Finite Group Databasebeta

← #12070499

Subgroups — #12070499

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
1#10614883C211yesmaximal, characteristic
2#10614863C211yesmaximal, characteristic
3#10611046C211yesmaximal, characteristic, complemented
4C5×#1494C211yesmaximal, characteristic
5#10601590C211yesmaximal, characteristic, complemented
6C2×#64676C211yesmaximal, characteristic, complemented
7#10600517C211yesmaximal, characteristic, complemented
8#10599018C211yesmaximal, characteristic, complemented
9#10599015C211yesmaximal, characteristic, complemented
10#10599014C211yesmaximal, characteristic, complemented
11#10599006C211yesmaximal, characteristic, complemented
12#10598954C211yesmaximal, characteristic, complemented
13#10598952C211yesmaximal, characteristic, complemented
14#10598949C211yesmaximal, characteristic, complemented
15#10598942C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C2×C4×Dic10C2211yescharacteristic
18C5×#432C2211yescharacteristic
19C2×C4×C5×C8C2211yescharacteristic
20#65352C411yescharacteristic
21#65352C411yescharacteristic
22#65343C411yescharacteristic
23#65343C411yescharacteristic
24#65339C411yescharacteristic
25#65332C411yescharacteristic
26#65329C411yescharacteristic
27#65322C411yescharacteristic
28C4×#689C2211yescharacteristic
29C4×#689C2211yescharacteristic
30#65313C2211yescharacteristic
31Q8×#168C2211yescharacteristic
32C4×#687C2211yescharacteristic
33C4×#687C2211yescharacteristic
34#65301C2211yescharacteristic
35#65300—21no—
36D4×#168—21no—
37D4×#168C2211yescharacteristic
38#65289—21no—
39#65288—21no—
40#65214C2211yescharacteristic
41#65214C2211yescharacteristic
42C2×C4⋊#168C2211yescharacteristic
43#65120C2211yescharacteristic
44#65120C2211yescharacteristic
45#65119C2211yescharacteristic
46#65119C2211yescharacteristic
47#65008—21no—
48#65007—21no—
49#64990—21no—
50#64990—21no—
51C5×Q8⋊C8C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×D4⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic
56#64700C2211yescharacteristic
57#64699C2211yescharacteristic
58#64699C2211yescharacteristic
59#64676C2211yescharacteristic
60#64676C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64675C2211yescharacteristic
64#64675C2211yescharacteristic
65C8×#168C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18017—51nomaximal, Sylow
68C22×Dic10C2×C411yescharacteristic
69C22×C5×C8—21no—
70C5×#126—21no—
71C5×#125C2×C411yescharacteristic
72C5×#124C2×C411yescharacteristic
73C5×#123—21no—
74C5×C22⋊Q8C2×C411yescharacteristic
75C5×#121C2×C411yescharacteristic
76C4×C5×Q8C2311yescharacteristic
77C4×C5×D4—21no—
78C4×C5×D4C2311yescharacteristic
79C5×#117—21no—
80C2×C42×C5C2311yescharacteristic
81C2×#689C2×C411yescharacteristic
82C2×#689C2×C411yescharacteristic
83C2×#687C2×C411yescharacteristic
84C2×#687C2×C411yescharacteristic
85C2×C4⋊Dic5C2×C411yescharacteristic
86C2×#683—21no—
87C2×C4×Dic5—21no—
88C2×#681—21no—
89C22×#168—21no—
90C22×#168—21no—
91C4×Dic10—21no—
92C4×Dic10—21no—
93C4×Dic10C2×C411yescharacteristic
94C4×Dic10C2×C411yescharacteristic
95C4×Dic10C2311yescharacteristic
96C4×Dic10C2311yescharacteristic
97C5×C4⋊C8C2311yescharacteristic
98C5×C4⋊C8C2311yescharacteristic
99C5×C22⋊C8—21no—
100C5×#97—21no—
101C4×C5×C8—21no—
102C4×C5×C8C2311yescharacteristic
103C4×C5×C8C2311yescharacteristic
104#3967C2×C411yescharacteristic
105#3967C2×C411yescharacteristic
106#3964C2×C411yescharacteristic
107#3964C2×C411yescharacteristic
108C22⋊#168—21no—
109C22⋊#168—21no—
110C22⋊#168C2×C411yescharacteristic
111C22⋊#168C2×C411yescharacteristic
112C22⋊#168D411yescharacteristic
113C22⋊#168D411yescharacteristic
114#3947—21no—
115#3947—21no—
116#3946—21no—
117#3946—21no—
118#3946—21no—
119#3946—21no—
120C8×Dic5—21no—
121C8×Dic5—21no—
122#3942C2×C411yescharacteristic
123#3942C2×C411yescharacteristic
124#3942C2×C411yescharacteristic
125#3942C2×C411yescharacteristic
