Finite Group Databasebeta

← #12071039

Subgroups — #12071039

Order 1280.

718 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D5×D8C211yesmaximal, characteristic
2#10611273C211yesmaximal, characteristic, complemented
3#10611158C211yesmaximal, characteristic, complemented
4C5×#1581C211yesmaximal, characteristic, complemented
5#10601672C211yesmaximal, characteristic, complemented
6#10601654C211yesmaximal, characteristic, complemented
7#10601633C211yesmaximal, characteristic, complemented
8#10599363C211yesmaximal, characteristic, complemented
9#10599352C211yesmaximal, characteristic, complemented
10#10598968C211yesmaximal, characteristic, complemented
11#10598968C211yesmaximal, characteristic, complemented
12#10598956C211yesmaximal, characteristic, complemented
13#10598944C211yesmaximal, characteristic, complemented
14#10598871C211yesmaximal, characteristic, complemented
15#10598863C211yesmaximal, characteristic, complemented
16C2×D5×D8C411yescharacteristic
17C4×D4×D5C2211yescharacteristic
18C4×D4×D5C2211yescharacteristic
19C4×C5×D8C2211yescharacteristic
20C5×#436C2211yescharacteristic, complemented
21C5×C8×D4C2211yescharacteristic, complemented
22D8×Dic5C411yescharacteristic
23#65416—21no—
24#65415—21no—
25#65400—21no—
26C2×#3952—21no—
27C4×#686C2211yescharacteristic
28C4×#686C2211yescharacteristic
29#65301C2211yescharacteristic, complemented
30D4×#168C2211yescharacteristic, complemented
31D5×#107C411yescharacteristic
32#65161C411yescharacteristic
33#65127C2211yescharacteristic, complemented
34#65124C2211yescharacteristic
35#65124C2211yescharacteristic
36#65123C2211yescharacteristic, complemented
37D5×#102C411yescharacteristic
38D5×#102C411yescharacteristic
39#65045C411yescharacteristic
40#65045C411yescharacteristic
41#65019—21no—
42#65017—21no—
43#65015—21no—
44D5×C22⋊C8—21no—
45C4×D40C2211yescharacteristic
46#64977C2211yescharacteristic, complemented
47C4×#676C2211yescharacteristic
48C8×D20C2211yescharacteristic, complemented
49#64974C2211yescharacteristic
50C4×C8×D5C2211yescharacteristic
51C5×#335C2211yescharacteristic, 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#64700C2211yescharacteristic, complemented
60#64700C2211yescharacteristic, complemented
61#64679C2211yescharacteristic, complemented
62#64679C2211yescharacteristic, complemented
63#64678C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#18064—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×#676—21no—
90C2×C8×D5—21no—
91C2×C8×D5—21no—
92C2×C8×D5C2×C411yescharacteristic
93C2×C8×D5C2×C411yescharacteristic
94#4039C2×C411yescharacteristic
95#4039C2×C411yescharacteristic
96D5×C4⋊C4C2×C411yescharacteristic
97D5×C4⋊C4C2×C411yescharacteristic
98#4027—21no—
99#4027—21no—
100D5×C22⋊C4—21no—
101D5×C22⋊C4—21no—
102C4×D20C2311yescharacteristic
103C4×D20C2311yescharacteristic
104C42×D5C2311yescharacteristic
105C5×#107C2×C411yescharacteristic
106C5×C4⋊C8C2311yescharacteristic
107C5×C4⋊C8C2311yescharacteristic
108C5×#102C2×C411yescharacteristic
109C5×#102C2×C411yescharacteristic
110C5×C22⋊C8—21no—
111C5×C22⋊C8—21no—
112C4×C5×C8C2311yescharacteristic
113C4×C5×C8C2311yescharacteristic
114C4×C5×C8C2311yescharacteristic
