Finite Group Databasebeta

← #12104201

Subgroups — #12104201

Order 1280.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64979C211yesmaximal, characteristic
2#10605491C211yesmaximal, characteristic
3#10605481C211yesmaximal, characteristic
4C4×C5×#107C211yesmaximal, characteristic, complemented
5#10601426C211yesmaximal, characteristic
6#10601425C211yesmaximal, characteristic
7#10601409C211yesmaximal, characteristic, complemented
8#10601408C211yesmaximal, characteristic, complemented
9C4×#3949C211yesmaximal, characteristic, complemented
10#10600274C211yesmaximal, characteristic, complemented
11#10600274C211yesmaximal, characteristic, complemented
12#10599669C211yesmaximal, characteristic
13#10599668C211yesmaximal, characteristic
14#10599590C211yesmaximal, characteristic, complemented
15#10599589C211yesmaximal, characteristic, complemented
16C2×#4038C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×#4018C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C4×C5×C8C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C4×C5×C4⋊C4C2211yescharacteristic
24C2×#3952C2211yescharacteristic
25C2×#3952C2211yescharacteristic
26C2×#3949C2211yescharacteristic
27C2×#3949C2211yescharacteristic
28C2×#3946C2211yescharacteristic
29C2×#3946C2211yescharacteristic
30#65276C2211yescharacteristic
31#65276C2211yescharacteristic
32#65266C2211yescharacteristic
33#65265C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40#65229—21no—
41C4×#685—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44#65222—21no—
45C4×#683—21no—
46C2×#3935C2211yescharacteristic
47#64979C418yescomplemented
48#64958—21no—
49#64955—21no—
50#64941—21no—
51#64938—21no—
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21367—51nomaximal, Sylow
61C22×C4×D5—21no—
62C22×C4×D5C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C2×C5×C4⋊C4C2311yescharacteristic
66C2×C5×C4⋊C4C2311yescharacteristic
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C42×C5—21no—
70C2×C42×C5—21no—
71C2×C42×C5C2311yescharacteristic
72C2×#685—21no—
73C2×#685—21no—
74C2×#685—21no—
75C2×#685D411yescharacteristic
76C2×#685D411yescharacteristic
77C2×C4⋊Dic5C2311yescharacteristic
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×#683—21no—
82C2×#683—21no—
83C2×#683—21no—
84C2×#683D411yescharacteristic
85C2×#683D411yescharacteristic
86C2×C4×Dic5—21no—
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5C2311yescharacteristic
92C22×#168C2311yescharacteristic
93C22×#168C2311yescharacteristic
94#4038—22no—
95#4038—22no—
96D5×C4⋊C4—22no—
97D5×C4⋊C4—22no—
98#4018C2×C414yes—
99#4018Q814yes—
100C5×#107—22no—
101C5×#107—22no—
102C4×C5×C8C2×C414yescomplemented
103C5×#95—21no—
104C5×#95—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3952C2×C414yes—
114#3952C2×C414yes—
115#3949—22no—
116#3949—22no—
117#3946C2×C414yescomplemented
118#3946C2×C414yescomplemented
119#3940—22no—
120#3940—22no—
121#3939—22no—
122#3939—22no—
123#3935C2×C414yescomplemented
124C2×#433—51no—
125#2314—51no—
126#2274—51no—
127#1949—51no—
128#1949—51no—
129#1948—51no—
130#1947—51no—
131#1854—51no—
132#1854—51no—
133#1853—51no—
134#1852—51no—
135#1776—51no—
136#1776—51no—
137C4×#107D511yescharacteristic, complemented
138C4×#106—51no—
139C23×D5C2×D411yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2411yescharacteristic
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5C2×D411yescharacteristic
152C22×Dic5C2×D411yescharacteristic
153C22×Dic5C2×D411yescharacteristic
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—24no—
159C2×C4×D5—81no—
160C2×C4×D5—81no—
161C2×C4×D5C22×C412yes—
162C2×C4×D5C2×Q812yes—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8C22×C412yes—
168C2×C5×C8C22×C412yes—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4#4112yes—
