Finite Group Databasebeta

← #12068968

Subgroups — #12068968

Order 1280.

726 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D5×D8C211yesmaximal, characteristic
2#10611274C211yesmaximal, characteristic, complemented
3#10611157C211yesmaximal, characteristic, complemented
4C5×#1586C211yesmaximal, characteristic, complemented
5#10601673C211yesmaximal, characteristic, complemented
6#10601655C211yesmaximal, characteristic, complemented
7#10601634C211yesmaximal, characteristic, complemented
8#10599320C211yesmaximal, characteristic, complemented
9#10599314C211yesmaximal, characteristic, complemented
10#10598960C211yesmaximal, characteristic, complemented
11#10598960C211yesmaximal, characteristic, complemented
12#10598946C211yesmaximal, characteristic, complemented
13#10598945C211yesmaximal, characteristic, complemented
14#10598874C211yesmaximal, characteristic, complemented
15#10598864C211yesmaximal, characteristic, complemented
16C2×D5×D8C411yescharacteristic
17C4×D4×D5C2211yescharacteristic
18C4×D4×D5C2211yescharacteristic
19C4×C5×D8C2211yescharacteristic
20C5×#436C2211yescharacteristic, complemented
21C5×C8×D4C2211yescharacteristic, complemented
22D8×Dic5C411yescharacteristic
23#65417—21no—
24#65415—21no—
25C8×C22⋊D5—21no—
26C2×#3952—21no—
27C4×#686C2211yescharacteristic
28C4×#686C2211yescharacteristic
29#65301C2211yescharacteristic, complemented
30D4×#168C2211yescharacteristic, complemented
31D5×#107C411yescharacteristic
32#65161C411yescharacteristic
33#65127C2211yescharacteristic, complemented
34#65123C2211yescharacteristic, complemented
35#65122C2211yescharacteristic
36#65122C2211yescharacteristic
37D5×#102C411yescharacteristic
38D5×#102C411yescharacteristic
39#65045C411yescharacteristic
40#65045C411yescharacteristic
41#65018—21no—
42#65015—21no—
43#65014—21no—
44D5×C22⋊C8—21no—
45C4×D40C2211yescharacteristic
46#64977C2211yescharacteristic, complemented
47C8×D20C2211yescharacteristic, complemented
48#64974C2211yescharacteristic
49#64974C2211yescharacteristic
50C4×C8×D5C2211yescharacteristic
51C5×#334C2211yescharacteristic, complemented
52C5×D4⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic, complemented
54C5×#322C2211yescharacteristic, complemented
55D4⋊#168C2211yescharacteristic, complemented
56D4⋊#168C2211yescharacteristic, complemented
57#64703C2211yescharacteristic, complemented
58#64703C2211yescharacteristic, complemented
59#64699C2211yescharacteristic, complemented
60#64699C2211yescharacteristic, complemented
61#64679C2211yescharacteristic, complemented
62#64679C2211yescharacteristic, complemented
63#64677C2211yescharacteristic, complemented
64#64675C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#17877—51nomaximal, Sylow
68C2×D4×D5C2×C411yescharacteristic
69C2×D4×D5C2×C411yescharacteristic
70C22×C4×D5—21no—
71C22×C4×D5—21no—
72C2×C5×D8C2×C411yescharacteristic
73C2×C5×M16—21no—
74C22×C5×C8—21no—
75C4×C5×D4C2311yescharacteristic
76C4×C5×D4C2311yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78D4×Dic5C2×C411yescharacteristic
