Finite Group Databasebeta

← #13031487

Subgroups — #13031487

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617143C211yesmaximal, characteristic
2#10617137C211yesmaximal, characteristic
3#10611184C211yesmaximal, characteristic
4#10604740C211yesmaximal, characteristic, complemented
5#10604739C211yesmaximal, characteristic, complemented
6#10604697C211yesmaximal, characteristic, complemented
7C2×#64883C211yesmaximal, characteristic, complemented
8#10604020C211yesmaximal, characteristic, complemented
9#10604018C211yesmaximal, characteristic, complemented
10#10603902C211yesmaximal, characteristic, complemented
11#10603901C211yesmaximal, characteristic, complemented
12#10603898C211yesmaximal, characteristic, complemented
13#10603897C211yesmaximal, characteristic, complemented
14#10603867C211yesmaximal, characteristic, complemented
15#10603865C211yesmaximal, characteristic, complemented
16C2×#4131—21no—
17C4×#711C2211yescharacteristic
18#65775—21no—
19#65759C2211yescharacteristic
20#65758C2211yescharacteristic
21#65758C2211yescharacteristic
22#65758C2211yescharacteristic
23#65748C2211yescharacteristic
24C2×C4⋊#170C2211yescharacteristic
25C2×C4⋊#170C2211yescharacteristic
26C2×C4⋊#170C2211yescharacteristic
27#65708—21no—
28#65706—21no—
29#65697—21no—
30#65696—21no—
31#65696—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#64884C2211yescharacteristic
54#64884C2211yescharacteristic
55#64883C2211yescharacteristic
56#64883C2211yescharacteristic
57#64883C2211yescharacteristic
58#64883C2211yescharacteristic
59#64883C2211yescharacteristic
60#64883C2211yescharacteristic
61#64882C2211yescharacteristic
62#64882C2211yescharacteristic
63#64882C2211yescharacteristic
64#64882C2211yescharacteristic
65#64881C2211yescharacteristic
66#64881C2211yescharacteristic
67#17830—51nomaximal, Sylow
68C2×#711D411yescharacteristic
69C2×#704—21no—
70C2×#704—21no—
71C2×#704—21no—
72C22×#170—21no—
73C22×#170—21no—
74C22×#170—21no—
75#4131—44no—
76C2×#700—21no—
77C2×D5⋊C8—21no—
78C2×C5×M16C2×C411yescharacteristic
79C22×C5×C8C2×C411yescharacteristic
80C4×C5×D4C2×C411yescharacteristic
81D4×Dic5Q811yescharacteristic
82C4×C22⋊D5C2×C411yescharacteristic
83C4×C22⋊D5C2×C411yescharacteristic
84C2×C4×Dic5C2311yescharacteristic
85C2×C4×Dic5C2311yescharacteristic
86C2×#681C2×C411yescharacteristic
87C22×#168C2×C411yescharacteristic
88C2×#676C2×C411yescharacteristic
89C2×#676C2×C411yescharacteristic
90#4038D411yescharacteristic
91#4033Q811yescharacteristic
92#4027Q811yescharacteristic
93#4027Q811yescharacteristic
94#4023D411yescharacteristic
95#4023D411yescharacteristic
96C42×D5C2311yescharacteristic
97C4×Dic10C2×C411yescharacteristic
98C22⋊#170—21no—
99C22⋊#170—21no—
100#4004—21no—
101#4004—21no—
102#4004—21no—
103#4004—21no—
104#4003—21no—
105#4003—21no—
106#4002—21no—
107#4002—21no—
108C4⋊#170—21no—
109C4⋊#170—21no—
110C4⋊#170—21no—
111C4⋊#170—21no—
112C4⋊#170C2311yescharacteristic
113C4⋊#170C2311yescharacteristic
114C4⋊#170C2311yescharacteristic
115C4⋊#170C2311yescharacteristic
116C4⋊#170C2311yescharacteristic
117C4⋊#170C2311yescharacteristic
118C4⋊#170C2311yescharacteristic
119C4⋊#170C2311yescharacteristic
120C4×#170—21no—
121C4×#170—21no—
122C5×C4⋊C8C2×C411yescharacteristic
123C5×C22⋊C8C2×C411yescharacteristic
124C5×C22⋊C8C2×C411yescharacteristic
