Finite Group Databasebeta

← #12070387

Subgroups — #12070387

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615083C211yesmaximal, characteristic
2#10615061C211yesmaximal, characteristic, complemented
3#10611059C211yesmaximal, characteristic
4C5×#1497C211yesmaximal, characteristic, complemented
5#10601590C211yesmaximal, characteristic, complemented
6#10601548C211yesmaximal, characteristic
7#10601536C211yesmaximal, characteristic, complemented
8#10599020C211yesmaximal, characteristic, complemented
9#10599018C211yesmaximal, characteristic, complemented
10#10599014C211yesmaximal, characteristic, complemented
11#10599013C211yesmaximal, characteristic, complemented
12#10599011C211yesmaximal, characteristic, complemented
13#10599009C211yesmaximal, characteristic, complemented
14#10599007C211yesmaximal, characteristic, complemented
15#10599005C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C4×#709C2211yescharacteristic
18C5×#432C2211yescharacteristic
19C5×#431C2211yescharacteristic
20#65383C411yescharacteristic
21#65379C411yescharacteristic
22#65376C411yescharacteristic
23#65372C411yescharacteristic
24#65336C411yescharacteristic
25#65336C411yescharacteristic
26#65334C411yescharacteristic
27#65334C411yescharacteristic
28C4×#689C2211yescharacteristic
29C4×#689C2211yescharacteristic
30C4×#688C2211yescharacteristic
31C4×#688C2211yescharacteristic
32#65313—21no—
33#65313—21no—
34#65313C2211yescharacteristic
35#65313C2211yescharacteristic
36Q8×#168C2211yescharacteristic
37Q8×#168C2211yescharacteristic
38#65288—21no—
39#65286—21no—
40#65214C2211yescharacteristic
41C2×C4⋊#168C2211yescharacteristic
42C4×#681C2211yescharacteristic
43#65123C2211yescharacteristic
44#65123C2211yescharacteristic
45#65120C2211yescharacteristic
46#65120C2211yescharacteristic
47#65017—21no—
48#65017—21no—
49#64994—21no—
50D5×#97—21no—
51C5×Q8⋊C8C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×Q8⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic
56#64700C2211yescharacteristic
57#64699C2211yescharacteristic
58#64699C2211yescharacteristic
59#64679C2211yescharacteristic
60#64679C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18009—51nomaximal, Sylow
68C2×#709C2×C411yescharacteristic
69C5×C4⋊Q8C2×C411yescharacteristic
70C5×C4⋊Q8C2×C411yescharacteristic
71C5×#125—21no—
72C5×C22⋊Q8—21no—
73C5×C22⋊Q8C2×C411yescharacteristic
74C5×C22⋊Q8C2×C411yescharacteristic
75C4×C5×Q8—21no—
76C4×C5×Q8C2311yescharacteristic
77C4×C5×Q8C2311yescharacteristic
78C5×#117—21no—
79C2×C42×C5C2311yescharacteristic
80C2×#689C2×C411yescharacteristic
81C2×#689C2×C411yescharacteristic
82C2×#688C2×C411yescharacteristic
83C2×#688C2×C411yescharacteristic
84C4×C22⋊D5—21no—
85C4×C22⋊D5—21no—
86#4072C2×C411yescharacteristic
87C2×#681D411yescharacteristic
88C2×#681D411yescharacteristic
89C22×#168—21no—
90C2×C8×D5—21no—
91C2×C8×D5—21no—
92C4×D20C2×C411yescharacteristic
93C4×D20C2311yescharacteristic
94#4018—21no—
95C42×D5—21no—
96C4×Dic10C2×C411yescharacteristic
97C4×Dic10C2311yescharacteristic
98C5×C4⋊C8—21no—
99C5×C4⋊C8C2311yescharacteristic
100C5×C4⋊C8C2311yescharacteristic
101C5×C22⋊C8—21no—
102C5×C22⋊C8—21no—
103C5×#97—21no—
104C4×C5×C8C2311yescharacteristic
105C4×C5×C8C2311yescharacteristic
106#3967C2×C411yescharacteristic
107#3967C2×C411yescharacteristic
108#3967C2×C411yescharacteristic
109#3967C2×C411yescharacteristic
110C22⋊#168C2×C411yescharacteristic
111C22⋊#168C2×C411yescharacteristic
112#3952—21no—
113#3952—21no—
114#3947—21no—
115#3947—21no—
116#3946—21no—
117#3946—21no—
118#3942C2×C411yescharacteristic
119#3942C2×C411yescharacteristic
120#3941C2×C411yescharacteristic
121#3941C2×C411yescharacteristic
122#3940C2×C411yescharacteristic
123#3940C2×C411yescharacteristic
124#3939C2×C411yescharacteristic
125#3939C2×C411yescharacteristic
126C4⋊#168—21no—
127C4⋊#168—21no—
128C4⋊#168—21no—
129C4⋊#168—21no—
130C4⋊#168—21no—
131C4⋊#168C2×C411yescharacteristic
132C4⋊#168C2×C411yescharacteristic
