Finite Group Databasebeta

← #12107153

Subgroups — #12107153

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3076C211yesmaximal, characteristic
2#10615060C211yesmaximal, characteristic, complemented
3#10614242C211yesmaximal, characteristic
4#10602634C211yesmaximal, characteristic, complemented
5#10602439C211yesmaximal, characteristic
6#10601454C211yesmaximal, characteristic, complemented
7#10601454C211yesmaximal, characteristic, complemented
8#10601453C211yesmaximal, characteristic, complemented
9#10601452C211yesmaximal, characteristic, complemented
10#10601267C211yesmaximal, characteristic, complemented
11#10601260C211yesmaximal, characteristic, complemented
12#10601085C211yesmaximal, characteristic
13#10601085C211yesmaximal, characteristic
14#10601083C211yesmaximal, characteristic
15#10601082C211yesmaximal, characteristic
16C5×#533C2211yescharacteristic
17C4×C5×#41C2211yescharacteristic
18C2×#4094C2211yescharacteristic
19C2×#4094C2211yescharacteristic
20C5×#479C411yescharacteristic, complemented
21C5×#479C411yescharacteristic, complemented
22C5×#478C411yescharacteristic, complemented
23C5×#478C411yescharacteristic, complemented
24C5×#477C411yescharacteristic, complemented
25C5×#476C411yescharacteristic, complemented
26C5×#475C411yescharacteristic, complemented
27C5×#474C411yescharacteristic, complemented
28C5×#427C2211yescharacteristic
29C5×#427C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C5×#416C2211yescharacteristic
32C5×#416C2211yescharacteristic
33C2×#3969C2211yescharacteristic
34C2×#3969C2211yescharacteristic
35C2×#3951C2211yescharacteristic
36C2×#3951C2211yescharacteristic
37C2×#3947C2211yescharacteristic
38C2×C8×Dic5C2211yescharacteristic
39#65313—21no—
40#65313—21no—
41#65313—21no—
42#65313—21no—
43#65288C2211yescharacteristic
44#65288C2211yescharacteristic
45#65286—21no—
46#65286—21no—
47#65286C2211yescharacteristic
48#65286C2211yescharacteristic
49#65286C2211yescharacteristic
50#65286C2211yescharacteristic
51C4×C4⋊Dic5C2211yescharacteristic
52#65213C2211yescharacteristic
53C4×#681—21no—
54C4×#681C2211yescharacteristic
55C2×#3935—21no—
56C2×#3935C2211yescharacteristic
57#64772C2211yescharacteristic
58#64772C2211yescharacteristic
59#64770C2211yescharacteristic
60#64770C2211yescharacteristic
61#64752C2211yescharacteristic
62#64752C2211yescharacteristic
63#64752C2211yescharacteristic
64#64752C2211yescharacteristic
65#64752C2211yescharacteristic
66#64752C2211yescharacteristic
67#21629—51nomaximal, Sylow
68C2×C5×#41C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C5×C4⋊Q8C2×C411yescharacteristic
72C5×C4⋊Q8C2×C411yescharacteristic
73C5×#125C2×C411yescharacteristic
74C5×#125C2×C411yescharacteristic
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8—21no—
77C4×C5×Q8—21no—
78C4×C5×Q8—21no—
79C4×C5×Q8C2×C411yescharacteristic
80C4×C5×Q8C2×C411yescharacteristic
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C4×C5×D4C2×C411yescharacteristic
84C4×C5×D4C2×C411yescharacteristic
85C5×#117—21no—
86C5×#117C2311yescharacteristic
87C5×#117C2311yescharacteristic
