Finite Group Databasebeta

← #12116661

Subgroups — #12116661

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2924C211yesmaximal, characteristic, complemented
2C2×#65291C211yesmaximal, characteristic
3#10610331C211yesmaximal, characteristic
4#10602383C211yesmaximal, characteristic, complemented
5#10601338C212yesmaximal, complemented
6#10601328C212yesmaximal, complemented
7#10600784C211yesmaximal, characteristic
8#10600775C211yesmaximal, characteristic, complemented
9#10600740C211yesmaximal, characteristic, complemented
10#10600693C212yesmaximal, complemented
11#10600680C212yesmaximal, complemented
12C22×#709C2211yescharacteristic
13C2×C5×#117C2211yescharacteristic
14C23×#168C2211yescharacteristic
15C2×#4047C2212yes—
16C5×#433—22no—
17C5×#432—21no—
18C5×#431—21no—
19C5×#424C2212yescomplemented
20C5×#407C2211yescharacteristic
21C2×C5×C22⋊C8C2211yescharacteristic
22C5×#405C2212yescomplemented
23C4×C22⋊Dic5C2211yescharacteristic
24#65496C2211yescharacteristic
25C2×#3957C2212yes—
26C2×#3957C2212yes—
27C2×#3954C2212yescomplemented
28#65399C2212yes—
29C2×C8×Dic5C2212yescomplemented
30#65291C411yescharacteristic, complemented
31#65291C411yescharacteristic, complemented
32#65291C411yescharacteristic, complemented
33#65291C411yescharacteristic, complemented
34#65291C2211yescharacteristic
35#65291C2211yescharacteristic
36#65291C2211yescharacteristic
37#65291C2211yescharacteristic
38C2×#3942C411yescharacteristic, complemented
39C2×#3942C411yescharacteristic, complemented
40C2×#3941C411yescharacteristic, complemented
41C2×#3941C411yescharacteristic, complemented
42#65016—22no—
43#65015—21no—
44D5×C22⋊C8—21no—
45#64778C2212yescomplemented
46#64770C2212yescomplemented
47#64752C2212yescomplemented
48#64752C2212yescomplemented
49#22587—51nomaximal, Sylow
50C23×C4×C5C2311yescharacteristic
51C22×C22⋊D5—21no—
52C2×#709—21no—
53C2×#709—21no—
54C2×#709—24no—
55C2×#709—42no—
56C2×#709C2×C411yescharacteristic
57C2×#709C2×C411yescharacteristic
58C2×#709C2311yescharacteristic
59C2×#709C2311yescharacteristic
60C22×D20C2×C411yescharacteristic
61C22×C4×D5—21no—
62C22×Dic10C2×C411yescharacteristic
63C2×C5×M16C2312yes—
64C22×C5×C8C2312yes—
65C5×#117—21no—
66C5×#117—21no—
67C5×#117C2×C411yescharacteristic
68C5×#117C2×C411yescharacteristic
69C5×#117C2311yescharacteristic
70C5×#117C2311yescharacteristic
71C2×C5×C4⋊C4C2×C411yescharacteristic
72C2×C5×C4⋊C4C2×C411yescharacteristic
73C2×C5×C22⋊C4—21no—
74C2×C42×C5—21no—
75C2×C22⋊Dic5—21no—
76C2×C4×Dic5C2312yes—
77C2×#681C2312yes—
78C22×#168—42no—
79C22×#168C2×C411yescharacteristic
80C22×#168C2×C411yescharacteristic
81C22×#168C2×C411yescharacteristic
82C22×#168C2×C411yescharacteristic
83C22×#168C2311yescharacteristic
84C22×#168C2311yescharacteristic
85#4047—24no—
86#4047—42no—
87C2×#676—22no—
88C2×C8×D5—22no—
89C5×C4⋊C8—22no—
90C5×C4⋊C8—22no—
91C5×C22⋊C8—21no—
92C5×C22⋊C8—21no—
93C5×C22⋊C8D411yescharacteristic
94C5×C22⋊C8D411yescharacteristic
95C5×C22⋊C8D412yes—
96C5×#97—22no—
97C4×C5×C8—22no—
98#3963—21no—
99C22⋊#168—21no—
100C22⋊#168—21no—
101#3957—24no—
102#3957—42no—
103#3954—42no—
104#3952—22no—
105#3952—22no—
106C8×Dic5—42no—
107#3942C2×C411yescharacteristic
108#3942C2×C411yescharacteristic
109#3942C2×C411yescharacteristic
110#3942C2×C411yescharacteristic
111#3942C2×C411yescharacteristic
