Finite Group Databasebeta

← #12068995

Subgroups — #12068995

Order 1280.

626 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611694C211yesmaximal, characteristic
2#10611651C211yesmaximal, characteristic
3C4×D5×Q16C211yesmaximal, characteristic
4C5×#1587C211yesmaximal, characteristic, complemented
5#10601749C211yesmaximal, characteristic, complemented
6#10601727C211yesmaximal, characteristic, complemented
7#10601697C211yesmaximal, characteristic, complemented
8#10599320C211yesmaximal, characteristic
9#10599315C211yesmaximal, characteristic, complemented
10#10599024C211yesmaximal, characteristic
11#10599024C211yesmaximal, characteristic
12#10599012C211yesmaximal, characteristic, complemented
13#10599011C211yesmaximal, characteristic, complemented
14#10598880C211yesmaximal, characteristic, complemented
15#10598864C211yesmaximal, characteristic
16C2×D5×Q16C411yescharacteristic
17C4×Q8×D5C2211yescharacteristic
18C4×Q8×D5C2211yescharacteristic
19C5×#446C2211yescharacteristic
20C5×C8×Q8C2211yescharacteristic
21C4×C5×Q16C2211yescharacteristic
22Q16×Dic5C411yescharacteristic
23C4×#689C2211yescharacteristic
24C4×#689C2211yescharacteristic
25#65313C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27D5×#107C411yescharacteristic
28#65162C411yescharacteristic
29#65124—21no—
30#65122—21no—
31#65122C2211yescharacteristic
32#65122C2211yescharacteristic
33#65120C2211yescharacteristic
34#65119—21no—
35#65119C2211yescharacteristic
36#65117—21no—
37D5×#103C411yescharacteristic
38D5×#103C411yescharacteristic
39#65079C411yescharacteristic
40#65079C411yescharacteristic
41#64994—21no—
42#64990—21no—
43C4×Dic20C2211yescharacteristic
44#64974—21no—
45#64974C2211yescharacteristic
46#64974C2211yescharacteristic
47C4×C8×D5C2211yescharacteristic
48#64968C2211yescharacteristic
49C8×Dic10—21no—
50C8×Dic10C2211yescharacteristic
51C5×#334C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64699C2211yescharacteristic
60#64699C2211yescharacteristic
61#64677C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64674C2211yescharacteristic
66#64674C2211yescharacteristic
67#17880—51nomaximal, Sylow
68C2×Q8×D5C2×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×#689C2×C411yescharacteristic
77D5×Q16—24no—
78C2×Dic20C2×C411yescharacteristic
79C2×C8×D5C2×C411yescharacteristic
80C2×C8×D5C2×C411yescharacteristic
81D5×C4⋊C4—21no—
82D5×C4⋊C4—21no—
83D5×C4⋊C4C2×C411yescharacteristic
84D5×C4⋊C4C2×C411yescharacteristic
85#4033—21no—
86#4033—21no—
87#4033C2×C411yescharacteristic
88#4033C2×C411yescharacteristic
89C42×D5—21no—
90C42×D5—21no—
91C42×D5C2311yescharacteristic
92C4×Dic10—21no—
93C4×Dic10—21no—
94C4×Dic10C2311yescharacteristic
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#3952—21no—
111#3952—21no—
112#3952—21no—
113#3952D411yescharacteristic
114#3952D411yescharacteristic
115#3950C2×C411yescharacteristic
116#3948C2×C411yescharacteristic
117#3948C2×C411yescharacteristic
118#3947—21no—
119#3947—21no—
120#3946—21no—
121#3946—21no—
122#3946—21no—
123#3946—21no—
124#3946—21no—
125#3946D411yescharacteristic
126#3946D411yescharacteristic
127C8×Dic5—21no—
128C8×Dic5—21no—
129C8×Dic5—21no—
130C8×Dic5—21no—
131C8×Dic5C2×C411yescharacteristic
132C8×Dic5C2×C411yescharacteristic
133#3942C2×C411yescharacteristic
134#3942C2×C411yescharacteristic
135#3939C2×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#2983—51no—
147#2982—51no—
148C2×C4×Q16—51no—
149#1587—51no—
150#1587—51no—
151#1587—51no—
152#1587D511yescharacteristic, complemented
153#1584—51no—
154#1584—51no—
155#1584—51no—
156#1584—51no—
157#1564—51no—
158#1479—51no—
159#1479—51no—
