Finite Group Databasebeta

← #12004839

Subgroups — #12004839

Order 1280.

1186 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66079C211yesmaximal, characteristic
2C2×#65428C211yesmaximal, characteristic
3C2×#65255C211yesmaximal, characteristic
4C2×C5×#343C211yesmaximal, characteristic, complemented
5C2×#64779C211yesmaximal, characteristic, complemented
6C2×#64780C211yesmaximal, characteristic, complemented
7#10602351C211yesmaximal, characteristic, complemented
8C22×#709C2211yescharacteristic
9C22×C5×M16C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C2×#4072C2211yescharacteristic
13C22×#681C2211yescharacteristic
14C22×#681C2211yescharacteristic
15#66079—22no—
16#66079—22no—
17#66079—22no—
18#66079C414yescomplemented
19C2×#4053—22no—
20C2×D5×M16—22no—
21C2×#4047—22no—
22#65428—22no—
23#65428C414yescomplemented
24C2×#3957—22no—
25C2×#3942C412yescomplemented
26#65255—22no—
27#65255—22no—
28C2×#3941C412yescomplemented
29C5×#343—22no—
30#64780—22no—
31#64779—22no—
32#64749—22no—
33#10784—51nomaximal, Sylow
34C23×C4×C5—21no—
35C23×C4×C5C2311yescharacteristic
36C22×C22⋊D5—21no—
37C2×#709—21no—
38C2×#709—21no—
39C2×#709—21no—
40C2×#709—21no—
41C2×#709—21no—
42C2×#709—21no—
43C2×#709C2×C412yes—
44C2×#709C2×C412yes—
45C2×#709D412yes—
46C2×#709D412yes—
47C2×#709D412yes—
48C2×#709Q812yes—
49C22×D20C2×C411yescharacteristic
50C22×C4×D5—21no—
51C22×Dic10C2×C411yescharacteristic
52C2×C5×M16—21no—
53C2×C5×M16—21no—
54C2×C5×M16—21no—
55C2×C5×M16—21no—
56C2×C5×M16—21no—
57C2×C5×M16—21no—
58C2×C5×M16—21no—
59C2×C5×M16—21no—
60C2×C5×M16C2×C412yes—
61C2×C5×M16C2×C412yes—
62C2×C5×M16D412yes—
63C2×C5×M16D412yes—
64C22×C5×C8—21no—
65C22×C5×C8—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C2×C412yes—
72C2×C22⋊Dic5—21no—
73#4072—21no—
74#4072—21no—
75#4072—21no—
76#4072C2×C412yes—
77C2×C4⋊Dic5—21no—
78C2×C4×Dic5—21no—
79C2×#681—21no—
80C2×#681—21no—
81C2×#681—21no—
82C2×#681—21no—
83C2×#681—21no—
84C2×#681—21no—
85C2×#681—21no—
86C2×#681—21no—
87C2×#681—21no—
88C2×#681—21no—
89C2×#681C2×C412yes—
90C2×#681D412yes—
91C22×#168C2×C412yes—
92C22×#168D412yes—
93#4053—28no—
94#4053—28no—
95D5×M16—28no—
96D5×M16—28no—
97#4047—28no—
98#4047—28no—
99C2×#676—24no—
100C2×C8×D5—24no—
101#3957—28no—
102#3942—24no—
103#3941—24no—
104C2×#568—51no—
105C2×#421—51no—
106C2×#417—51no—
107C2×#344—51no—
108C2×#343D511yescharacteristic, complemented
109#1736—51no—
110C2×#338—51no—
111C24×C5#4111yescharacteristic
112C23×D5—21no—
113C22×C4×C5—22no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—82no—
117C22×C4×C5C22×C411yescharacteristic
118C22×C4×C5C22×C411yescharacteristic
119C22×C4×C5C22×C411yescharacteristic
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2×D411yescharacteristic
123C22×C4×C5C2×D411yescharacteristic
124C22×C4×C5C2×D411yescharacteristic
125C22×C4×C5C2×D411yescharacteristic
126C22×C4×C5C2×D411yescharacteristic
127C22×C4×C5C2×Q811yescharacteristic
128C22×C4×C5#4111yescharacteristic
129C22×C4×C5#4111yescharacteristic
130C22×C4×C5#4111yescharacteristic
131C2×C22⋊D5—22no—
132C2×C22⋊D5—22no—
133C2×C22⋊D5—22no—
134C2×C22⋊D5—22no—
135C2×C22⋊D5—22no—
136C2×C22⋊D5—22no—
137C22×Dic5—21no—
138C22×Dic5—41no—
139#709—22no—
140#709—22no—
141#709—22no—
142#709—22no—
143#709—22no—
144#709—22no—
145#709—22no—
146#709—22no—
147#709—22no—
148#709—22no—
149#709—22no—
150#709—22no—
151#709C22⋊C414yes—
152#709C22⋊C414yes—
153#709C4⋊C414yes—
154#709C4⋊C414yes—