133C4⋊#168C2311yescharacteristic
134C4⋊#168C2311yescharacteristic
135#3935—21no—
136#3935—21no—
137#3935D411yescharacteristic
138#3935D411yescharacteristic
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3107—51no—
146#2970—51no—
147#2962—51no—
148#1593—51no—
149#1591—51no—
150#1587—51no—
151#1585—51no—
152#1584—51no—
153#1582—51no—
154SD16⋊C8—51no—
155C8×SD16—51no—
156#1573—51no—
157#1497D511yescharacteristic, complemented
158#1477—51no—
159#1453—51no—
160C2×C5×Q8—21no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×Q8C22×C411yescharacteristic
163C22×C4×C5C22×C411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5#4111yescharacteristic
166C2×C22⋊D5—21no—
167#709—22no—
168#709—41no—
169C2×D20C22×C411yescharacteristic
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×Dic10C22×C411yescharacteristic
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4C22×C411yescharacteristic
186C5×C4⋊C4C22×C411yescharacteristic
187C5×C22⋊C4—21no—
188C5×C22⋊C4—21no—
189C42×C5—21no—
190C42×C5—21no—
191C42×C5C22×C411yescharacteristic
192C42×C5C2×D411yescharacteristic
193C42×C5#4111yescharacteristic
194C42×C5C2411yescharacteristic
195C22⋊Dic5—21no—
196#689—41no—
197#689—41no—
198#688—22no—
199#688—22no—
200#685—21no—
201#685—21no—
202C4⋊Dic5C22×C411yescharacteristic
203C4⋊Dic5C22×C411yescharacteristic
204#683—21no—
205#683—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209#681—22no—
210#681—41no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—42no—
214C2×#168C22×C411yescharacteristic
215C2×#168C22×C411yescharacteristic
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C2×D411yescharacteristic
219C2×#168C2×D411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C8×D5—42no—
223C8×D5—42no—
224#533C2×D511yescharacteristic
225C4×#41—51no—
226#485—51no—
227#485—51no—
228#475—51no—
229#474—51no—
230#462—51no—
231#461—51no—
232#452—51no—
233#452—51no—
234#446—51no—
235#446—51no—
236#446—51no—
237#446—51no—
238#446—101no—
239#446—101no—
240C8×Q8—51no—
241C8×Q8—51no—
242C4×Q16—51no—
243C4×Q16—51no—
244C4×SD16—51no—
245C4×SD16—51no—
246#435—101no—
247#435—101no—
248C8×D4—51no—
249C8×D4—51no—
250#432—101no—
251#432C2×D511yescharacteristic
252#431—51no—
253#431C2×D511yescharacteristic
254#424—101no—
255C2×C4⋊C8—51no—
256#405—101no—
257C4×M16—51no—
258C2×#97—101no—
259#335—51no—
260#335—51no—
261#334—51no—
262#334—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8C2×D511yescharacteristic
266Q8⋊C8C2×D511yescharacteristic
267Q8⋊C8C2×D511yescharacteristic
268Q8⋊C8C2×D511yescharacteristic
269D4⋊C8—51no—
270D4⋊C8—51no—
271#322—51no—
272#322—51no—
273#322—51no—
274C82—51no—
275C23×C5C4×D411yescharacteristic
276C22×D5—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8—81no—
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—21no—
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
297C22⋊D5—42no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301D20—21no—
302D20#13112yes—
303C4×D5—42no—
304C4×D5—41no—
305C4×D5—41no—
306C4×D5—81no—
307Dic10—21no—
308Dic10—21no—
309C5×C8—41no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—41no—
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—
322#168#13712yes—
323C2×#41—51no—
324C2×Q16—51no—
325C2×Q16—51no—
326C2×SD16—51no—
327C2×SD16—51no—
328C2×M16—51no—
329C2×M16—51no—
330C22×C8—101no—
331C22×C8—101no—
332C22×C8—101no—
333C4⋊Q8C4×D511yescharacteristic
334C4⋊Q8C4×D511yescharacteristic
335#125—21no—
336C22⋊Q8—21no—
337C22⋊Q8C4×D511yescharacteristic
338C22⋊Q8C4×D511yescharacteristic
339C4×Q8—21no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8C22×D511yescharacteristic
343C4×Q8C22×D511yescharacteristic
344C4×D4—51no—
345C4×D4—51no—
346C4×D4—101no—
347C4×D4—101no—
348#117—21no—
349#117—51no—
350#117—101no—
351C2×C42—101no—
352C2×C42C22×D511yescharacteristic
353#107—51no—
354#107—51no—
355#106—51no—
356#106—51no—
357C4⋊C8—21no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—51no—