160#1452—51no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×Q8C22×C411yescharacteristic
163Q8×D5—22no—
164Q8×D5—22no—
165Q8×D5—22no—
166Q8×D5M1614yes—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5C22×C411yescharacteristic
172C2×C4×D5C2×D411yescharacteristic
173C2×C4×D5#4111yescharacteristic
174C2×Dic10—21no—
175C2×Dic10—21no—
176C2×Dic10C22×C411yescharacteristic
177C2×Dic10C22×C411yescharacteristic
178C5×Q16—22no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8C22×C411yescharacteristic
183C2×C5×C8C22×C411yescharacteristic
184C2×C5×C8C2×D411yescharacteristic
185C2×C5×C8C2×D411yescharacteristic
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4C22×C411yescharacteristic
189C5×C4⋊C4C22×C411yescharacteristic
190C42×C5—21no—
191C42×C5—21no—
192C42×C5C2411yescharacteristic
193#689—22no—
194#689—22no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5C22×C411yescharacteristic
198C4⋊Dic5C22×C411yescharacteristic
199#683—21no—
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×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
221Dic20—22no—
222C8×D5—22no—
223C8×D5—22no—
224C22×Q16—51no—
225C2×C4×Q8—51no—
226C2×C4×Q8—51no—
227#446—51no—
228#446—51no—
229#446—51no—
230#446—101no—
231#446—101no—
232#446C2×D511yescharacteristic
233C8×Q8—51no—
234C8×Q8—51no—
235C8×Q8—51no—
236C8×Q8—101no—
237C8×Q8—101no—
238C8×Q8C2×D511yescharacteristic
239C4×Q16—51no—
240C4×Q16—51no—
241C4×Q16—51no—
242C4×Q16—51no—
243C4×Q16—51no—
244C4×Q16—51no—
245C4×Q16—51no—
246C4×Q16C2×D511yescharacteristic
247#432—101no—
248#432—101no—
249#431—51no—
250#431—51no—
251#431—51no—
252#431—51no—
253#431—101no—
254#431—101no—
255C2×#107—51no—
256C2×#103—51no—
257C2×#103—51no—
258C2×C4×C8—51no—
259#335—51no—
260#335—51no—
261#334—51no—
262#334C2×D511yescharacteristic
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269Q8⋊C8C2×D511yescharacteristic
270Q8⋊C8C2×D511yescharacteristic
271#322—51no—
272#322—51no—
273#322—51no—
274#322C2×D511yescharacteristic
275C22×D5C4×D411yescharacteristic
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8C2×M1612yes—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5C23×C411yescharacteristic
285C2×C4×C5C22×D411yescharacteristic
286C2×C4×C5C2×#4111yescharacteristic
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5C4×D411yescharacteristic
292C2×Dic5C4×D411yescharacteristic
293C2×Dic5C4×D411yescharacteristic
294C4×D5—24no—
295C4×D5—21no—
296C4×D5—21no—
297C4×D5—41no—
298C4×D5—42no—
299C4×D5—81no—
300C4×D5—81no—
301C4×D5C2×M1612yes—
302C4×D5#13112yes—
303Dic10—21no—
304Dic10—24no—
305Dic10—21no—
306Dic10—21no—
307Dic10—42no—
308Dic10C2×M1612yes—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8—41no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—41no—
321#168—41no—
322#168—41no—
323C22×Q8—51no—
324C22×Q8—51no—
325C2×Q16—51no—
326C2×Q16—51no—
327C2×Q16—51no—
328C2×Q16—104no—
329C2×Q16C4×D511yescharacteristic
330C22×C8—51no—
331C22×C8—51no—
332C4×Q8—51no—
333C4×Q8—51no—
334C4×Q8—51no—
335C4×Q8—51no—
336C4×Q8—51no—
337C4×Q8—51no—
338C4×Q8—101no—
339C4×Q8—101no—
340C4×Q8—101no—
341C4×Q8—101no—
342C4×Q8C22×D511yescharacteristic
343C4×Q8C22×D511yescharacteristic
344C2×C4⋊C4—51no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C42—51no—
349C2×C42—101no—
350C2×C42—101no—
351#107—51no—
352#107—51no—
353#107—51no—
354#107C4×D511yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
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⋊C8—101no—
368C4⋊C8C22×D511yescharacteristic
369C4⋊C8C22×D511yescharacteristic
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#103C4×D511yescharacteristic
377#103C4×D511yescharacteristic
378C22⋊C8—51no—
379C22⋊C8—51no—
