Finite Group Databasebeta

← #13031490

Subgroups — #13031490

Order 1280.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617145C211yesmaximal, characteristic
2#10617143C211yesmaximal, characteristic
3#10611184C211yesmaximal, characteristic
4#10604740C211yesmaximal, characteristic, complemented
5#10604738C211yesmaximal, characteristic, complemented
6#10604699C211yesmaximal, characteristic, complemented
7#10604694C211yesmaximal, characteristic, complemented
8#10604020C211yesmaximal, characteristic, complemented
9#10604018C211yesmaximal, characteristic, complemented
10#10603902C211yesmaximal, characteristic, complemented
11#10603901C211yesmaximal, characteristic, complemented
12#10603899C211yesmaximal, characteristic, complemented
13#10603899C211yesmaximal, characteristic, complemented
14#10603866C211yesmaximal, characteristic, complemented
15#10603865C211yesmaximal, characteristic, complemented
16C4×#711C2211yescharacteristic
17#65776—21no—
18#65775—21no—
19#65759C2211yescharacteristic
20#65759C2211yescharacteristic
21#65759C2211yescharacteristic
22#65758C2211yescharacteristic
23#65748C2211yescharacteristic
24#65748C2211yescharacteristic
25#65748C2211yescharacteristic
26C2×C4⋊#170C2211yescharacteristic
27#65706—21no—
28#65701—21no—
29#65697—21no—
30#65697—21no—
31#65697—21no—
32#65691—21no—
33#65683C2211yescharacteristic
34#65681C2211yescharacteristic
35#65680C2211yescharacteristic
36D5⋊(C4⋊C8)C2211yescharacteristic
37C5×#435C411yescharacteristic
38#65417C411yescharacteristic
39M16×Dic5C2211yescharacteristic
40#65400C411yescharacteristic
41C2×C8×Dic5C2211yescharacteristic
42#65300C411yescharacteristic
43#65122C2211yescharacteristic
44#65117C411yescharacteristic
45#65019C411yescharacteristic
46#65018C411yescharacteristic
47#65007C2211yescharacteristic
48#65007C2211yescharacteristic
49#64996C2211yescharacteristic
50#64990C411yescharacteristic
51#64884C2211yescharacteristic
52#64884C2211yescharacteristic
53#64883C2211yescharacteristic
54#64883C2211yescharacteristic
55#64883C2211yescharacteristic
56#64883C2211yescharacteristic
57#64882C2211yescharacteristic
58#64882C2211yescharacteristic
59#64882C2211yescharacteristic
60#64882C2211yescharacteristic
61#64882C2211yescharacteristic
62#64882C2211yescharacteristic
63#64881C2211yescharacteristic
64#64881C2211yescharacteristic
65#64881C2211yescharacteristic
66#64881C2211yescharacteristic
67#17831—51nomaximal, Sylow
68C2×#711D411yescharacteristic
69C2×#704—21no—
70C22×#170—21no—
71C2×#700—21no—
72C2×D5⋊C8—21no—
73C2×C5×M16C2×C411yescharacteristic
74C22×C5×C8C2×C411yescharacteristic
75C4×C5×D4C2×C411yescharacteristic
76D4×Dic5Q811yescharacteristic
77C4×C22⋊D5C2×C411yescharacteristic
78C4×C22⋊D5C2×C411yescharacteristic
79C2×C4×Dic5C2311yescharacteristic
80C2×C4×Dic5C2311yescharacteristic
81C2×#681C2×C411yescharacteristic
82C22×#168C2×C411yescharacteristic
83C2×#676C2×C411yescharacteristic
84C2×#676C2×C411yescharacteristic
85#4038D411yescharacteristic
86#4033Q811yescharacteristic
87#4027Q811yescharacteristic
88#4027Q811yescharacteristic
89#4023D411yescharacteristic
90#4023D411yescharacteristic
91C42×D5C2311yescharacteristic
92C4×Dic10C2×C411yescharacteristic
93C22⋊#170—21no—
94C22⋊#170—21no—
95C22⋊#170—21no—
96C22⋊#170—21no—
97C22⋊#170—21no—
98C22⋊#170—21no—
99#4004—21no—
100#4004—21no—
101#4003—21no—
102#4003—21no—
103#4002—21no—
104#4002—21no—
105#4002—21no—
