Finite Group Databasebeta

← #12070298

Subgroups — #12070298

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611691C211yesmaximal, characteristic
2Q8×#676C211yesmaximal, characteristic
3#10611453C211yesmaximal, characteristic
4C5×#1587C211yesmaximal, characteristic, complemented
5#10601745C211yesmaximal, characteristic, complemented
6#10601725C211yesmaximal, characteristic, complemented
7#10601695C211yesmaximal, characteristic, complemented
8#10599325C211yesmaximal, characteristic
9#10599317C211yesmaximal, characteristic, complemented
10#10599033C211yesmaximal, characteristic
11D5×Q8⋊C8C211yesmaximal, characteristic
12#10599014C211yesmaximal, characteristic, complemented
13#10599014C211yesmaximal, characteristic, complemented
14#10598880C211yesmaximal, characteristic, complemented
15#10598862C211yesmaximal, characteristic
16#65912C2211yescharacteristic
17C4×Q8×D5C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic
20C4×C5×Q16C2211yescharacteristic
21#65475C411yescharacteristic
22#65471C411yescharacteristic
23C4×#689C2211yescharacteristic
24C4×#689C2211yescharacteristic
25Q8×#168C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27#65173C411yescharacteristic
28#65164C411yescharacteristic
29#65128—21no—
30#65126—21no—
31#65126C2211yescharacteristic
32D5×C4⋊C8C2211yescharacteristic
33#65120—21no—
34#65120—21no—
35#65120C2211yescharacteristic
36#65120C2211yescharacteristic
37#65098C411yescharacteristic
38#65097C411yescharacteristic
39#65083C411yescharacteristic
40#65082C411yescharacteristic
41#64997—21no—
42#64990—21no—
43C4×Dic20C2211yescharacteristic
44C4×#676—21no—
45C4×#676C2211yescharacteristic
46#64974C2211yescharacteristic
47C4×C8×D5C2211yescharacteristic
48#64968—21no—
49#64968C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51C5×#334C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64700C2211yescharacteristic
60#64700C2211yescharacteristic
61#64677C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64675C2211yescharacteristic
66#64674C2211yescharacteristic
67#18003—51nomaximal, Sylow
68C2×Q8×D5C2×C411yescharacteristic
69C2×C5×Q16C2×C411yescharacteristic
70C4×C5×Q8C2311yescharacteristic
71C4×C5×Q8C2311yescharacteristic
72#4092C2×C411yescharacteristic
73Q8×Dic5C2×C411yescharacteristic
74#4090C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76C2×#689C2×C411yescharacteristic
77C2×Dic20C2×C411yescharacteristic
78C2×#676—21no—
79C2×#676D411yescharacteristic
80C2×#676D411yescharacteristic
81C2×C8×D5—21no—
82C2×C8×D5—21no—
83#4043C2×C411yescharacteristic
84#4042—21no—
85D5×C4⋊C4—21no—
86D5×C4⋊C4C2×C411yescharacteristic
87#4035—21no—
88#4034C2×C411yescharacteristic
89#4033—21no—
90#4033C2×C411yescharacteristic
91#4018—21no—
92C42×D5—21no—
93C42×D5C2311yescharacteristic
94C4×Dic10—21no—
95C4×Dic10—21no—
96C4×Dic10C2311yescharacteristic
97C4×Dic10C2311yescharacteristic
98C5×#107C2×C411yescharacteristic
99C5×C4⋊C8—21no—
100C5×C4⋊C8—21no—
101C5×C4⋊C8C2311yescharacteristic
102C5×C4⋊C8C2311yescharacteristic
103C5×#103C2×C411yescharacteristic
104C5×#103C2×C411yescharacteristic
105C5×#97—21no—
106C4×C5×C8—21no—
107C4×C5×C8C2311yescharacteristic
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110#3967C2×C411yescharacteristic
111#3967C2×C411yescharacteristic
112#3952C2×C411yescharacteristic
113#3952C2×C411yescharacteristic
114#3950C2×C411yescharacteristic
115#3948C2×C411yescharacteristic
116#3948C2×C411yescharacteristic
117#3947—21no—
118#3947—21no—
119#3947—21no—
120#3947D411yescharacteristic