88C5×#117C2311yescharacteristic
89C2×C42×C5—21no—
90C2×C42×C5C2311yescharacteristic
91#4094—22no—
92#4094—22no—
93#4094—22no—
94#4094Q814yescomplemented
95C2×C4⋊Dic5—21no—
96C2×C4×Dic5C2311yescharacteristic
97C2×C4×Dic5C2311yescharacteristic
98C2×#681—21no—
99C2×#681—21no—
100C2×#681C2311yescharacteristic
101C2×#681C2311yescharacteristic
102C2×#681C2311yescharacteristic
103C2×#681C2311yescharacteristic
104C22×#168—21no—
105C22×#168—21no—
106C22×#168C2311yescharacteristic
107C22×#168C2311yescharacteristic
108C5×#107C2×C411yescharacteristic
109C5×#107C2×C411yescharacteristic
110C5×#107C2×C411yescharacteristic
111C5×#107C2×C411yescharacteristic
112C5×#106C2×C411yescharacteristic
113C5×#106C2×C411yescharacteristic
114C5×#106C2×C411yescharacteristic
115C5×#106C2×C411yescharacteristic
116C5×C4⋊C8C2×C411yescharacteristic
117C5×C4⋊C8C2×C411yescharacteristic
118C5×C4⋊C8C2×C411yescharacteristic
119C5×C4⋊C8C2×C411yescharacteristic
120C5×#103C2×C411yescharacteristic
121C5×#103C2×C411yescharacteristic
122C5×#103C2×C411yescharacteristic
123C5×#103C2×C411yescharacteristic
124C5×#102C2×C411yescharacteristic
125C5×#102C2×C411yescharacteristic
126C5×#102C2×C411yescharacteristic
127C5×#102C2×C411yescharacteristic
128#3969—22no—
129#3969—22no—
130#3963—21no—
131#3951—22no—
132#3951—22no—
133#3947—22no—
134C8×Dic5—22no—
135C4⋊#168—21no—
136C4⋊#168—21no—
137C4⋊#168—21no—
138C4⋊#168—21no—
139C4⋊#168—21no—
140C4⋊#168—21no—
141#3935—21no—
142#3935—21no—
143#3935—21no—
144#3935—21no—
145#3935—21no—
146#3935D411yescharacteristic
147#3935D411yescharacteristic
148#3935D411yescharacteristic
149#3935D411yescharacteristic
150C4×#168—21no—
151C4×#168—21no—
152C4×#168—21no—
153C4×#168—21no—
154C4×#168—21no—
155#3076D511yescharacteristic
156#2961—51no—
157#2875—51no—
158#1986—51no—
159#1950—51no—
160#1922—51no—
161#1922—51no—
162#1866—51no—
163#1866—51no—
164#1806—51no—
165#1773—51no—
166#1772—51no—
167#1771—51no—
168#1765—51no—
169#1764—51no—
170C5×#41—21no—
171C5×#41—21no—
172C5×#41C2×Q812yes—
173C5×#41#4112yes—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8C22×C411yescharacteristic
177C2×C5×D4—21no—
178C2×C5×D4C22×C411yescharacteristic
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5#4111yescharacteristic
183C22×C4×C5#4111yescharacteristic
184C22×C4×C5C2411yescharacteristic
185C22×Dic5—21no—
186C22×Dic5—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8C22×C411yescharacteristic
192C2×C5×C8C22×C411yescharacteristic
193C2×C5×C8C22×C411yescharacteristic
194C2×C5×C8C22×C411yescharacteristic
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4C22×C411yescharacteristic
204C5×C4⋊C4C22×C411yescharacteristic
205C5×C4⋊C4C22×C411yescharacteristic
206C5×C4⋊C4C22×C411yescharacteristic
207C5×C4⋊C4C22×C411yescharacteristic
208C5×C4⋊C4C22×C411yescharacteristic
209C5×C22⋊C4—21no—
210C5×C22⋊C4—21no—
211C5×C22⋊C4—21no—
212C5×C22⋊C4—21no—
213C5×C22⋊C4—21no—
214C42×C5—21no—
215C42×C5—21no—
216C42×C5—21no—
217C42×C5—21no—
218C42×C5—21no—
219C42×C5C22×C411yescharacteristic
220C42×C5C22×C411yescharacteristic
