Finite Group Databasebeta

← #12065225

Subgroups — #12065225

Order 1280.

1206 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65880C211yesmaximal, characteristic
2#10610365C212yesmaximal, complemented
3C5×#1465C211yesmaximal, characteristic, complemented
4#10602395C211yesmaximal, characteristic, complemented
5#10600764C212yesmaximal, complemented
6#10598937C212yesmaximal, complemented
7#10598918C212yesmaximal, complemented
8#10598914C212yesmaximal, complemented
9#10598893C212yesmaximal, complemented
10C22×#711C411yescharacteristic
11C2×C4×C5×D4C2211yescharacteristic
12C2×D4×Dic5C411yescharacteristic
13C2×C4×C22⋊D5C411yescharacteristic
14C2×C4×C22⋊D5C2211yescharacteristic
15C22×#683C411yescharacteristic
16C22×#683C2211yescharacteristic
17#65880—24no—
18#65880—24no—
19C2×D5×C4⋊C4C2211yescharacteristic
20C2×#4033C2211yescharacteristic
21C2×#4027C411yescharacteristic
22C2×#4027C2211yescharacteristic
23C2×#4023C411yescharacteristic
24C2×#4023C2211yescharacteristic
25C2×#4018C411yescharacteristic
26C2×C4×Dic10C411yescharacteristic
27C5×#407C2212yes—
28#65496C2212yes—
29#65417—24no—
30#65018—24no—
31#65015C2214yes—
32#65007C2214yes—
33C5×#324C2212yes—
34C5×#323C2212yes—
35#64748C2212yes—
36#64745C2212yes—
37#64689C2214yes—
38#64689C2214yes—
39#17370—51nomaximal, Sylow
40C22×C5×D4C2×C411yescharacteristic
41C23×C4×C5C2×C411yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C22×C22⋊D5C2×C411yescharacteristic
44C22×C22⋊D5C2×C411yescharacteristic
45C23×Dic5C2×C411yescharacteristic
46C23×Dic5C2×C411yescharacteristic
47C23×Dic5C2×C411yescharacteristic
48C23×Dic5C2×C411yescharacteristic
49C2×#711—24no—
50C2×#711—24no—
51C2×#711—24no—
52C22×C4×D5C2×C411yescharacteristic
53C22×C4×D5C2×C411yescharacteristic
54C22×C4×D5C2311yescharacteristic
55C22×Dic10C2×C411yescharacteristic
56C2×C5×M16—22no—
57C4×C5×D4—22no—
58C4×C5×D4—22no—
59C2×C5×C4⋊C4C2311yescharacteristic
60C2×C5×C22⋊C4C2×C411yescharacteristic
61C2×C5×C22⋊C4C2311yescharacteristic
62C2×C42×C5C2×C411yescharacteristic
63C2×C22⋊Dic5C2×C411yescharacteristic
64C2×C22⋊Dic5C2×C411yescharacteristic
65D4×Dic5—24no—
66C4×C22⋊D5—22no—
67C4×C22⋊D5—22no—
68C4×C22⋊D5D414yes—
69C4×C22⋊D5D414yes—
70C2×#685C2×C411yescharacteristic
71C2×#685C2×C411yescharacteristic
72C2×C4⋊Dic5C2×C411yescharacteristic
73C2×#683—22no—
74C2×#683—22no—
75C2×#683—22no—
76C2×#683—22no—
77C2×#683C2×C411yescharacteristic
78C2×#683C2×C411yescharacteristic
79C2×#683C2×C411yescharacteristic
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2311yescharacteristic
84C2×#683C2311yescharacteristic
85C2×C4×Dic5C2×C411yescharacteristic
86C2×C4×Dic5C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2×C411yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×#681—22no—
91C2×#676—24no—
92D5×C4⋊C4—24no—
93#4033—24no—
94#4027—24no—
95#4027—24no—
96#4023—24no—
97#4023—24no—
98#4018—22no—
99#4018—22no—
100C4×Dic10—22no—
101C4×Dic10—22no—
