Finite Group Databasebeta

← #12099250

Subgroups — #12099250

Order 1280.

1318 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65880C211yesmaximal, characteristic
2#10605176C212yesmaximal, complemented
3C4×C5×#99C211yesmaximal, characteristic, complemented
4C4×#3966C211yesmaximal, characteristic, complemented
5#10600821C212yesmaximal, complemented
6#10600820C212yesmaximal
7C4×#3938C212yesmaximal, complemented
8#10599752C212yesmaximal, complemented
9#10599746C212yesmaximal, complemented
10C22×#711C2211yescharacteristic
11C2×C4×C5×D4C2211yescharacteristic
12C2×D4×Dic5C2211yescharacteristic
13C2×C4×C22⋊D5C411yescharacteristic, complemented
14C2×C4×C22⋊D5C2211yescharacteristic
15C22×#683C411yescharacteristic, complemented
16C22×#683C2211yescharacteristic
17#65880—24no—
18#65880—24no—
19C2×D5×C4⋊C4C411yescharacteristic, complemented
20C2×#4033C411yescharacteristic, complemented
21C2×#4027C411yescharacteristic, complemented
22C2×#4027C2211yescharacteristic
23C2×#4023C411yescharacteristic, complemented
24C2×#4023C2211yescharacteristic
25C2×#4018C411yescharacteristic, complemented
26C2×C4×Dic10C411yescharacteristic, complemented
27C2×C5×#99C2212yes—
28C4×C5×C22⋊C4C2212yes—
29C2×#3966C2212yes—
30C4×C22⋊Dic5C2212yes—
31C2×#3938C2214yes—
32#65232C2214yes—
33#65231C2214yes—
34#65222—24no—
35#64941—24no—
36C5×#342C2212yes—
37#64747C2214yes—
38#64746C2212yes—
39#20725—51nomaximal, Sylow
40C22×C5×D4C2311yescharacteristic
41C23×C4×C5C2×C411yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C22×C22⋊D5C2×C411yescharacteristic
44C22×C22⋊D5C2311yescharacteristic
45C23×Dic5C2×C411yescharacteristic
46C23×Dic5C2×C411yescharacteristic
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C2×#711—24no—
50C2×#711—24no—
51C2×#711—24no—
52C22×C4×D5C2×C411yescharacteristic
53C22×C4×D5C2×C411yescharacteristic
54C22×C4×D5C2×C411yescharacteristic
55C22×Dic10C2×C411yescharacteristic
56C4×C5×D4—22no—
57C4×C5×D4—22no—
58C2×C5×C4⋊C4C2×C411yescharacteristic
59C2×C5×C22⋊C4C2×C411yescharacteristic
60C2×C5×C22⋊C4C2314yes—
61C2×C5×C22⋊C4C2311yescharacteristic
62C2×C42×C5—22no—
63C2×C42×C5C2×C411yescharacteristic
64C2×C22⋊Dic5C2×C411yescharacteristic
65C2×C22⋊Dic5C2314yes—
66C2×C22⋊Dic5C2311yescharacteristic
67D4×Dic5—24no—
68C4×C22⋊D5—22no—
69C4×C22⋊D5—22no—
70C4×C22⋊D5—22no—
71C4×C22⋊D5—22no—
72C2×#685C2×C411yescharacteristic
73C2×#685C2×C411yescharacteristic
74C2×C4⋊Dic5C2×C411yescharacteristic
75C2×#683—22no—
76C2×#683—22no—
77C2×#683—24no—
78C2×#683C2×C411yescharacteristic
79C2×#683C2×C411yescharacteristic
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683D414yes—
87C2×#683D414yes—
88C2×C4×Dic5—22no—
89C2×C4×Dic5C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2×C411yescharacteristic
92C2×C4×Dic5C2×C411yescharacteristic
93C2×C4×Dic5C2×C411yescharacteristic
94D5×C4⋊C4—24no—
95#4033—24no—
96#4027—24no—
97#4027—24no—
98#4023—24no—
99#4023—24no—
100#4018—22no—
101#4018—22no—
102C4×Dic10—22no—
103C4×Dic10—22no—
104C5×#99—24no—
105C5×#95—22no—
106#3966—24no—
107#3963—22no—
108#3963—24no—
109#3963—28no—
110#3938—28no—