79C2×#686C2×C411yescharacteristic
80C2×#686C2×C411yescharacteristic
81C4×C22⋊D5—21no—
82C4×C22⋊D5—21no—
83C2×#681—21no—
84C22×#168—21no—
85D5×D8—24no—
86C2×D40C2×C411yescharacteristic
87C2×#676—21no—
88C2×#676—21no—
89C2×C8×D5—21no—
90C2×C8×D5—21no—
91C2×C8×D5C2×C411yescharacteristic
92C2×C8×D5C2×C411yescharacteristic
93#4039C2×C411yescharacteristic
94#4039C2×C411yescharacteristic
95D5×C4⋊C4C2×C411yescharacteristic
96D5×C4⋊C4C2×C411yescharacteristic
97#4027—21no—
98#4027—21no—
99D5×C22⋊C4—21no—
100D5×C22⋊C4—21no—
101C4×D20C2311yescharacteristic
102C4×D20C2311yescharacteristic
103C42×D5C2311yescharacteristic
104C5×#107C2×C411yescharacteristic
105C5×C4⋊C8C2311yescharacteristic
106C5×C4⋊C8C2311yescharacteristic
107C5×#102C2×C411yescharacteristic
108C5×#102C2×C411yescharacteristic
109C5×C22⋊C8—21no—
110C5×C22⋊C8—21no—
111C4×C5×C8C2311yescharacteristic
112C4×C5×C8C2311yescharacteristic
113C4×C5×C8C2311yescharacteristic
114#3964C2×C411yescharacteristic
115#3964C2×C411yescharacteristic
116C22⋊#168—21no—
117C22⋊#168—21no—
118#3953C2×C411yescharacteristic
119#3953C2×C411yescharacteristic
120#3952—21no—
121#3952—21no—
122#3952—21no—
123#3952—21no—
124#3952—21no—
125#3952—21no—
126#3952—21no—
127#3952D411yescharacteristic
128#3952D411yescharacteristic
129#3950C2×C411yescharacteristic
130#3946—21no—
131#3946D411yescharacteristic
132#3946D411yescharacteristic
133C8×Dic5—21no—
134C8×Dic5—21no—
135C8×Dic5C2×C411yescharacteristic
136C8×Dic5C2×C411yescharacteristic
137#3941C2×C411yescharacteristic
138#3941C2×C411yescharacteristic
139#3939C2×C411yescharacteristic
140#3939C2×C411yescharacteristic
141C4⋊#168C2311yescharacteristic
142C4⋊#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146#2975—51no—
147#2972—51no—
148C2×C4×D8—51no—
149#1586—51no—
150#1586—51no—
151#1586—51no—
152#1586D511yescharacteristic, complemented
153#1581—51no—
154#1581—51no—
155#1581—51no—
156#1581—51no—
157#1564—51no—
158#1478—51no—
159#1478—51no—
160#1452—51no—
161C23×D5—21no—
162C23×D5—21no—
163C2×C5×D4C22×C411yescharacteristic
164C2×C5×D4C22×C411yescharacteristic
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C2×C22⋊D5—21no—
168C2×C22⋊D5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171D4×D5—22no—
172D4×D5—22no—
173D4×D5—22no—
174D4×D5M1614yescomplemented
175C2×D20C22×C411yescharacteristic
176C2×D20C22×C411yescharacteristic
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×C4×D5—21no—
182C2×C4×D5—21no—
183C2×C4×D5—81no—
184C2×C4×D5—81no—
185C2×C4×D5—81no—
186C2×C4×D5—81no—
187C2×C4×D5C22×C411yescharacteristic
188C2×C4×D5C2×D411yescharacteristic
189C2×C4×D5#4111yescharacteristic
190C5×D8—22no—
191C5×M16—81no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—81no—
196C2×C5×C8C22×C411yescharacteristic
197C2×C5×C8C22×C411yescharacteristic
198C2×C5×C8C2×D411yescharacteristic
199C2×C5×C8C2×D411yescharacteristic
200C5×C4⋊C4C22×C411yescharacteristic
201C5×C4⋊C4C22×C411yescharacteristic
202C5×C22⋊C4—21no—
203C5×C22⋊C4—21no—
204C42×C5C2411yescharacteristic
205C22⋊Dic5—21no—