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20C4212yes—
159C2×D20C22⋊C412yes—
160C2×D20C4⋊C412yes—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—22no—
166C2×C4×D5—22no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10C4212yes—
171C2×Dic10C22⋊C412yes—
172C2×Dic10C4⋊C412yes—
173C5×M16—22no—
174C5×M16—22no—
175C5×M16—22no—
176C5×M16—22no—
177C5×M16—22no—
178C5×M16—41no—
179C5×M16—41no—
180C5×M16C22⋊C414yes—
181C2×C5×C8—22no—
182C2×C5×C8—22no—
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—41no—
186C2×C5×C8—41no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—41no—
190C5×C4⋊C4—41no—
191C22⋊Dic5—22no—
192C22⋊Dic5—41no—
193C4⋊Dic5—22no—
194C4⋊Dic5—41no—
195C4×Dic5—22no—
196C4×Dic5—41no—
197#681—22no—
198#681—22no—
199#681—22no—
200#681—22no—
201#681—41no—
202#681—41no—
203#681—41no—
204#681—41no—
205C2×#168—22no—
206C2×#168—22no—
207C2×#168—22no—
208C2×#168—22no—
209C2×#168—22no—
210C2×#168C22⋊C414yes—
211#676—216no—
212C8×D5—216no—
213C22×#41—51no—
214#568—54no—
215#568—102no—
216#568—102no—
217#568—102no—
218C2×#131—102no—
219C2×#131—102no—
220C22×M16—51no—
221C22×M16—51no—
222C22×M16—102no—
223C22×M16C2×D511yescharacteristic
224C22×M16C2×D511yescharacteristic
225C2×#117—51no—
226C22×C4⋊C4C2×D511yescharacteristic
227#421—54no—
228#421—102no—
229C2×#104—102no—
230#417—102no—
231#417—102no—
232C2×#103—52no—
233C2×#102—52no—
234#344—102no—
235#343—22no—
236#340—102no—
237#338—102no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5#11711yescharacteristic
241C23×C5C4×D411yescharacteristic
242C23×C5C4×D411yescharacteristic
243C23×C5#12111yescharacteristic
244C23×C5C22⋊Q811yescharacteristic
245C23×C5#12311yescharacteristic
246C23×C5#12311yescharacteristic
247C22×D5—22no—
248C22×D5—22no—
249C22×D5—22no—
250C22×D5—81no—
251C22×D5—81no—
252C2×C4×C5—42no—
253C2×C4×C5—82no—
254C2×C4×C5—82no—
255C2×C4×C5—82no—
256C2×C4×C5C2×C4211yescharacteristic
257C2×C4×C5C2×C22⋊C411yescharacteristic
258C2×C4×C5C2×C22⋊C411yescharacteristic
259C2×C4×C5C2×C22⋊C411yescharacteristic
260C2×C4×C5C2×C22⋊C411yescharacteristic
261C2×C4×C5C2×C22⋊C411yescharacteristic
262C2×C4×C5C2×C4⋊C411yescharacteristic
263C2×C4×C5C2×C4⋊C411yescharacteristic
264C2×C4×C5C2×C4⋊C411yescharacteristic
265C2×C4×C5#11711yescharacteristic
266C2×C4×C5C4×D411yescharacteristic
267C2×C4×C5C4×D411yescharacteristic
268C2×C4×C5C4×D411yescharacteristic
269C2×C4×C5C4×D411yescharacteristic
270C2×C4×C5C4×D411yescharacteristic
271C2×C4×C5C4×D411yescharacteristic
272C2×C4×C5#12011yescharacteristic
273C2×C4×C5#12011yescharacteristic
274C2×C4×C5#12011yescharacteristic
275C2×C4×C5#12011yescharacteristic
276C2×C4×C5#12111yescharacteristic
277C2×C4×C5#12111yescharacteristic
278C2×C4×C5#12111yescharacteristic
279C2×C4×C5C22⋊Q811yescharacteristic
280C2×C4×C5C22⋊Q811yescharacteristic
281C2×C4×C5C22⋊Q811yescharacteristic
282C2×C4×C5#12311yescharacteristic
283C2×C4×C5#12311yescharacteristic
284C22⋊D5—24no—
285C22⋊D5—24no—
286C22⋊D5—24no—
287C22⋊D5—24no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—42no—
292C2×Dic5—81no—
293C2×Dic5—81no—
294D20—22no—
295D20—22no—
296D20—22no—
297D20#9514yes—
298C4×D5—24no—
299C4×D5—24no—
300C4×D5—24no—
301C4×D5—24no—
302Dic10—22no—
303Dic10—22no—
304Dic10—22no—
305Dic10#9514yes—
306C5×C8—24no—
307C5×C8—42no—
308#168—24no—
309#168—42no—
310C2×#41—52no—
311C2×#41—52no—
312C2×#41—52no—
313C2×#41—52no—
314C2×#41—52no—
315C2×#41—52no—
