Finite Group Databasebeta

← #13034742

Subgroups — #13034742

Order 1280.

1646 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5⋊M16C211yesmaximal, characteristic
2C2×#65756C211yesmaximal, characteristic
3C2×#65682C211yesmaximal, characteristic, complemented
4C2×#65681C211yesmaximal, characteristic, complemented
5C4×D5×C22⋊C4C211yesmaximal, characteristic
6#10604232C214yesmaximal, complemented
7#10604172C211yesmaximal, characteristic, complemented
8#10604172C211yesmaximal, characteristic, complemented
9#10603785C214yesmaximal, complemented
10C23×C4×D5C2211yescharacteristic
11C22×#704C2212yes—
12C2×D5⋊M16—24no—
13C2×D5⋊M16—24no—
14C2×D5⋊M16—24no—
15C22×#700C2211yescharacteristic
16C22×#700C2211yescharacteristic
17C22×#700C2211yescharacteristic
18C22×#700C2211yescharacteristic
19C22×D5⋊C8C2212yes—
20C2×D5×C22⋊C4C412yes—
21C2×C42×D5C2211yescharacteristic
22C2×C42×D5C2211yescharacteristic
23C2×C22⋊#170C2212yes—
24#65756—24no—
25C2×#4004C2214yescomplemented
26C2×#4003C2212yes—
27C2×C4⋊#170C2214yescomplemented
28#65682—24no—
29#65681—24no—
30C4×C5×C22⋊C4C411yescharacteristic
31C4×C22⋊Dic5C411yescharacteristic
32C22⋊C4×Dic5C2212yes—
33C4×#685C411yescharacteristic
34C4×#685C411yescharacteristic
35#64955C2212yes—
36D5×#95C412yes—
37#64918C2214yescomplemented
38#64918C2214yescomplemented
39#20837—51nomaximal, Sylow
40C24×D5C2×C411yescharacteristic
41C23×C4×C5C2×C411yescharacteristic
42C23×Dic5C2311yescharacteristic
43C22×C4×D5—22no—
44C22×C4×D5—22no—
45C22×C4×D5—22no—
46C22×C4×D5—22no—
47C22×C4×D5C2×C412yes—
48C22×C4×D5C2×C412yes—
49C22×C4×D5C2×C411yescharacteristic
50C22×C4×D5C2×C411yescharacteristic
51C22×C4×D5D414yes—
52C22×C4×D5Q814yes—
53C22×C4×D5C2311yescharacteristic
54C22×C4×D5C2311yescharacteristic
55C2×#704—24no—
56C2×#704—24no—
57C2×#704—24no—
58C22×#170C2312yes—
59C22×#170C2312yes—
60C22×#170C2312yes—
61C22×#170C2312yes—
62D5⋊M16—232no—
63C2×#700—22no—
64C2×#700—22no—
65C2×#700—22no—
66C2×#700—22no—
67C2×#700—22no—
68C2×#700—22no—
69C2×#700—22no—
70C2×#700—22no—
71C2×#700—22no—
72C2×#700—22no—
73C2×#700D414yes—
74C2×#700D414yes—
75C2×D5⋊C8—24no—
76C2×D5⋊C8—24no—
77C2×D5⋊C8—24no—
78C2×C5×C22⋊C4C2×C412yes—
79C2×C42×C5C2×C411yescharacteristic
80C2×C42×C5C2×C411yescharacteristic
81C2×C22⋊Dic5C2×C412yes—
82C2×#685C2×C412yes—
83C2×#685C2×C412yes—
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5C2×C411yescharacteristic
86C2×C4×Dic5C2312yes—
87C2×C4×Dic5C2312yes—
88D5×C22⋊C4—28no—
89C42×D5—22no—
90C42×D5—22no—
91C42×D5—22no—
92C42×D5—22no—
93C22⋊#170—24no—
94#4004—28no—
95#4003—24no—
96C4⋊#170—28no—
97C5×#95C2×C412yes—
98#3963C2×C412yes—
99#3963C2×C412yes—
100#3963C2×C412yes—
101C23×M16—51no—
102C2×#423—51no—
103C2×#423—51no—
104C2×#407—51no—
105C2×C4×C22⋊C4—51no—
106#1851—54no—
107#1850—54no—
108#1728—51no—
109#1728—51no—
110C24×C5C22×C411yescharacteristic
111C23×D5—22no—
112C23×D5—22no—
113C23×D5—24no—
114C23×D5—42no—
115C23×D5C4⋊C414yes—
116C23×D5C22×C411yescharacteristic
117C23×D5C22×C411yescharacteristic
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5C4⋊C414yes—
121C22×C4×C5C22×C412yes—
122C22×C4×C5C22×C411yescharacteristic
