Finite Group Databasebeta

← #12129351

Subgroups — #12129351

Order 1280.

752 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4070C211yesmaximal, characteristic
2#10613791C211yesmaximal, characteristic
3C4×C5×C22⋊C8C211yesmaximal, characteristic
4#10600733C211yesmaximal, characteristic
5#10600731C211yesmaximal, characteristic
6#10600730C211yesmaximal, characteristic
7#10600729C211yesmaximal, characteristic
8C4×#3950C211yesmaximal, characteristic, complemented
9C4×#3949C211yesmaximal, characteristic, complemented
10C4×#3948C211yesmaximal, characteristic, complemented
11C4×#3948C211yesmaximal, characteristic, complemented
12#10599486C211yesmaximal, characteristic, complemented
13#10599437C211yesmaximal, characteristic, complemented
14#10599434C211yesmaximal, characteristic, complemented
15#10599431C211yesmaximal, characteristic, complemented
16C22×C42×C5C2211yescharacteristic
17C2×#4070C2211yescharacteristic
18C2×C4×Dic10C2211yescharacteristic
19C2×C5×C22⋊C8C2211yescharacteristic
20C2×C5×C22⋊C8C2211yescharacteristic
21C2×C4×C5×C8C2211yescharacteristic
22C2×C4×C5×C8C2211yescharacteristic
23#65501C2211yescharacteristic
24#65501C2211yescharacteristic
25#65501C2211yescharacteristic
26#65500—21no—
27#65499—21no—
28C4×C22⋊Dic5—21no—
29C4×C22⋊Dic5—21no—
30C2×#3950C2211yescharacteristic
31C2×#3950C2211yescharacteristic
32C2×#3949C2211yescharacteristic
33C2×#3949C2211yescharacteristic
34C2×#3948C2211yescharacteristic
35C2×#3948C2211yescharacteristic
36C2×#3948C2211yescharacteristic
37C2×#3948C2211yescharacteristic
38#65226—21no—
39#65225C2211yescharacteristic
40#65225C2211yescharacteristic
41C4×C4⋊Dic5C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44#65222—21no—
45#65221—21no—
46C4×#683—21no—
47#65218C2211yescharacteristic
48#65217C2211yescharacteristic
49C5×#336C2211yescharacteristic
50C5×#336C2211yescharacteristic
51#64771C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64771C2211yescharacteristic
59#23759—51nomaximal, Sylow
60C23×C4×C5D411yescharacteristic
61C23×C4×C5D411yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C22×Dic10C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C2×C42×C5—22no—
69C2×C42×C5—22no—
70C2×C42×C5D411yescharacteristic
71C2×C42×C5D411yescharacteristic
72C2×C42×C5C2311yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C22⋊Dic5—21no—
75C2×C22⋊Dic5—21no—
76C2×C22⋊Dic5—21no—
77C2×C22⋊Dic5—21no—
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
82C2×C4⋊Dic5C2311yescharacteristic
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85#4070—22no—
86#4070—22no—
87C2×#683—21no—
88C2×#683—21no—
89C2×#683—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C4×Dic10—22no—
95C4×Dic10—22no—
96C5×C22⋊C8—22no—
97C5×C22⋊C8—22no—
98C4×C5×C8—22no—
99C4×C5×C8—22no—
100#3963—21no—
101#3963—21no—
102#3963—21no—
103#3963—21no—
104#3963—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3950—22no—
114#3950—22no—
115#3949—22no—
116#3949—22no—
117#3948—22no—
118#3948—22no—
119#3948—22no—
120#3948—22no—
121C4×C22⋊Q8—51no—
122#2283—51no—
123#2101—51no—
124#2097—51no—
125#2085—51no—
126#2077—51no—
127#2075—51no—
128#2074—51no—
129#2036—51no—
130#2035—51no—
131C4×#107—51no—
132C4×#106—51no—
133C4×#103—51no—
134C4×#103—51no—
135C4×C22⋊C8D511yescharacteristic
136C24×C5C2×D411yescharacteristic
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—41no—
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2411yescharacteristic
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5—21no—
163C2×Dic10—21no—
164C2×Dic10—21no—
165C2×Dic10—21no—
166C2×Dic10—21no—