221C42×C5C2×D411yescharacteristic
222C42×C5C2×D411yescharacteristic
223C4⋊Dic5—42no—
224C4×Dic5—21no—
225C4×Dic5—21no—
226C4×Dic5—21no—
227C4×Dic5—21no—
228#681—24no—
229#681—21no—
230#681—21no—
231#681—24no—
232#681—21no—
233#681—21no—
234#681—21no—
235#681—21no—
236#681C2×Q812yes—
237#681#4112yes—
238C2×#168—24no—
239C2×#168—21no—
240C2×#168—21no—
241C2×#168—21no—
242C2×#168—21no—
243C2×#168—24no—
244C2×#168—21no—
245C2×#168—21no—
246C2×#168C2×D411yescharacteristic
247C2×#168C2×D411yescharacteristic
248C2×#168C2×D411yescharacteristic
249C2×#168C2×D411yescharacteristic
250C2×#168C2×Q812yes—
251C2×#168#4112yes—
252C2×#131—51no—
253C2×#131—51no—
254#533C2×D511yescharacteristic
255C4×#41C2×D511yescharacteristic
256#479Dic511yescharacteristic, complemented
257#479Dic511yescharacteristic, complemented
258#478Dic511yescharacteristic, complemented
259#478Dic511yescharacteristic, complemented
260#477Dic511yescharacteristic, complemented
261#476Dic511yescharacteristic, complemented
262#475Dic511yescharacteristic, complemented
263#474Dic511yescharacteristic, complemented
264#446—101no—
265#446—101no—
266#446—101no—
267#446—101no—
268C2×#108—51no—
269C2×#108—51no—
270#427C2×D511yescharacteristic
271#427C2×D511yescharacteristic
272#424—51no—
273#424—51no—
274#423—51no—
275C2×C4⋊C8C2×D511yescharacteristic
276C2×#104—51no—
277C2×#104—51no—
278#416C2×D511yescharacteristic
279#416C2×D511yescharacteristic
280#405—51no—
281#405—51no—
282#405—51no—
283#405—51no—
284#405—101no—
285#405—101no—
286C4×M16—51no—
287C4×M16—101no—
288C2×#97—51no—
289C2×#97—51no—
290C2×#97—101no—
291C2×C4×C8—51no—
292C4×C4⋊C4—51no—
293#341—51no—
294#341—51no—
295#339—51no—
296#339—51no—
297#339—51no—
298#339—51no—
299#339—51no—
300#339—51no—
301#336—51no—
302#336—51no—
303C23×C5—21no—
304C23×C5C2×#4111yescharacteristic
305C5×Q8—21no—
306C5×Q8—81no—
307C5×Q8—81no—
308C5×Q8C4×Q812yes—
309C5×D4—22no—
310C5×D4—22no—
311C5×D4—21no—
312C5×D4C4×Q812yes—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—81no—
325C2×C4×C5—81no—
326C2×C4×C5C4×D411yescharacteristic
327C2×C4×C5C4×D411yescharacteristic
328C2×C4×C5C4×D411yescharacteristic
329C2×C4×C5C4×D411yescharacteristic
330C2×C4×C5C23×C411yescharacteristic
331C2×C4×C5C22×D411yescharacteristic
332C2×C4×C5C22×Q811yescharacteristic
333C2×C4×C5C2×#4111yescharacteristic
334C2×C4×C5C2×#4111yescharacteristic
335C2×C4×C5C2×#4111yescharacteristic
336C2×Dic5—22no—
337C2×Dic5—41no—
338C2×Dic5—41no—
339C2×Dic5—41no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342C5×C8—21no—
343C5×C8—21no—
344C5×C8—21no—
345C5×C8—21no—
346#168—22no—
347#168—21no—
348#168—22no—
349#168—21no—
350#168—41no—
351#168—41no—
352#168C22⋊Q812yes—
353#168C22⋊Q812yes—
354C2×#41C22×D511yescharacteristic
355#131—54no—
356#131—102no—
357#131—102no—
358#131—102no—
359C2×M16—51no—
360C2×M16—51no—
361C2×M16—51no—
362C2×M16—51no—
363C2×M16—101no—
364C2×M16—101no—
365C22×C8—51no—
366C22×C8—51no—
367C22×C8—101no—
368C22×C8—101no—
369C22×C8C22×D511yescharacteristic
370C22×C8C22×D511yescharacteristic