123C22×C4×C5C22×C412yes—
124C22×C4×C5C22×C411yescharacteristic
125C22×Dic5—21no—
126C22×Dic5—21no—
127C22×Dic5—21no—
128C22×Dic5—21no—
129C22×Dic5C22×C412yes—
130C22×Dic5C22×C411yescharacteristic
131C22×Dic5C22×C412yes—
132C22×Dic5C2×D412yes—
133C22×Dic5C2×Q812yes—
134C22×Dic5C2411yescharacteristic
135C2×C4×D5—22no—
136C2×C4×D5—22no—
137C2×C4×D5—22no—
138C2×C4×D5—22no—
139C2×C4×D5—21no—
140C2×C4×D5—21no—
141C2×C4×D5—21no—
142C2×C4×D5—21no—
143C2×C4×D5—28no—
144C2×C4×D5—28no—
145C2×C4×D5—28no—
146C2×C4×D5—28no—
147C2×C4×D5—24no—
148C2×C4×D5—24no—
149C2×C4×D5—24no—
150C2×C4×D5—24no—
151C2×C4×D5—42no—
152C2×C4×D5—42no—
153C2×C4×D5C4⋊C414yes—
154C2×C4×D5C4⋊C414yes—
155C2×C4×D5C2×D412yes—
156C2×C4×D5C2×D412yes—
157C2×C4×D5C2×D412yes—
158C2×C4×D5C2×D412yes—
159C2×C4×D5C2×Q812yes—
160C2×C4×D5C2×Q812yes—
161C2×C4×D5#4112yes—
162C2×C4×D5#4112yes—
163#704—216no—
164C2×#170—22no—
165C2×#170—22no—
166C2×#170—22no—
167C2×#170—22no—
168C2×#170—22no—
169C2×#170—22no—
170C2×#170—22no—
171C2×#170—22no—
172C2×#170—22no—
173C2×#170—22no—
174C2×#170C2×D414yes—
175C2×#170C2×D414yes—
176#700—28no—
177#700—28no—
178#700—44no—
179#700—44no—
180D5⋊C8—216no—
181C5×C22⋊C4—24no—
182C42×C5—22no—
183C42×C5—22no—
184C22⋊Dic5—24no—
185#685—24no—
186#685M1618yescomplemented
187C4×Dic5—22no—
188C4×Dic5—22no—
189C4×Dic5—22no—
190C4×Dic5—22no—
191C4×Dic5—22no—
192C4×Dic5—22no—
193C24×C4—51no—
194C22×M16—51no—
195C22×M16—51no—
196C22×M16—52no—
197C22×M16—51no—
198C22×M16—51no—
199C22×M16—104no—
200C22×M16—104no—
201C22×M16—104no—
202C23×C8—52no—
203C22×C22⋊C4—52no—
204C22×C42—51no—
205C22×C42—51no—
206#423—104no—
207#423—104no—
208C2×C4⋊C8—54no—
209C2×C4⋊C8—54no—
210#407—104no—
211C2×C22⋊C8—52no—
212C2×C22⋊C8—52no—
213C4×C22⋊C4—51no—
214C4×C22⋊C4—52no—
215C4×C22⋊C4—51no—
216C4×C22⋊C4—51no—
217C4×C22⋊C4—52no—
218C4×C22⋊C4AGL(1,𝔽5)11yescharacteristic
219C2×#95—52no—
220#336—54no—
221#336—54no—
222C23×C5—21no—
223C23×C5—21no—
224C23×C5—22no—
225C23×C5—22no—
226C23×C5C2×C4⋊C412yes—
227C23×C5C23×C411yescharacteristic
228C22×D5—21no—
229C22×D5—21no—
230C22×D5—22no—
231C22×D5—22no—
232C22×D5—22no—
233C22×D5—28no—
234C22×D5—28no—
235C22×D5—44no—
236C22×D5—48no—
237C22×D5—48no—
238C22×D5C2×C4⋊C412yes—
239C22×D5C2×C4⋊C412yes—
240C22×D5C4×D412yes—
241C22×D5C4×D412yes—
242C22×D5C2×M1614yes—
243C2×C4×C5—22no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—22no—
247C2×C4×C5—28no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5C2×C4⋊C412yes—
252C2×C4×C5C2×C4⋊C412yes—
253C2×C4×C5C4×D412yes—
254C2×C4×C5C4×D412yes—
255C2×C4×C5C2×M1614yescomplemented
256C2×Dic5—22no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—22no—
260C2×Dic5—22no—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—22no—
264C2×Dic5—22no—
265C2×Dic5—22no—
266C2×Dic5—22no—
267C2×Dic5C2×C4⋊C412yes—
268C2×Dic5C2×M1614yescomplemented
269C2×Dic5C22×D411yescharacteristic
270C2×Dic5C22×D411yescharacteristic
271C2×Dic5C22×D411yescharacteristic
272C2×Dic5C22×Q811yescharacteristic
273C2×Dic5C2×#4111yescharacteristic
274C2×Dic5C2×#4111yescharacteristic
275C4×D5—28no—
276C4×D5—28no—