167C2×Dic10—21no—
168C2×Dic10#4112yes—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8#4112yes—
180C2×C5×C8#4112yes—
181C42×C5—22no—
182C42×C5—22no—
183C42×C5—21no—
184C42×C5—21no—
185C42×C5#4112yes—
186C42×C5#4112yes—
187C22⋊Dic5—24no—
188C22⋊Dic5—42no—
189C22⋊Dic5—42no—
190C22⋊Dic5—42no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5#4112yes—
205#683—24no—
206#683—42no—
207#683—42no—
208C4×Dic5—42no—
209C4×Dic5—42no—
210C4×Dic5—42no—
211C4×Dic5—42no—
212C2×C22⋊Q8—51no—
213C2×C4×Q8—51no—
214C22×C42C2×D511yescharacteristic
215C2×#107—51no—
216C2×#107—51no—
217C2×#106—51no—
218C2×#106—51no—
219C2×#103—51no—
220C2×#103—51no—
221C2×#103—51no—
222C2×#103—51no—
223C2×C22⋊C8C2×D511yescharacteristic
224C2×C22⋊C8C2×D511yescharacteristic
225C2×C4×C8C2×D511yescharacteristic
226C2×C4×C8C2×D511yescharacteristic
227#391—51no—
228#389—51no—
229#387—101no—
230#385—101no—
231#383—101no—
232#382—51no—
233#382—51no—
234#381—101no—
235#380—51no—
236#380—51no—
237#380—51no—
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—101no—
242C4×C22⋊C4—101no—
243C4×C22⋊C4—101no—
244#376—101no—
245#340—51no—
246#340—51no—
247#340—51no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#336C2×D511yescharacteristic
254#336C2×D511yescharacteristic
255C23×C5—21no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5#13512yes—
262C23×C5C22×D411yescharacteristic
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—44no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—44no—
280C2×C4×C5#12312yes—
281C2×C4×C5#12312yes—
282C2×C4×C5#13512yes—
283C2×C4×C5#13712yes—
284C2×C4×C5C2×#4111yescharacteristic
285C2×C4×C5C2×#4111yescharacteristic
286C2×C4×C5C2×#4111yescharacteristic
287C2×C4×C5C2×#4111yescharacteristic
288C2×C4×C5C2×#4111yescharacteristic
289C2×C4×C5C2×#4111yescharacteristic
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314Dic10—22no—
315Dic10—22no—
316Dic10—41no—
317Dic10—41no—
318C5×C8—22no—
319C5×C8—22no—
320C5×C8—41no—
321C5×C8—41no—
322C22×Q8—51no—
323C23×C4D2011yescharacteristic
324C23×C4D2011yescharacteristic
325C23×C4C22×D511yescharacteristic
326C22×C8C22×D511yescharacteristic
327C22×C8C22×D511yescharacteristic
328C22×C8C22×D511yescharacteristic
329C22×C8C22×D511yescharacteristic
330C22⋊Q8—102no—
331C22⋊Q8—102no—
332C4×Q8—102no—
333C4×Q8—102no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—51no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—101no—
342C2×C4⋊C4—101no—
343C2×C4⋊C4—101no—
344C2×C22⋊C4—101no—
345C2×C22⋊C4—101no—
346C2×C22⋊C4—101no—
347C2×C22⋊C4—101no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—101no—
351C2×C42—101no—
352C2×C42—101no—
353C2×C42—101no—
354C2×C42D2011yescharacteristic
355C2×C42D2011yescharacteristic
356C2×C42C22×D511yescharacteristic
357C2×C42C22×D511yescharacteristic
358#107—102no—
359#107—102no—
360#106—102no—
361#106—102no—
362#103—102no—
363#103—102no—
364#103—102no—
365#103—102no—
366C22⋊C8—22no—
367C22⋊C8—22no—
368C4×C8—22no—
369C4×C8—22no—
370#95—101no—
371#95—101no—
372#95—101no—
373#95—101no—
374#95—101no—
375#95—101no—
376#95—101no—
377#95—101no—
378#95—101no—
379#95—101no—
380#95—101no—
381#95—101no—
382#95—101no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—41no—
387C22×C5—41no—
388C22×C5—41no—
389C22×C5—41no—
390C22×C5C2×#12311yescharacteristic
391C22×C5#52511yescharacteristic
392C22×C5#53211yescharacteristic
393C22×C5C2×#13511yescharacteristic
394C22×C5C2×#13511yescharacteristic
395C22×C5C2×#13711yescharacteristic
396C22×C5#57511yescharacteristic
397C4×C5—22no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5#48514yes—