316C2×#41—101no—
317C2×#41—101no—
318C2×#41—101no—
319C2×#41—101no—
320C2×#41—101no—
321C2×#41—101no—
322C22×Q8—51no—
323C22×D4—51no—
324C22×D4—101no—
325C23×C4—21no—
326C23×C4—101no—
327C23×C4C22×D511yescharacteristic
328#131—108no—
329#131—108no—
330#131—108no—
331#131—108no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—52no—
341C2×M16—52no—
342C2×M16—104no—
343C2×M16—108no—
344C2×M16—101no—
345C2×M16—101no—
346C2×M16—101no—
347C2×M16—101no—
348C2×M16—108no—
349C2×M16—101no—
350C2×M16—101no—
351C2×M16—101no—
352C2×M16—101no—
353C2×M16—101no—
354C2×M16—101no—
355C2×M16C4×D512yes—
356C2×M16C4×D512yes—
357C2×M16D2012yes—
358C2×M16C22⋊D512yes—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—52no—
362C22×C8—52no—
363C22×C8—104no—
364#117—52no—
365#117—101no—
366#117—101no—
367#117—101no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—101no—
374C2×C4⋊C4C4×D512yes—
375C2×C22⋊C4—101no—
376C2×C42—101no—
377#104—108no—
378#103—104no—
379#102—104no—
380C22×C5—21no—
381C22×C5—21no—
382C22×C5—21no—
383C22×C5—21no—
384C22×C5—21no—
385C22×C5—21no—
386C22×C5—41no—
387C22×C5—41no—
388C22×C5—41no—
389C22×C5—41no—
390C22×C5C4×C22⋊C411yescharacteristic
391C22×C5#38011yescharacteristic
392C22×C5#38111yescharacteristic
393C22×C5#38511yescharacteristic
394C22×C5#38511yescharacteristic
395C22×C5#38611yescharacteristic
396C22×C5#38611yescharacteristic
397C2×D5—24no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—82no—
401C2×D5—82no—
402C4×C5—82no—
403C4×C5C2×#9511yescharacteristic
404C4×C5C4×C22⋊C411yescharacteristic
405C4×C5#37911yescharacteristic
406C4×C5#38011yescharacteristic
407C4×C5#38511yescharacteristic
408C4×C5#38511yescharacteristic
409C4×C5#38611yescharacteristic
410C4×C5#38611yescharacteristic
411Dic5—24no—
412Dic5—82no—
413C24—101no—
414C24#70911yescharacteristic
415#41—54no—
416#41—54no—
417#41—54no—
418#41—54no—
419#41—102no—
420#41—102no—
421#41—102no—
422#41—102no—
423#41—102no—
424#41—102no—
425#41—102no—
426#41—102no—
427#41—102no—
428#41—102no—
429#41—102no—
430#41—102no—
431C2×Q8—52no—
432C2×Q8—52no—
433C2×Q8—52no—
434C2×Q8—101no—
435C2×Q8—101no—
436C2×Q8—101no—
437C2×D4—52no—
438C2×D4—52no—
439C2×D4—52no—
440C2×D4—102no—
441C2×D4—102no—
442C2×D4—102no—
443C2×D4—102no—
444C2×D4—102no—
445C2×D4—102no—
446C2×D4—101no—
447C2×D4—101no—
448C2×D4—101no—
449C22×C4—22no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—82no—
453C22×C4—101no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—201no—
461C22×C4C2×C4×D511yescharacteristic
462C22×C4C2×C4×D511yescharacteristic
463C22×C4C2×C4×D511yescharacteristic
464C22×C4C2×D2011yescharacteristic
465C22×C4#70911yescharacteristic
466C22×C4D4×D511yescharacteristic
467C22×C4D4×D511yescharacteristic
468C22×C4D4×D511yescharacteristic
469C22×C4D4×D511yescharacteristic
470C22×C4D4×D511yescharacteristic
471C22×C4#71111yescharacteristic
472C22×C4Q8×D511yescharacteristic
473C22×C4#71311yescharacteristic
474C22×C4C2×C22⋊D511yescharacteristic
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—1016no—
483M16—102no—
484M16—102no—
485M16—102no—
486M16—102no—
487M16—201no—
488M16—201no—
489M16—201no—
490M16—201no—
491M16#68514yes—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—54no—
499C2×C8—1016no—
500C2×C8—102no—
501C2×C8—102no—
502C2×C8—102no—
503C2×C8—102no—
504C2×C8—102no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—102no—
510C4⋊C4—201no—
511C22⋊C4—102no—
512C22⋊C4—201no—