176C5×C4⋊C4#4112yes—
177C42×C5—81no—
178C42×C5—81no—
179C42×C5C22×C412yes—
180C42×C5C2×Q812yes—
181#685—24no—
182#685—81no—
183#685—81no—
184#685C4⋊C414yes—
185#685C4⋊C414yes—
186C4⋊Dic5—21no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5#4112yes—
193C4⋊Dic5#4112yes—
194#683—24no—
195#683—81no—
196#683—81no—
197#683C4⋊C414yes—
198#683C4⋊C414yes—
199C4×Dic5—24no—
200C4×Dic5—81no—
201C4×Dic5—81no—
202C4×Dic5—81no—
203C4×Dic5—81no—
204C4×Dic5C22×C412yes—
205C4×Dic5C2×Q812yes—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168C22×C412yes—
211C2×#168C22×C412yes—
212C2×#117—51no—
213C2×#117—51no—
214C22×C4⋊C4—51no—
215#433—58no—
216C2×#107—51no—
217C2×#107—51no—
218C2×#107C2×D511yescharacteristic
219C2×#107C2×D511yescharacteristic
220C2×#106—51no—
221C2×#106—51no—
222C2×#106—51no—
223C2×#106—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×C22⋊C8—51no—
227C2×C22⋊C8—51no—
228C2×#97—51no—
229C2×C4×C8C2×D511yescharacteristic
230#388—101no—
231#388—101no—
232#387—101no—
233#387—101no—
234#384—51no—
235#382—51no—
236#380—51no—
237#380—51no—
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—51no—
242C4×C4⋊C4—101no—
243C4×C4⋊C4—101no—
244C4×C4⋊C4C2×D511yescharacteristic
245C4×C4⋊C4C2×D511yescharacteristic
246C4×C22⋊C4—101no—
247C4×C22⋊C4—101no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340C2×D511yescharacteristic
255#340C2×D511yescharacteristic
256C23×C5C22×D411yescharacteristic
257C22×D5—21no—
258C22×D5—21no—
259C22×D5—21no—
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5C2×C4⋊C412yes—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5C2×C4⋊C412yes—
281C2×C4×C5C2×C4⋊C412yes—
282C2×C4×C5C23×C411yescharacteristic
283C2×C4×C5C22×Q811yescharacteristic
284C2×C4×C5C2×#4111yescharacteristic
285C2×C4×C5C2×#4111yescharacteristic
286C2×C4×C5C2×#4111yescharacteristic
287C2×C4×C5C2×#4111yescharacteristic
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5C2×C4⋊C412yes—
307C2×Dic5C2×C4⋊C412yes—
308C2×Dic5C2×C4⋊C412yes—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—22no—
312C4×D5—22no—
313C4×D5—84no—
314C5×C8—22no—
315C5×C8—22no—
316#168—22no—
317#168—22no—
318C23×C4—51no—
319C23×C4—101no—
320C22×C8—51no—
321C22×C8—51no—
322C22×C8C22×D511yescharacteristic
323C22×C8C22×D511yescharacteristic
324#117—54no—
325#117—54no—
326#117—102no—
327#117—102no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—51no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—101no—
336C2×C4⋊C4—102no—
337C2×C4⋊C4—101no—
338C2×C4⋊C4—101no—
339C2×C4⋊C4C22×D511yescharacteristic
340C2×C4⋊C4C22×D511yescharacteristic
341C2×C4⋊C4C22×D511yescharacteristic
342C2×C4⋊C4C22×D511yescharacteristic
343C2×C22⋊C4—51no—
344C2×C22⋊C4—51no—
345C2×C22⋊C4—101no—
346C2×C22⋊C4—101no—
347C2×C22⋊C4—101no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—51no—
351C2×C42—101no—
352C2×C42—101no—
353C2×C42—101no—
354C2×C42—101no—
355C2×C42—101no—
356C2×C42C22×D511yescharacteristic
357#107—22no—
358#107—22no—
359#107—102no—
360#107—102no—
361#106—102no—
362#106—102no—
363#106—102no—
364#106—102no—
365C4⋊C8—54no—
366C4⋊C8—54no—
367C22⋊C8—54no—
368C22⋊C8—54no—
369#97—54no—
370C4×C8C4×D514yescomplemented
371#95—21no—
372#95—21no—
373#95—101no—
374#95—101no—
375#95—101no—
376#95—101no—
377#95—101no—
378#95—101no—
379#95—101no—
380#95—101no—
381C22×C5C22×C4⋊C411yescharacteristic
382C22×C5#52511yescharacteristic
383C22×C5#52511yescharacteristic
384C22×C5#57611yescharacteristic
385C22×C5#57711yescharacteristic
386C22×C5#57711yescharacteristic
387C22×C5#57811yescharacteristic
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—41no—
392C2×D5—41no—
393C2×D5—41no—
394C2×D5—41no—
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—42no—
