Finite Group Databasebeta

← #12106324

Subgroups — #12106324

Order 1280.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64977C211yesmaximal, characteristic
2C2×C4×#676C211yesmaximal, characteristic, complemented
3C4×#4040C211yesmaximal, characteristic
4C5×C8×C4⋊C4C211yesmaximal, characteristic, complemented
5#10601271C211yesmaximal, characteristic, complemented
6#10601243C211yesmaximal, characteristic, complemented
7#10600576C211yesmaximal, characteristic, complemented
8#10600574C211yesmaximal, characteristic, complemented
9#10600574C211yesmaximal, characteristic, complemented
10#10600574C211yesmaximal, characteristic, complemented
11#10600275C211yesmaximal, characteristic, complemented
12#10599462C211yesmaximal, characteristic
13#10599457C211yesmaximal, characteristic, complemented
14#10599450C211yesmaximal, characteristic, complemented
15#10599407C211yesmaximal, characteristic, complemented
16C22×#676C2211yescharacteristic
17C22×#676C2211yescharacteristic
18C22×#676C2211yescharacteristic
19C2×#4040C411yescharacteristic
20C2×C4×D20C2211yescharacteristic
21C2×C42×D5C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C4×C5×C8C2211yescharacteristic
24C2×C4×C5×C8C2211yescharacteristic
25C2×C4×C5×C8C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C2×#3952C2211yescharacteristic
28C2×#3952C2211yescharacteristic
29C2×#3952C2211yescharacteristic
30C2×#3952C2211yescharacteristic
31C2×#3952C2211yescharacteristic
32C2×#3947C2211yescharacteristic
33C2×#3947C2211yescharacteristic
34C2×#3947C2211yescharacteristic
35C2×#3946C2211yescharacteristic
36#65279C411yescharacteristic
37#65278C411yescharacteristic
38#65270C411yescharacteristic
39C4×#685C2211yescharacteristic
40C4×#685C2211yescharacteristic
41C4×#685C2211yescharacteristic
42C4×#683C2211yescharacteristic
43C2×C4⋊#168C2211yescharacteristic
44C2×C4×#168C2211yescharacteristic
45#64977—24no—
46C4×#676—24no—
47#64958C411yescharacteristic
48#64954C411yescharacteristic
49#64953C411yescharacteristic
50#64944C411yescharacteristic
51C5×#336C2211yescharacteristic
52C5×#336C2211yescharacteristic
53#64770C2211yescharacteristic
54#64770C2211yescharacteristic
55#64770C2211yescharacteristic
56#64770C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#64744C2211yescharacteristic
60#64744C2211yescharacteristic
61#21565—51nomaximal, Sylow
62C22×D20C2×C411yescharacteristic
63C22×C4×D5C2×C411yescharacteristic
64C22×C4×D5C2×C411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×C4×D5C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C2×C5×C4⋊C4C2×C411yescharacteristic
72C2×C5×C4⋊C4C2×C411yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C42×C5C2311yescharacteristic
75C2×C42×C5C2311yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79C2×#685C2×C411yescharacteristic
80C2×#685C2×C411yescharacteristic
81C2×#685C2×C411yescharacteristic
82C2×#685C2×C411yescharacteristic
83C2×#685C2×C411yescharacteristic
84C2×C4⋊Dic5C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2×C411yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×C4×Dic5C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C2×#676—22no—
96C2×#676—22no—
97C2×#676—22no—
98C2×#676—22no—
99C2×#676—22no—
100C2×#676—22no—
101C2×#676—22no—
102C2×#676—22no—
103C2×#676D414yes—
104#4040—24no—
105C4×D20—22no—
106C4×D20—22no—
107C42×D5—22no—
108C42×D5—22no—
109C5×C4⋊C8—22no—
110C4×C5×C8—22no—
111C4×C5×C8—22no—
112C4×C5×C8—22no—
113C5×#95C2×C411yescharacteristic
114C5×#95C2×C411yescharacteristic
115#3963C2×C411yescharacteristic
116#3963C2×C411yescharacteristic
