Finite Group Databasebeta

← #12065222

Subgroups — #12065222

Order 1280.

1206 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65838C211yesmaximal, characteristic
2#10610365C212yesmaximal, complemented
3C5×#1463C211yesmaximal, characteristic, complemented
4#10602345C211yesmaximal, characteristic, complemented
5#10600761C212yesmaximal, complemented
6#10598938C212yesmaximal, complemented
7#10598937C212yesmaximal, complemented
8#10598918C212yesmaximal, complemented
9#10598917C212yesmaximal, complemented
10C22×#709C411yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C2×C4×C22⋊D5C411yescharacteristic
13C2×C4×C22⋊D5C411yescharacteristic
14C2×C4×C22⋊D5C2211yescharacteristic
15C2×C4×C22⋊D5C2211yescharacteristic
16C2×#4072C411yescharacteristic
17#65838—24no—
18#65838—24no—
19C2×#4039C411yescharacteristic
20C2×#4039C2211yescharacteristic
21C2×#4038C411yescharacteristic
22C2×#4038C2211yescharacteristic
23C2×D5×C4⋊C4C411yescharacteristic
24C2×D5×C4⋊C4C2211yescharacteristic
25C2×#4033C411yescharacteristic
26C2×#4033C2211yescharacteristic
27C5×#407C2212yes—
28#65496C2212yes—
29#65417—24no—
30#65018—24no—
31#65015C2214yes—
32#65007C2214yes—
33C5×#324C2212yes—
34C5×#324C2212yes—
35#64748C2212yes—
36#64748C2212yes—
37#64689C2214yes—
38#64688C2214yes—
39#17370—51nomaximal, Sylow
40C23×C4×C5C2×C411yescharacteristic
41C23×C4×C5C2×C411yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C22×C22⋊D5C2×C411yescharacteristic
44C22×C22⋊D5C2×C411yescharacteristic
45C2×#709—22no—
46C2×#709—22no—
47C2×#709—24no—
48C2×#709—24no—
49C22×D20C2×C411yescharacteristic
50C22×C4×D5C2×C411yescharacteristic
51C22×C4×D5C2×C411yescharacteristic
52C22×C4×D5C2×C411yescharacteristic
53C22×C4×D5C2×C411yescharacteristic
54C22×C4×D5C2×C411yescharacteristic
55C22×C4×D5C2311yescharacteristic
56C22×Dic10C2×C411yescharacteristic
57C2×C5×M16—22no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4C2×C411yescharacteristic
61C2×C5×C4⋊C4C2×C411yescharacteristic
62C2×C5×C4⋊C4C2311yescharacteristic
63C2×C5×C4⋊C4C2311yescharacteristic
64C2×C22⋊Dic5C2×C411yescharacteristic
65C2×C22⋊Dic5C2×C411yescharacteristic
66C4×C22⋊D5—22no—
67C4×C22⋊D5—22no—
68C4×C22⋊D5—22no—
69C4×C22⋊D5—22no—
70C4×C22⋊D5—22no—
71C4×C22⋊D5—22no—
72C4×C22⋊D5D414yes—
73C4×C22⋊D5D414yes—
74C2×#685C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2311yescharacteristic
78#4072—22no—
79#4072—22no—
80C2×C4⋊Dic5C2×C411yescharacteristic
81C2×C4⋊Dic5C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2311yescharacteristic
86C2×C4×Dic5C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2×C411yescharacteristic
89C2×C4×Dic5C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×#681—22no—
93C2×#676—24no—
94#4039—24no—
95#4039—24no—
96#4038—24no—
97#4038—24no—
98D5×C4⋊C4—24no—
99D5×C4⋊C4—24no—
100#4033—24no—
101#4033—24no—
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—52no—
113#1463—52no—
114#1463—51no—
