Finite Group Databasebeta

← #12151192

Subgroups — #12151192

Order 1280.

774 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
1C5×#2580C211yesmaximal, characteristic
2#10614214C211yesmaximal, characteristic, complemented
3C2×Q8×#168C211yesmaximal, characteristic, complemented
4C2×#65298C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic
6#10600446C211yesmaximal, characteristic
7#10600445C211yesmaximal, characteristic
8#10600437C211yesmaximal, characteristic
9#10600437C211yesmaximal, characteristic
10#10600416C211yesmaximal, characteristic, complemented
11#10600412C211yesmaximal, characteristic, complemented
12#10600411C211yesmaximal, characteristic, complemented
13#10600403C211yesmaximal, characteristic, complemented
14#10600347C211yesmaximal, characteristic, complemented
15#10600333C211yesmaximal, characteristic, complemented
16C2×C4×C5×Q8C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×#4016C2211yescharacteristic
19C5×#399—21no—
20C5×#393—21no—
21C5×#390C2211yescharacteristic
22C5×#390C2211yescharacteristic
23C5×#389C2211yescharacteristic
24C5×#389C2211yescharacteristic
25C5×#385—21no—
26C5×#385—21no—
27C5×#382C2211yescharacteristic
28#65518—21no—
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31C2×#3964C2211yescharacteristic
32C2×#3964C2211yescharacteristic
33Q8×#168—24no—
34#65298—24no—
35#65269—21no—
36#65261—21no—
37#65261—21no—
38C2×#3940C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C2×#3939C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65217C2211yescharacteristic
44#65217C2211yescharacteristic
45#65217C2211yescharacteristic
46#65217C2211yescharacteristic
47C2×C4⋊#168C2211yescharacteristic
48C2×C4⋊#168C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50C2×C4×#168C2211yescharacteristic
51C2×C4×#168C2211yescharacteristic
52C2×C4×#168C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#64749C2211yescharacteristic
61#25473—51nomaximal, Sylow
62C22×C5×Q8D411yescharacteristic
63C22×C5×D4C2311yescharacteristic
64C23×C4×C5—21no—
65C4×C5×Q8—22no—
66C4×C5×Q8—22no—
67C4×C5×D4—22no—
68C4×C5×D4—22no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4D411yescharacteristic
72C2×C5×C4⋊C4D411yescharacteristic
73C2×C5×C4⋊C4D411yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4—21no—
82C2×C42×C5C2311yescharacteristic
83C2×C42×C5C2311yescharacteristic
84C2×C42×C5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×#683—21no—
90C2×#683—21no—
91C2×#683—21no—
92C2×#683—21no—
93C2×#683—21no—
94C2×#683—21no—
95C2×C4×Dic5—21no—
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100#4016—22no—
101#4016—22no—
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105C5×#95—21no—
106#3964—22no—
107#3964—22no—
108#3964—22no—
109#3964Q814yescomplemented
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3940—22no—
116#3940—22no—
117#3939—22no—
118#3939—22no—
119C4⋊#168—22no—
120C4⋊#168—22no—
121C4⋊#168D414yes—
122C4×#168—22no—
123C4×#168—22no—
124C4×#168—22no—
125C2×#478—51no—
126C2×C8×Q8—51no—
127#2584—51no—
128#2580D511yescharacteristic
129#2088—51no—
130#2087—51no—
131#2067—51no—
132#2065—51no—
133#1991—51no—
134#1949—51no—
135#1942—51no—
136#1941—51no—
137#1934—51no—
138#1934—51no—
139C4×#102—51no—
140C24×C5—21no—
141C2×C5×Q8—22no—
142C2×C5×Q8—22no—
143C2×C5×Q8—22no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4C2×Q812yes—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—42no—
154C22×C4×C5—81no—
155C22×C4×C5—81no—