380C22⋊C8—101no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383#97—21no—
384#97—101no—
385#97—101no—
386#97—101no—
387C4×C8—21no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C4×C8—101no—
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C4×C8C22×D511yescharacteristic
401C22×C5C2×C4×D411yescharacteristic
402C2×D5—21no—
403C2×D5—21no—
404C2×D5#43512yes—
405C4×C5—22no—
406C4×C5—21no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5C22×M1611yescharacteristic
411C4×C5C2×#13111yescharacteristic
412C4×C5#57811yescharacteristic
413C4×C5#57811yescharacteristic
414Dic5—22no—
415Dic5—21no—
416Dic5—21no—
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420Dic5#43512yes—
421C2×Q8—54no—
422C2×Q8—51no—
423C2×Q8—51no—
424C2×Q8—101no—
425C2×Q8—101no—
426C2×Q8—102no—
427C2×Q8—102no—
428C2×Q8—102no—
429C2×Q8C2×C4×D511yescharacteristic
430C2×Q8C2×C4×D511yescharacteristic
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438Q16—22no—
439Q16—102no—
440Q16—102no—
441Q16—102no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—51no—
446C2×C8—51no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—102no—
450C2×C8—102no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8C2×C4×D511yescharacteristic
455C2×C8C2×C4×D511yescharacteristic
456C2×C8D4×D511yescharacteristic
457C2×C8D4×D511yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—51no—
461C4⋊C4—51no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4C2×C4×D511yescharacteristic
471C4⋊C4C2×C4×D511yescharacteristic
472C42—21no—
473C42—21no—
474C42—51no—
475C42—51no—
476C42—51no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42—101no—
482C42—101no—
483C42C23×D511yescharacteristic
484C2×C5C2×#43511yescharacteristic
485C2×C5#295011yescharacteristic
486C2×C5#295711yescharacteristic
487D5—22no—
488C23—51no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—52no—
493Q8—104no—
494Q8—101no—
495Q8—101no—
496Q8—101no—
497Q8—202no—
498Q8D5×M1612yes—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—51no—
504C2×C4—52no—
505C2×C4—52no—
506C2×C4—51no—
507C2×C4—51no—
508C2×C4—104no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—201no—
516C2×C4—202no—
517C2×C4—401no—
518C2×C4—401no—
519C2×C4C22×C4×D511yescharacteristic
520C2×C4C2×D4×D511yescharacteristic
521C2×C4D5×#4111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—101no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—201no—
534C8—201no—
535C8—201no—
536C5#1788011yescharacteristic, complemented, Sylow
537C22—52no—
538C22—101no—
539C22—101no—
540C22C4×D4×D511yescharacteristic
541C4—22no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—52no—
547C4—102no—
548C4—101no—
549C4—101no—
550C4—201no—
551C4—201no—
552C4—201no—
553C4C2×D5×M1611yescharacteristic
554C4D5×#13111yescharacteristic
555C4#6611311yescharacteristic
556C4#6611311yescharacteristic
557C2—102no—
558C2D5×#43511yescharacteristic
559C2#1061156211yescharacteristic
560C2#1061162111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1587C2
socleC22×C5C2×C4×D4
prime radicalC22×D5C4×D4
cosocleC42×C5C24
hypercenter#1587D5
hypocenterC5#17880
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
4. C5×#1587C2semidirect
5. #10601749C2semidirect
6. #10601727C2semidirect
7. #10601697C2semidirect
9. #10599315C2semidirect
12. #10599012C2semidirect
13. #10599011C2semidirect
14. #10598880C2semidirect
152. #1587D5semidirect
536. C5#17880semidirect

Maximal subgroups

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

subgroupindex
#106116942
#106116512
C4×D5×Q162
C5×#15872
#106017492
#106017272
#106016972
#105993202
#105993152
#105990242
#105990122
#105990112
#105988802
#105988642
#178805