115#1463D511yescharacteristic, complemented
116#1461—52no—
117#1458—52no—
118C24×C5C22×C411yescharacteristic
119C23×D5C22×C411yescharacteristic
120C23×D5C22×C411yescharacteristic
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—81no—
128C22×C4×C5—81no—
129C22×C4×C5C22×C411yescharacteristic
130C22×C4×C5C22×C411yescharacteristic
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C22×C411yescharacteristic
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C2×D412yes—
135C22×C4×C5C2×D412yes—
136C22×C4×C5C2411yescharacteristic
137C2×C22⋊D5—21no—
138C2×C22⋊D5—21no—
139C2×C22⋊D5—22no—
140C2×C22⋊D5—22no—
141C2×C22⋊D5—22no—
142C2×C22⋊D5—22no—
143C2×C22⋊D5C22⋊C412yes—
144C2×C22⋊D5C22⋊C412yes—
145C22×Dic5C22×C411yescharacteristic
146C22×Dic5C22×C411yescharacteristic
147C22×Dic5C22×C411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151#709—216no—
152#709—216no—
153C2×D20—22no—
154C2×D20—22no—
155C2×D20—22no—
156C2×C4×D5—22no—
157C2×C4×D5—22no—
158C2×C4×D5—22no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—81no—
165C2×C4×D5—81no—
166C2×C4×D5—81no—
167C2×C4×D5—81no—
168C2×C4×D5M1614yescomplemented
169C2×C4×D5C2×D414yes—
170C2×Dic10—22no—
171C2×Dic10—22no—
172C2×Dic10M1614yescomplemented
173C5×M16—82no—
174C2×C5×C8—24no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C22⋊Dic5—21no—
180C22⋊Dic5—21no—
181C22⋊Dic5C22⋊C412yes—
182C22⋊Dic5C22⋊C412yes—
183#685—22no—
184#685—22no—
185#685—22no—
186#685C22⋊C414yes—
187C4⋊Dic5—22no—
188C4⋊Dic5—22no—
189#683—22no—
190#683—22no—
191#683—22no—
192#683C22⋊C414yes—
193C4×Dic5—22no—
194C4×Dic5—22no—
195C4×Dic5—22no—
196C4×Dic5—22no—
197C4×Dic5—22no—
198C4×Dic5C2×D414yes—
199#681—82no—
200C2×#168—24no—
201#676—84no—
202C22×#41—51no—
203#520—104no—
204#520—104no—
205C2×C4×Q8—51no—
206C2×C4×Q8—51no—
207C2×C4×D4—51no—
208C2×C4×D4—51no—
209C2×C4×D4—51no—
210C2×C4×D4—51no—
211C2×C4×D4—51no—
212C2×C4×D4—51no—
213C2×#117—51no—
214C2×#117—51no—
215C2×#117—51no—
216C22×C4⋊C4—51no—
217C22×C4⋊C4—51no—
218C22×C4⋊C4C2×D511yescharacteristic
219#436—104no—
220#436—104no—
221#431—54no—
222#407—52no—
223#407—54no—
224#407C2×D512yes—
225#324—52no—
226#324—52no—
227#324—54no—
228#324C2×D512yes—
229#324C2×D512yes—
230#323—54no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—41no—
234C23×C5—41no—
235C23×C5C2×C22⋊C411yescharacteristic
236C23×C5C2×C22⋊C411yescharacteristic
237C23×C5C23×C411yescharacteristic
238C22×D5—21no—
239C22×D5—21no—
240C22×D5—21no—
241C22×D5—21no—
242C22×D5—41no—
243C22×D5—41no—
244C22×D5—41no—
245C22×D5—41no—
246C22×D5C2×C22⋊C412yes—
247C22×D5C2×M1612yes—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—81no—
263C2×C4×C5—81no—
264C2×C4×C5C2×C22⋊C412yes—
265C2×C4×C5C2×M1612yes—
266C2×C4×C5C2×M1612yes—
267C2×C4×C5C22×D412yes—
268C22⋊D5—24no—
269C22⋊D5—24no—
270C22⋊D5—24no—
271C22⋊D5—24no—
272C2×Dic5—21no—
273C2×Dic5—21no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—41no—
