Finite Group Databasebeta

← #12069409

Subgroups — #12069409

Order 1280.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611033C211yesmaximal, characteristic
2#10611022C211yesmaximal, characteristic
3#10610997C211yesmaximal, characteristic, complemented
4C5×#1454C211yesmaximal, characteristic, complemented
5#10601561C211yesmaximal, characteristic, complemented
6#10601556C211yesmaximal, characteristic
7#10601545C211yesmaximal, characteristic, complemented
8#10598880C211yesmaximal, characteristic, complemented
9#10598879C211yesmaximal, characteristic, complemented
10#10598877C211yesmaximal, characteristic, complemented
11#10598873C211yesmaximal, characteristic, complemented
12#10598872C211yesmaximal, characteristic, complemented
13#10598869C211yesmaximal, characteristic, complemented
14C8×Dic20C211yesmaximal, characteristic, complemented
15C8×#677C211yesmaximal, characteristic, complemented
16C4×#709C2211yescharacteristic
17#65804C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C5×#431C2211yescharacteristic
21#65215C2211yescharacteristic
22C2×C4⋊#168C2211yescharacteristic
23#65140C411yescharacteristic
24#65138C411yescharacteristic
25#65135C411yescharacteristic
26#65130C411yescharacteristic
27#65122—21no—
28D5×C4⋊C8—21no—
29#65117—21no—
30#65117—21no—
31#65022C411yescharacteristic
32#65022C411yescharacteristic
33#65014—21no—
34#65014—21no—
35#65012C411yescharacteristic
36#65012C411yescharacteristic
37#65009—21no—
38#65009—21no—
39C4×Dic20C2211yescharacteristic
40C4×Dic20C2211yescharacteristic
41C4×#677C2211yescharacteristic
42C4×#677C2211yescharacteristic
43C8×D20C2211yescharacteristic
44C8×D20C2211yescharacteristic
45#64968C2211yescharacteristic
46#64968C2211yescharacteristic
47C8×Dic10C2211yescharacteristic
48C8×Dic10C2211yescharacteristic
49C8×Dic10C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51C5×#322C2211yescharacteristic
52C5×#322C2211yescharacteristic
53C5×#322C2211yescharacteristic
54C5×C82C2211yescharacteristic
55#64679C2211yescharacteristic
56#64679C2211yescharacteristic
57#64678C2211yescharacteristic
58#64678C2211yescharacteristic
59#64677C2211yescharacteristic
60#64677C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64676C2211yescharacteristic
65#64676C2211yescharacteristic
66#64676C2211yescharacteristic
67#17921—51nomaximal, Sylow
68C2×#709C2×C411yescharacteristic
69C2×C42×C5C2311yescharacteristic
70C4×C22⋊D5—21no—
71C4×C22⋊D5—21no—
72#4072—21no—
73#4072C2×C411yescharacteristic
74#4070—21no—
75#4070C2×C411yescharacteristic
76#4070C2×C411yescharacteristic
77C22×#168—21no—
78C2×Dic20C2×C411yescharacteristic
79C2×Dic20C2×C411yescharacteristic
80C2×#677C2×C411yescharacteristic
81C2×#677C2×C411yescharacteristic
82C2×C8×D5—21no—
83C2×C8×D5—21no—
84C4×D20C2×C411yescharacteristic
85C4×D20C2311yescharacteristic
86#4018—21no—
87C42×D5—21no—
88#4016—21no—
89#4015C2×C411yescharacteristic
90#4015C2×C411yescharacteristic
91C4×Dic10—21no—
92C4×Dic10C2×C411yescharacteristic
93C4×Dic10C2311yescharacteristic
94C4×Dic10C2311yescharacteristic
95C4×Dic10C2311yescharacteristic
96C5×C4⋊C8—21no—
97C5×C4⋊C8C2×C411yescharacteristic
