Finite Group Databasebeta

← #12069374

Subgroups — #12069374

Order 1280.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611678C211yesmaximal, characteristic
2#10611651C211yesmaximal, characteristic, complemented
3#10611454C211yesmaximal, characteristic
4C5×#1587C211yesmaximal, characteristic, complemented
5#10601749C211yesmaximal, characteristic, complemented
6#10601726C211yesmaximal, characteristic, complemented
7Q16×#168C211yesmaximal, characteristic, complemented
8#10599328C211yesmaximal, characteristic, complemented
9#10599309C211yesmaximal, characteristic, complemented
10#10599029C211yesmaximal, characteristic, complemented
11#10599026C211yesmaximal, characteristic
12#10599008C211yesmaximal, characteristic, complemented
13#10599007C211yesmaximal, characteristic, complemented
14#10598881C211yesmaximal, characteristic, complemented
15#10598867C211yesmaximal, characteristic, complemented
16#65914C2211yescharacteristic
17C4×Q8×D5C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic
20C4×C5×Q16C2211yescharacteristic
21#65475C411yescharacteristic
22#65474C411yescharacteristic
23C4×#689C2211yescharacteristic
24C4×#688C2211yescharacteristic
25Q8×#168C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27#65171C411yescharacteristic
28#65166C411yescharacteristic
29#65128—21no—
30#65127—21no—
31#65126C2211yescharacteristic
32#65123C2211yescharacteristic
33#65122—21no—
34#65122C2211yescharacteristic
35#65119—21no—
36#65119C2211yescharacteristic
37#65095C411yescharacteristic
38#65094C411yescharacteristic
39#65088C411yescharacteristic
40#65087C411yescharacteristic
41#64998—21no—
42#64995—21no—
43C4×#677C2211yescharacteristic
44#64977C2211yescharacteristic
45#64974—21no—
46#64974C2211yescharacteristic
47#64974C2211yescharacteristic
48#64974C2211yescharacteristic
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#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#17919—51nomaximal, Sylow
68C2×Q8×D5C2×C411yescharacteristic
69C2×C5×Q16C2×C411yescharacteristic
70C4×C5×Q8C2311yescharacteristic
71C4×C5×Q8C2311yescharacteristic
72#4093C2×C411yescharacteristic
73#4092C2×C411yescharacteristic
74Q8×Dic5C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77C2×#677C2×C411yescharacteristic
78C2×#676—21no—
79C2×#676—21no—
80C2×C8×D5—21no—
81#4044—21no—
82#4041C2×C411yescharacteristic
83#4040—21no—
84D5×C4⋊C4—21no—
85D5×C4⋊C4C2×C411yescharacteristic
86#4036C2×C411yescharacteristic
87#4033—21no—
88#4033C2×C411yescharacteristic
89C4×D20—21no—
90C4×D20C2311yescharacteristic
91#4018—21no—
92C42×D5—21no—
93C42×D5C2311yescharacteristic
94C4×Dic10—21no—
95C4×Dic10C2311yescharacteristic
96C5×#107C2×C411yescharacteristic
97C5×C4⋊C8—21no—
98C5×C4⋊C8—21no—
99C5×C4⋊C8C2311yescharacteristic
100C5×C4⋊C8C2311yescharacteristic
101C5×#103C2×C411yescharacteristic
102C5×#103C2×C411yescharacteristic
103C5×#97—21no—
104C4×C5×C8—21no—
105C4×C5×C8C2311yescharacteristic
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2311yescharacteristic
108#3967C2×C411yescharacteristic
109#3967C2×C411yescharacteristic
110#3953C2×C411yescharacteristic
111#3952—21no—
112#3952—21no—
113#3952—21no—
114#3952—21no—
115#3952C2×C411yescharacteristic
116#3952C2×C411yescharacteristic
117#3952D411yescharacteristic
118#3952D411yescharacteristic
119#3949C2×C411yescharacteristic
120#3948C2×C411yescharacteristic
121#3946—21no—
122#3946—21no—
123#3946—21no—
124#3946—21no—
125#3946C2×C411yescharacteristic
126#3946C2×C411yescharacteristic
127#3946D411yescharacteristic
128#3946D411yescharacteristic
129C8×Dic5—21no—
130C8×Dic5—21no—
131C8×Dic5—21no—
132#3942C2×C411yescharacteristic
133#3941C2×C411yescharacteristic
134#3940C2×C411yescharacteristic
135#3939C2×C411yescharacteristic
136C4⋊#168—21no—
137C4⋊#168—21no—
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140C4×#168—21no—
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3108—51no—
146#2993—51no—
147#2982—51no—
148#1588—51no—