126#3940C2×C411yescharacteristic
127#3940C2×C411yescharacteristic
128#3939C2×C411yescharacteristic
129#3939C2×C411yescharacteristic
130C4⋊#168—21no—
131C4⋊#168—21no—
132C4⋊#168—21no—
133C4⋊#168C2×C411yescharacteristic
134C4⋊#168C2×C411yescharacteristic
135C4⋊#168D411yescharacteristic
136C4⋊#168D411yescharacteristic
137C4⋊#168C2311yescharacteristic
138C4⋊#168C2311yescharacteristic
139#3935—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3108—51no—
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#1494D511yescharacteristic
158C2×Q8⋊C8—51no—
159#1450—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C22×C411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5C22×C411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5#4111yescharacteristic
167C22×Dic5—21no—
168C22×Dic5—21no—
169C2×Dic10—22no—
170C2×Dic10—21no—
171C2×Dic10—41no—
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C2×C5×C8—24no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4C22×C411yescharacteristic
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C22⋊C4—21no—
186C5×C22⋊C4—21no—
187C5×C22⋊C4—21no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—21no—
190C42×C5—21no—
191C42×C5C22×C411yescharacteristic
192C42×C5C2×D411yescharacteristic
193C42×C5#4111yescharacteristic
194C42×C5C2411yescharacteristic
195#689—22no—
196#689—41no—
197#687—22no—
198#687—41no—
199C4⋊Dic5—21no—
200C4⋊Dic5C22×C411yescharacteristic
201C4⋊Dic5C22×C411yescharacteristic
202#683—21no—
203#683—21no—
204#683—21no—
205#683—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210#681—81no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—81no—
214C2×#168—81no—
215C2×#168C22×C411yescharacteristic
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C22×C411yescharacteristic
219C2×#168C2×D411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223#529C2×D511yescharacteristic
224C2×C4×Q8—51no—
225#483—51no—
226#480—51no—
227#479—51no—
228#479—51no—
229#464—51no—
230#464—51no—
231#451—51no—
232#448—51no—
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×Q16—51no—
242C4×Q16—51no—
243C4×SD16—51no—
244C4×SD16—51no—
245#436—51no—
246#435—101no—
247C8×D4—51no—
248C8×D4—101no—
249#433—101no—
250#432—101no—
251#432C2×D511yescharacteristic
252#431—51no—
253#431—51no—
254#431—101no—
255#424—101no—
256C2×C4⋊C8—51no—
257C2×C4×C8C2×D511yescharacteristic
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⋊C8C2×D511yescharacteristic
267Q8⋊C8C2×D511yescharacteristic
268D4⋊C8C2×D511yescharacteristic
269D4⋊C8C2×D511yescharacteristic
270#322—51no—
271#322—51no—
272C82—51no—
273C82—51no—
274C23×C5—21no—
275C23×C5C4×D411yescharacteristic
276C5×Q8—21no—
277C5×Q8—21no—
278C5×D4—21no—
279C5×D4—21no—
280C5×D4—42no—
281C2×C4×C5—22no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5C4×D411yescharacteristic
292C2×C4×C5C4×D411yescharacteristic
293C2×C4×C5C4×D411yescharacteristic
294C2×C4×C5C23×C411yescharacteristic
295C2×C4×C5C22×D411yescharacteristic
296C2×C4×C5C2×#4111yescharacteristic
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303Dic10—21no—
304Dic10—21no—
305Dic10—21no—
306Dic10—42no—
307Dic10#13112yes—
308C5×C8—22no—
309C5×C8—22no—
310C5×C8—41no—
311C5×C8—41no—
312#168—21no—
313#168—21no—
314#168—21no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—41no—
321#168—41no—
322C22×Q8—51no—
323C2×Q16—51no—
324C2×Q16—51no—
325C2×SD16—51no—
326C2×SD16—51no—
327C2×M16—101no—
328C22×C8—21no—
329C22×C8—101no—
330C22×C8—101no—
331#126—21no—
332#125C4×D511yescharacteristic
333#124C4×D511yescharacteristic
334#123—21no—
335C22⋊Q8C4×D511yescharacteristic
336#121C4×D511yescharacteristic
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—101no—
342C4×Q8—101no—
343C4×Q8C22×D511yescharacteristic
344C4×D4—21no—
345C4×D4C22×D511yescharacteristic
346#117—21no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—101no—
349C2×C42—101no—