111C2×#520—51no—
112#2313—52no—
113#1820—52no—
114#1799—52no—
115#1799—52no—
116#1782—52no—
117C4×#99—52no—
118C4×#99—51no—
119C4×#99D511yescharacteristic, complemented
120C24×C5C22×C411yescharacteristic
121C24×C5C2411yescharacteristic
122C23×D5C22×C411yescharacteristic
123C2×C5×D4—22no—
124C2×C5×D4—22no—
125C2×C5×D4#4114yes—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—24no—
129C22×C4×C5—81no—
130C22×C4×C5—81no—
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C22×C411yescharacteristic
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C22×C411yescharacteristic
135C22×C4×C5C22×C411yescharacteristic
136C22×C4×C5C2×D412yes—
137C22×C4×C5C2×D412yes—
138C2×C22⋊D5—22no—
139C2×C22⋊D5—22no—
140C2×C22⋊D5—22no—
141C2×C22⋊D5—22no—
142C2×C22⋊D5—22no—
143C2×C22⋊D5#4114yes—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—24no—
151C22×Dic5—81no—
152C22×Dic5—81no—
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C22×C411yescharacteristic
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C2×D414yes—
161C22×Dic5C2×D414yes—
162#711—232no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—22no—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—81no—
169C2×C4×D5—81no—
170C2×Dic10—22no—
171C2×Dic10—22no—
172C2×Dic10—22no—
173C5×C4⋊C4—22no—
174C5×C22⋊C4—22no—
175C5×C22⋊C4—22no—
176C5×C22⋊C4—24no—
177C5×C22⋊C4—24no—
178C42×C5—21no—
179C42×C5—21no—
180C42×C5—82no—
181C22⋊Dic5—22no—
182C22⋊Dic5—22no—
183C22⋊Dic5—24no—
184C22⋊Dic5—24no—
185#685—21no—
186#685—21no—
187#685—22no—
188C4⋊Dic5—22no—
189#683—21no—
190#683—21no—
191#683—22no—
192#683—22no—
193#683—22no—
194#683—84no—
195#683C22⋊C412yes—
196#683C22⋊C412yes—
197#683C22⋊C412yes—
198#683C22⋊C412yes—
199#683C22⋊C414yes—
200#683C22⋊C414yes—
201C4×Dic5—22no—
202C4×Dic5—22no—
203C4×Dic5—22no—
204C4×Dic5—22no—
205C4×Dic5—22no—
206C4×Dic5—82no—
207C22×#41—51no—
208#520—104no—
209#520—104no—
210C2×C4×Q8—51no—
211C2×C4×Q8—51no—
212C2×C4×D4—51no—
213C2×C4×D4—51no—
214C2×C4×D4—51no—
215C2×C4×D4—51no—
216C2×C4×D4—51no—
217C2×C4×D4C2×D511yescharacteristic
218C2×#117—51no—
219C2×#117—51no—
220C2×#117—51no—
221C22×C4⋊C4—51no—
222C22×C4⋊C4—51no—
223C22×C4⋊C4—51no—
224C2×#99—52no—
225C2×#99—54no—
226C2×#99C2×D512yes—
227#387—104no—
228#387—104no—
229#381—54no—
230#380—54no—
231C4×C22⋊C4—52no—
232C4×C22⋊C4C2×D512yes—
233#342—52no—
234#342—54no—
235#342C2×D512yes—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5#11712yes—
243C23×C5C23×C411yescharacteristic
244C23×C5C22×D412yes—
245C23×C5C2×#4112yes—
246C23×C5C2×#4112yes—
247C22×D5—21no—
248C22×D5—21no—
249C22×D5—41no—
250C22×D5—41no—
251C22×D5#11712yes—
252C5×D4—28no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—44no—
264C2×C4×C5—44no—
265C2×C4×C5—44no—
266C2×C4×C5—81no—
267C2×C4×C5—81no—
268C2×C4×C5C2×C22⋊C412yes—
269C2×C4×C5C2×C22⋊C411yescharacteristic
270C2×C4×C5C2×C22⋊C411yescharacteristic
271C2×C4×C5#11712yes—
272C22⋊D5—28no—
273C22⋊D5—28no—
274C2×Dic5—28no—
275C2×Dic5—21no—
276C2×Dic5—21no—