106#4002—21no—
107C4⋊#170—21no—
108C4⋊#170—21no—
109C4⋊#170C2311yescharacteristic
110C4⋊#170C2311yescharacteristic
111C4⋊#170C2311yescharacteristic
112C4⋊#170C2311yescharacteristic
113C4⋊#170C2311yescharacteristic
114C4⋊#170C2311yescharacteristic
115C4⋊#170C2311yescharacteristic
116C4⋊#170C2311yescharacteristic
117C4×#170—21no—
118C4×#170—21no—
119C4×#170—21no—
120C4×#170—21no—
121C5×C4⋊C8C2×C411yescharacteristic
122C5×C22⋊C8C2×C411yescharacteristic
123C5×C22⋊C8C2×C411yescharacteristic
124C5×#97C2×C411yescharacteristic
125C22⋊#168C2×C411yescharacteristic
126C22⋊#168C2×C411yescharacteristic
127#3952C2×C411yescharacteristic
128#3952C2×C411yescharacteristic
129#3947C2×C411yescharacteristic
130#3947C2×C411yescharacteristic
131#3946C2×C411yescharacteristic
132#3946C2×C411yescharacteristic
133#3946C2×C411yescharacteristic
134#3946C2×C411yescharacteristic
135C8×Dic5C2×C411yescharacteristic
136C8×Dic5C2×C411yescharacteristic
137C8×Dic5C2311yescharacteristic
138C8×Dic5C2311yescharacteristic
139C8×Dic5C2311yescharacteristic
140C8×Dic5C2311yescharacteristic
141C4⋊#168C2×C411yescharacteristic
142#3935C2×C411yescharacteristic
143#2965—51no—
144#2925—51no—
145#2925—51no—
146#1574—51no—
147#1574—51no—
148#1573—51no—
149#1573—51no—
150#1572—51no—
151#1572—51no—
152#1569—51no—
153#1569—51no—
154#1568—51no—
155#1565—51no—
156#1565—51no—
157#1564—51no—
158C2×C5×D4C4⋊C411yescharacteristic
159C22×C4×C5C22×C411yescharacteristic
160C22×C4×C5C22×C411yescharacteristic
161C2×C22⋊D5C4⋊C411yescharacteristic
162C2×C22⋊D5C4⋊C411yescharacteristic
163C22×Dic5C2×D411yescharacteristic
164C22×Dic5C2×D411yescharacteristic
165C22×Dic5C2×Q811yescharacteristic
166C22×Dic5C2×Q811yescharacteristic
167#711—41no—
168#711—41no—
169C2×C4×D5C22×C411yescharacteristic
170C2×C4×D5C2×D411yescharacteristic
171C2×C4×D5C2×Q811yescharacteristic
172C2×Dic10C4⋊C411yescharacteristic
173#704—42no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—42no—
183#700—42no—
184D5⋊C8—42no—
185C5×M16—22no—
186C2×C5×C8—22no—
187C2×C5×C8C22×C411yescharacteristic
188C2×C5×C8C22×C411yescharacteristic
189C2×C5×C8C22×C411yescharacteristic
190C2×C5×C8C22×C411yescharacteristic
191C5×C4⋊C4C4⋊C411yescharacteristic
192C5×C22⋊C4C4⋊C411yescharacteristic
193C5×C22⋊C4C4⋊C411yescharacteristic
194C42×C5C22×C411yescharacteristic
195C22⋊Dic5C4⋊C411yescharacteristic
196C22⋊Dic5C4⋊C411yescharacteristic
197#685C4⋊C411yescharacteristic
198#685C4⋊C411yescharacteristic
199C4⋊Dic5C4⋊C411yescharacteristic
200#683C4⋊C411yescharacteristic
201#683C4⋊C411yescharacteristic
202#683C4⋊C411yescharacteristic
203#683C4⋊C411yescharacteristic
204C4×Dic5C22×C411yescharacteristic
205C4×Dic5C22×C411yescharacteristic
206C4×Dic5C2×D411yescharacteristic
207C4×Dic5C2×D411yescharacteristic
208C4×Dic5C2×D411yescharacteristic
209C4×Dic5C2×Q811yescharacteristic
210C4×Dic5C2×Q811yescharacteristic
211C4×Dic5C2×Q811yescharacteristic
212C4×Dic5C2411yescharacteristic
213#681—41no—
214C2×#168—41no—
215C2×#168C22×C411yescharacteristic
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C22×C411yescharacteristic
219#676—22no—
220#676—41no—
221C4×#41—51no—
222#446—51no—
223#446—51no—
224#436—51no—
225#436—51no—
226#435—51no—
227#435—51no—
228#435—51no—
229#435AGL(1,𝔽5)11yescharacteristic
230#433—101no—
231#433—101no—
232#433—101no—
233#433—101no—
234#432—51no—
235#432—51no—
236#432—51no—
237#432—51no—
238#431—51no—
239#431—51no—