125C5×#97C2×C411yescharacteristic
126C22⋊#168C2×C411yescharacteristic
127C22⋊#168C2×C411yescharacteristic
128#3952C2×C411yescharacteristic
129#3952C2×C411yescharacteristic
130#3947C2×C411yescharacteristic
131#3947C2×C411yescharacteristic
132#3946C2×C411yescharacteristic
133#3946C2×C411yescharacteristic
134#3946C2×C411yescharacteristic
135#3946C2×C411yescharacteristic
136C8×Dic5C2×C411yescharacteristic
137C8×Dic5C2×C411yescharacteristic
138C8×Dic5C2311yescharacteristic
139C8×Dic5C2311yescharacteristic
140C8×Dic5C2311yescharacteristic
141C8×Dic5C2311yescharacteristic
142C4⋊#168C2×C411yescharacteristic
143#3935C2×C411yescharacteristic
144#2965—51no—
145#2925—51no—
146#2906—51no—
147#1574—51no—
148#1574—51no—
149#1573—51no—
150#1573—51no—
151#1571—51no—
152#1570—51no—
153#1569—51no—
154#1569—51no—
155#1567—51no—
156#1565—51no—
157#1565—51no—
158C2×#334—51no—
159C2×C5×D4C4⋊C411yescharacteristic
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C22×C411yescharacteristic
162C2×C22⋊D5C4⋊C411yescharacteristic
163C2×C22⋊D5C4⋊C411yescharacteristic
164C22×Dic5C2×D411yescharacteristic
165C22×Dic5C2×D411yescharacteristic
166C22×Dic5C2×Q811yescharacteristic
167C22×Dic5C2×Q811yescharacteristic
168#711—22no—
169#711—22no—
170C2×C4×D5C22×C411yescharacteristic
171C2×C4×D5C2×D411yescharacteristic
172C2×C4×D5C2×Q811yescharacteristic
173C2×Dic10C4⋊C411yescharacteristic
174#704—42no—
175#704—42no—
176#704—42no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—21no—
183C2×#170—21no—
184C2×#170—21no—
185C2×#170—42no—
186C2×#170—42no—
187C2×#170—42no—
188#700—42no—
189D5⋊C8—42no—
190C5×M16—41no—
191C2×C5×C8—41no—
192C2×C5×C8C22×C411yescharacteristic
193C2×C5×C8C22×C411yescharacteristic
194C2×C5×C8C22×C411yescharacteristic
195C2×C5×C8C22×C411yescharacteristic
196C5×C4⋊C4C4⋊C411yescharacteristic
197C5×C22⋊C4C4⋊C411yescharacteristic
198C5×C22⋊C4C4⋊C411yescharacteristic
199C42×C5C22×C411yescharacteristic
200C22⋊Dic5C4⋊C411yescharacteristic
201C22⋊Dic5C4⋊C411yescharacteristic
202#685C4⋊C411yescharacteristic
203#685C4⋊C411yescharacteristic
204C4⋊Dic5C4⋊C411yescharacteristic
205#683C4⋊C411yescharacteristic
206#683C4⋊C411yescharacteristic
207#683C4⋊C411yescharacteristic
208#683C4⋊C411yescharacteristic
209C4×Dic5C22×C411yescharacteristic
210C4×Dic5C22×C411yescharacteristic
211C4×Dic5C2×D411yescharacteristic
212C4×Dic5C2×D411yescharacteristic
213C4×Dic5C2×D411yescharacteristic
214C4×Dic5C2×Q811yescharacteristic
215C4×Dic5C2×Q811yescharacteristic
216C4×Dic5C2×Q811yescharacteristic
217C4×Dic5C2411yescharacteristic
218#681—22no—
219C2×#168—22no—
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222C2×#168C22×C411yescharacteristic
223C2×#168C22×C411yescharacteristic
224#676—22no—
225#676—41no—
226C2×#131—101no—
227C4×#41—51no—
228#446—51no—
229#446—51no—
230#436—51no—
231#436—51no—
232#435—51no—
233#435—51no—
234#435—51no—
235#435AGL(1,𝔽5)11yescharacteristic
236#433—101no—
237#433—101no—
238#432—51no—
239#432—51no—
240#431—51no—
241#431—51no—
242#431—51no—
243#431—51no—
244#431—51no—
245#424—101no—
246#424—101no—
247#424—101no—
248#423—51no—
249#423—51no—
250#423—51no—
251#423—51no—
252C2×C4⋊C8—51no—
253C2×C4⋊C8—51no—
254C2×C4⋊C8—51no—
255C2×C4⋊C8—51no—
256#408—101no—
257#405—101no—
258C4×M16—51no—
259C4×M16—51no—
260C2×C4×C8—51no—
261#335—51no—