277C2×Dic5—41no—
278C2×Dic5—41no—
279C2×Dic5—41no—
280C2×Dic5C2×C22⋊C412yes—
281C2×Dic5C2×C22⋊C412yes—
282C2×Dic5C2×C22⋊C412yes—
283C2×Dic5C2×M1612yes—
284C2×Dic5C2×M1612yes—
285C2×Dic5C2×M1612yes—
286D20—28no—
287C4×D5—28no—
288C4×D5—28no—
289C4×D5—44no—
290C4×D5—82no—
291C4×D5—82no—
292C4×D5—82no—
293Dic10—28no—
294C5×C8—44no—
295#168—44no—
296C2×#41—104no—
297C2×#41—102no—
298C2×#41—102no—
299C2×#41—104no—
300C22×Q8—51no—
301C22×D4—51no—
302C22×D4—51no—
303C22×D4—51no—
304C23×C4—51no—
305C23×C4—51no—
306C23×C4—51no—
307C23×C4—51no—
308C23×C4—51no—
309C23×C4—51no—
310C23×C4C4×D511yescharacteristic
311C23×C4C4×D511yescharacteristic
312C23×C4C22×D511yescharacteristic
313C2×M16—22no—
314C2×M16—104no—
315C2×M16—102no—
316C4×Q8—104no—
317C4×Q8—104no—
318C4×D4—54no—
319C4×D4—54no—
320C4×D4—104no—
321C4×D4—102no—
322C4×D4—102no—
323C4×D4—104no—
324C4×D4—102no—
325C4×D4—102no—
326C4×D4—102no—
327C4×D4—102no—
328#117—104no—
329#117—104no—
330#117—102no—
331#117—102no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—51no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—104no—
341C2×C4⋊C4—104no—
342C2×C4⋊C4C4×D511yescharacteristic
343C2×C4⋊C4C4×D511yescharacteristic
344C2×C4⋊C4C22×D511yescharacteristic
345C2×C4⋊C4C22×D511yescharacteristic
346C2×C22⋊C4—51no—
347C2×C22⋊C4—51no—
348C2×C22⋊C4—51no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—51no—
352C2×C42—51no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—51no—
356C2×C42—51no—
357C2×C42—51no—
358C4⋊C8—104no—
359C22⋊C8—22no—
360C22⋊C8—54no—
361C22⋊C8—104no—
362C22⋊C8—102no—
363C22⋊C8C22×D514yes—
364C4×C8—104no—
365C22×C5—21no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—21no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5C22×C22⋊C411yescharacteristic
376C22×C5C22×M1611yescharacteristic
377C22×C5C22×M1611yescharacteristic
378C2×D5—22no—
379C2×D5—22no—
380C2×D5—22no—
381C2×D5—22no—
382C2×D5—42no—
383C2×D5—42no—
384C2×D5—42no—
385C2×D5—41no—
386C2×D5—41no—
387C2×D5—42no—
388C4×C5—22no—
389C4×C5—22no—
390C4×C5—22no—
391C4×C5—22no—
392C4×C5—41no—
393C4×C5—41no—
394Dic5—22no—
395Dic5—22no—
396Dic5—22no—
397Dic5—41no—
398Dic5—41no—
399Dic5#40714yes—
400C24—51no—
401C24—51no—
402C24C2×C4×D511yescharacteristic
403#41—1016no—
404#41—1016no—
405C2×Q8—54no—
406C2×Q8—102no—
407C2×Q8—102no—
408C2×D4—52no—
409C2×D4—52no—
410C2×D4—102no—
411C2×D4—102no—
412C2×D4—102no—
413C2×D4—102no—
414C2×D4—102no—
415C2×D4—102no—
416C2×D4—101no—
417C2×D4—101no—
418C2×D4—102no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—54no—
430C22×C4—54no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—102no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—401no—
444C22×C4—401no—
445C22×C4—401no—
446C22×C4—401no—
447C22×C4C2×C4×D511yescharacteristic
448C22×C4C2×C4×D511yescharacteristic
449C22×C4C2×C4×D511yescharacteristic
450C22×C4C2×C4×D511yescharacteristic
451C22×C4C2×C4×D511yescharacteristic