121#3947D411yescharacteristic
122#3946—21no—
123#3946—21no—
124#3946—21no—
125#3946—21no—
126#3946—21no—
127#3946—21no—
128#3946C2×C411yescharacteristic
129#3946C2×C411yescharacteristic
130C8×Dic5—21no—
131C8×Dic5—21no—
132#3942C2×C411yescharacteristic
133#3942C2×C411yescharacteristic
134#3939C2×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#3104—51no—
146Q8×M16—51no—
147#2962—51no—
148#1593—51no—
149#1593—51no—
150#1587—51no—
151#1587—51no—
152#1587—51no—
153#1587D511yescharacteristic, complemented
154#1579—51no—
155#1579—51no—
156#1570—51no—
157#1493—51no—
158C2×Q8⋊C8—51no—
159#1451—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×Q8C22×C411yescharacteristic
162Q8×D5—22no—
163Q8×D5—41no—
164C2×C4×D5—21no—
165C2×C4×D5—21no—
166C2×C4×D5C22×C411yescharacteristic
167C2×C4×D5C2×D411yescharacteristic
168C2×C4×D5#4111yescharacteristic
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10C22×C411yescharacteristic
172C2×Dic10C22×C411yescharacteristic
173C5×Q16—22no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8C22×C411yescharacteristic
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C2×D411yescharacteristic
180C2×C5×C8C2×D411yescharacteristic
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4C22×C411yescharacteristic
184C5×C4⋊C4C22×C411yescharacteristic
185C42×C5—21no—
186C42×C5—21no—
187C42×C5C2411yescharacteristic
188#689—22no—
189#689—41no—
190#685—21no—
191#685—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5C22×C411yescharacteristic
195C4⋊Dic5C22×C411yescharacteristic
196#683—21no—
197#683—21no—
198#683—21no—
199#683—21no—
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204C4×Dic5—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
218Dic20—41no—
219#676—22no—
220#676—22no—
221#676—42no—
222C8×D5—42no—
223C8×D5—42no—
224#533—51no—
225C2×C4×Q8—51no—
226#484—51no—
227#484—51no—
228#477—51no—
229#477—51no—
230#462—51no—
231#462—51no—
232#451—51no—
233#451—51no—
234#446—51no—
235#446—51no—
236#446—51no—
237#446—101no—
238#446—101no—
239#446—101no—
240#446—101no—
241#446C2×D511yescharacteristic
242C8×Q8—51no—
243C8×Q8—51no—
244C8×Q8—51no—
245C8×Q8C2×D511yescharacteristic
246C4×Q16—51no—
247C4×Q16—51no—
248C4×Q16—51no—
249C4×Q16C2×D511yescharacteristic
250#431—51no—
251#424—101no—
252#423—51no—
253#423—101no—
254C2×C4⋊C8—51no—
255#405—101no—
256C4×M16—51no—
257C4×M16—101no—
258C2×C4×C8—51no—
259#334—51no—
260#334—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×Q8#13112yes—
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—21no—
295C4×D5—21no—
296C4×D5—41no—
297C4×D5—42no—
298C4×D5—81no—
299C4×D5#13712yes—
300C4×D5#13712yes—
301Dic10—21no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10—42no—
306Dic10—81no—
307C5×C8—22no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
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×Q16—51no—
324C2×Q16—51no—
325C2×Q16C4×D511yescharacteristic
326C2×M16—51no—
327C2×M16—51no—
328C2×M16—101no—
329C22×C8—101no—
330C22×C8—101no—
331C4⋊Q8—51no—
332C4⋊Q8—51no—
333#125—101no—
334C22⋊Q8—51no—
335C22⋊Q8—51no—
336C22⋊Q8—101no—
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—101no—
342C4×Q8—101no—
343C4×Q8—101no—
344C4×Q8C22×D511yescharacteristic
345C4×Q8C22×D511yescharacteristic
346#117—101no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—101no—
349C2×C42—51no—
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⋊C8—101no—
369C4⋊C8C22×D511yescharacteristic
370C4⋊C8C22×D511yescharacteristic
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#103—51no—