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#102—51no—
378#102—51no—
379C22⋊C8—21no—
380C22⋊C8—21no—
381C22⋊C8—51no—
382C22⋊C8—51no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—21no—
386#97—51no—
387#97—51no—
388#97—101no—
389#97—101no—
390#97—101no—
391#97—101no—
392C4×C8—51no—
393C4×C8—51no—
394C4×C8—51no—
395C4×C8—51no—
396C4×C8—101no—
397C4×C8—101no—
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—21no—
403C22×C5C2×C4×D411yescharacteristic
404C2×D5—22no—
405C2×D5—41no—
406C2×D5—41no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5C2×#13111yescharacteristic
416C4×C5#56811yescharacteristic
417C4×C5C2×#13711yescharacteristic
418C4×C5#57511yescharacteristic
419Dic5—41no—
420Dic5—41no—
421Dic5—41no—
422#41—102no—
423#41—201no—
424C2×Q8—21no—
425C2×Q8—51no—
426C2×Q8C2×C4×D511yescharacteristic
427C2×Q8C2×C4×D511yescharacteristic
428C2×D4—51no—
429C2×D4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4C2×C4×D511yescharacteristic
434C22×C4D4×D511yescharacteristic
435C22×C4#71111yescharacteristic
436Q16—201no—
437Q16—201no—
438SD16—102no—
439SD16—102no—
440M16—102no—
441M16—201no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—51no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—51no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—202no—
457C2×C8—202no—
458C2×C8—202no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—51no—
467C4⋊C4—51no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4C2×C4×D511yescharacteristic
471C4⋊C4C2×C4×D511yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—101no—
475C22⋊C4—101no—
476C22⋊C4—101no—
477C42—21no—
478C42—21no—
479C42—101no—
480C42—101no—
481C42—101no—
482C42C2×C4×D511yescharacteristic
483C42D4×D511yescharacteristic
484C42#71111yescharacteristic
485C42C23×D511yescharacteristic
486C2×C5—41no—
487C2×C5#293311yescharacteristic
488C2×C5C4×#13711yescharacteristic
489C2×C5#295711yescharacteristic
490D5—42no—
491C23—101no—
492C23#402711yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—81no—
498Q8—101no—
499Q8—101no—
500D4—52no—
501D4—101no—
502D4—202no—
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—41no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—202no—
516C2×C4—201no—
517C2×C4—201no—
518C2×C4—401no—
519C2×C4#402711yescharacteristic
520C2×C4#402711yescharacteristic
521C2×C4#402711yescharacteristic
522C2×C4C22×C4×D511yescharacteristic
523C2×C4C2×D4×D511yescharacteristic
524C2×C4C2×#71111yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—52no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—101no—
534C8—101no—
535C8—101no—
536C8—101no—
537C8—201no—
538C8—201no—
539C5#1800911yescharacteristic, complemented, Sylow
540C22—21no—
541C22—21no—
542C22—21no—
543C22—102no—
544C22—201no—
545C22—201no—
546C22C2×#402711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—201no—
556C4—201no—
557C4—201no—
558C4D5×#13111yescharacteristic
559C4#6608411yescharacteristic
560C4D5×#13711yescharacteristic
561C4#6611111yescharacteristic
562C2—41no—
563C2—202no—
564C2#1061039011yescharacteristic
565C2#1061067711yescharacteristic
566C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1497C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenter#1497D5
hypocenterC5#18009
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #10615061C2semidirect
4. C5×#1497C2semidirect
5. #10601590C2semidirect
7. #10601536C2semidirect
8. #10599020C2semidirect
9. #10599018C2semidirect
10. #10599014C2semidirect
11. #10599013C2semidirect
12. #10599011C2semidirect
13. #10599009C2semidirect
14. #10599007C2semidirect
15. #10599005C2semidirect
157. #1497D5semidirect
539. C5#18009semidirect

Maximal subgroups

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

subgroupindex
#106150832
#106150612
#106110592
C5×#14972
#106015902
#106015482
#106015362
#105990202
#105990182
#105990142
#105990132
#105990112
#105990092
#105990072
#105990052
#180095