112#3942C2×C411yescharacteristic
113#3942C2×C411yescharacteristic
114#3942C2×C411yescharacteristic
115#3941C2×C411yescharacteristic
116#3941C2×C411yescharacteristic
117#3941C2×C411yescharacteristic
118#3941C2×C411yescharacteristic
119#3941C2×C411yescharacteristic
120#3941C2×C411yescharacteristic
121#3941C2×C411yescharacteristic
122#3941C2×C411yescharacteristic
123#2924D511yescharacteristic, complemented
124C2×#416—51no—
125#2880—51no—
126#1937—52no—
127#1929—52no—
128#1866—52no—
129#1826—51no—
130#1810—51no—
131#1789—51no—
132#1764—52no—
133C8×C22⋊C4—51no—
134C24×C5#4111yescharacteristic
135C23×D5—21no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5#4111yescharacteristic
145C22×C4×C5C2411yescharacteristic
146C2×C22⋊D5—21no—
147C2×C22⋊D5—21no—
148C2×C22⋊D5—21no—
149C2×C22⋊D5—21no—
150C2×C22⋊D5—44no—
151C22×Dic5—21no—
152C22×Dic5—22no—
153#709—22no—
154#709—22no—
155#709—22no—
156#709—22no—
157#709—22no—
158#709—41no—
159#709—41no—
160#709—44no—
161#709—44no—
162#709#4114yes—
163C2×D20—22no—
164C2×D20—21no—
165C2×D20—41no—
166C2×D20C22×C411yescharacteristic
167C2×D20C22×C411yescharacteristic
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—44no—
173C2×Dic10—22no—
174C2×Dic10—21no—
175C2×Dic10—41no—
176C2×Dic10C22×C411yescharacteristic
177C2×Dic10C22×C411yescharacteristic
178C5×M16—22no—
179C5×M16—22no—
180C2×C5×C8—22no—
181C2×C5×C8—22no—
182C2×C5×C8—22no—
183C2×C5×C8C2×D412yes—
184C2×C5×C8C2×D412yes—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4C22×C411yescharacteristic
188C5×C4⋊C4C22×C411yescharacteristic
189C5×C4⋊C4C22×C411yescharacteristic
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C22⋊C4—21no—
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C42×C5—21no—
196C42×C5—21no—
197C42×C5—21no—
198C42×C5—21no—
199C22⋊Dic5—24no—
200C4×Dic5—22no—
201C4×Dic5—22no—
202#681—22no—
203#681—22no—
204C2×#168—22no—
205C2×#168—22no—
206C2×#168—22no—
207C2×#168—41no—
208C2×#168—41no—
209C2×#168—41no—
210C2×#168—41no—
211C2×#168C22×C411yescharacteristic
212C2×#168C22×C411yescharacteristic
213C2×#168C22×C411yescharacteristic
214C2×#168C22×C411yescharacteristic
215#676—44no—
216C8×D5—44no—
217C22×#41—51no—
218C2×#131—52no—
219C23×C8—51no—
220C2×#117C2×D511yescharacteristic
221#433—22no—
222#432—21no—
223#431—21no—
224C2×#108—52no—
225#424C2×D512yescomplemented
226C2×#104—52no—
227C2×#104—52no—
228#416—51no—
229#416—51no—
230#416—51no—
231#416—51no—
232#416—51no—
233#416—51no—
234#416—51no—
235#416—51no—
236C2×#103—51no—
237C2×#103—51no—
238C2×#102—51no—
239C2×#102—51no—
240#408—52no—
241#408—102no—
242#407—51no—
243#407—101no—
244#407C2×D511yescharacteristic
245C2×C22⋊C8—101no—
246C2×C22⋊C8C2×D511yescharacteristic
247#405C2×D512yescomplemented
248C2×C4×C8—52no—
249C4×C22⋊C4—51no—
250#341—52no—
251#339—52no—
252#339—52no—
253#336—52no—
254C23×C5—22no—
255C23×C5—22no—
256C23×C5—41no—
257C23×C5C4×D411yescharacteristic
258C23×C5C4×D411yescharacteristic
259C23×C5C2×#4111yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—42no—
263C22×D5—42no—
264C22×D5—81no—
265C2×C4×C5—22no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—42no—
277C2×C4×C5—81no—
278C2×C4×C5C4×D411yescharacteristic
279C2×C4×C5C4×D411yescharacteristic
280C2×C4×C5C23×C411yescharacteristic
281C2×C4×C5C22×D411yescharacteristic