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2411yescharacteristic
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—81no—
177C5×C4⋊C4—81no—
178C5×C22⋊C4—42no—
179C5×C22⋊C4—42no—
180C5×C22⋊C4—42no—
181C5×C22⋊C4—81no—
182C5×C22⋊C4—81no—
183C42×C5—21no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5—21no—
187C42×C5C2×D412yes—
188C42×C5#4112yes—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5C2×Q812yes—
196C4⋊Dic5#4112yes—
197#683—42no—
198#683—42no—
199#683—42no—
200#683—42no—
201#683—81no—
202#683—81no—
203C4×Dic5—81no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168C2×D412yes—
214C2×#168C2×D412yes—
215C2×#168C2×Q812yes—
216C2×#125—51no—
217C2×C4×Q8C2×D511yescharacteristic
218C2×C4×D4C2×D511yescharacteristic
219#478—104no—
220C8×Q8—104no—
221C2×#107—51no—
222C2×#107—51no—
223C2×#106—51no—
224C2×#106—51no—
225C2×C4⋊C8—51no—
226C2×C4⋊C8—51no—
227C2×C4⋊C8—51no—
228C2×#102—51no—
229C2×#102—51no—
230C2×#102—51no—
231C2×#102—51no—
232C2×C4×C8—51no—
233C2×C4×C8—51no—
234C2×C4×C8—51no—
235#399—21no—
236#398—101no—
237#395—101no—
238#393—21no—
239#390C2×D511yescharacteristic
240#390C2×D511yescharacteristic
241#389—51no—
242#389—51no—
243#389—51no—
244#389—51no—
245#389—101no—
246#389—101no—
247#389C2×D511yescharacteristic
248#389C2×D511yescharacteristic
249#385—21no—
250#385—21no—
251#382C2×D511yescharacteristic
252C4×C4⋊C4—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#340—51no—
261C23×C5—22no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5C22×D411yescharacteristic
269C5×Q8—28no—
270C5×D4—22no—
271C5×D4—22no—
272C5×D4—41no—
273C5×D4—41no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—84no—
298C2×C4×C5#12112yes—
299C2×C4×C5#12112yes—
300C2×C4×C5#13512yes—
301C2×C4×C5#13512yes—
302C2×C4×C5C22×D411yescharacteristic
303C2×C4×C5C22×Q811yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×C4×C52−1+411yescharacteristic
307C2×C4×C52−1+411yescharacteristic
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320#168—22no—
321#168—22no—
322#168—22no—
323#168—41no—
324C22×Q8C22⋊D511yescharacteristic
325C22×D4C22×D511yescharacteristic
326C23×C4—21no—
327C22×C8—51no—
328C22×C8—51no—
329C22×C8—51no—
330C22×C8—51no—
331#125—102no—
332#125—102no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×D4—22no—
336C4×D4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—101no—
344C2×C4⋊C4—101no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4C22⋊D511yescharacteristic
350C2×C4⋊C4C22⋊D511yescharacteristic
351C2×C4⋊C4C22⋊D511yescharacteristic
352C2×C4⋊C4C22×D511yescharacteristic
353C2×C4⋊C4C22×D511yescharacteristic
354C2×C4⋊C4C22×D511yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C42—101no—
361C2×C42C22×D511yescharacteristic
362C2×C42C22×D511yescharacteristic
363C2×C42C22×D511yescharacteristic
364#107—102no—
365#107—102no—
366#106—102no—
367#106—102no—
368C4⋊C8—54no—
369C4⋊C8—102no—
370C4⋊C8—102no—
371#102—54no—
372#102—102no—
373#102—102no—
374#102—102no—
375C4×C8—102no—
376C4×C8—102no—
377C4×C8—102no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386#95—101no—
387C22×C5—42no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—81no—
391C22×C5—81no—
392C22×C5—81no—
393C22×C5—81no—
394C22×C5C2×#12111yescharacteristic
395C22×C5#54811yescharacteristic
396C22×C5D4×Q811yescharacteristic
397C22×C5C2×#13511yescharacteristic
398C22×C5C2×#13511yescharacteristic
399C22×C5#57611yescharacteristic
400C22×C5#57711yescharacteristic
401C4×C5—22no—
402C4×C5—22no—
403C4×C5—22no—