102C5×C22⋊C8—22no—
103C5×C22⋊C8C2314yes—
104C22⋊#168—22no—
105C22⋊#168C2314yes—
106#3952—24no—
107#3946—24no—
108C8×Dic5—24no—
109C2×#520—51no—
110#2975—52no—
111#1465—52no—
112#1465—51no—
113#1465D511yescharacteristic, complemented
114#1463—52no—
115#1463—52no—
116#1461—52no—
117#1458—52no—
118C24×C5C22×C411yescharacteristic
119C24×C5C22×C411yescharacteristic
120C23×D5C22×C411yescharacteristic
121C2×C5×D4—22no—
122C2×C5×D4—22no—
123C2×C5×D4—22no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—81no—
127C22×C4×C5—81no—
128C22×C4×C5C22×C411yescharacteristic
129C22×C4×C5C22×C411yescharacteristic
130C22×C4×C5C22×C411yescharacteristic
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C2×D412yes—
133C22×C4×C5C2×D412yes—
134C22×C4×C5C2411yescharacteristic
135C2×C22⋊D5—22no—
136C2×C22⋊D5—22no—
137C2×C22⋊D5—22no—
138C2×C22⋊D5—22no—
139C2×C22⋊D5—22no—
140C2×C22⋊D5C22⋊C414yes—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—81no—
149C22×Dic5—81no—
150C22×Dic5M1614yescomplemented
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C22×C411yescharacteristic
157C22×Dic5C22×C411yescharacteristic
158#711—232no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—81no—
164C2×C4×D5—81no—
165C2×C4×D5C2×D414yes—
166C2×Dic10—22no—
167C2×Dic10—22no—
168C2×Dic10M1614yescomplemented
169C5×M16—82no—
170C2×C5×C8—24no—
171C5×C4⋊C4—22no—
172C5×C22⋊C4—22no—
173C5×C22⋊C4—22no—
174C42×C5—21no—
175C42×C5—21no—
176C22⋊Dic5—22no—
177C22⋊Dic5C22⋊C414yes—
178#685—22no—
179#685C22⋊C412yes—
180#685C22⋊C412yes—
181C4⋊Dic5—22no—
182#683—21no—
183#683—21no—
184#683—21no—
185#683—21no—
186#683—22no—
187#683—22no—
188#683—22no—
189#683—22no—
190#683—22no—
191#683C22⋊C412yes—
192#683C22⋊C412yes—
193C4×Dic5—22no—
194C4×Dic5—22no—
195C4×Dic5—22no—
196C4×Dic5—22no—
197C4×Dic5C2×D414yes—
198#681—82no—
199C2×#168—24no—
200#676—84no—
201C22×#41—51no—
202#520—104no—
203#520—104no—
204C2×C4×Q8—51no—
205C2×C4×Q8—51no—
206C2×C4×D4—51no—
207C2×C4×D4—51no—
208C2×C4×D4—51no—
209C2×C4×D4—51no—
210C2×C4×D4—51no—
211C2×C4×D4C2×D511yescharacteristic
212C2×#117—51no—
213C2×#117—51no—
214C2×#117—51no—
215C22×C4⋊C4—51no—
216C22×C4⋊C4—51no—
217C22×C4⋊C4—51no—
218#436—104no—
219#436—104no—
220#431—54no—
221#407—52no—
222#407—54no—
223#407C2×D512yes—
224#324—52no—
225#324—54no—
226#324—54no—
227#324C2×D512yes—
228#323—52no—
229#323C2×D512yes—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5—41no—
235C23×C5—41no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5C2×C22⋊C412yes—
239C23×C5C2×M1612yes—
240C23×C5C23×C411yescharacteristic
241C22×D5—21no—
242C22×D5—21no—
243C22×D5—41no—
244C22×D5—41no—
245C22×D5C2×C22⋊C412yes—
246C5×D4—28no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—81no—
258C2×C4×C5—81no—
259C2×C4×C5C2×C22⋊C411yescharacteristic
260C2×C4×C5C2×C22⋊C411yescharacteristic
261C2×C4×C5C2×M1612yes—
262C2×C4×C5C22×D412yes—
263C22⋊D5—28no—
264C22⋊D5—28no—