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—28no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5—44no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287C2×Dic5—41no—
288C2×Dic5—41no—
289C2×Dic5—44no—
290C2×Dic5—44no—
291C2×Dic5—44no—
292C2×Dic5—82no—
293C2×Dic5C2×C22⋊C412yes—
294C2×Dic5C2×C22⋊C412yes—
295C2×Dic5C2×C22⋊C412yes—
296C2×Dic5C2×C22⋊C412yes—
297C2×Dic5#11712yes—
298C4×D5—28no—
299C4×D5—82no—
300C4×D5—82no—
301Dic10—28no—
302C2×#41—104no—
303C2×#41—104no—
304C2×#41—104no—
305C22×Q8—51no—
306C22×D4—51no—
307C22×D4—51no—
308C22×D4C22×D511yescharacteristic
309C23×C4—51no—
310C23×C4—51no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—51no—
314C23×C4—51no—
315C23×C4—51no—
316C23×C4C4×D511yescharacteristic
317C23×C4C22×D511yescharacteristic
318C4×Q8—102no—
319C4×Q8—102no—
320C4×Q8—104no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—104no—
324C4×D4—104no—
325C4×D4—102no—
326C4×D4—102no—
327C4×D4—104no—
328C4×D4—102no—
329C4×D4—102no—
330#117—102no—
331#117—102no—
332#117—104no—
333#117—104no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—54no—
339C2×C4⋊C4—54no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—104no—
346C2×C4⋊C4—102no—
347C2×C4⋊C4—102no—
348C2×C4⋊C4—104no—
349C2×C4⋊C4C4×D511yescharacteristic
350C2×C22⋊C4—51no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—51no—
353C2×C22⋊C4—51no—
354C2×C22⋊C4—54no—
355C2×C22⋊C4C4×D511yescharacteristic
356C2×C22⋊C4C22×D514yes—
357C2×C22⋊C4C22×D511yescharacteristic
358C2×C42—22no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—102no—
365C2×C42C4×D511yescharacteristic
366#99—24no—
367#99—108no—
368#99—104no—
369#95—22no—
370#95—104no—
371#95—108no—
372#95—102no—
373C22×C5—22no—
374C22×C5—21no—
375C22×C5—22no—
376C22×C5—21no—
377C22×C5—22no—
378C22×C5—42no—
379C22×C5—42no—
380C22×C5—42no—
381C22×C5—42no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5C22×C22⋊C411yescharacteristic
385C22×C5C2×#11711yescharacteristic
386C22×C5C2×#11711yescharacteristic
387C22×C5#52514yes—
388C2×D5—22no—
389C2×D5—42no—
390C2×D5—41no—
391C2×D5—41no—
392C2×D5—42no—
393C4×C5—22no—
394C4×C5—21no—
395C4×C5—21no—
396C4×C5—22no—
397C4×C5—41no—
398C4×C5—41no—
399C4×C5—84no—
400Dic5—22no—
401Dic5—22no—
402Dic5—22no—
403Dic5—22no—
404Dic5—22no—
405Dic5—41no—
406Dic5—41no—
407Dic5—84no—
408C24—51no—
409C24C2×C4×D511yescharacteristic
410C24C23×D511yescharacteristic
411#41—1032no—
412C2×Q8—102no—
413C2×Q8—102no—
414C2×Q8—102no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—54no—
418C2×D4—102no—
419C2×D4—102no—
420C2×D4—102no—
421C2×D4—102no—
422C2×D4—102no—
423C2×D4#70914yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—54no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—54no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—104no—
450C22×C4—401no—
451C22×C4—401no—
452C22×C4—401no—
453C22×C4—401no—
454C22×C4C2×C4×D511yescharacteristic
455C22×C4C2×C4×D511yescharacteristic
456C22×C4C2×C4×D511yescharacteristic
457C22×C4C2×C4×D511yescharacteristic
458C22×C4C2×C4×D511yescharacteristic
459C22×C4D4×D512yes—
460C22×C4D4×D512yes—
461C4⋊C4—22no—
462C4⋊C4—52no—
463C4⋊C4—52no—
464C4⋊C4—54no—