117#3963C2×C411yescharacteristic
118#3963C2×C411yescharacteristic
119#3963C2×C411yescharacteristic
120#3963C2×C411yescharacteristic
121#3963C2×C411yescharacteristic
122#3963C2×C411yescharacteristic
123#3952—22no—
124#3952—22no—
125#3952—22no—
126#3952—22no—
127#3952—22no—
128#3947—22no—
129#3947—22no—
130#3947—22no—
131#3946—22no—
132C4⋊#168—22no—
133C4×#168—22no—
134C2×#436—51no—
135C2×C4×M16—51no—
136C4×#123—51no—
137#1924—51no—
138#1923—51no—
139#1917—51no—
140#1916—51no—
141#1870—51no—
142#1851—51no—
143#1817—51no—
144#1771—51no—
145C8×C4⋊C4D511yescharacteristic, complemented
146#1753—51no—
147#1753—51no—
148#1753—51no—
149C23×D5C22×C411yescharacteristic
150C23×D5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5C22×C411yescharacteristic
154C22×C4×C5C22×C411yescharacteristic
155C22×C4×C5C22×C411yescharacteristic
156C22×C4×C5C22×C411yescharacteristic
157C22×C4×C5C2411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C2×D20—22no—
165C2×D20—22no—
166C2×D20—41no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—22no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×C4×D5—41no—
182C2×C4×D5—41no—
183C2×C4×D5C2×D412yes—
184C2×C4×D5#4112yes—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8C2×D412yes—
194C2×C5×C8#4112yes—
195C2×C5×C8#4112yes—
196C2×C5×C8#4112yes—
197C5×C4⋊C4—22no—
198C5×C4⋊C4M1614yescomplemented
199C42×C5—21no—
200C42×C5—21no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205#685—22no—
206#685—22no—
207#685—22no—
208#685—22no—
209#685—22no—
210#685—22no—
211#685—41no—
212#685—41no—
213C4⋊Dic5—22no—
214#683—22no—
215#683—41no—
216C4×Dic5—21no—
217C4×Dic5—21no—
218C4×Dic5—21no—
219C4×Dic5—21no—
220C4×Dic5—22no—
221C4×Dic5—22no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—21no—
225C2×#168—21no—
226C2×#168—21no—
227C2×#168—21no—
228C2×#168—21no—
229C2×#168—21no—
230C2×#168—21no—
231C2×#168—21no—
232C2×#168C2×D412yes—
233C2×#168#4112yes—
234#676—28no—
235#676—28no—
236#676—44no—
237C22×M16—51no—
238C22×M16—51no—
239C22×M16—51no—
240C2×#123—51no—
241C2×C4×D4—51no—
242C22×C42—51no—
243#436—104no—
244C2×C4⋊C8—51no—
245C2×C4⋊C8—51no—
246C2×C4⋊C8C2×D511yescharacteristic
247C2×C22⋊C8—51no—
248C2×C22⋊C8—51no—
249C2×C22⋊C8—51no—
250C2×C22⋊C8—51no—
251C2×C22⋊C8—51no—
252C4×M16—104no—
253C2×#97—51no—
254C2×#97—51no—
255C2×#97—51no—
256C2×C4×C8—51no—
257C2×C4×C8C2×D511yescharacteristic
258C2×C4×C8C2×D511yescharacteristic
259C2×C4×C8C2×D511yescharacteristic
260#388—51no—
261#388—51no—
262#387—51no—
263#387—51no—
264#386—51no—
265#385—51no—
266#381—51no—
267C4×C4⋊C4—51no—
268C4×C4⋊C4C2×D511yescharacteristic
269C4×C22⋊C4—51no—
270C4×C22⋊C4—51no—
271C4×C22⋊C4—51no—
272#336—51no—
273#336—51no—
274#336—51no—
275#336—51no—
276#336—51no—
277#336—51no—
278#336—51no—
279#336—51no—
280#336C2×D511yescharacteristic
281#336C2×D511yescharacteristic
282C23×C5C23×C411yescharacteristic
283C22×D5—21no—
284C22×D5—21no—
285C22×D5—21no—
286C22×D5—21no—
287C22×D5—21no—
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C22×D5—21no—
292C22×D5—21no—
293C22×D5—21no—
294C22×D5—21no—
295C22×D5—21no—
296C22×D5C4×D412yes—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5C2×M1612yes—
312C2×C4×C5C2×M1612yes—
313C2×C4×C5C2×M1612yes—
314C2×C4×C5#13112yes—
315C2×C4×C5C22×D411yescharacteristic
316C2×C4×C5C2×#4111yescharacteristic
317C2×C4×C5C2×#4111yescharacteristic
318C2×C4×C5C2×#4111yescharacteristic
319C2×C4×C5C2×#4111yescharacteristic
320C2×C4×C5C2×#4111yescharacteristic
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—21no—
331C2×Dic5—21no—
332C2×Dic5—21no—