282C2×C4×C5C2×#4112yes—
283C2×C4×C5H(5,𝔽2)12yes—
284C22⋊D5—24no—
285C22⋊D5—42no—
286C22⋊D5—42no—
287C22⋊D5—42no—
288C2×Dic5—21no—
289C2×Dic5—24no—
290C2×Dic5—21no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294D20—21no—
295D20—21no—
296D20—21no—
297D20—42no—
298D20#11712yes—
299C4×D5—24no—
300C4×D5—42no—
301C4×D5—42no—
302C4×D5—42no—
303Dic10—21no—
304Dic10—21no—
305Dic10—21no—
306Dic10—42no—
307Dic10#11712yes—
308C5×C8—22no—
309C5×C8—22no—
310C5×C8—42no—
311#168—21no—
312#168—21no—
313#168—21no—
314#168—21no—
315#168—42no—
316C2×#41—51no—
317C2×#41—51no—
318C2×#41—51no—
319C2×#41—51no—
320C2×#41—104no—
321C2×#41—101no—
322C2×#41—101no—
323C2×#41—202no—
324C22×Q8—51no—
325C22×D4—51no—
326C22×D4—101no—
327C23×C4—101no—
328C23×C4C22×D511yescharacteristic
329#131—104no—
330#131—202no—
331C2×M16—52no—
332C2×M16—102no—
333C2×M16C22×D512yes—
334C22×C8—51no—
335C22×C8—51no—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8—51no—
339C22×C8—51no—
340C22×C8—102no—
341C22×C8—202no—
342C22×C8C22×D512yes—
343#117—21no—
344#117—21no—
345#117C4×D511yescharacteristic
346#117C4×D511yescharacteristic
347#117C22×D511yescharacteristic
348#117C22×D511yescharacteristic
349C2×C4⋊C4C4×D511yescharacteristic
350C2×C4⋊C4C4×D511yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—101no—
353C2×C42—21no—
354C2×C42—52no—
355#108—202no—
356C4⋊C8—22no—
357C4⋊C8—22no—
358#104—104no—
359#104—202no—
360#103—51no—
361#103—51no—
362#103—51no—
363#103—51no—
364#103—51no—
365#103—51no—
366#103—51no—
367#103—51no—
368#102—51no—
369#102—51no—
370#102—51no—
371#102—51no—
372#102—51no—
373#102—51no—
374#102—51no—
375#102—51no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8—101no—
379C22⋊C8—101no—
380C22⋊C8—102no—
381C22⋊C8—102no—
382C22⋊C8C22⋊D511yescharacteristic
383C22⋊C8C22⋊D511yescharacteristic
384C22⋊C8C22⋊D512yes—
385#97—22no—
386C4×C8—22no—
387C4×C8—202no—
388#95—101no—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—21no—
393C22×C5—21no—
394C22×C5—21no—
395C22×C5—21no—
396C22×C5—44no—
397C22×C5#44312yes—
398C22×C5C2×C4×D411yescharacteristic
399C22×C5#55112yes—
400C2×D5—22no—
401C2×D5—41no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—41no—
406C2×D5—84no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5C2×#11711yescharacteristic
414C4×C5#51811yescharacteristic
415C4×C5#54612yes—
416Dic5—22no—
417Dic5—44no—
418Dic5—41no—
419C24—101no—
420C24#70911yescharacteristic
421#41—54no—
422#41—102no—
423#41—102no—
424#41—102no—
425#41—102no—
426#41—102no—
427#41—204no—
428#41—201no—
429#41—201no—
430#41—204no—
431C2×Q8—51no—
432C2×Q8—51no—
433C2×Q8—102no—
434C2×Q8—101no—
435C2×Q8—201no—
436C2×D4—51no—
437C2×D4—51no—
438C2×D4—102no—
439C2×D4—101no—
440C2×D4—101no—
441C2×D4—101no—
442C2×D4—101no—
443C2×D4—101no—
444C2×D4—201no—
445C2×D4—204no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—101no—
451C22×C4—102no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—204no—
457C22×C4C2×C4×D511yescharacteristic
458C22×C4C2×C4×D511yescharacteristic
459C22×C4#70911yescharacteristic
460C22×C4C2×C22⋊D511yescharacteristic
461C22×C4C2×C22⋊D511yescharacteristic
462C22×C4C23×D511yescharacteristic
463M16—22no—
464M16—22no—
465M16—102no—
466M16—102no—
467M16—204no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—51no—