465C4⋊C4—52no—
466C4⋊C4—52no—
467C4⋊C4—54no—
468C4⋊C4—102no—
469C4⋊C4—102no—
470C4⋊C4—102no—
471C4⋊C4—102no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—404no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—102no—
480C22⋊C4—102no—
481C22⋊C4—102no—
482C22⋊C4—101no—
483C22⋊C4—101no—
484C22⋊C4—104no—
485C22⋊C4—104no—
486C42—21no—
487C42—21no—
488C42—82no—
489C42—102no—
490C42—102no—
491C42—102no—
492C42—102no—
493C42—102no—
494C42—402no—
495C2×C5—24no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—42no—
499C2×C5#228011yescharacteristic
500C2×C5#288311yescharacteristic
501C2×C5#288411yescharacteristic
502D5—42no—
503C23—21no—
504C23—21no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—52no—
510C23—101no—
511C23—101no—
512C23—201no—
513C23—201no—
514C23#401812yes—
515C23C22×C4×D511yescharacteristic
516C23C2×#70912yes—
517C23C2×D4×D512yes—
518C23D5×#4112yes—
519Q8—108no—
520D4—28no—
521D4—108no—
522D4—108no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—52no—
539C2×C4—52no—
540C2×C4—52no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—108no—
544C2×C4—108no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—101no—
551C2×C4—108no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—204no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—201no—
559C2×C4—204no—
560C2×C4—204no—
561C2×C4—204no—
562C2×C4—402no—
563C2×C4—402no—
564C2×C4—402no—
565C2×C4#401812yes—
566C2×C4D5×C22⋊C411yescharacteristic
567C2×C4D5×C22⋊C411yescharacteristic
568C2×C4D5×C22⋊C412yes—
569C5#2072511yescharacteristic, complemented, Sylow
570C22—22no—
571C22—21no—
572C22—22no—
573C22—21no—
574C22—22no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—41no—
581C22—102no—
582C22—202no—
583C22—202no—
584C22—201no—
585C22—201no—
586C22C2×#401811yescharacteristic
587C22C2×D5×C22⋊C411yescharacteristic
588C22D5×#11711yescharacteristic
589C22#6588114yes—
590C4—22no—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—84no—
597C4—102no—
598C4—102no—
599C4—102no—
600C4—102no—
601C4—102no—
602C4—201no—
603C4—201no—
604C4—404no—
605C2—24no—
606C2—21no—
607C2—21no—
608C2—42no—
609C2—202no—
610C2#1060529211yescharacteristic
611C2#1061041911yescharacteristic
612C2#1061042011yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC4×C5×#99C2
socleC22×C5C22×C22⋊C4
prime radicalC22×#711C22
cosocleC24×C5C24
hypercenterC4×#99D5
hypocenterC5#20725
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #10605176C2semidirect
3. C4×C5×#99C2semidirect
4. C4×#3966C2semidirect
5. #10600821C2semidirect
7. C4×#3938C2semidirect
8. #10599752C2semidirect
9. #10599746C2semidirect
13. C2×C4×C22⋊D5C4semidirect
15. C22×#683C4semidirect
19. C2×D5×C4⋊C4C4semidirect
20. C2×#4033C4semidirect
21. C2×#4027C4semidirect
23. C2×#4023C4semidirect
25. C2×#4018C4semidirect
26. C2×C4×Dic10C4semidirect
119. C4×#99D5semidirect
569. C5#20725semidirect

Maximal subgroups

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

subgroupindex
C2×#658802
#106051762
C4×C5×#992
C4×#39662
#106008212
#106008202
C4×#39382
#105997522
#105997462
#207255