277C4×D5—22no—
278C4×D5—22no—
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—48no—
282C4×D5—48no—
283C4×D5#12014yes—
284C4×D5C22⋊Q814yes—
285C4×D5C22⋊Q814yes—
286C4×D5#12314yes—
287#170—24no—
288#170—24no—
289#170—42no—
290#170—42no—
291C25—51no—
292C23×C4—51no—
293C23×C4—51no—
294C23×C4—54no—
295C23×C4—54no—
296C23×C4—51no—
297C23×C4—51no—
298C23×C4—51no—
299C23×C4—52no—
300C23×C4—52no—
301C23×C4—102no—
302C23×C4—102no—
303C23×C4—102no—
304C23×C4—102no—
305C23×C4C2×AGL(1,𝔽5)11yescharacteristic
306C2×M16—54no—
307C2×M16—54no—
308C2×M16—104no—
309C2×M16—104no—
310C2×M16—102no—
311C2×M16—102no—
312C2×M16—102no—
313C2×M16—102no—
314C2×M16—104no—
315C2×M16—1032no—
316C2×M16—102no—
317C2×M16—102no—
318C2×M16—102no—
319C2×M16—102no—
320C2×M16—102no—
321C2×M16—102no—
322C22×C8—52no—
323C22×C8—52no—
324C22×C8—52no—
325C22×C8—52no—
326C22×C8—104no—
327C22×C8—104no—
328C22×C8—104no—
329C2×C22⋊C4—52no—
330C2×C22⋊C4—52no—
331C2×C22⋊C4—52no—
332C2×C22⋊C4—108no—
333C2×C22⋊C4C2×AGL(1,𝔽5)12yes—
334C2×C42—52no—
335C2×C42—52no—
336C2×C42—51no—
337C2×C42—51no—
338C2×C42—102no—
339C2×C42—102no—
340C2×C42—102no—
341C2×C42—102no—
342C2×C42C2×AGL(1,𝔽5)11yescharacteristic
343C2×C42C2×AGL(1,𝔽5)11yescharacteristic
344C4⋊C8—108no—
345C4⋊C8—108no—
346C22⋊C8—104no—
347C22⋊C8—104no—
348#95—52no—
349#95—52no—
350#95—52no—
351#95C2×AGL(1,𝔽5)12yes—
352C22×C5—22no—
353C22×C5—22no—
354C22×C5—22no—
355C22×C5—42no—
356C22×C5—42no—
357C22×C5C22×C4⋊C411yescharacteristic
358C22×C5C2×C4×D411yescharacteristic
359C22×C5C2×C4×D411yescharacteristic
360C22×C5C22×M1612yes—
361C22×C5#56812yes—
362C2×D5—22no—
363C2×D5—22no—
364C2×D5—22no—
365C2×D5—24no—
366C2×D5—24no—
367C2×D5—24no—
368C2×D5—24no—
369C2×D5—22no—
370C2×D5—416no—
371C2×D5#38514yes—
372C2×D5#42314yescomplemented
373C4×C5—24no—
374C4×C5—22no—
375C4×C5—42no—
376C4×C5#38514yes—
377Dic5—24no—
378Dic5—22no—
379Dic5—42no—
380Dic5C2×#12011yescharacteristic
381Dic5C2×C22⋊Q811yescharacteristic
382Dic5C2×C22⋊Q811yescharacteristic
383Dic5C2×#12311yescharacteristic
384C24—51no—
385C24—51no—
386C24—54no—
387C24—104no—
388C24—102no—
389C24—102no—
390C24—202no—
391C24C22×AGL(1,𝔽5)11yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—51no—
395C22×C4—52no—
396C22×C4—52no—
397C22×C4—52no—
398C22×C4—52no—
399C22×C4—52no—
400C22×C4—52no—
401C22×C4—52no—
402C22×C4—52no—
403C22×C4—51no—
404C22×C4—52no—
405C22×C4—52no—
406C22×C4—54no—
407C22×C4—54no—
408C22×C4—52no—
409C22×C4—52no—
410C22×C4—101no—
411C22×C4—101no—
412C22×C4—108no—
413C22×C4—101no—
414C22×C4—101no—
415C22×C4—108no—
416C22×C4—108no—
417C22×C4—108no—
418C22×C4—104no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—104no—
422C22×C4—104no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—104no—
430C22×C4—202no—
431C22×C4—202no—
432C22×C4C4⋊AGL(1,𝔽5)14yes—
433C22×C4C22×AGL(1,𝔽5)12yes—
434C22×C4C22×AGL(1,𝔽5)12yes—
435C22×C4C22×AGL(1,𝔽5)11yescharacteristic
436C22×C4C22×AGL(1,𝔽5)11yescharacteristic
437M16—108no—
438M16—108no—
439M16—1016no—
440M16—204no—
441M16—204no—
442C2×C8—54no—
443C2×C8—54no—
444C2×C8—102no—
445C2×C8—102no—
446C2×C8—102no—
447C2×C8—102no—