98C5×C4⋊C8C2×C411yescharacteristic
99C5×C4⋊C8D411yescharacteristic
100C5×C4⋊C8D411yescharacteristic
101C5×C22⋊C8—21no—
102C5×C22⋊C8C2×C411yescharacteristic
103C5×C22⋊C8C2×C411yescharacteristic
104C5×C22⋊C8D411yescharacteristic
105C5×C22⋊C8D411yescharacteristic
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2311yescharacteristic
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112C22⋊#168—21no—
113#3953C2×C411yescharacteristic
114#3953C2×C411yescharacteristic
115#3952—21no—
116#3952—21no—
117#3950C2×C411yescharacteristic
118#3950C2×C411yescharacteristic
119#3949C2×C411yescharacteristic
120#3949C2×C411yescharacteristic
121#3948C2×C411yescharacteristic
122#3948C2×C411yescharacteristic
123#3948C2×C411yescharacteristic
124#3948C2×C411yescharacteristic
125#3948C2×C411yescharacteristic
126#3948C2×C411yescharacteristic
127#3947—21no—
128#3947—21no—
129#3946—21no—
130#3946—21no—
131#3946—21no—
132#3946—21no—
133#3946—21no—
134#3946—21no—
135C8×Dic5—21no—
136C8×Dic5—21no—
137C8×Dic5—21no—
138C8×Dic5—21no—
139C4⋊#168—21no—
140C4⋊#168C2311yescharacteristic
141C4⋊#168C2311yescharacteristic
142C4⋊#168C2311yescharacteristic
143C4⋊#168C2311yescharacteristic
144#3935—21no—
145#3107—51no—
146#2988—51no—
147#2985—51no—
148#1587—51no—
149#1585—51no—
150#1584—51no—
151#1582—51no—
152#1579—51no—
153SD16⋊C8—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1573—51no—
157#1488—51no—
158#1481—51no—
159#1454D511yescharacteristic, complemented
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C2×C22⋊D5—21no—
164#709—22no—
165#709—22no—
166C2×D20C22×C411yescharacteristic
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×Dic10—21no—
171C2×Dic10C22×C411yescharacteristic
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8C22×C411yescharacteristic
177C2×C5×C8C22×C411yescharacteristic
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C2×D411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C2×C5×C8C2×D411yescharacteristic
184C42×C5C22×C411yescharacteristic
185C42×C5C2×D411yescharacteristic
186C42×C5#4111yescharacteristic
187C42×C5C2411yescharacteristic
188C22⋊Dic5—21no—
189C22⋊Dic5—21no—
190C22⋊Dic5—21no—
191#685—21no—
192#685—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5C22×C411yescharacteristic
197C4⋊Dic5C22×C411yescharacteristic
198C4⋊Dic5C22×C411yescharacteristic
199C4⋊Dic5C22×C411yescharacteristic
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205#683—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—81no—
216Dic20—22no—
217Dic20—22no—
218#677—22no—
219#677—22no—
220C8×D5—81no—
221C8×D5—81no—
222#533—51no—
223C4×#41—51no—
224#485—51no—
225#485—51no—
226#475—51no—
227#474—51no—
228#462—51no—
229#461—51no—
230#452—51no—
231#452—51no—
232#446—51no—
233#446—51no—
234#446—101no—
235#446—101no—
236C8×Q8—51no—
237C8×Q8—51no—
238C8×Q8—51no—
239C8×Q8—51no—
240C4×Q16—51no—
241C4×Q16—51no—
242C4×SD16—51no—
243C4×SD16—51no—
244C8×D4—51no—
245C8×D4—51no—
246C8×D4—101no—
247C8×D4—101no—
248#433—101no—
249#433—101no—
250#432—51no—
251#431—101no—
252#431C2×D511yescharacteristic
253#431C2×D511yescharacteristic
254#431C2×D511yescharacteristic
255C2×C4⋊C8—51no—
