Finite Group Databasebeta

← #12070495

Subgroups — #12070495

Order 1280.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3108C211yesmaximal, characteristic
2#10614863C211yesmaximal, characteristic
3#10614168C211yesmaximal, characteristic, complemented
4#10602545C211yesmaximal, characteristic
5C2×Q8⋊#168C211yesmaximal, characteristic, complemented
6#10601698C211yesmaximal, characteristic, complemented
7#10601697C211yesmaximal, characteristic, complemented
8#10601697C211yesmaximal, characteristic, complemented
9Q16×#168C211yesmaximal, characteristic, complemented
10#10601692C211yesmaximal, characteristic, complemented
11#10601691C211yesmaximal, characteristic, complemented
12#10601690C211yesmaximal, characteristic, complemented
13SD16×#168C211yesmaximal, characteristic, complemented
14#10601545C211yesmaximal, characteristic, complemented
15#10601533C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C5×#483C411yescharacteristic
19C5×#480C411yescharacteristic
20C5×#479C411yescharacteristic
21C5×#479C411yescharacteristic
22C5×#464C411yescharacteristic
23C5×#464C411yescharacteristic
24C5×#451C411yescharacteristic
25C5×#448C411yescharacteristic
26C4×C5×Q16C2211yescharacteristic
27C4×C5×Q16C2211yescharacteristic
28C4×C5×SD16C2211yescharacteristic
29C4×C5×SD16C2211yescharacteristic
30C5×#431C2211yescharacteristic
31#65313—21no—
32#65313—21no—
33#65313C2211yescharacteristic
34#65313C2211yescharacteristic
35#65313C2211yescharacteristic
36Q8×#168C2211yescharacteristic
37Q8×#168C2211yescharacteristic
38Q8×#168C2211yescharacteristic
39#65301C2211yescharacteristic
40#65300—21no—
41D4×#168—21no—
42D4×#168C2211yescharacteristic
43#65289—21no—
44#65288—21no—
45#65215—21no—
46#65215C2211yescharacteristic
47#65214—21no—
48#65214C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50C2×C4×#168C2211yescharacteristic
51Q8⋊#168C2211yescharacteristic
52Q8⋊#168C2211yescharacteristic
53Q8⋊#168C2211yescharacteristic
54Q8⋊#168C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57D4⋊#168C2211yescharacteristic
58D4⋊#168C2211yescharacteristic
59#64678C2211yescharacteristic
60#64678C2211yescharacteristic
61#64677C2211yescharacteristic
62#64677C2211yescharacteristic
63#64674C2211yescharacteristic
64#64674C2211yescharacteristic
65C8×#168C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18017—51nomaximal, Sylow
68C22×C5×Q8C2×C411yescharacteristic
69C2×C5×Q16C2×C411yescharacteristic
70C2×C5×Q16C2×C411yescharacteristic
71C2×C5×SD16C2×C411yescharacteristic
72C2×C5×SD16C2×C411yescharacteristic
73C5×#126—21no—
74C5×#125C2×C411yescharacteristic
75C5×#124C2×C411yescharacteristic
76C5×#123—21no—
77C5×C22⋊Q8C2×C411yescharacteristic
78C5×#121C2×C411yescharacteristic
79C4×C5×Q8—21no—
80C4×C5×Q8—21no—
81C4×C5×Q8C2×C411yescharacteristic
82C4×C5×Q8C2×C411yescharacteristic
83C4×C5×Q8C2311yescharacteristic
84C4×C5×Q8C2311yescharacteristic
85C4×C5×Q8C2311yescharacteristic
86C4×C5×D4—21no—
87C4×C5×D4C2311yescharacteristic
88C5×#117—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4C2×C411yescharacteristic
91C2×C42×C5—21no—
92C2×C42×C5C2311yescharacteristic
93C2×#681—21no—
94C22×#168—21no—
95C22×#168—21no—
96C22×#168—21no—
97C5×#107C2×C411yescharacteristic
98C5×#107C2×C411yescharacteristic
99C5×#106C2×C411yescharacteristic
100C5×#106C2×C411yescharacteristic
101C5×C4⋊C8C2×C411yescharacteristic
102C5×C4⋊C8C2×C411yescharacteristic
103C5×#103C2×C411yescharacteristic
104C5×#103C2×C411yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#103C2×C411yescharacteristic
107C5×#103C2×C411yescharacteristic
108C5×#103C2×C411yescharacteristic
109C5×#102C2×C411yescharacteristic
110C5×#102C2×C411yescharacteristic
111C5×C22⋊C8C2×C411yescharacteristic
112C5×C22⋊C8C2×C411yescharacteristic
113C4×C5×C8C2311yescharacteristic
114C4×C5×C8C2311yescharacteristic
115C22⋊#168—21no—
116C22⋊#168—21no—
117C22⋊#168—21no—
118C22⋊#168D411yescharacteristic
119C22⋊#168D411yescharacteristic
120C4⋊#168—21no—
121C4⋊#168—21no—
122C4⋊#168—21no—
123C4⋊#168—21no—
124C4⋊#168—21no—
125C4⋊#168—21no—
126C4⋊#168—21no—
127C4⋊#168D411yescharacteristic
128C4⋊#168D411yescharacteristic
129C4⋊#168C2311yescharacteristic
130C4⋊#168C2311yescharacteristic