115#3964C2×C411yescharacteristic
116#3964C2×C411yescharacteristic
117C22⋊#168—21no—
118C22⋊#168—21no—
119#3953C2×C411yescharacteristic
120#3953C2×C411yescharacteristic
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#3947—21no—
131#3947—21no—
132#3947—21no—
133#3946D411yescharacteristic
134#3946D411yescharacteristic
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#2974—51no—
147#2974—51no—
148C2×C4×D8—51no—
149#1594—51no—
150#1594—51no—
151#1581—51no—
152#1581—51no—
153#1581—51no—
154#1581D511yescharacteristic, complemented
155#1580—51no—
156#1580—51no—
157#1568—51no—
158#1490—51no—
159#1490—51no—
160#1451—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—41no—
174D4×D5—41no—
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#686M1614yescomplemented
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—42no—
231#676—81no—
232#676—81no—
233C8×D5—22no—
234C8×D5—41no—
235C8×D5—81no—
236C8×D5—81no—
237C22×D8—51no—
238C2×C4×D4—51no—
239C2×C4×D4—51no—
240C4×D8—51no—
241C4×D8—51no—
242C4×D8—51no—
243C4×D8—51no—
244C4×D8—51no—
245C4×D8—51no—
246C4×D8—51no—
247C4×D8C2×D511yescharacteristic
248#436—51no—
249#436—51no—
250#436—51no—
251#436C2×D511yescharacteristic, complemented
252#435—101no—
253#435—101no—
254#435—101no—
255#435—101no—
256C8×D4—51no—
257C8×D4—51no—
258C8×D4—51no—
259C8×D4C2×D511yescharacteristic, complemented
260#432—51no—
261#432—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—
270C4×M16—51no—
271C2×C4×C8—51no—
272#335—51no—
273#335C2×D511yescharacteristic, complemented
274#334—51no—
275#334—51no—
276D4⋊C8—51no—
277D4⋊C8—51no—
278D4⋊C8—51no—
279D4⋊C8—51no—
280D4⋊C8—51no—
281D4⋊C8—51no—
282D4⋊C8C2×D511yescharacteristic, complemented
283D4⋊C8C2×D511yescharacteristic, complemented
284#322—51no—
285#322—51no—
286#322—51no—
287#322C2×D511yescharacteristic, complemented
288C23×C5—21no—
289C23×C5—21no—
290C22×D5—21no—
291C22×D5—21no—
292C22×D5—42no—
293C22×D5—42no—
294C22×D5—42no—
295C22×D5—42no—
296C22×D5—81no—
297C22×D5—81no—
298C22×D5C4×D411yescharacteristic
299C5×D4—21no—
300C5×D4—21no—
301C5×D4—21no—
302C5×D4C2×M1612yes—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5C23×C411yescharacteristic
310C2×C4×C5C22×D411yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C22⋊D5—42no—
313C22⋊D5—42no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—81no—
317C2×Dic5—81no—
318C2×Dic5C4×D411yescharacteristic
319C2×Dic5C4×D411yescharacteristic
320C2×Dic5C4×D411yescharacteristic
321D20—21no—
322D20—21no—
323D20—21no—
324D20C2×M1612yes—
325C4×D5—22no—
326C4×D5—21no—
327C4×D5—21no—
328C4×D5—21no—
329C4×D5—21no—
330C4×D5—41no—
331C4×D5—41no—
332C4×D5—41no—
333C4×D5—41no—
334C4×D5—81no—
335C4×D5—81no—
336C4×D5—81no—
337C4×D5—81no—
338C5×C8—21no—
339C5×C8—21no—
340C5×C8—21no—
341C5×C8—21no—
342C5×C8—41no—
343C5×C8—41no—
344C5×C8—41no—
345#168—21no—
346#168—21no—
347#168—21no—
348#168—41no—
349#168—41no—
350#168—41no—
351#168C2×M1612yes—
352C22×D4—51no—
353C22×D4—51no—
354C23×C4—101no—
355C23×C4—101no—
356C2×D8—51no—
357C2×D8—51no—
358C2×D8—51no—
359C2×D8—104no—
360C2×D8C4×D511yescharacteristic
361C2×M16—21no—
362C2×M16—101no—
363C2×M16—101no—