371C4⋊Q8C2×Dic511yescharacteristic
372C4⋊Q8C2×Dic511yescharacteristic
373#125C2×Dic511yescharacteristic
374#125C2×Dic511yescharacteristic
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C2×Dic511yescharacteristic
380C4×Q8C2×Dic511yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C2×Dic511yescharacteristic
384C4×D4C2×Dic511yescharacteristic
385#117—21no—
386#117C22×D511yescharacteristic
387#117C22×D511yescharacteristic
388#117C22×D511yescharacteristic
389C2×C4⋊C4—101no—
390C2×C42—21no—
391C2×C42—51no—
392C2×C42—51no—
393C2×C42C22×D511yescharacteristic
394#108—102no—
395#108—102no—
396#107C2×Dic511yescharacteristic
397#107C2×Dic511yescharacteristic
398#107C2×Dic511yescharacteristic
399#107C2×Dic511yescharacteristic
400#106C2×Dic511yescharacteristic
401#106C2×Dic511yescharacteristic
402#106C2×Dic511yescharacteristic
403#106C2×Dic511yescharacteristic
404C4⋊C8—101no—
405C4⋊C8—101no—
406C4⋊C8—101no—
407C4⋊C8—101no—
408C4⋊C8—101no—
409C4⋊C8—101no—
410C4⋊C8C2×Dic511yescharacteristic
411C4⋊C8C2×Dic511yescharacteristic
412C4⋊C8C2×Dic511yescharacteristic
413C4⋊C8C2×Dic511yescharacteristic
414#104—102no—
415#104—102no—
416#103C2×Dic511yescharacteristic
417#103C2×Dic511yescharacteristic
418#103C2×Dic511yescharacteristic
419#103C2×Dic511yescharacteristic
420#102C2×Dic511yescharacteristic
421#102C2×Dic511yescharacteristic
422#102C2×Dic511yescharacteristic
423#102C2×Dic511yescharacteristic
424#97—51no—
425#97—51no—
426#97—51no—
427#97—51no—
428#97—101no—
429#97—101no—
430#97—101no—
431#97—101no—
432#97—102no—
433#97—101no—
434C4×C8—101no—
435C4×C8—101no—
436C4×C8—101no—
437C4×C8—101no—
438C4×C8—102no—
439C4×C8—101no—
440#95—101no—
441C22×C5—21no—
442C22×C5—21no—
443C22×C5—22no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5C2×C4×D411yescharacteristic
447C22×C5#52911yescharacteristic
448C22×C5#53311yescharacteristic
449C4×C5—21no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—21no—
453C4×C5—22no—
454C4×C5—41no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5—41no—
458C4×C5—41no—
459C4×C5—41no—
460C4×C5C2×C4×Q811yescharacteristic
461C4×C5C4×#4111yescharacteristic
462C4×C5C2×C22⋊Q811yescharacteristic
463C4×C5#52511yescharacteristic
464Dic5—42no—
465Dic5—81no—
466#41—21no—
467#41—21no—
468#41Q8×D512yes—
469#41#71312yes—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8C22×Dic511yescharacteristic
473C2×D4—21no—
474C2×D4C22×Dic511yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4#71111yescharacteristic
481C22×C4#71111yescharacteristic
482C22×C4C23×D511yescharacteristic
483M16—52no—
484M16—52no—
485M16—104no—
486M16—104no—
487M16—101no—
488M16—101no—
489M16—101no—
490M16—101no—
491M16—101no—
492M16—101no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—51no—
498C2×C8—51no—
499C2×C8—52no—
500C2×C8—52no—
501C2×C8—51no—
502C2×C8—51no—
503C2×C8—104no—
504C2×C8—104no—
505C2×C8—101no—
506C2×C8—101no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—101no—
510C2×C8—101no—
511C2×C8C22×Dic511yescharacteristic
512C2×C8C22×Dic511yescharacteristic
513C2×C8C22×Dic511yescharacteristic