131C4⋊#168C2311yescharacteristic
132C4⋊#168C2311yescharacteristic
133#3935—21no—
134#3935—21no—
135#3935—21no—
136#3935—21no—
137C4×#168—21no—
138C4×#168—21no—
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3108D511yescharacteristic
146#2994—51no—
147#2984—51no—
148#1591—51no—
149#1590—51no—
150#1588—51no—
151#1587—51no—
152#1587—51no—
153#1585—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1573—51no—
157#1494—51no—
158C2×Q8⋊C8—51no—
159#1450—51no—
160C2×C5×Q8—21no—
161C2×C5×Q8—22no—
162C2×C5×Q8—41no—
163C2×C5×Q8C22×C411yescharacteristic
164C2×C5×Q8C22×C411yescharacteristic
165C2×C5×Q8C22×C411yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4C22×C411yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5C22×C411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C5×Q16—22no—
175C5×Q16—41no—
176C5×SD16—22no—
177C5×SD16—41no—
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C22×C411yescharacteristic
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C4⋊C4C22×C411yescharacteristic
193C5×C4⋊C4C22×C411yescharacteristic
194C5×C4⋊C4C22×C411yescharacteristic
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C42×C5—21no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5C22×C411yescharacteristic
206C42×C5C2×D411yescharacteristic
207C42×C5#4111yescharacteristic
208C42×C5C2411yescharacteristic
209#681—81no—
210C2×#168—24no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—81no—
218C2×#168—81no—
219C2×#168C2×D411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223#529C2×D511yescharacteristic
224C2×C4×Q8C2×D511yescharacteristic
225#483Dic511yescharacteristic
226#480Dic511yescharacteristic
227#479Dic511yescharacteristic
228#479Dic511yescharacteristic
229#464Dic511yescharacteristic
230#464Dic511yescharacteristic
231#451Dic511yescharacteristic
232#448Dic511yescharacteristic
233#446—51no—
234#446—51no—
235#446—51no—
236#446—101no—
237#446—101no—
238C8×Q8—51no—
239C8×Q8—51no—
240C8×Q8—51no—
241C4×Q16C2×D511yescharacteristic
242C4×Q16C2×D511yescharacteristic
243C4×SD16C2×D511yescharacteristic
244C4×SD16C2×D511yescharacteristic
245#436—51no—
246#435—101no—
247C8×D4—51no—
248C8×D4—101no—
249#433—101no—
250#432—51no—
251#432—101no—
252#431—51no—
253#431—101no—
254#431C2×D511yescharacteristic
255#424—101no—
256C2×C4⋊C8—51no—
257C2×C4×C8—51no—
258#335—51no—
259#335—51no—
260#334—51no—
261#334—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268D4⋊C8—51no—
269D4⋊C8—51no—
270#322—51no—
271#322—51no—
272C82—51no—
273C82—51no—
274C23×C5—21no—
275C23×C5C4×D411yescharacteristic
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8—42no—
282C5×Q8#13112yes—
283C5×D4—21no—
284C5×D4—21no—
285C5×D4—42no—
286C2×C4×C5—21no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5C4×D411yescharacteristic
303C2×C4×C5C4×D411yescharacteristic
304C2×C4×C5C4×D411yescharacteristic
305C2×C4×C5C23×C411yescharacteristic
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5C2×#4111yescharacteristic
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312#168—22no—
313#168—22no—
314#168—21no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—41no—
319#168—41no—
320#168—41no—
321#168—41no—
322C22×Q8C2×Dic511yescharacteristic
323C2×Q16C2×Dic511yescharacteristic
324C2×Q16C2×Dic511yescharacteristic
325C2×SD16C2×Dic511yescharacteristic
326C2×SD16C2×Dic511yescharacteristic
327C2×M16—101no—
328C22×C8—101no—
329C22×C8—101no—
330C22×C8—101no—
331#126—21no—
332#125C2×Dic511yescharacteristic
333#124C2×Dic511yescharacteristic
334#123—21no—
335C22⋊Q8C2×Dic511yescharacteristic
336#121C2×Dic511yescharacteristic
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8C2×Dic511yescharacteristic
340C4×Q8C2×Dic511yescharacteristic
341C4×Q8C22×D511yescharacteristic
342C4×Q8C22×D511yescharacteristic
343C4×Q8C22×D511yescharacteristic
344C4×D4—21no—
345C4×D4C22×D511yescharacteristic
346#117—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4C2×Dic511yescharacteristic
349C2×C42—21no—
350C2×C42C22×D511yescharacteristic
351#107C2×Dic511yescharacteristic
352#107C2×Dic511yescharacteristic
353#106C2×Dic511yescharacteristic
354#106C2×Dic511yescharacteristic
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⋊C8—101no—