402C4×C5#52911yescharacteristic
403C4×C5#52911yescharacteristic
404C4×C5#52911yescharacteristic
405C4×C5#52911yescharacteristic
406Dic5—42no—
407Dic5—42no—
408Dic5—81no—
409Dic5—81no—
410Dic5—81no—
411Dic5—81no—
412Dic5—81no—
413Dic5—81no—
414C24C2×D2011yescharacteristic
415C2×Q8—52no—
416C2×Q8—101no—
417C2×Q8—101no—
418C2×Q8—101no—
419C2×Q8—101no—
420C2×Q8—101no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4C2×D2011yescharacteristic
442C22×C4C2×D2011yescharacteristic
443C22×C4C2×D2011yescharacteristic
444C22×C4C2×D2011yescharacteristic
445C22×C4C2×D2011yescharacteristic
446C22×C4C23×D511yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8#70912yes—
458C2×C8#70912yes—
459C4⋊C4—52no—
460C4⋊C4—104no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—202no—
475C4⋊C4—202no—
476C22⋊C4—104no—
477C22⋊C4—202no—
478C22⋊C4—202no—
479C22⋊C4—202no—
480C42—21no—
481C42—21no—
482C42—22no—
483C42—22no—
484C42—202no—
485C42—202no—
486C42—202no—
487C42—202no—
488C42#71112yes—
489C42#71112yes—
490C2×C5—42no—
491C2×C5#239511yescharacteristic
492C2×C5C2×#48511yescharacteristic
493C2×C5#309111yescharacteristic
494C2×C5#310211yescharacteristic
495C2×C5#310811yescharacteristic
496C2×C5#316811yescharacteristic
497C2×C5#317211yescharacteristic
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#405012yes—
505C23C22×D2011yescharacteristic
506Q8—102no—
507Q8—102no—
508Q8—201no—
509Q8—201no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—44no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—201no—
540C2×C4—201no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4#403212yes—
552C2×C4#403212yes—
553C2×C4#405012yes—
554C2×C4#405512yes—
555C2×C4C2×#70911yescharacteristic
556C2×C4C2×#70911yescharacteristic
557C2×C4C2×#71111yescharacteristic
558C2×C4C2×#71111yescharacteristic
559C2×C4D5×#4111yescharacteristic
560C2×C4D5×#4111yescharacteristic
561C8—22no—
562C8—22no—
563C8—41no—
564C8—41no—
565C5#2375911yescharacteristic, complemented, Sylow
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#6581111yescharacteristic
574C22C2×#403211yescharacteristic
575C22#6585811yescharacteristic
576C22C2×#405011yescharacteristic
577C22C2×#405011yescharacteristic
578C22C2×#405511yescharacteristic
579C22#6608211yescharacteristic
580C4—22no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—202no—
585C4—202no—
586C4—401no—
587C4—401no—
588C4—401no—
589C4—401no—
590C4—401no—
591C4—401no—
592C4#6501214yes—
593C4#6587211yescharacteristic
594C4#6587211yescharacteristic
595C4#6589111yescharacteristic
596C4#6589111yescharacteristic
597C2—42no—
598C2#1060531411yescharacteristic
599C2#1061020011yescharacteristic
600C2#1061027011yescharacteristic
601C2C2×#6501211yescharacteristic
602C2#1061032211yescharacteristic
603C2#1061103011yescharacteristic
604C2#1061104211yescharacteristic
subgroupG/H
centerC22×C4C2×D20
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC4×C5×C22⋊C8C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenterC4×C22⋊C8D5
hypocenterC5#23759
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
8. C4×#3950C2semidirect
9. C4×#3949C2semidirect
10. C4×#3948C2semidirect
11. C4×#3948C2semidirect
12. #10599486C2semidirect
13. #10599437C2semidirect
14. #10599434C2semidirect
15. #10599431C2semidirect
565. C5#23759semidirect

Maximal subgroups

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

subgroupindex
C4×#40702
#106137912
C4×C5×C22⋊C82
#106007332
#106007312
#106007302
#106007292
C4×#39502
C4×#39492
C4×#39482
#105994862
#105994372
#105994342
#105994312
#237595