448C2×C8—1016no—
449C2×C8—102no—
450C2×C8—102no—
451C2×C8—102no—
452C2×C8—102no—
453C2×C8—102no—
454C2×C8—102no—
455C22⋊C4—24no—
456C22⋊C4—58no—
457C22⋊C4—104no—
458C22⋊C4—104no—
459C42—22no—
460C42—22no—
461C42—102no—
462C42—102no—
463C42—102no—
464C42—102no—
465C42—102no—
466C42—102no—
467C2×C5—42no—
468C2×C5C2×#38511yescharacteristic
469C2×C5C2×#42311yescharacteristic
470C2×C5#290511yescharacteristic
471C2×C5D4×M1612yes—
472C2×C5D4×M1612yes—
473D5—24no—
474D5—24no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—54no—
480C23—52no—
481C23—52no—
482C23—52no—
483C23—52no—
484C23—108no—
485C23—108no—
486C23—102no—
487C23—101no—
488C23—101no—
489C23—102no—
490C23—102no—
491C23—204no—
492C23—208no—
493C23—208no—
494C23C2×C4⋊AGL(1,𝔽5)12yes—
495C23C23×AGL(1,𝔽5)11yescharacteristic
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—28no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—51no—
507C2×C4—51no—
508C2×C4—51no—
509C2×C4—51no—
510C2×C4—54no—
511C2×C4—54no—
512C2×C4—54no—
513C2×C4—54no—
514C2×C4—54no—
515C2×C4—52no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—108no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—102no—
529C2×C4—108no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—208no—
534C2×C4—208no—
535C2×C4D5⋊M1614yescomplemented
536C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
537C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
538C2×C4D4×AGL(1,𝔽5)12yes—
539C2×C4D4×AGL(1,𝔽5)12yes—
540C8—104no—
541C8—104no—
542C8—202no—
543C8—202no—
544C5#2083711yescharacteristic, complemented, Sylow
545C22—22no—
546C22—22no—
547C22—22no—
548C22—42no—
549C22—42no—
550C22—54no—
551C22—54no—
552C22—102no—
553C22—102no—
554C22—104no—
555C22—104no—
556C22—104no—
557C22—104no—
558C22—102no—
559C22—102no—
560C22—2016no—
561C22C2×D5⋊M1612yes—
562C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
563C22C2×D4×AGL(1,𝔽5)11yescharacteristic
564C22C2×D4×AGL(1,𝔽5)11yescharacteristic
565C22#6626412yes—
566C4—24no—
567C4—22no—
568C4—42no—
569C4—51no—
570C4—51no—
571C4—51no—
572C4—51no—
573C4—104no—
574C4—102no—
575C4—202no—
576C4#6569914yes—
577C2—42no—
578C2—104no—
579C2—104no—
580C2D5⋊#42311yescharacteristic
581C2C2×#6569911yescharacteristic
582C2#1061710811yescharacteristic
583C2#1061715012yes—
584C2#1061715212yes—
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC4×C5×C22⋊C4C4
prime radicalC24×D5C2×C4
cosocleC22×Dic5C24
hypercenterC4×C22⋊C4AGL(1,𝔽5)
hypocenterC5#20837
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#65682C2semidirect
4. C2×#65681C2semidirect
6. #10604232C2semidirect
7. #10604172C2semidirect
8. #10604172C2semidirect
9. #10603785C2semidirect
25. C2×#4004C22semidirect
27. C2×C4⋊#170C22semidirect
37. #64918C22semidirect
38. #64918C22semidirect
186. #685M16semidirect
255. C2×C4×C5C2×M16semidirect
268. C2×Dic5C2×M16semidirect
372. C2×D5#423semidirect
535. C2×C4D5⋊M16semidirect
544. C5#20837semidirect

Maximal subgroups

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

subgroupindex
C22×D5⋊M162
C2×#657562
C2×#656822
C2×#656812
C4×D5×C22⋊C42
#106042322
#106041722
#106037852
#208375