149#1587D511yescharacteristic, complemented
150#1584—51no—
151#1583—51no—
152#1579—51no—
153SD16⋊C8—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1574—51no—
157#1487—51no—
158#1482—51no—
159#1454—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×Q8C22×C411yescharacteristic
162Q8×D5—22no—
163Q8×D5—22no—
164C2×D20—21no—
165C2×D20C22×C411yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5C22×C411yescharacteristic
170C2×C4×D5C2×D411yescharacteristic
171C2×C4×D5#4111yescharacteristic
172C2×Dic10—21no—
173C2×Dic10C22×C411yescharacteristic
174C5×Q16—22no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C2×D411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C4⋊C4C22×C411yescharacteristic
186C42×C5—21no—
187C42×C5—21no—
188C42×C5C2411yescharacteristic
189#689—22no—
190#688—22no—
191#685—21no—
192#685—21no—
193#685—21no—
194#685—21no—
195#685—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5C22×C411yescharacteristic
199C4⋊Dic5C22×C411yescharacteristic
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×Dic5C22×C411yescharacteristic
209C4×Dic5C2×D411yescharacteristic
210C4×Dic5#4111yescharacteristic
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168C22×C411yescharacteristic
215C2×#168C22×C411yescharacteristic
216C2×#168C2×D411yescharacteristic
217C2×#168C2×D411yescharacteristic
218#677—22no—
219#676—81no—
220#676—81no—
221C8×D5—81no—
222#529—51no—
223C2×C4×Q8—51no—
224#483—51no—
225#480—51no—
226#479—51no—
227#479—51no—
228#464—51no—
229#464—51no—
230#451—51no—
231#448—51no—
232#446C2×D511yescharacteristic
233C8×Q8—51no—
234C8×Q8—51no—
235C8×Q8—51no—
236C8×Q8—51no—
237C8×Q8—101no—
238C8×Q8—101no—
239C8×Q8C2×D511yescharacteristic
240C4×Q16—51no—
241C4×Q16C2×D511yescharacteristic
242C4×SD16—51no—
243C4×SD16—51no—
244#436—51no—
245#436—101no—
246#435—101no—
247C8×D4—51no—
248#433—101no—
249#431—51no—
250#431—51no—
251#431—51no—
252#431—51no—
253#431—101no—
254#431—101no—
255#424—101no—
256#423—51no—
257#335—51no—
258#335—51no—
259#334—51no—
260#334C2×D511yescharacteristic
261Q8⋊C8—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8C2×D511yescharacteristic
266Q8⋊C8C2×D511yescharacteristic
267D4⋊C8—51no—
268D4⋊C8—51no—
269#322—51no—
270#322—51no—
271#322C2×D511yescharacteristic
272C82—51no—
273C22×D5—21no—
274C22×D5C4×D411yescharacteristic
275C5×Q8—21no—
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8#13112yes—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5C23×C411yescharacteristic
284C2×C4×C5C22×D411yescharacteristic
285C2×C4×C5C2×#4111yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5C4×D411yescharacteristic
290C2×Dic5C4×D411yescharacteristic
291C2×Dic5C4×D411yescharacteristic
292D20—21no—
293D20—21no—
294D20—81no—
295C4×D5—24no—
296C4×D5—21no—
297C4×D5—21no—
298C4×D5—21no—
299C4×D5—21no—
300C4×D5—41no—
301C4×D5—41no—
302C4×D5—41no—
303C4×D5—81no—
304Dic10—24no—
305Dic10—21no—
306Dic10#13112yes—
307C5×C8—21no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314#168—21no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—41no—
319#168—41no—
320#168—41no—
321C22×Q8—51no—
322C2×Q16—51no—
323C2×Q16C4×D511yescharacteristic
324C2×SD16—51no—
325C2×SD16—51no—
326C2×M16—101no—
327C2×M16—101no—
328C22×C8—101no—
329#126—101no—
330#125—51no—
331#124—51no—
332#123—101no—
333C22⋊Q8—51no—
334#121—51no—
335C4×Q8—51no—
336C4×Q8—51no—
337C4×Q8—51no—
338C4×Q8—101no—
339C4×Q8—101no—
340C4×Q8C22×D511yescharacteristic
341C4×Q8C22×D511yescharacteristic
342C4×D4—51no—
343C4×D4—101no—
344#117—101no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—101no—
347C2×C42—51no—
348C2×C42—101no—
349#107—51no—
350#107C4×D511yescharacteristic
351#106—51no—
352#106—51no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—51no—
356C4⋊C8—51no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8C22×D511yescharacteristic
368C4⋊C8C22×D511yescharacteristic
369#103—51no—
370#103—51no—
371#103—51no—
372#103—51no—