240#431—51no—
241#431—51no—
242#431—51no—
243#431—51no—
244#431—51no—
245#423—51no—
246#423—51no—
247C2×C4⋊C8—51no—
248C2×C4⋊C8—51no—
249#408—101no—
250#408—101no—
251#405—101no—
252#405—101no—
253C4×M16—51no—
254C4×M16—51no—
255C2×C4×C8—51no—
256#335—51no—
257#335—51no—
258#335—51no—
259#335—51no—
260#335—51no—
261#335—51no—
262#335—51no—
263#335—51no—
264#334—51no—
265#334—51no—
266#334—51no—
267#334—51no—
268#334—51no—
269#334—51no—
270#334—51no—
271#334—51no—
272C23×C5C2×C4⋊C411yescharacteristic
273C23×C5C2×C4⋊C411yescharacteristic
274C22×D5C2×C4⋊C411yescharacteristic
275C5×D4—41no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5C2×C4⋊C411yescharacteristic
281C2×C4×C5C2×C4⋊C411yescharacteristic
282C2×C4×C5C2×C4⋊C411yescharacteristic
283C2×C4×C5C2×C4⋊C411yescharacteristic
284C2×C4×C5C23×C411yescharacteristic
285C22⋊D5—41no—
286C22⋊D5—41no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—41no—
292C2×Dic5—41no—
293C2×Dic5C2×C4⋊C411yescharacteristic
294C2×Dic5C2×C4⋊C411yescharacteristic
295C2×Dic5C2×C4⋊C411yescharacteristic
296C2×Dic5C2×C4⋊C411yescharacteristic
297C2×Dic5C2×C4⋊C411yescharacteristic
298C2×Dic5C22×D411yescharacteristic
299C2×Dic5C22×Q811yescharacteristic
300C4×D5—21no—
301C4×D5—21no—
302C4×D5—21no—
303C4×D5—21no—
304C4×D5—41no—
305Dic10—41no—
306#170—41no—
307#170—41no—
308#170—41no—
309#170—41no—
310#170—41no—
311#170—41no—
312#170—41no—
313#170—41no—
314C5×C8—21no—
315C5×C8—21no—
316C5×C8—21no—
317C5×C8#13112yes—
318#168—21no—
319#168—21no—
320#168—21no—
321#168—21no—
322C2×#41—51no—
323C2×M16—51no—
324C2×M16—51no—
325C2×M16—51no—
326C2×M16—101no—
327C2×M16—101no—
328C2×M16C2×AGL(1,𝔽5)11yescharacteristic
329C22×C8—51no—
330C22×C8—101no—
331C22×C8—101no—
332C22×C8C2×AGL(1,𝔽5)11yescharacteristic
333C4×Q8—51no—
334C4×Q8—51no—
335C4×D4—51no—
336C4×D4—51no—
337C4×D4—51no—
338C4×D4—51no—
339C4×D4—51no—
340C4×D4C2×AGL(1,𝔽5)11yescharacteristic
341#117—51no—
342#117—51no—
343#117—51no—
344C2×C42—51no—
345C2×C42—51no—
346C2×C42—51no—
347C4⋊C8—51no—
348C4⋊C8—51no—
349C4⋊C8—51no—
350C4⋊C8—51no—
351C4⋊C8—51no—
352C4⋊C8—51no—
353C4⋊C8—51no—
354C4⋊C8—51no—
355C4⋊C8—51no—
356C4⋊C8—51no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—101no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8C2×AGL(1,𝔽5)11yescharacteristic
365C22⋊C8—51no—
366C22⋊C8—51no—
367C22⋊C8—51no—
368C22⋊C8—51no—
369C22⋊C8—101no—
370C22⋊C8—101no—
371C22⋊C8—101no—
372C22⋊C8—101no—
373C22⋊C8—101no—
374C22⋊C8—101no—
375C22⋊C8—101no—
376C22⋊C8—101no—
377C22⋊C8C2×AGL(1,𝔽5)11yescharacteristic
378C22⋊C8C2×AGL(1,𝔽5)11yescharacteristic
379#97—51no—
380#97—51no—
381#97—51no—
382#97—101no—
383#97—101no—
384#97—101no—
385#97—101no—
386#97C2×AGL(1,𝔽5)11yescharacteristic
387C4×C8—51no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C22×C5—21no—
398C22×C5—21no—
399C22×C5—21no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—21no—
403C22×C5C22×C4⋊C411yescharacteristic
404C2×D5—21no—
405C2×D5—21no—
406C2×D5—21no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5C2×#13111yescharacteristic
412C4×C5#56811yescharacteristic
413Dic5—21no—
414Dic5—21no—
415Dic5—21no—
416Dic5—21no—
417Dic5—21no—
418Dic5—21no—
419Dic5#57511yescharacteristic
420Dic5#57511yescharacteristic
421#41—201no—
422#41—201no—
423C2×Q8—51no—
424C2×D4—51no—
425C2×D4—51no—
426C2×D4C4⋊AGL(1,𝔽5)11yescharacteristic