404C4×C5—22no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5—81no—
408C4×C5—81no—
409C4×C5—81no—
410C4×C5#53311yescharacteristic
411C4×C5#54111yescharacteristic
412C4×C5#54711yescharacteristic
413C4×C5D4×Q811yescharacteristic
414Dic5—42no—
415Dic5—42no—
416Dic5—81no—
417Dic5—81no—
418C24—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4Q8×D512yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4C2×C22⋊D511yescharacteristic
439C22×C4C2×C22⋊D511yescharacteristic
440C22×C4C2×C22⋊D511yescharacteristic
441C22×C4C2×C22⋊D511yescharacteristic
442C22×C4C2×C22⋊D511yescharacteristic
443C22×C4C2×C22⋊D511yescharacteristic
444C22×C4C23×D511yescharacteristic
445C2×C8—52no—
446C2×C8—52no—
447C2×C8—52no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—52no—
467C4⋊C4—52no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—202no—
477C4⋊C4—202no—
478C4⋊C4—202no—
479C4⋊C4—202no—
480C4⋊C4—401no—
481C4⋊C4—401no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—401no—
492C42D4×D512yes—
493C42#71112yes—
494C2×C5—82no—
495C2×C5#242911yescharacteristic
496C2×C5#305011yescharacteristic
497C2×C5#306211yescharacteristic
498C2×C5#336111yescharacteristic
499C2×C5#336511yescharacteristic
500C2×C5#338011yescharacteristic
501C2×C5#338111yescharacteristic
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C22×C22⋊D511yescharacteristic
510Q8—28no—
511D4—22no—
512D4—22no—
513D4—41no—
514D4—41no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—84no—
539C2×C4—102no—
540C2×C4—102no—
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#408512yes—
552C2×C4#408512yes—
553C2×C4#409612yes—
554C2×C4#409612yes—
555C2×C4C2×D4×D511yescharacteristic
556C2×C4C2×#71111yescharacteristic
557C2×C4C2×Q8×D511yescharacteristic
558C2×C4#414711yescharacteristic
559C2×C4D5×#4111yescharacteristic
560C2×C4#415011yescharacteristic
561C8—102no—
562C8—102no—
563C8—102no—
564C8—201no—
565C5#2547311yescharacteristic, complemented, Sylow
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C2×#408511yescharacteristic
574C22Q8×C22⋊D511yescharacteristic
575C22C2×#409611yescharacteristic
576C22C2×#409611yescharacteristic
577C22#6616511yescharacteristic
578C22#6616911yescharacteristic
579C22#6617011yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—202no—
590C4—202no—
591C4—401no—
592C4—401no—
593C4#6595611yescharacteristic
594C4#6595911yescharacteristic
595C4#6596511yescharacteristic
596C4#6596611yescharacteristic
597C2—82no—
598C2#1061448911yescharacteristic
599C2#1061465311yescharacteristic
600C2#1061511011yescharacteristic
601C2#1061535911yescharacteristic
602C2#1061536011yescharacteristic
603C2#1061544411yescharacteristic
604C2#1061544811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2580C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
hypercenter#2580D5
hypocenterC5#25473
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2580

Complements

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

NH ≅ G/Ntype
2. #10614214C2semidirect
3. C2×Q8×#168C2semidirect
10. #10600416C2semidirect
11. #10600412C2semidirect
12. #10600411C2semidirect
13. #10600403C2semidirect
14. #10600347C2semidirect
15. #10600333C2semidirect
109. #3964Q8semidirect
565. C5#25473semidirect

Maximal subgroups

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

subgroupindex
C5×#25802
#106142142
C2×Q8×#1682
C2×#652982
C4×#39642
#106004462
#106004452
#106004372
#106004162
#106004122
#106004112
#106004032
#106003472
#106003332
#254735