364C2×M16—101no—
365C2×M16—101no—
366C22×C8—21no—
367C22×C8—51no—
368C22×C8—51no—
369C22×C8—101no—
370C22×C8—101no—
371C22×C8—101no—
372C4×D4—51no—
373C4×D4—51no—
374C4×D4—51no—
375C4×D4—51no—
376C4×D4—51no—
377C4×D4—51no—
378C4×D4—101no—
379C4×D4—101no—
380C4×D4—101no—
381C4×D4—101no—
382C4×D4C22×D511yescharacteristic
383C4×D4C22×D511yescharacteristic
384C2×C4⋊C4—51no—
385C2×C4⋊C4—51no—
386C2×C22⋊C4—101no—
387C2×C22⋊C4—101no—
388C2×C42—51no—
389#107—51no—
390#107—51no—
391#107—51no—
392#107C4×D511yescharacteristic
393C4⋊C8—51no—
394C4⋊C8—51no—
395C4⋊C8—51no—
396C4⋊C8—51no—
397C4⋊C8C22×D511yescharacteristic
398C4⋊C8C22×D511yescharacteristic
399#102—51no—
400#102—51no—
401#102—51no—
402#102—51no—
403#102—51no—
404#102—51no—
405#102C4×D511yescharacteristic
406#102C4×D511yescharacteristic
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—51no—
410C22⋊C8—51no—
411C22⋊C8—101no—
412C22⋊C8—101no—
413C22⋊C8—101no—
414C22⋊C8—101no—
415C22⋊C8—101no—
416C22⋊C8—101no—
417C22⋊C8—101no—
418C22⋊C8—101no—
419#97—101no—
420#97—101no—
421#97—101no—
422C4×C8—51no—
423C4×C8—51no—
424C4×C8—51no—
425C4×C8—51no—
426C4×C8—51no—
427C4×C8C22×D511yescharacteristic
428C4×C8C22×D511yescharacteristic
429C4×C8C22×D511yescharacteristic
430C22×C5—22no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5C2×C4×D411yescharacteristic
437C2×D5—21no—
438C2×D5—21no—
439C2×D5—22no—
440C2×D5—41no—
441C2×D5—41no—
442C2×D5—41no—
443C2×D5—41no—
444C2×D5—41no—
445C2×D5—84no—
446C2×D5—84no—
447C2×D5#44412yes—
448C4×C5—21no—
449C4×C5—41no—
450C4×C5—41no—
451C4×C5C22×M1611yescharacteristic
452C4×C5#56811yescharacteristic
453C4×C5#57611yescharacteristic
454C4×C5#57611yescharacteristic
455Dic5—21no—
456Dic5—21no—
457Dic5—21no—
458Dic5—41no—
459Dic5—41no—
460C24—101no—
461C24—101no—
462C2×D4—51no—
463C2×D4—51no—
464C2×D4—101no—
465C2×D4—101no—
466C2×D4—102no—
467C2×D4—102no—
468C2×D4—201no—
469C2×D4—201no—
470C2×D4C2×C4×D511yescharacteristic
471C2×D4C2×C4×D511yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—401no—
486C22×C4—401no—
487C22×C4—401no—
488C22×C4—401no—
489D8—22no—
490D8—54no—
491D8—102no—
492D8—102no—
493M16—81no—
494M16—202no—
495M16—401no—
496M16—401no—
497M16—401no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—51no—
502C2×C8—51no—
503C2×C8—51no—
504C2×C8—51no—
505C2×C8—81no—
506C2×C8—102no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—101no—
510C2×C8—201no—
511C2×C8—401no—
512C2×C8—401no—
513C2×C8—401no—
514C2×C8C2×C4×D511yescharacteristic
515C2×C8C2×C4×D511yescharacteristic
516C2×C8D4×D511yescharacteristic
517C2×C8D4×D511yescharacteristic
518C4⋊C4—51no—
519C4⋊C4—51no—
520C4⋊C4—101no—
521C4⋊C4—101no—
522C4⋊C4C2×C4×D511yescharacteristic
523C4⋊C4C2×C4×D511yescharacteristic
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—101no—
527C22⋊C4—101no—
528C22⋊C4—101no—
529C22⋊C4—101no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C42—51no—
533C42—51no—
534C42—51no—
535C42C23×D511yescharacteristic
536C2×C5—42no—
537C2×C5—81no—
538C2×C5D4×M1611yescharacteristic
539C2×C5#294811yescharacteristic
540C2×C5C2×#44411yescharacteristic
541D5—22no—
542D5—42no—
543D5—81no—
544C23—21no—