452C22×C4D4×D512yes—
453C22×C4D4×D512yes—
454C22×C4C23×D511yescharacteristic
455M16—82no—
456M16—404no—
457M16—402no—
458C2×C8—24no—
459C2×C8—104no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—54no—
465C4⋊C4—102no—
466C4⋊C4—102no—
467C4⋊C4—102no—
468C4⋊C4—102no—
469C4⋊C4—102no—
470C22⋊C4—52no—
471C22⋊C4—52no—
472C22⋊C4—54no—
473C22⋊C4—102no—
474C22⋊C4—102no—
475C22⋊C4—101no—
476C22⋊C4—101no—
477C22⋊C4—102no—
478C42—54no—
479C42—102no—
480C42—102no—
481C42—102no—
482C42—102no—
483C42—102no—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—41no—
487C2×C5—41no—
488C2×C5C2×#40711yescharacteristic
489C2×C5#288311yescharacteristic
490C2×C5#288911yescharacteristic
491D5—42no—
492D5—42no—
493C23—21no—
494C23—21no—
495C23—41no—
496C23—41no—
497C23—52no—
498C23—52no—
499C23—101no—
500C23—101no—
501C23—101no—
502C23—101no—
503C23—201no—
504C23—201no—
505C23—201no—
506C23—201no—
507C23D5×C22⋊C411yescharacteristic
508C23D5×C22⋊C411yescharacteristic
509C23C22×C4×D511yescharacteristic
510Q8—108no—
511D4—108no—
512D4—104no—
513D4—104no—
514D4—104no—
515D4—104no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—52no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—52no—
535C2×C4—52no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4—108no—
539C2×C4—108no—
540C2×C4—101no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—101no—
544C2×C4—204no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—402no—
550C2×C4—402no—
551C2×C4—402no—
552C2×C4D5×C22⋊C412yes—
553C2×C4D5×M1612yes—
554C2×C4D5×M1612yes—
555C2×C4C2×D4×D512yes—
556C8—44no—
557C8—204no—
558C5#1737011yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—42no—
569C22—102no—
570C22—102no—
571C22—102no—
572C22—102no—
573C22—202no—
574C22—202no—
575C22—202no—
576C22—202no—
577C22—201no—
578C22—201no—
579C22C2×D5×C22⋊C411yescharacteristic
580C22C2×D5×M1611yescharacteristic
581C22C2×D5×M1611yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—54no—
589C4—102no—
590C4—102no—
591C4—102no—
592C4—201no—
593C4—201no—
594C2—21no—
595C2—21no—
596C2—41no—
597C2—41no—
598C2—202no—
599C2—202no—
600C2D5×#40711yescharacteristic
601C2#1061041911yescharacteristic
602C2#1061043711yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1463C2
socleC22×C5C22×C22⋊C4
prime radicalC22×#709C4
cosocleC22×C4×C5C24
hypercenter#1463D5
hypocenterC5#17370
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #10610365C2semidirect
3. C5×#1463C2semidirect
4. #10602345C2semidirect
5. #10600761C2semidirect
6. #10598938C2semidirect
7. #10598937C2semidirect
8. #10598918C2semidirect
9. #10598917C2semidirect
115. #1463D5semidirect
168. C2×C4×D5M16semidirect
172. C2×Dic10M16semidirect
558. C5#17370semidirect

Maximal subgroups

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

subgroupindex
C2×#658382
#106103652
C5×#14632
#106023452
#106007612
#105989382
#105989372
#105989182
#105989172
#173705