265C2×Dic5—28no—
266C2×Dic5—21no—
267C2×Dic5—21no—
268C2×Dic5—21no—
269C2×Dic5—21no—
270C2×Dic5—28no—
271C2×Dic5—21no—
272C2×Dic5—21no—
273C2×Dic5—41no—
274C2×Dic5—41no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—82no—
278C2×Dic5—82no—
279C2×Dic5C2×C22⋊C412yes—
280C2×Dic5C2×C22⋊C412yes—
281C2×Dic5C2×C22⋊C412yes—
282C2×Dic5C2×M1612yes—
283C2×Dic5C2×M1612yes—
284C2×Dic5C2×M1612yes—
285C2×Dic5C2×M1612yes—
286C4×D5—28no—
287C4×D5—44no—
288C4×D5—82no—
289Dic10—28no—
290C5×C8—44no—
291#168—44no—
292C2×#41—104no—
293C2×#41—104no—
294C2×#41—104no—
295C22×Q8—51no—
296C22×D4—51no—
297C22×D4—51no—
298C22×D4C4×D511yescharacteristic
299C23×C4—51no—
300C23×C4—51no—
301C23×C4—51no—
302C23×C4—51no—
303C23×C4—51no—
304C23×C4—51no—
305C23×C4—51no—
306C23×C4C4×D511yescharacteristic
307C23×C4C22×D511yescharacteristic
308C2×M16—22no—
309C2×M16—104no—
310C2×M16—102no—
311C4×Q8—102no—
312C4×Q8—102no—
313C4×Q8—104no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—54no—
317C4×D4—54no—
318C4×D4—104no—
319C4×D4—104no—
320C4×D4—102no—
321C4×D4—102no—
322C4×D4—104no—
323#117—102no—
324#117—102no—
325#117—104no—
326#117—104no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—51no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—104no—
337C2×C4⋊C4—102no—
338C2×C4⋊C4—102no—
339C2×C4⋊C4—102no—
340C2×C4⋊C4—102no—
341C2×C4⋊C4C22×D511yescharacteristic
342C2×C22⋊C4—51no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—51no—
345C2×C22⋊C4—51no—
346C2×C22⋊C4C4×D511yescharacteristic
347C2×C22⋊C4C22×D511yescharacteristic
348C2×C42—51no—
349C2×C42—51no—
350C2×C42—51no—
351C2×C42—51no—
352C2×C42—51no—
353C2×C42C4×D511yescharacteristic
354C4⋊C8—104no—
355C22⋊C8—22no—
356C22⋊C8—54no—
357C22⋊C8—104no—
358C22⋊C8—102no—
359C22⋊C8C22×D514yes—
360C4×C8—104no—
361C22×C5—21no—
362C22×C5—21no—
363C22×C5—22no—
364C22×C5—22no—
365C22×C5—22no—
366C22×C5—22no—
367C22×C5—42no—
368C22×C5—42no—
369C22×C5—42no—
370C22×C5—42no—
371C22×C5—41no—
372C22×C5—41no—
373C22×C5C22×C22⋊C411yescharacteristic
374C22×C5C22×M1611yescharacteristic
375C22×C5C22×M1611yescharacteristic
376C2×D5—22no—
377C2×D5—22no—
378C2×D5—22no—
379C2×D5—42no—
380C2×D5—42no—
381C4×C5—22no—
382C4×C5—22no—
383C4×C5—21no—
384C4×C5—21no—
385C4×C5—41no—
386C4×C5—41no—
387Dic5—22no—
388Dic5—22no—
389Dic5—22no—
390Dic5—22no—
391Dic5—41no—
392Dic5—41no—
393Dic5#40714yes—
394C24—51no—
395C24C2×C4×D511yescharacteristic
396C24C2×C4×D511yescharacteristic
397#41—1032no—
398C2×Q8—54no—
399C2×Q8—102no—
400C2×Q8—102no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—54no—
405C2×D4—102no—
406C2×D4—102no—
407C2×D4—102no—
408C2×D4—102no—
409C2×D4—102no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—54no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—54no—
419C22×C4—51no—
420C22×C4—51no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—102no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—401no—