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4C22×AGL(1,𝔽5)11yescharacteristic
435C22×C4C22×AGL(1,𝔽5)11yescharacteristic
436M16—22no—
437M16—102no—
438M16—201no—
439M16—201no—
440M16—202no—
441M16—202no—
442C2×C8—22no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—51no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—201no—
456C2×C8—202no—
457C2×C8—202no—
458C2×C8C22×AGL(1,𝔽5)11yescharacteristic
459C2×C8C22×AGL(1,𝔽5)11yescharacteristic
460C2×C8C22×AGL(1,𝔽5)11yescharacteristic
461C2×C8C22×AGL(1,𝔽5)11yescharacteristic
462C4⋊C4—51no—
463C4⋊C4—51no—
464C4⋊C4—51no—
465C4⋊C4—51no—
466C4⋊C4—51no—
467C4⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
468C22⋊C4—51no—
469C22⋊C4—51no—
470C22⋊C4—51no—
471C22⋊C4—51no—
472C22⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
473C22⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
474C42—51no—
475C42—51no—
476C42—51no—
477C42—51no—
478C42—51no—
479C42—51no—
480C42—51no—
481C42—51no—
482C42—51no—
483C42C22×AGL(1,𝔽5)11yescharacteristic
484C2×C5—41no—
485C2×C5—41no—
486C2×C5#290611yescharacteristic
487C2×C5#291111yescharacteristic
488C2×C5#291611yescharacteristic
489D5—41no—
490C23—51no—
491C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
492C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
493Q8—201no—
494D4—41no—
495D4—201no—
496D4—201no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—51no—
502C2×C4—51no—
503C2×C4—51no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—51no—
507C2×C4—51no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—101no—
516C2×C4—201no—
517C2×C4—201no—
518C2×C4—201no—
519C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
520C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
521C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
522C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
523C2×C4C23×AGL(1,𝔽5)11yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—101no—
528C8—101no—
529C8—101no—
530C8—101no—
531C8—201no—
532C8—201no—
533C8—201no—
534C8—201no—
535C8—201no—
536C8—201no—
537C8—201no—
538C8—201no—
539C8#413112yes—
540C5#1783111yescharacteristic, complemented, Sylow
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—101no—
548C22—101no—
549C22—101no—
550C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—51no—
556C4—51no—
557C4—101no—
558C4—101no—
559C4—101no—
560C4—101no—
561C4—101no—
562C4—101no—
563C4C2×#413111yescharacteristic
564C4#6626411yescharacteristic
565C2—41no—
566C2—41no—
567C2—201no—
568C2#1061713711yescharacteristic
569C2#1061740911yescharacteristic
570C2#1061741911yescharacteristic
subgroupG/H
centerC22C22×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#435C4
socleC22×C5C22×C4⋊C4
prime radicalC2×#711D4
cosocleC4×Dic5C24
hypercenter#435AGL(1,𝔽5)
hypocenterC5#17831
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
4. #10604740C2semidirect
5. #10604738C2semidirect
6. #10604699C2semidirect
7. #10604694C2semidirect
8. #10604020C2semidirect
9. #10604018C2semidirect
10. #10603902C2semidirect
11. #10603901C2semidirect
12. #10603899C2semidirect
13. #10603899C2semidirect
14. #10603866C2semidirect
15. #10603865C2semidirect
540. C5#17831semidirect

Maximal subgroups

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

subgroupindex
#106171452
#106171432
#106111842
#106047402
#106047382
#106046992
#106046942
#106040202
#106040182
#106039022
#106039012
#106038992
#106038662
#106038652
#178315