514C2×C8C22×Dic511yescharacteristic
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—202no—
524C4⋊C4C22×Dic511yescharacteristic
525C4⋊C4C22×Dic511yescharacteristic
526C4⋊C4C22×Dic511yescharacteristic
527C4⋊C4C22×Dic511yescharacteristic
528C4⋊C4C22×Dic511yescharacteristic
529C4⋊C4C22×Dic511yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—101no—
541C42—101no—
542C42—101no—
543C42—101no—
544C42D4×D511yescharacteristic
545C42D4×D511yescharacteristic
546C42C22×Dic511yescharacteristic
547C42C22×Dic511yescharacteristic
548C2×C5—21no—
549C2×C5—21no—
550C2×C5—42no—
551C2×C5C4×C22⋊Q811yescharacteristic
552C2×C5#295611yescharacteristic
553C2×C5#295711yescharacteristic
554C23—21no—
555C23C2×#71111yescharacteristic
556Q8—21no—
557Q8—81no—
558Q8—81no—
559Q8Q8×Dic512yes—
560D4—22no—
561D4—22no—
562D4—21no—
563D4Q8×Dic512yes—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—102no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4D4×Dic511yescharacteristic
584C2×C4D4×Dic511yescharacteristic
585C2×C4D4×Dic511yescharacteristic
586C2×C4D4×Dic511yescharacteristic
587C2×C4C2×D4×D511yescharacteristic
588C2×C4C2×Q8×D511yescharacteristic
589C2×C4C2×#71311yescharacteristic
590C2×C4D5×#4111yescharacteristic
591C2×C4D5×#4111yescharacteristic
592C2×C4C23×Dic511yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—52no—
598C8—52no—
599C8—102no—
600C8—101no—
601C8—101no—
602C8—102no—
603C8—201no—
604C8—201no—
605C5#2162911yescharacteristic, complemented, Sylow
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22#6595611yescharacteristic
612C22#6595811yescharacteristic
613C22C2×D4×Dic511yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—202no—
626C4—401no—
627C4D5×C22⋊Q811yescharacteristic
628C4#6596111yescharacteristic
629C4C2×Q8×Dic511yescharacteristic
630C4#41×Dic511yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2Dic5×C22⋊Q811yescharacteristic
635C2#1061564111yescharacteristic
636C2#1061573111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#3076C2
socleC22×C5C2×C4×D4
prime radicalC2×C5×#41C23
cosocleC22×C4×C5C24
hypercenter#3076D5
hypocenterC5#21629
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
2. #10615060C2semidirect
4. #10602634C2semidirect
6. #10601454C2semidirect
7. #10601454C2semidirect
8. #10601453C2semidirect
9. #10601452C2semidirect
10. #10601267C2semidirect
11. #10601260C2semidirect
20. C5×#479C4semidirect
21. C5×#479C4semidirect
22. C5×#478C4semidirect
23. C5×#478C4semidirect
24. C5×#477C4semidirect
25. C5×#476C4semidirect
26. C5×#475C4semidirect
27. C5×#474C4semidirect
94. #4094Q8semidirect
256. #479Dic5semidirect
257. #479Dic5semidirect
258. #478Dic5semidirect
259. #478Dic5semidirect
260. #477Dic5semidirect
261. #476Dic5semidirect
262. #475Dic5semidirect
263. #474Dic5semidirect
605. C5#21629semidirect

Maximal subgroups

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

subgroupindex
C5×#30762
#106150602
#106142422
#106026342
#106024392
#106014542
#106014532
#106014522
#106012672
#106012602
#106010852
#106010832
#106010822
#216295