333C2×Dic5—21no—
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—21no—
337C2×Dic5—21no—
338C2×Dic5C4×D412yes—
339D20—44no—
340C4×D5—22no—
341C4×D5—22no—
342C4×D5—22no—
343C4×D5—22no—
344C4×D5—44no—
345C4×D5—44no—
346C4×D5—41no—
347C4×D5—41no—
348C4×D5—41no—
349C4×D5—41no—
350C5×C8—22no—
351C5×C8—41no—
352C5×C8—41no—
353C5×C8#12314yescomplemented
354#168—22no—
355#168—22no—
356#168—41no—
357#168—41no—
358C22×D4—51no—
359C23×C4—51no—
360C23×C4—51no—
361C23×C4—51no—
362C23×C4—51no—
363C2×M16—54no—
364C2×M16—102no—
365C2×M16—102no—
366C2×M16—102no—
367C2×M16—102no—
368C2×M16—102no—
369C2×M16—102no—
370C2×M16—102no—
371C2×M16—102no—
372C22×C8—51no—
373C22×C8—51no—
374C22×C8—51no—
375C22×C8—51no—
376C22×C8C22×D511yescharacteristic
377C22×C8C22×D511yescharacteristic
378C22×C8C22×D511yescharacteristic
379C22×C8C22×D511yescharacteristic
380#123—104no—
381C4×D4—102no—
382C4×D4—102no—
383C2×C4⋊C4—51no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—51no—
386C2×C4⋊C4C4×D511yescharacteristic
387C2×C4⋊C4C4×D511yescharacteristic
388C2×C22⋊C4—51no—
389C2×C22⋊C4—51no—
390C2×C22⋊C4—51no—
391C2×C22⋊C4—51no—
392C2×C22⋊C4—51no—
393C2×C22⋊C4—51no—
394C2×C22⋊C4—51no—
395C2×C22⋊C4—51no—
396C2×C42—51no—
397C2×C42—51no—
398C2×C42—51no—
399C2×C42—51no—
400C2×C42—102no—
401C2×C42—102no—
402C2×C42C22×D511yescharacteristic
403C2×C42C22×D511yescharacteristic
404C2×C42C22×D511yescharacteristic
405C4⋊C8—22no—
406C4⋊C8—102no—
407C4⋊C8—102no—
408C22⋊C8—102no—
409C22⋊C8—102no—
410C22⋊C8—102no—
411C22⋊C8—102no—
412C22⋊C8—102no—
413#97—102no—
414#97—102no—
415#97—102no—
416C4×C8—22no—
417C4×C8—22no—
418C4×C8—22no—
419C4×C8—102no—
420#95—51no—
421#95—51no—
422#95—51no—
423#95—51no—
424#95—51no—
425#95—51no—
426#95—51no—
427#95—51no—
428#95C4×D511yescharacteristic
429#95C4×D511yescharacteristic
430C22×C5C2×C4×D411yescharacteristic
431C22×C5C4×#4111yescharacteristic
432C22×C5C4×#4111yescharacteristic
433C22×C5C22×M1611yescharacteristic
434C22×C5C2×#13111yescharacteristic
435C22×C5#56811yescharacteristic
436C22×C5#56811yescharacteristic
437C2×D5—22no—
438C2×D5—22no—
439C2×D5—22no—
440C2×D5—41no—
441C2×D5—41no—
442C2×D5—41no—
443C2×D5—41no—
444C2×D5—41no—
445C2×D5—41no—
446C2×D5—41no—
447C2×D5—41no—
448C2×D5—41no—
449C2×D5—41no—
450C2×D5—41no—
451C4×C5—22no—
452C4×C5—22no—
453C4×C5—22no—
454C4×C5—22no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5C2×#12311yescharacteristic
458C4×C5#52511yescharacteristic
459C4×C5#52911yescharacteristic
460C4×C5#52911yescharacteristic
461Dic5—22no—
462Dic5—41no—
463Dic5—41no—
464Dic5—41no—
465Dic5—41no—
466Dic5—41no—
467C24—51no—
468C24—51no—
469C2×D4—102no—
470C2×D4—102no—
471C2×D4—201no—
472C22×C4—51no—
473C22×C4—52no—
474C22×C4—52no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—101no—
487C22×C4—101no—
488C22×C4—101no—
489C22×C4—101no—
490C22×C4—101no—
491C22×C4—101no—
492C22×C4—102no—
493C22×C4—102no—
494C22×C4—201no—
495C22×C4—201no—
496C22×C4C2×C4×D511yescharacteristic
497C22×C4C2×C4×D511yescharacteristic
498C22×C4C2×C4×D511yescharacteristic
499C22×C4C2×C4×D511yescharacteristic
500C22×C4C2×C4×D511yescharacteristic
501C22×C4C2×C4×D511yescharacteristic
502C22×C4C23×D511yescharacteristic
503M16—108no—
504M16—108no—
505M16—204no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—52no—
515C2×C8—52no—
516C2×C8—101no—
517C2×C8—101no—
518C2×C8—101no—
519C2×C8—101no—
520C2×C8—101no—
521C2×C8—101no—
522C2×C8—101no—
523C2×C8—101no—
524C2×C8—101no—
525C2×C8—101no—
526C2×C8#70912yes—
527C2×C8#70912yes—
528C2×C8D4×D512yes—
529C2×C8#71312yes—