262#335—51no—
263#335—51no—
264#335—51no—
265#335—51no—
266#335—51no—
267#335—51no—
268#335—51no—
269#334—51no—
270#334—51no—
271#334—51no—
272#334—51no—
273#334—51no—
274#334—51no—
275#334—51no—
276#334—51no—
277C23×C5C2×C4⋊C411yescharacteristic
278C23×C5C2×C4⋊C411yescharacteristic
279C22×D5C2×C4⋊C411yescharacteristic
280C5×D4—22no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5C2×C4⋊C411yescharacteristic
286C2×C4×C5C2×C4⋊C411yescharacteristic
287C2×C4×C5C2×C4⋊C411yescharacteristic
288C2×C4×C5C2×C4⋊C411yescharacteristic
289C2×C4×C5C23×C411yescharacteristic
290C22⋊D5—22no—
291C22⋊D5—22no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5C2×C4⋊C411yescharacteristic
297C2×Dic5C2×C4⋊C411yescharacteristic
298C2×Dic5C2×C4⋊C411yescharacteristic
299C2×Dic5C2×C4⋊C411yescharacteristic
300C2×Dic5C2×C4⋊C411yescharacteristic
301C2×Dic5AGL(1,ℤ/8)12yes—
302C2×Dic5#13712yes—
303C2×Dic5C22×D411yescharacteristic
304C2×Dic5C22×Q811yescharacteristic
305C4×D5—21no—
306C4×D5—21no—
307C4×D5—21no—
308C4×D5—21no—
309C4×D5—41no—
310Dic10—22no—
311#170—41no—
312#170—41no—
313#170—41no—
314#170—41no—
315#170—41no—
316#170—41no—
317#170—41no—
318#170—41no—
319C5×C8—21no—
320C5×C8—21no—
321C5×C8—21no—
322C5×C8—21no—
323#168—21no—
324#168—21no—
325#168—21no—
326#168#13112yescomplemented
327C2×#41—51no—
328#131—204no—
329C2×M16—51no—
330C2×M16—51no—
331C2×M16—51no—
332C2×M16—101no—
333C2×M16—101no—
334C2×M16—101no—
335C2×M16—101no—
336C2×M16C2×AGL(1,𝔽5)11yescharacteristic
337C22×C8—51no—
338C22×C8—101no—
339C22×C8—101no—
340C22×C8—101no—
341C22×C8—101no—
342C22×C8C2×AGL(1,𝔽5)11yescharacteristic
343C4×Q8—51no—
344C4×Q8—51no—
345C4×D4—51no—
346C4×D4—51no—
347C4×D4—51no—
348C4×D4—51no—
349C4×D4—51no—
350C4×D4C2×AGL(1,𝔽5)11yescharacteristic
351#117—51no—
352#117—51no—
353#117—51no—
354C2×C42—51no—
355C2×C42—51no—
356C2×C42—51no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—51no—
362C4⋊C8—51no—
363C4⋊C8—51no—
364C4⋊C8—51no—
365C4⋊C8—51no—
366C4⋊C8—51no—
367C4⋊C8—51no—
368C4⋊C8—51no—
369C4⋊C8—51no—
370C4⋊C8—101no—
371C4⋊C8—101no—
372C4⋊C8—101no—
373C4⋊C8—101no—
374C4⋊C8—101no—
375C4⋊C8—101no—
376C4⋊C8—101no—
377C4⋊C8—101no—
378C4⋊C8C2×AGL(1,𝔽5)11yescharacteristic
379C22⋊C8—51no—
380C22⋊C8—51no—
381C22⋊C8—51no—
382C22⋊C8—51no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385C22⋊C8—101no—
386C22⋊C8—101no—
387C22⋊C8C2×AGL(1,𝔽5)11yescharacteristic
388C22⋊C8C2×AGL(1,𝔽5)11yescharacteristic
389#97—51no—
390#97—51no—
391#97—51no—
392#97—101no—
393#97—101no—
394#97C2×AGL(1,𝔽5)11yescharacteristic
395C4×C8—51no—
396C4×C8—51no—
397C4×C8—51no—
398C4×C8—51no—
399C4×C8—51no—
400C4×C8—51no—
401C4×C8—101no—
402C4×C8—101no—
403C22×C5—21no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—21no—
407C22×C5—21no—
408C22×C5#42812yes—
409C22×C5C22×C4⋊C411yescharacteristic
410C2×D5—21no—
411C2×D5—21no—
412C2×D5—21no—
413C4×C5—21no—
414C4×C5—21no—
415C4×C5—21no—
416C4×C5—21no—
417C4×C5C2×#13111yescharacteristic
418C4×C5#56811yescharacteristic
419Dic5—21no—
420Dic5—21no—
421Dic5—21no—
422Dic5—21no—
423Dic5—21no—
424Dic5#42812yes—
425Dic5C2×AGL(1,ℤ/8)11yescharacteristic
426Dic5C2×#13711yescharacteristic
427#41—102no—
428#41—102no—
429C2×Q8—51no—
430C2×D4—51no—
431C2×D4—51no—
432C2×D4C4⋊AGL(1,𝔽5)11yescharacteristic