398C4×C5—42no—
399C4×C5—81no—
400C4×C5—81no—
401C4×C5C4×#4111yescharacteristic
402C4×C5C4×#4111yescharacteristic
403C4×C5#53311yescharacteristic
404C4×C5#53311yescharacteristic
405Dic5—22no—
406Dic5—22no—
407Dic5—22no—
408Dic5—42no—
409Dic5—42no—
410Dic5—81no—
411Dic5—81no—
412C24—51no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—51no—
420C22×C4—52no—
421C22×C4—52no—
422C22×C4—104no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—401no—
432C22×C4—401no—
433C22×C4D4×D511yescharacteristic
434C22×C4D4×D511yescharacteristic
435C22×C4C23×D511yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—52no—
441C2×C8—52no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8C2×C4×D512yes—
447C2×C8C2×C4×D512yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—54no—
455C4⋊C4—54no—
456C4⋊C4—52no—
457C4⋊C4—52no—
458C4⋊C4—104no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—401no—
466C4⋊C4—401no—
467C4⋊C4#70912yes—
468C4⋊C4#70912yes—
469C22⋊C4—54no—
470C22⋊C4—54no—
471C22⋊C4—104no—
472C22⋊C4—401no—
473C22⋊C4—401no—
474C42—52no—
475C42—52no—
476C42—81no—
477C42—81no—
478C42—104no—
479C42—401no—
480C42—401no—
481C42—401no—
482C42—401no—
483C42C2×C4×D512yes—
484C42Q8×D512yes—
485C2×C5#229611yescharacteristic
486C2×C5#291211yescharacteristic
487C2×C5#291311yescharacteristic
488C2×C5#311811yescharacteristic
489C2×C5#311911yescharacteristic
490C2×C5#312011yescharacteristic
491C2×C5#312111yescharacteristic
492D5—42no—
493C23—52no—
494C23—101no—
495C23—101no—
496C23—101no—
497C23—101no—
498C23—101no—
499C23—101no—
500C23C2×D4×D511yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—201no—
540C2×C4—201no—
541C2×C4—201no—
542C2×C4—404no—
543C2×C4D5×C4⋊C412yes—
544C2×C4D5×C4⋊C412yes—
545C2×C4C22×C4×D511yescharacteristic
546C2×C4C2×#70911yescharacteristic
547C2×C4C2×#70911yescharacteristic
548C2×C4C2×Q8×D511yescharacteristic
549C2×C4D5×#4111yescharacteristic
550C2×C4D5×#4111yescharacteristic
551C8—22no—
552C8—22no—
553C8—102no—
554C8—102no—
555C5#2136711yescharacteristic, complemented, Sylow
556C22—102no—
557C22—102no—
558C22—102no—
559C22—201no—
560C22—201no—
561C22—201no—
562C22—201no—
563C22C2×D5×C4⋊C411yescharacteristic
564C22#6588111yescharacteristic
565C22#6588111yescharacteristic
566C22#6609111yescharacteristic
567C22#6610011yescharacteristic
568C22#6610411yescharacteristic
569C22#6610411yescharacteristic
570C4—22no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—102no—
577C4—102no—
578C4—102no—
579C4—202no—
580C4—202no—
581C4—401no—
582C4—401no—
583C4C4×#70911yescharacteristic
584C4#6585611yescharacteristic
585C4#6591211yescharacteristic
586C4#6591211yescharacteristic
587C2—202no—
588C2#1060548611yescharacteristic
589C2#1061087711yescharacteristic
590C2#1061090911yescharacteristic
591C2#1061132511yescharacteristic
592C2#1061132611yescharacteristic
593C2#1061147911yescharacteristic
594C2#1061148111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×#107C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenterC4×#107D5
hypocenterC5#21367
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
4. C4×C5×#107C2semidirect
7. #10601409C2semidirect
8. #10601408C2semidirect
9. C4×#3949C2semidirect
10. #10600274C2semidirect
11. #10600274C2semidirect
14. #10599590C2semidirect
15. #10599589C2semidirect
47. #64979C4semidirect
102. C4×C5×C8C2×C4semidirect
117. #3946C2×C4semidirect
118. #3946C2×C4semidirect
123. #3935C2×C4semidirect
137. C4×#107D5semidirect
370. C4×C8C4×D5semidirect
555. C5#21367semidirect

Maximal subgroups

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

subgroupindex
C2×#649792
#106054912
#106054812
C4×C5×#1072
#106014262
#106014252
#106014092
#106014082
C4×#39492
#106002742
#105996692
#105996682
#105995902
#105995892
#213675