530C4⋊C4—22no—
531C4⋊C4—102no—
532C4⋊C4—102no—
533C4⋊C4—201no—
534C4⋊C4#67614yescomplemented
535C22⋊C4—102no—
536C22⋊C4—102no—
537C22⋊C4—102no—
538C22⋊C4—102no—
539C22⋊C4—102no—
540C22⋊C4—102no—
541C22⋊C4—201no—
542C22⋊C4—201no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—102no—
550C42—102no—
551C42—101no—
552C42—101no—
553C42—101no—
554C42—101no—
555C2×C5C4×#12311yescharacteristic
556C2×C5#293311yescharacteristic
557C2×C5D4×M1611yescharacteristic
558C2×C5#296511yescharacteristic
559C2×C5#296711yescharacteristic
560C2×C5#296911yescharacteristic
561C2×C5#297111yescharacteristic
562D5—42no—
563D5—81no—
564C23—52no—
565C23—101no—
566C23—101no—
567C23—101no—
568C23—101no—
569C23—101no—
570C23—101no—
571C23—101no—
572C23—101no—
573C23—101no—
574C23—101no—
575C23—101no—
576C23—101no—
577C23—101no—
578C23C22×C4×D511yescharacteristic
579D4—204no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—52no—
595C2×C4—101no—
596C2×C4—101no—
597C2×C4—102no—
598C2×C4—102no—
599C2×C4—102no—
600C2×C4—102no—
601C2×C4—101no—
602C2×C4—101no—
603C2×C4—101no—
604C2×C4—101no—
605C2×C4—101no—
606C2×C4—101no—
607C2×C4—101no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—204no—
617C2×C4—204no—
618C2×C4—201no—
619C2×C4—201no—
620C2×C4—201no—
621C2×C4—201no—
622C2×C4C2×#67612yes—
623C2×C4C2×#67612yes—
624C2×C4C2×#67612yes—
625C2×C4#404712yes—
626C2×C4C2×#70911yescharacteristic
627C2×C4C2×#70911yescharacteristic
628C2×C4C2×D4×D511yescharacteristic
629C2×C4C2×#71311yescharacteristic
630C2×C4D5×#4111yescharacteristic
631C2×C4D5×#4111yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—102no—
636C8—102no—
637C8—201no—
638C8—201no—
639C8#404014yescomplemented
640C5#2156511yescharacteristic, complemented, Sylow
641C22—102no—
642C22—102no—
643C22—102no—
644C22—201no—
645C22—201no—
646C22—201no—
647C22—201no—
648C22—201no—
649C22—201no—
650C22—201no—
651C22—201no—
652C22—201no—
653C22—201no—
654C22—201no—
655C22C4×#70911yescharacteristic
656C22C4×D4×D511yescharacteristic
657C22C4×#71311yescharacteristic
658C22C22×#67611yescharacteristic
659C22C2×#404711yescharacteristic
660C22#6608411yescharacteristic
661C22#6608411yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—102no—
669C4—201no—
670C4—201no—
671C4—201no—
672C4—201no—
673C4—201no—
674C4C2×#404011yescharacteristic
675C4#6586211yescharacteristic
676C4#6588111yescharacteristic
677C4#6591411yescharacteristic
678C2—202no—
679C2—401no—
680C2C4×#404011yescharacteristic
681C2#1061017811yescharacteristic
682C2#1061028811yescharacteristic
683C2#1061115411yescharacteristic
684C2D4×#67611yescharacteristic
685C2#1061163511yescharacteristic
686C2#1061163611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×C8×C4⋊C4C2
prime radicalC22×D20C2×C4
cosocleC22×C4×C5C24
hypercenterC8×C4⋊C4D5
hypocenterC5#21565
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#676C2semidirect
4. C5×C8×C4⋊C4C2semidirect
5. #10601271C2semidirect
6. #10601243C2semidirect
7. #10600576C2semidirect
8. #10600574C2semidirect
9. #10600574C2semidirect
10. #10600574C2semidirect
11. #10600275C2semidirect
13. #10599457C2semidirect
14. #10599450C2semidirect
15. #10599407C2semidirect
145. C8×C4⋊C4D5semidirect
198. C5×C4⋊C4M16semidirect
353. C5×C8#123semidirect
534. C4⋊C4#676semidirect
639. C8#4040semidirect
640. C5#21565semidirect

Maximal subgroups

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

subgroupindex
C2×#649772
C2×C4×#6762
C4×#40402
C5×C8×C4⋊C42
#106012712
#106012432
#106005762
#106005742
#106002752
#105994622
#105994572
#105994502
#105994072
#215655