373#103C4×D511yescharacteristic
374#103C4×D511yescharacteristic
375#102—51no—
376#102—51no—
377C22⋊C8—51no—
378C22⋊C8—51no—
379C22⋊C8—51no—
380C22⋊C8—51no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—21no—
386C4×C8—21no—
387C4×C8—51no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—101no—
391C4×C8—101no—
392C4×C8—101no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8C22×D511yescharacteristic
396C4×C8C22×D511yescharacteristic
397C4×C8C22×D511yescharacteristic
398C22×C5C2×C4×D411yescharacteristic
399C2×D5—21no—
400C2×D5—21no—
401C2×D5—21no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—41no—
405C4×C5—22no—
406C4×C5—21no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5C2×#13111yescharacteristic
411C4×C5C2×#13111yescharacteristic
412C4×C5#57711yescharacteristic
413C4×C5#57811yescharacteristic
414Dic5—21no—
415Dic5—22no—
416Dic5—21no—
417Dic5—21no—
418Dic5—41no—
419Dic5—41no—
420C2×Q8—51no—
421C2×Q8—101no—
422C2×Q8—102no—
423C2×Q8—102no—
424C2×Q8C2×C4×D511yescharacteristic
425C2×Q8C2×C4×D511yescharacteristic
426C2×D4—51no—
427C2×D4—101no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4—101no—
434Q16—22no—
435Q16—102no—
436SD16—102no—
437SD16—102no—
438M16—401no—
439M16—401no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—51no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—401no—
451C2×C8C2×C4×D511yescharacteristic
452C2×C8C2×C4×D511yescharacteristic
453C2×C8D4×D511yescharacteristic
454C2×C8D4×D511yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—51no—
458C4⋊C4—51no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4C2×C4×D511yescharacteristic
467C4⋊C4C2×C4×D511yescharacteristic
468C22⋊C4—101no—
469C22⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C22⋊C4—101no—
473C42—21no—
474C42—21no—
475C42—51no—
476C42—51no—
477C42—51no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42C23×D511yescharacteristic
482C2×C5#292911yescharacteristic
483C2×C5#294711yescharacteristic
484C2×C5#295711yescharacteristic
485D5—41no—
486D5—81no—
487C23—51no—
488C23—101no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—52no—
493Q8—104no—
494Q8—101no—
495Q8#405312yes—
496D4—101no—
497D4—101no—
498D4—401no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—51no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—104no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—201no—
515C2×C4—201no—
516C2×C4—201no—
517C2×C4—401no—
518C2×C4C22×C4×D511yescharacteristic
519C2×C4C2×D4×D511yescharacteristic
520C2×C4D5×#4111yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—101no—
529C8—101no—
530C8—101no—
531C8—101no—
532C8—201no—
533C8—201no—
534C8—201no—
535C5#1791911yescharacteristic, complemented, Sylow
536C22—101no—
537C22—101no—
538C22—101no—
539C22—201no—
540C22—201no—
541C22—201no—
542C22C4×D4×D511yescharacteristic
543C4—22no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—101no—
549C4—102no—
550C4—101no—
551C4—101no—
552C4—201no—
553C4—201no—
554C4C2×#405311yescharacteristic
555C4D5×#13111yescharacteristic
556C4#6611211yescharacteristic
557C4#6611311yescharacteristic
558C2—201no—
559C2—401no—
560C2#1061120911yescharacteristic
561C2#1061156111yescharacteristic
562C2#1061162111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1587C2
socleC22×C5C2×C4×D4
prime radical#4041C2×C4
cosocleC42×C5C24
hypercenter#1587D5
hypocenterC5#17919
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. Q16×#168C2semidirect
8. #10599328C2semidirect
9. #10599309C2semidirect
10. #10599029C2semidirect
12. #10599008C2semidirect
13. #10599007C2semidirect
14. #10598881C2semidirect
15. #10598867C2semidirect
149. #1587D5semidirect
535. C5#17919semidirect

Maximal subgroups

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

subgroupindex
#106116782
#106116512
#106114542
C5×#15872
#106017492
#106017262
Q16×#1682
#105993282
#105993092
#105990292
#105990262
#105990082
#105990072
#105988812
#105988672
#179195