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—51no—
438C22×C4—51no—
439C22×C4—51no—
440C22×C4C22×AGL(1,𝔽5)11yescharacteristic
441C22×C4C22×AGL(1,𝔽5)11yescharacteristic
442M16—41no—
443M16—102no—
444M16—102no—
445M16—201no—
446M16—202no—
447M16—202no—
448M16—202no—
449M16—202no—
450C2×C8—41no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—51no—
454C2×C8—51no—
455C2×C8—102no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—202no—
465C2×C8—202no—
466C2×C8—202no—
467C2×C8—202no—
468C2×C8C22×AGL(1,𝔽5)11yescharacteristic
469C2×C8C22×AGL(1,𝔽5)11yescharacteristic
470C2×C8C22×AGL(1,𝔽5)11yescharacteristic
471C2×C8C22×AGL(1,𝔽5)11yescharacteristic
472C4⋊C4—51no—
473C4⋊C4—51no—
474C4⋊C4—51no—
475C4⋊C4—51no—
476C4⋊C4—51no—
477C4⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
478C22⋊C4—51no—
479C22⋊C4—51no—
480C22⋊C4—51no—
481C22⋊C4—51no—
482C22⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
483C22⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
484C42—51no—
485C42—51no—
486C42—51no—
487C42—51no—
488C42—51no—
489C42—51no—
490C42—51no—
491C42—51no—
492C42—51no—
493C42C22×AGL(1,𝔽5)11yescharacteristic
494C2×C5—22no—
495C2×C5—41no—
496C2×C5#290611yescharacteristic
497C2×C5C2×#42811yescharacteristic
498C2×C5#291611yescharacteristic
499D5—41no—
500C23—51no—
501C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
502C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
503Q8—102no—
504D4—22no—
505D4—102no—
506D4—102no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—52no—
512C2×C4—52no—
513C2×C4—51no—
514C2×C4—51no—
515C2×C4—51no—
516C2×C4—51no—
517C2×C4—51no—
518C2×C4—51no—
519C2×C4—51no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
530C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
531C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
532C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
533C2×C4C23×AGL(1,𝔽5)11yescharacteristic
534C8—21no—
535C8—21no—
536C8—21no—
537C8—21no—
538C8—52no—
539C8—101no—
540C8—101no—
541C8—101no—
542C8—201no—
543C8—201no—
544C8—201no—
545C8—201no—
546C8—201no—
547C8—201no—
548C8—201no—
549C8—201no—
550C5#1783011yescharacteristic, complemented, Sylow
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—101no—
557C22—101no—
558C22—101no—
559C22#6572712yes—
560C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—51no—
566C4—51no—
567C4—52no—
568C4—101no—
569C4—101no—
570C4—101no—
571C4—101no—
572C4—101no—
573C4#6625611yescharacteristic
574C4D5⋊#13111yescharacteristic
575C2—22no—
576C2—41no—
577C2—201no—
578C2#1061713811yescharacteristic
579C2C2×#6572711yescharacteristic
580C2#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#17830
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. #10604739C2semidirect
6. #10604697C2semidirect
7. C2×#64883C2semidirect
8. #10604020C2semidirect
9. #10604018C2semidirect
10. #10603902C2semidirect
11. #10603901C2semidirect
12. #10603898C2semidirect
13. #10603897C2semidirect
14. #10603867C2semidirect
15. #10603865C2semidirect
326. #168#131semidirect
550. C5#17830semidirect

Maximal subgroups

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

subgroupindex
#106171432
#106171372
#106111842
#106047402
#106047392
#106046972
C2×#648832
#106040202
#106040182
#106039022
#106039012
#106038982
#106038972
#106038672
#106038652
#178305