474C2×C8—51no—
475C2×C8—102no—
476C2×C8—102no—
477C2×C8—102no—
478C2×C8—204no—
479C2×C8—201no—
480C2×C8—201no—
481C2×C8—201no—
482C2×C8—201no—
483C2×C8C2×C22⋊D512yes—
484C2×C8C2×C22⋊D512yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4C2×C4×D511yescharacteristic
488C4⋊C4C2×C4×D511yescharacteristic
489C4⋊C4C2×C4×D511yescharacteristic
490C4⋊C4C2×C4×D511yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—104no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—102no—
501C42—102no—
502C2×C5—22no—
503C2×C5—22no—
504C2×C5—41no—
505C2×C5#234211yescharacteristic
506C2×C5C2×#44311yescharacteristic
507C2×C5#295711yescharacteristic
508D5—42no—
509D5—81no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—101no—
514C23—101no—
515C23—202no—
516C23—202no—
517C23—401no—
518C23C4×C22⋊D511yescharacteristic
519C23C4×C22⋊D511yescharacteristic
520C23C2×#70911yescharacteristic
521Q8—52no—
522Q8—101no—
523Q8—101no—
524Q8—101no—
525Q8—202no—
526D4—52no—
527D4—104no—
528D4—101no—
529D4—101no—
530D4—101no—
531D4—202no—
532D4—202no—
533D4—202no—
534D4—202no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—101no—
549C2×C4—104no—
550C2×C4—104no—
551C2×C4—101no—
552C2×C4—202no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4—202no—
558C2×C4C4×C22⋊D511yescharacteristic
559C2×C4C4×C22⋊D511yescharacteristic
560C2×C4C22×C4×D511yescharacteristic
561C2×C4D5×#4112yes—
562C2×C4#414912yes—
563C2×C4C22×C22⋊D511yescharacteristic
564C8—22no—
565C8—22no—
566C8—42no—
567C8—101no—
568C8—101no—
569C8—101no—
570C8—101no—
571C8—202no—
572C5#2258711yescharacteristic, complemented, Sylow
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—44no—
581C22—102no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22—201no—
586C22—201no—
587C22—404no—
588C22#6543312yes—
589C22#6586112yes—
590C22C2×C4×C22⋊D511yescharacteristic
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—102no—
598C4—204no—
599C4—201no—
600C4D5×#11711yescharacteristic
601C4#6585511yescharacteristic
602C4#6616312yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—202no—
607C2—401no—
608C2#1061400211yescharacteristic
609C2C2×#6543311yescharacteristic
610C2#1061554311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2924C2
socleC22×C5C2×C4×D4
prime radicalC22×#709C22
cosocleC22×C4×C5C24
hypercenter#2924D5
hypocenterC5#22587
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. C5×#2924C2semidirect
4. #10602383C2semidirect
5. #10601338C2semidirect
6. #10601328C2semidirect
8. #10600775C2semidirect
9. #10600740C2semidirect
10. #10600693C2semidirect
11. #10600680C2semidirect
19. C5×#424C22semidirect
22. C5×#405C22semidirect
27. C2×#3954C22semidirect
29. C2×C8×Dic5C22semidirect
30. #65291C4semidirect
31. #65291C4semidirect
32. #65291C4semidirect
33. #65291C4semidirect
38. C2×#3942C4semidirect
39. C2×#3942C4semidirect
40. C2×#3941C4semidirect
41. C2×#3941C4semidirect
45. #64778C22semidirect
46. #64770C22semidirect
47. #64752C22semidirect
48. #64752C22semidirect
123. #2924D5semidirect
225. #424C2×D5semidirect
247. #405C2×D5semidirect
572. C5#22587semidirect

Maximal subgroups

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

subgroupindex
C5×#29242
C2×#652912
#106103312
#106023832
#106013382
#106013282
#106007842
#106007752
#106007402
#106006932
#106006802
#225875