368C4⋊C8C2×Dic511yescharacteristic
369C4⋊C8C2×Dic511yescharacteristic
370#103C2×Dic511yescharacteristic
371#103C2×Dic511yescharacteristic
372#103C2×Dic511yescharacteristic
373#103C2×Dic511yescharacteristic
374#103C2×Dic511yescharacteristic
375#103C2×Dic511yescharacteristic
376#102C2×Dic511yescharacteristic
377#102C2×Dic511yescharacteristic
378C22⋊C8—51no—
379C22⋊C8—51no—
380C22⋊C8—101no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8C2×Dic511yescharacteristic
384C22⋊C8C2×Dic511yescharacteristic
385#97—101no—
386#97—101no—
387#97—101no—
388#97—101no—
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×C8C22×D511yescharacteristic
398C4×C8C22×D511yescharacteristic
399C22×C5—21no—
400C22×C5—21no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5#44312yes—
405C22×C5C2×C4×D411yescharacteristic
406C4×C5—21no—
407C4×C5—22no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5—41no—
416C4×C5—41no—
417C4×C5C2×#13111yescharacteristic
418C4×C5#56811yescharacteristic
419C4×C5#57711yescharacteristic
420C4×C5#57811yescharacteristic
421C2×Q8—21no—
422C2×Q8—22no—
423C2×Q8—41no—
424C2×Q8C22×Dic511yescharacteristic
425C2×Q8C22×Dic511yescharacteristic
426C2×Q8C22×Dic511yescharacteristic
427C2×D4—21no—
428C2×D4C22×Dic511yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4D4×D511yescharacteristic
433C22×C4#71111yescharacteristic
434C22×C4C22×Dic511yescharacteristic
435Q16—22no—
436Q16—41no—
437SD16—22no—
438SD16—41no—
439M16—401no—
440C2×C8—51no—
441C2×C8—51no—
442C2×C8—51no—
443C2×C8—51no—
444C2×C8—104no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—401no—
452C2×C8—401no—
453C2×C8C22×Dic511yescharacteristic
454C2×C8C22×Dic511yescharacteristic
455C2×C8C22×Dic511yescharacteristic
456C2×C8C22×Dic511yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4C22×Dic511yescharacteristic
467C4⋊C4C22×Dic511yescharacteristic
468C4⋊C4C22×Dic511yescharacteristic
469C4⋊C4C22×Dic511yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42D4×D511yescharacteristic
481C42#71111yescharacteristic
482C42C22×Dic511yescharacteristic
483C42C23×D511yescharacteristic
484C2×C5—22no—
485C2×C5—81no—
486C2×C5#293311yescharacteristic
487C2×C5#294711yescharacteristic
488C2×C5C2×#44311yescharacteristic
489C23—21no—
490C23D4×Dic511yescharacteristic
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—42no—
497Q8#409412yes—
498D4—21no—
499D4—21no—
500D4—42no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4D4×Dic511yescharacteristic
518C2×C4D4×Dic511yescharacteristic
519C2×C4D4×Dic511yescharacteristic
520C2×C4C2×D4×D511yescharacteristic
521C2×C4C2×#71111yescharacteristic
522C2×C4C23×Dic511yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—102no—
528C8—102no—
529C8—101no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—201no—
534C8—201no—
535C8—201no—
536C8—201no—
537C5#1801711yescharacteristic, complemented, Sylow
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#6548512yes—
544C22C2×D4×Dic511yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—22no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4#6611211yescharacteristic
557C4#6611311yescharacteristic
558C4C2×#409411yescharacteristic
559C4#6615311yescharacteristic
560C2—22no—
561C2—81no—
562C2#1061464911yescharacteristic
563C2C2×#6548511yescharacteristic
564C2#1061569611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#3108C2
socleC22×C5C2×C4×D4
prime radicalC5×#121C2×C4
cosocleC42×C5C24
hypercenter#3108D5
hypocenterC5#18017
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3108

Complements

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

NH ≅ G/Ntype
3. #10614168C2semidirect
5. C2×Q8⋊#168C2semidirect
6. #10601698C2semidirect
7. #10601697C2semidirect
8. #10601697C2semidirect
9. Q16×#168C2semidirect
10. #10601692C2semidirect
11. #10601691C2semidirect
12. #10601690C2semidirect
13. SD16×#168C2semidirect
14. #10601545C2semidirect
15. #10601533C2semidirect
537. C5#18017semidirect

Maximal subgroups

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

subgroupindex
C5×#31082
#106148632
#106141682
#106025452
C2×Q8⋊#1682
#106016982
#106016972
Q16×#1682
#106016922
#106016912
#106016902
SD16×#1682
#106015452
#106015332
#180175