206C22⋊Dic5—21no—
207#686—22no—
208#686—22no—
209#685—21no—
210#685—21no—
211#685—21no—
212#685—21no—
213C4⋊Dic5C22×C411yescharacteristic
214C4⋊Dic5C22×C411yescharacteristic
215#683—21no—
216#683—21no—
217C4×Dic5C22×C411yescharacteristic
218C4×Dic5C2×D411yescharacteristic
219C4×Dic5#4111yescharacteristic
220#681—81no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—81no—
225C2×#168C22×C411yescharacteristic
226C2×#168C22×C411yescharacteristic
227C2×#168C2×D411yescharacteristic
228C2×#168C2×D411yescharacteristic
229D40—22no—
230#676—81no—
231#676—81no—
232C8×D5—22no—
233C8×D5—22no—
234C8×D5—81no—
235C8×D5—81no—
236C22×D8—51no—
237C2×C4×D4—51no—
238C2×C4×D4—51no—
239C4×D8—51no—
240C4×D8—51no—
241C4×D8—51no—
242C4×D8—51no—
243C4×D8—51no—
244C4×D8—51no—
245C4×D8—51no—
246C4×D8C2×D511yescharacteristic
247#436—51no—
248#436—51no—
249#436—51no—
250#436—101no—
251#436—101no—
252#436C2×D511yescharacteristic, complemented
253C8×D4—51no—
254C8×D4—51no—
255C8×D4—51no—
256C8×D4—101no—
257C8×D4—101no—
258C8×D4C2×D511yescharacteristic, complemented
259#431—51no—
260#431—51no—
261#431—51no—
262#431—51no—
263C2×#107—51no—
264C2×#102—51no—
265C2×#102—51no—
266#407—101no—
267#407—101no—
268C2×C22⋊C8—101no—
269C2×C22⋊C8—101no—
270C2×C4×C8—51no—
271#335—51no—
272#335—51no—
273#334—51no—
274#334C2×D511yescharacteristic, complemented
275D4⋊C8—51no—
276D4⋊C8—51no—
277D4⋊C8—51no—
278D4⋊C8—51no—
279D4⋊C8—51no—
280D4⋊C8—51no—
281D4⋊C8C2×D511yescharacteristic, complemented
282D4⋊C8C2×D511yescharacteristic, complemented
283#322—51no—
284#322—51no—
285#322—51no—
286#322C2×D511yescharacteristic, complemented
287C23×C5—21no—
288C23×C5—21no—
289C22×D5—21no—
290C22×D5—24no—
291C22×D5—21no—
292C22×D5—42no—
293C22×D5—81no—
294C22×D5—81no—
295C22×D5—81no—
296C22×D5—81no—
297C22×D5C4×D411yescharacteristic
298C5×D4—21no—
299C5×D4—21no—
300C5×D4—21no—
301C5×D4C2×M1612yes—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5C23×C411yescharacteristic
309C2×C4×C5C22×D411yescharacteristic
310C2×C4×C5C2×#4111yescharacteristic
311C22⋊D5—24no—
312C22⋊D5—42no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—81no—
316C2×Dic5—81no—
317C2×Dic5C4×D411yescharacteristic
318C2×Dic5C4×D411yescharacteristic
319C2×Dic5C4×D411yescharacteristic
320D20—21no—
321D20—21no—
322D20—21no—
323D20C2×M1612yes—
324C4×D5—21no—
325C4×D5—21no—
326C4×D5—41no—
327C4×D5—41no—
328C4×D5—41no—
329C4×D5—41no—
330C4×D5—41no—
331C4×D5—81no—
332C4×D5—81no—
333C4×D5—81no—
334C4×D5—81no—
335C4×D5C2×M1612yes—
336C4×D5#13112yes—
337C5×C8—21no—
338C5×C8—21no—
339C5×C8—21no—
340C5×C8—21no—
341C5×C8—41no—
342C5×C8—41no—
343C5×C8—41no—
344#168—21no—
345#168—21no—
346#168—21no—
347#168—21no—
348#168—41no—
349#168—41no—
350#168—41no—
351C22×D4—51no—
352C22×D4—51no—
353C23×C4—101no—
354C23×C4—101no—
355C2×D8—51no—
356C2×D8—51no—
357C2×D8—51no—
358C2×D8—104no—
359C2×D8C4×D511yescharacteristic
360C2×M16—21no—
361C2×M16—101no—
362C2×M16—101no—
363C2×M16—101no—
364C22×C8—21no—
365C22×C8—51no—
366C22×C8—51no—
367C22×C8—101no—
368C22×C8—101no—