256C2×C4⋊C8—101no—
257#335—51no—
258#335—51no—
259#334—51no—
260#334—51no—
261Q8⋊C8—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267D4⋊C8—51no—
268D4⋊C8—51no—
269#322C2×D511yescharacteristic
270#322C2×D511yescharacteristic
271#322C2×D511yescharacteristic
272C82C2×D511yescharacteristic
273C23×C5C4×D411yescharacteristic
274C22×D5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—41no—
280C2×C4×C5C4×D411yescharacteristic
281C2×C4×C5C4×D411yescharacteristic
282C2×C4×C5C4×D411yescharacteristic
283C2×C4×C5C23×C411yescharacteristic
284C2×C4×C5C22×D411yescharacteristic
285C2×C4×C5C2×#4111yescharacteristic
286C22⋊D5—24no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294D20—21no—
295D20#13112yes—
296C4×D5—24no—
297C4×D5—41no—
298C4×D5—41no—
299C4×D5—81no—
300Dic10—21no—
301Dic10—21no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10—81no—
306Dic10#13112yes—
307C5×C8—21no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—21no—
314C5×C8—21no—
315C5×C8—41no—
316C5×C8—41no—
317#168—41no—
318#168—41no—
319#168—41no—
320#168—41no—
321C2×#41—51no—
322C2×Q16—51no—
323C2×Q16—51no—
324C2×SD16—51no—
325C2×SD16—51no—
326C22×C8—101no—
327C22×C8—101no—
328C22×C8—101no—
329C4⋊Q8—51no—
330C4⋊Q8—51no—
331#125—101no—
332C22⋊Q8—51no—
333C22⋊Q8—51no—
334C22⋊Q8—101no—
335C4×Q8—51no—
336C4×Q8—51no—
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—101no—
340C4×D4—51no—
341C4×D4—51no—
342C4×D4—101no—
343C4×D4—101no—
344#117—51no—
345#117—101no—
346#117—101no—
347C2×C42—101no—
348C2×C42C22×D511yescharacteristic
349#107—51no—
350#107—51no—
351#106—51no—
352#106—51no—
353C4⋊C8—21no—
354C4⋊C8—51no—
355C4⋊C8—51no—
356C4⋊C8—51no—
357C4⋊C8—51no—
358C4⋊C8—101no—
359C4⋊C8—101no—
360C4⋊C8—101no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8C4×D511yescharacteristic
366C4⋊C8C4×D511yescharacteristic
367C4⋊C8D2011yescharacteristic
368C4⋊C8D2011yescharacteristic
369#103—51no—
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#102—51no—
376#102—51no—
377C22⋊C8—21no—
378C22⋊C8—101no—
379C22⋊C8—101no—
380C22⋊C8—101no—
381C22⋊C8C4×D511yescharacteristic
382C22⋊C8C4×D511yescharacteristic
383C22⋊C8D2011yescharacteristic
384C22⋊C8D2011yescharacteristic
385#97—101no—
386#97—101no—
387#97—101no—
388C4×C8—101no—
389C4×C8—101no—
390C4×C8—101no—
391C4×C8—101no—
392C4×C8C22×D511yescharacteristic
393C4×C8C22×D511yescharacteristic
394C4×C8C22×D511yescharacteristic
395C4×C8C22×D511yescharacteristic
396C4×C8C22×D511yescharacteristic
397C4×C8C22×D511yescharacteristic
398C22×C5—21no—
399C22×C5—21no—
400C22×C5—21no—
401C22×C5C2×C4×D411yescharacteristic
402C2×D5—22no—
403C2×D5—41no—
404C2×D5—41no—
405C4×C5—21no—
406C4×C5—21no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5C2×#13111yescharacteristic
410C4×C5C2×#13111yescharacteristic
411C4×C5#57711yescharacteristic
412C4×C5#57811yescharacteristic
413Dic5—22no—
414Dic5—41no—
415Dic5—41no—
416Dic5—41no—
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420#41—102no—
421#41—102no—
422C2×Q8—51no—
423C2×Q8—51no—
424C2×Q8—51no—
425C2×Q8—101no—
426C2×D4—51no—
427C2×D4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4C2×C4×D511yescharacteristic