435C22×C4—401no—
436C22×C4—401no—
437C22×C4—401no—
438C22×C4C2×C4×D511yescharacteristic
439C22×C4C2×C4×D511yescharacteristic
440C22×C4C2×C4×D511yescharacteristic
441C22×C4C2×C4×D511yescharacteristic
442C22×C4D4×D512yes—
443C22×C4D4×D512yes—
444C22×C4C23×D511yescharacteristic
445M16—82no—
446M16—404no—
447M16—402no—
448C2×C8—24no—
449C2×C8—104no—
450C4⋊C4—22no—
451C4⋊C4—52no—
452C4⋊C4—52no—
453C4⋊C4—102no—
454C4⋊C4—102no—
455C4⋊C4—102no—
456C4⋊C4—102no—
457C4⋊C4—102no—
458C4⋊C4—102no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—54no—
466C22⋊C4—52no—
467C22⋊C4—52no—
468C22⋊C4—102no—
469C22⋊C4—102no—
470C42—21no—
471C42—21no—
472C42—54no—
473C42—102no—
474C42—102no—
475C42—102no—
476C42—102no—
477C2×C5—21no—
478C2×C5—21no—
479C2×C5—42no—
480C2×C5—42no—
481C2×C5C2×#40711yescharacteristic
482C2×C5#288311yescharacteristic
483C2×C5#288911yescharacteristic
484D5—42no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—52no—
494C23—101no—
495C23—101no—
496C23—201no—
497C23—201no—
498C23D5×C22⋊C412yes—
499C23D5×M1612yes—
500C23C22×C4×D511yescharacteristic
501Q8—108no—
502D4—28no—
503D4—108no—
504D4—108no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—52no—
516C2×C4—52no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—81no—
523C2×C4—81no—
524C2×C4—108no—
525C2×C4—108no—
526C2×C4—108no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—204no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—402no—
539C2×C4—402no—
540C2×C4—402no—
541C2×C4D5×C22⋊C411yescharacteristic
542C2×C4D5×C22⋊C411yescharacteristic
543C2×C4D5×M1612yes—
544C2×C4C2×D4×D512yes—
545C8—44no—
546C8—204no—
547C5#1737011yescharacteristic, complemented, Sylow
548C22—21no—
549C22—21no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—102no—
561C22—102no—
562C22—102no—
563C22—202no—
564C22—202no—
565C22C2×D5×C22⋊C411yescharacteristic
566C22C2×D5×M1611yescharacteristic
567C22C2×D5×M1611yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—54no—
575C4—102no—
576C4—102no—
577C4—102no—
578C4—102no—
579C4—201no—
580C4—201no—
581C2—21no—
582C2—21no—
583C2—42no—
584C2—42no—
585C2—202no—
586C2D5×#40711yescharacteristic
587C2#1061041911yescharacteristic
588C2#1061044611yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1465C2
socleC22×C5C22×C22⋊C4
prime radicalC22×#711C4
cosocleC22×C4×C5C24
hypercenter#1465D5
hypocenterC5#17370
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #10610365C2semidirect
3. C5×#1465C2semidirect
4. #10602395C2semidirect
5. #10600764C2semidirect
6. #10598937C2semidirect
7. #10598918C2semidirect
8. #10598914C2semidirect
9. #10598893C2semidirect
113. #1465D5semidirect
150. C22×Dic5M16semidirect
168. C2×Dic10M16semidirect
547. C5#17370semidirect

Maximal subgroups

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

subgroupindex
C2×#658802
#106103652
C5×#14652
#106023952
#106007642
#105989372
#105989182
#105989142
#105988932
#173705