350C2×C42C22×D511yescharacteristic
351#107—51no—
352#107—51no—
353#106—51no—
354#106—51no—
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⋊C8C22×D511yescharacteristic
369C4⋊C8C22×D511yescharacteristic
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#102—51no—
377#102—51no—
378C22⋊C8—21no—
379C22⋊C8—51no—
380C22⋊C8—51no—
381C22⋊C8—51no—
382C22⋊C8—51no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—21no—
386#97—101no—
387#97—101no—
388#97—101no—
389C4×C8—21no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—51no—
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—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—41no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5C2×#13111yescharacteristic
414C4×C5#56811yescharacteristic
415C4×C5#57711yescharacteristic
416C4×C5#57811yescharacteristic
417Dic5—22no—
418Dic5—41no—
419Dic5—41no—
420Dic5—41no—
421C2×Q8—51no—
422C2×Q8—51no—
423C2×Q8—102no—
424C2×Q8—101no—
425C2×Q8—201no—
426C2×Q8C2×C4×D511yescharacteristic
427C2×D4—21no—
428C2×D4C2×C4×D511yescharacteristic
429C22×C4—21no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4C2×C4×D511yescharacteristic
433C22×C4D4×D511yescharacteristic
434C22×C4#71111yescharacteristic
435Q16—102no—
436Q16—201no—
437SD16—102no—
438SD16—201no—
439M16—401no—
440C2×C8—24no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—51no—
446C2×C8—51no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—401no—
456C2×C8—401no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—51no—
462C4⋊C4—51no—
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—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C42—21no—
476C42—101no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42C2×C4×D511yescharacteristic
481C42D4×D511yescharacteristic
482C42#71111yescharacteristic
483C42C23×D511yescharacteristic
484C2×C5—22no—
485C2×C5—81no—
486C2×C5#293311yescharacteristic
487C2×C5#294711yescharacteristic
488C2×C5C2×#44311yescharacteristic
489C23—21no—
490C23#402711yescharacteristic
491Q8—21no—
492Q8—21no—
493Q8—52no—
494Q8—101no—
495Q8—101no—
496Q8—101no—
497Q8—202no—
498D4—21no—
499D4—21no—
500D4—42no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—202no—
516C2×C4—202no—
517C2×C4#402711yescharacteristic
518C2×C4#402711yescharacteristic
519C2×C4#402711yescharacteristic
520C2×C4C22×C4×D511yescharacteristic
521C2×C4C2×D4×D511yescharacteristic
522C2×C4C2×#71111yescharacteristic
523C8—22no—
524C8—22no—
525C8—41no—
526C8—41no—
527C8—101no—
528C8—101no—
529C8—101no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—101no—
534C8—101no—
535C8—201no—
536C8—201no—
537C5#1801711yescharacteristic, complemented, Sylow
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#6511312yes—
544C22C2×#402711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—102no—
553C4—201no—
554C4—201no—
555C4—201no—
556C4D5×#13111yescharacteristic
557C4#6608411yescharacteristic
558C4#6610411yescharacteristic
559C4#6610511yescharacteristic
560C2—22no—
561C2—81no—
562C2#1061039011yescharacteristic
563C2#1061055211yescharacteristic
564C2C2×#6511311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1494C2
socleC22×C5C2×C4×D4
prime radicalC5×#121C2×C4
cosocleC42×C5C24
hypercenter#1494D5
hypocenterC5#18017
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #10611046C2semidirect
5. #10601590C2semidirect
6. C2×#64676C2semidirect
7. #10600517C2semidirect
8. #10599018C2semidirect
9. #10599015C2semidirect
10. #10599014C2semidirect
11. #10599006C2semidirect
12. #10598954C2semidirect
13. #10598952C2semidirect
14. #10598949C2semidirect
15. #10598942C2semidirect
537. C5#18017semidirect

Maximal subgroups

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

subgroupindex
#106148832
#106148632
#106110462
C5×#14942
#106015902
C2×#646762
#106005172
#105990182
#105990152
#105990142
#105990062
#105989542
#105989522
#105989492
#105989422
#180175