377#103C4×D511yescharacteristic
378#103C4×D511yescharacteristic
379C22⋊C8—51no—
380C22⋊C8—51no—
381#97—21no—
382#97—51no—
383#97—51no—
384#97—101no—
385#97—101no—
386#97—101no—
387C4×C8—21no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—51no—
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#44112yes—
402C4×C5—22no—
403C4×C5—21no—
404C4×C5—41no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5C2×#13111yescharacteristic
408C4×C5#56811yescharacteristic
409C4×C5C2×#13711yescharacteristic
410C4×C5C2×#13711yescharacteristic
411Dic5—21no—
412Dic5—21no—
413Dic5—41no—
414Dic5—41no—
415Dic5—41no—
416Dic5—41no—
417Dic5#44112yes—
418C2×Q8—51no—
419C2×Q8—51no—
420C2×Q8—101no—
421C2×Q8—101no—
422C2×Q8—102no—
423C2×Q8—201no—
424C2×Q8C2×C4×D511yescharacteristic
425C2×Q8C2×C4×D511yescharacteristic
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—101no—
430C22×C4—101no—
431Q16—22no—
432Q16—102no—
433Q16—201no—
434Q16—201no—
435M16—102no—
436M16—102no—
437M16—202no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—51no—
442C2×C8—51no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—202no—
449C2×C8—202no—
450C2×C8C2×C4×D511yescharacteristic
451C2×C8C2×C4×D511yescharacteristic
452C2×C8D4×D511yescharacteristic
453C2×C8D4×D511yescharacteristic
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—51no—
457C4⋊C4—51no—
458C4⋊C4—101no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4C2×C4×D511yescharacteristic
469C4⋊C4C2×C4×D511yescharacteristic
470C22⋊C4—101no—
471C22⋊C4—101no—
472C42—21no—
473C42—21no—
474C42—51no—
475C42—51no—
476C42—51no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42C23×D511yescharacteristic
482C2×C5#293311yescharacteristic
483C2×C5C2×#44111yescharacteristic
484C2×C5#295611yescharacteristic
485D5—22no—
486C23—51no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—101no—
491Q8—101no—
492Q8—101no—
493Q8—101no—
494Q8—202no—
495Q8—401no—
496Q8#405312yes—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—51no—
502C2×C4—52no—
503C2×C4—52no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—201no—
513C2×C4—202no—
514C2×C4—401no—
515C2×C4C22×C4×D511yescharacteristic
516C2×C4C2×D4×D511yescharacteristic
517C2×C4D5×#4111yescharacteristic
518C8—22no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—101no—
526C8—101no—
527C8—101no—
528C8—101no—
529C8—201no—
530C8—201no—
531C8—201no—
532C5#1800311yescharacteristic, complemented, Sylow
533C22—52no—
534C22—101no—
535C22—101no—
536C22C4×D4×D511yescharacteristic
537C4—22no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—52no—
543C4—101no—
544C4—101no—
545C4—201no—
546C4—201no—
547C4—201no—
548C4—201no—
549C4C2×#405311yescharacteristic
550C4#6608411yescharacteristic
551C4D5×#13711yescharacteristic
552C4D5×#13711yescharacteristic
553C2—102no—
554C2#1061121211yescharacteristic
555C2D5×#44111yescharacteristic
556C2#1061162011yescharacteristic
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#18003
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. #10601745C2semidirect
6. #10601725C2semidirect
7. #10601695C2semidirect
9. #10599317C2semidirect
12. #10599014C2semidirect
13. #10599014C2semidirect
14. #10598880C2semidirect
153. #1587D5semidirect
532. C5#18003semidirect

Maximal subgroups

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

subgroupindex
#106116912
Q8×#6762
#106114532
C5×#15872
#106017452
#106017252
#106016952
#105993252
#105993172
#105990332
D5×Q8⋊C82
#105990142
#105988802
#105988622
#180035