369C22×C8—101no—
370C4×D4—51no—
371C4×D4—51no—
372C4×D4—51no—
373C4×D4—51no—
374C4×D4—51no—
375C4×D4—51no—
376C4×D4—101no—
377C4×D4—101no—
378C4×D4—101no—
379C4×D4—101no—
380C4×D4C22×D511yescharacteristic
381C4×D4C22×D511yescharacteristic
382C2×C4⋊C4—51no—
383C2×C4⋊C4—51no—
384C2×C22⋊C4—101no—
385C2×C22⋊C4—101no—
386C2×C42—51no—
387#107—51no—
388#107—51no—
389#107—51no—
390#107C4×D511yescharacteristic
391C4⋊C8—51no—
392C4⋊C8—51no—
393C4⋊C8—51no—
394C4⋊C8—51no—
395C4⋊C8—101no—
396C4⋊C8C22×D511yescharacteristic
397C4⋊C8C22×D511yescharacteristic
398#102—51no—
399#102—51no—
400#102—51no—
401#102—51no—
402#102—51no—
403#102—51no—
404#102C4×D511yescharacteristic
405#102C4×D511yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—51no—
409C22⋊C8—51no—
410C22⋊C8—101no—
411C22⋊C8—101no—
412C22⋊C8—101no—
413C22⋊C8—101no—
414C22⋊C8—101no—
415C22⋊C8—101no—
416C22⋊C8—101no—
417C22⋊C8—101no—
418C22⋊C8—101no—
419C4×C8—51no—
420C4×C8—51no—
421C4×C8—51no—
422C4×C8—51no—
423C4×C8—51no—
424C4×C8—101no—
425C4×C8—101no—
426C4×C8C22×D511yescharacteristic
427C4×C8C22×D511yescharacteristic
428C4×C8C22×D511yescharacteristic
429C22×C5—22no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5C2×C4×D411yescharacteristic
436C2×D5—21no—
437C2×D5—21no—
438C2×D5—22no—
439C2×D5—41no—
440C2×D5—41no—
441C2×D5—41no—
442C2×D5—41no—
443C2×D5—41no—
444C2×D5—84no—
445C2×D5—84no—
446C2×D5#43512yes—
447C4×C5—21no—
448C4×C5—41no—
449C4×C5—41no—
450C4×C5C22×M1611yescharacteristic
451C4×C5C2×#13111yescharacteristic
452C4×C5#57611yescharacteristic
453C4×C5#57611yescharacteristic
454Dic5—21no—
455Dic5—21no—
456Dic5—41no—
457Dic5—41no—
458Dic5#43512yes—
459C24—101no—
460C24—101no—
461C2×D4—54no—
462C2×D4—51no—
463C2×D4—51no—
464C2×D4—102no—
465C2×D4—102no—
466C2×D4—102no—
467C2×D4—101no—
468C2×D4—101no—
469C2×D4C2×C4×D511yescharacteristic
470C2×D4C2×C4×D511yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—401no—
485C22×C4—401no—
486C22×C4—401no—
487C22×C4—401no—
488D8—22no—
489D8—102no—
490D8—102no—
491D8—102no—
492M16—81no—
493M16—401no—
494M16—401no—
495M16—401no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—51no—
500C2×C8—51no—
501C2×C8—51no—
502C2×C8—51no—
503C2×C8—81no—
504C2×C8—102no—
505C2×C8—102no—
506C2×C8—101no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—401no—
510C2×C8—401no—
511C2×C8—401no—
512C2×C8C2×C4×D511yescharacteristic
513C2×C8C2×C4×D511yescharacteristic
514C2×C8D4×D511yescharacteristic
515C2×C8D4×D511yescharacteristic
516C4⋊C4—51no—
517C4⋊C4—51no—
518C4⋊C4—101no—
519C4⋊C4—101no—
520C4⋊C4C2×C4×D511yescharacteristic
521C4⋊C4C2×C4×D511yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—101no—
525C22⋊C4—101no—
526C22⋊C4—101no—
527C22⋊C4—101no—
528C22⋊C4—101no—
529C22⋊C4—101no—
530C42—51no—
531C42—51no—
532C42—51no—
533C42C23×D511yescharacteristic
534C2×C5—42no—
535C2×C5—81no—
536C2×C5C2×#43511yescharacteristic
537C2×C5#294811yescharacteristic
538C2×C5#295711yescharacteristic
539D5—22no—
540D5—42no—
541D5—81no—
542C23—21no—
543C23—21no—
544C23—51no—
545C23—104no—