432C22×C4C2×D2011yescharacteristic
433C22×C4#70911yescharacteristic
434Q16—102no—
435Q16—102no—
436SD16—102no—
437SD16—102no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—101no—
441C2×C8—101no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—401no—
445C2×C8—401no—
446C2×C8—401no—
447C2×C8C2×C4×D511yescharacteristic
448C2×C8C2×C4×D511yescharacteristic
449C2×C8C2×C4×D511yescharacteristic
450C2×C8C2×C4×D511yescharacteristic
451C2×C8C2×D2011yescharacteristic
452C2×C8C2×D2011yescharacteristic
453C2×C8C2×D2011yescharacteristic
454C2×C8C2×D2011yescharacteristic
455C4⋊C4—51no—
456C4⋊C4—51no—
457C4⋊C4—51no—
458C4⋊C4—51no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C22⋊C4—101no—
469C22⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C22⋊C4—101no—
473C42—101no—
474C42—101no—
475C42—101no—
476C42—101no—
477C42—101no—
478C42C2×C4×D511yescharacteristic
479C42C2×D2011yescharacteristic
480C42#70911yescharacteristic
481C42C23×D511yescharacteristic
482C2×C5—41no—
483C2×C5#292911yescharacteristic
484C2×C5#294711yescharacteristic
485C2×C5#295711yescharacteristic
486D5—42no—
487C23—101no—
488C23C4×D2011yescharacteristic
489Q8—52no—
490Q8—101no—
491Q8—101no—
492Q8—101no—
493Q8—101no—
494Q8—101no—
495Q8—401no—
496D4—52no—
497D4—104no—
498D4—101no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—104no—
505C2×C4—101no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—201no—
513C2×C4—201no—
514C2×C4—401no—
515C2×C4C4×D2011yescharacteristic
516C2×C4C4×D2011yescharacteristic
517C2×C4C4×D2011yescharacteristic
518C2×C4C22×C4×D511yescharacteristic
519C2×C4C22×D2011yescharacteristic
520C2×C4C2×#70911yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—201no—
532C8—201no—
533C8—201no—
534C8—201no—
535C5#1792111yescharacteristic, complemented, Sylow
536C22—21no—
537C22—21no—
538C22—21no—
539C22—102no—
540C22—201no—
541C22—201no—
542C22C2×C4×D2011yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—102no—
548C4—201no—
549C4—201no—
550C4—201no—
551C4—201no—
552C4—201no—
553C4—201no—
554C4D5×#13111yescharacteristic
555C4D5×#13111yescharacteristic
556C4#6608511yescharacteristic
557C4#6608711yescharacteristic
558C2—41no—
559C2—202no—
560C2#1061028411yescharacteristic
561C2#1061030211yescharacteristic
562C2#1061031111yescharacteristic
subgroupG/H
centerC2×C4C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1454C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenter#1454D5
hypocenterC5#17921
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
3. #10610997C2semidirect
4. C5×#1454C2semidirect
5. #10601561C2semidirect
7. #10601545C2semidirect
8. #10598880C2semidirect
9. #10598879C2semidirect
10. #10598877C2semidirect
11. #10598873C2semidirect
12. #10598872C2semidirect
13. #10598869C2semidirect
14. C8×Dic20C2semidirect
15. C8×#677C2semidirect
159. #1454D5semidirect
535. C5#17921semidirect

Maximal subgroups

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

subgroupindex
#106110332
#106110222
#106109972
C5×#14542
#106015612
#106015562
#106015452
#105988802
#105988792
#105988772
#105988732
#105988722
#105988692
C8×Dic202
C8×#6772
#179215