545C23—21no—
546C23—51no—
547C23—101no—
548C23—101no—
549C23—202no—
550C23—202no—
551C23—202no—
552C23—202no—
553C23—401no—
554C23—401no—
555D4—21no—
556D4—21no—
557D4—21no—
558D4—52no—
559D4—101no—
560D4—101no—
561D4—101no—
562D4—202no—
563D4—202no—
564D4D5×M1612yes—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—51no—
572C2×C4—51no—
573C2×C4—51no—
574C2×C4—102no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—101no—
580C2×C4—101no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4—201no—
584C2×C4—201no—
585C2×C4—401no—
586C2×C4—401no—
587C2×C4—401no—
588C2×C4—401no—
589C2×C4—401no—
590C2×C4—401no—
591C2×C4C22×C4×D511yescharacteristic
592C2×C4C2×D4×D511yescharacteristic
593C2×C4D5×#4111yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—41no—
599C8—41no—
600C8—41no—
601C8—52no—
602C8—101no—
603C8—101no—
604C8—101no—
605C8—201no—
606C8—201no—
607C8—201no—
608C5#1806411yescharacteristic, complemented, Sylow
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—52no—
616C22—101no—
617C22—101no—
618C22—102no—
619C22—201no—
620C22—201no—
621C22—201no—
622C22—201no—
623C22—201no—
624C22—404no—
625C22—404no—
626C22C4×D4×D511yescharacteristic
627C4—21no—
628C4—41no—
629C4—41no—
630C4—101no—
631C4—101no—
632C4—101no—
633C4—201no—
634C4—201no—
635C4C2×D5×M1611yescharacteristic
636C4#6608411yescharacteristic
637C4#6609111yescharacteristic
638C4#6610311yescharacteristic
639C2—42no—
640C2—81no—
641C2—102no—
642C2—202no—
643C2—401no—
644C2#1061121411yescharacteristic
645C2#1061131911yescharacteristic
646C2D5×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1581C2
socleC22×C5C2×C4×D4
prime radicalC2×D5×D8C4
cosocleC42×C5C24
hypercenter#1581D5
hypocenterC5#18064
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #10611273C2semidirect
3. #10611158C2semidirect
4. C5×#1581C2semidirect
5. #10601672C2semidirect
6. #10601654C2semidirect
7. #10601633C2semidirect
8. #10599363C2semidirect
9. #10599352C2semidirect
10. #10598968C2semidirect
11. #10598968C2semidirect
12. #10598956C2semidirect
13. #10598944C2semidirect
14. #10598871C2semidirect
15. #10598863C2semidirect
20. C5×#436C22semidirect
21. C5×C8×D4C22semidirect
29. #65301C22semidirect
30. D4×#168C22semidirect
33. #65127C22semidirect
36. #65123C22semidirect
46. #64977C22semidirect
48. C8×D20C22semidirect
51. C5×#335C22semidirect
52. C5×D4⋊C8C22semidirect
53. C5×D4⋊C8C22semidirect
54. C5×#322C22semidirect
55. D4⋊#168C22semidirect
56. D4⋊#168C22semidirect
57. #64703C22semidirect
58. #64703C22semidirect
59. #64700C22semidirect
60. #64700C22semidirect
61. #64679C22semidirect
62. #64679C22semidirect
63. #64678C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
154. #1581D5semidirect
208. #686M16semidirect
251. #436C2×D5semidirect
259. C8×D4C2×D5semidirect
273. #335C2×D5semidirect
282. D4⋊C8C2×D5semidirect
283. D4⋊C8C2×D5semidirect
287. #322C2×D5semidirect
608. C5#18064semidirect

Maximal subgroups

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

subgroupindex
C4×D5×D82
#106112732
#106111582
C5×#15812
#106016722
#106016542
#106016332
#105993632
#105993522
#105989682
#105989562
#105989442
#105988712
#105988632
#180645