546C23—101no—
547C23—101no—
548C23—202no—
549C23—401no—
550C23—401no—
551C23—401no—
552C23—401no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—52no—
557D4—104no—
558D4—101no—
559D4—101no—
560D4—101no—
561D4—202no—
562D4D5×M1612yes—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—51no—
570C2×C4—52no—
571C2×C4—52no—
572C2×C4—51no—
573C2×C4—51no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4—401no—
584C2×C4—401no—
585C2×C4—401no—
586C2×C4—401no—
587C2×C4—401no—
588C2×C4—401no—
589C2×C4C22×C4×D511yescharacteristic
590C2×C4C2×D4×D511yescharacteristic
591C2×C4D5×#4111yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—41no—
599C8—101no—
600C8—101no—
601C8—101no—
602C8—101no—
603C8—201no—
604C8—201no—
605C8—201no—
606C5#1787711yescharacteristic, complemented, Sylow
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—52no—
614C22—101no—
615C22—101no—
616C22—102no—
617C22—201no—
618C22—201no—
619C22—201no—
620C22—201no—
621C22—201no—
622C22—404no—
623C22—404no—
624C22C4×D4×D511yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—52no—
629C4—101no—
630C4—101no—
631C4—201no—
632C4—201no—
633C4C2×D5×M1611yescharacteristic
634C4D5×#13111yescharacteristic
635C4#6610811yescharacteristic
636C4#6610811yescharacteristic
637C2—42no—
638C2—81no—
639C2—102no—
640C2—202no—
641C2—401no—
642C2D5×#43511yescharacteristic
643C2#1061159811yescharacteristic
644C2#1061162111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1586C2
socleC22×C5C2×C4×D4
prime radicalC2×D5×D8C4
cosocleC42×C5C24
hypercenter#1586D5
hypocenterC5#17877
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #10611274C2semidirect
3. #10611157C2semidirect
4. C5×#1586C2semidirect
5. #10601673C2semidirect
6. #10601655C2semidirect
7. #10601634C2semidirect
8. #10599320C2semidirect
9. #10599314C2semidirect
10. #10598960C2semidirect
11. #10598960C2semidirect
12. #10598946C2semidirect
13. #10598945C2semidirect
14. #10598874C2semidirect
15. #10598864C2semidirect
20. C5×#436C22semidirect
21. C5×C8×D4C22semidirect
29. #65301C22semidirect
30. D4×#168C22semidirect
33. #65127C22semidirect
34. #65123C22semidirect
46. #64977C22semidirect
47. C8×D20C22semidirect
51. C5×#334C22semidirect
52. C5×D4⋊C8C22semidirect
53. C5×D4⋊C8C22semidirect
54. C5×#322C22semidirect
55. D4⋊#168C22semidirect
56. D4⋊#168C22semidirect
57. #64703C22semidirect
58. #64703C22semidirect
59. #64699C22semidirect
60. #64699C22semidirect
61. #64679C22semidirect
62. #64679C22semidirect
63. #64677C22semidirect
64. #64675C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
152. #1586D5semidirect
174. D4×D5M16semidirect
252. #436C2×D5semidirect
258. C8×D4C2×D5semidirect
274. #334C2×D5semidirect
281. D4⋊C8C2×D5semidirect
282. D4⋊C8C2×D5semidirect
286. #322C2×D5semidirect
606. C5#17877semidirect

Maximal subgroups

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

subgroupindex
C4×D5×D82
#106112742
#106111572
C5×#15862
#106016732
#106016552
#106016342
#105993202
#105993142
#105989602
#105989462
#105989452
#105988742
#105988642
#178775