132
#105990222
D5×Q8⋊C82
#105990162
#105990152
#105988812
#105988622
#178745