513C42—102no—
514C42—201no—
515C2×C5—21no—
516C2×C5—21no—
517C2×C5—21no—
518C2×C5—21no—
519C2×C5—21no—
520C2×C5—21no—
521C2×C5C22⋊#9511yescharacteristic
522C2×C5#190211yescharacteristic
523C2×C5#190311yescharacteristic
524D5—44no—
525C23—41no—
526C23—41no—
527C23—102no—
528C23—102no—
529C23—102no—
530C23—401no—
531C23—401no—
532C23#401811yescharacteristic
533C23C4×D2011yescharacteristic
534C23#402911yescharacteristic
535C23#403011yescharacteristic
536C23#404011yescharacteristic
537C23#404211yescharacteristic
538C23C4×C22⋊D511yescharacteristic
539Q8—54no—
540Q8—102no—
541Q8—102no—
542Q8—102no—
543D4—54no—
544D4—104no—
545D4—104no—
546D4—104no—
547D4—104no—
548D4—102no—
549D4—102no—
550D4—102no—
551C2×C4—42no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—104no—
559C2×C4—104no—
560C2×C4—104no—
561C2×C4—104no—
562C2×C4—202no—
563C2×C4—401no—
564C2×C4—401no—
565C2×C4C42×D511yescharacteristic
566C2×C4C4×D2011yescharacteristic
567C2×C4D5×C22⋊C411yescharacteristic
568C2×C4D5×C22⋊C411yescharacteristic
569C2×C4D5×C22⋊C411yescharacteristic
570C2×C4D5×C22⋊C411yescharacteristic
571C2×C4#402711yescharacteristic
572C2×C4#402711yescharacteristic
573C2×C4#402811yescharacteristic
574C2×C4#402811yescharacteristic
575C2×C4#402911yescharacteristic
576C2×C4#403011yescharacteristic
577C2×C4D5×C4⋊C411yescharacteristic
578C2×C4D5×C4⋊C411yescharacteristic
579C2×C4D5×C4⋊C411yescharacteristic
580C2×C4#403811yescharacteristic
581C2×C4#403911yescharacteristic
582C2×C4#403911yescharacteristic
583C2×C4#404011yescharacteristic
584C2×C4#404111yescharacteristic
585C2×C4#404211yescharacteristic
586C2×C4#404311yescharacteristic
587C2×C4C2×#68511yescharacteristic
588C2×C4C4×C22⋊D511yescharacteristic
589C2×C4#408311yescharacteristic
590C2×C4#408311yescharacteristic
591C2×C4#408411yescharacteristic
592C2×C4#409211yescharacteristic
593C8—24no—
594C8—42no—
595C8—104no—
596C8—202no—
597C5#1078411yescharacteristic, complemented, Sylow
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—104no—
609C22—202no—
610C22—202no—
611C22—402no—
612C22—402no—
613C22#6495311yescharacteristic
614C22#6495411yescharacteristic
615C22#6495611yescharacteristic
616C22#6495711yescharacteristic
617C22C4×#68511yescharacteristic
618C22#6524511yescharacteristic
619C22#6527811yescharacteristic
620C4—82no—
621C4—104no—
622C4—402no—
623C4D5×#9511yescharacteristic
624C4#6495411yescharacteristic
625C4#6495511yescharacteristic
626C4#6495711yescharacteristic
627C4#6524411yescharacteristic
628C4#6524511yescharacteristic
629C4#6527611yescharacteristic
630C4#6527811yescharacteristic
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—204no—
638C2#1060021811yescharacteristic
639C2#1060088011yescharacteristic
640C2#1060091511yescharacteristic
subgroupG/H
centerC22#65245
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC2×C5×#343C2
socleC22×C5#386
prime radicalC22×#709C22
cosocleC23×C4×C5C23
hypercenterC2×#343D5
hypocenterC5#10784
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×C5×#343C2semidirect
5. C2×#64779C2semidirect
6. C2×#64780C2semidirect
7. #10602351C2semidirect
18. #66079C4semidirect
23. #65428C4semidirect
25. C2×#3942C4semidirect
28. C2×#3941C4semidirect
108. C2×#343D5semidirect
597. C5#10784semidirect

Maximal subgroups

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

subgroupindex
C2×#660792
C2×#654282
C2×#652552
C2×C5×#3432
C2×#647792
C2×#647802
#106023512
#107845