Finite Group Databasebeta

← #12099251

Subgroups — #12099251

Order 1280.

1318 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
1C2×#65880C211yesmaximal, characteristic
2#10605598C212yesmaximal, complemented
3C5×#1799C211yesmaximal, characteristic, complemented
4#10602412C211yesmaximal, characteristic, complemented
5#10600820C212yesmaximal
6Dic5×#99C212yesmaximal, complemented
7#10600323C212yesmaximal, complemented
8#10599746C212yesmaximal, complemented
9#10599745C212yesmaximal, 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—
28C5×#380C2212yes—
29C2×#3966C2212yes—
30#65501C2212yes—
31#65267—24no—
32C2×#3938C2214yes—
33#65232C2214yes—
34C22⋊C4×Dic5C2214yes—
35#64944—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—22no—
50C2×#711—22no—
51C2×#711—24no—
52C2×#711—24no—
53C22×C4×D5C2×C411yescharacteristic
54C22×C4×D5C2×C411yescharacteristic
55C22×C4×D5C2×C411yescharacteristic
56C22×Dic10C2×C411yescharacteristic
57C4×C5×D4—22no—
58C4×C5×D4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4C2×C411yescharacteristic
61C2×C5×C22⋊C4C2×C411yescharacteristic
62C2×C5×C22⋊C4C2314yes—
63C2×C5×C22⋊C4C2311yescharacteristic
64C2×C42×C5C2×C411yescharacteristic
65C2×C22⋊Dic5C2×C411yescharacteristic
66C2×C22⋊Dic5C2314yes—
67C2×C22⋊Dic5C2311yescharacteristic
68D4×Dic5—24no—
69C4×C22⋊D5—22no—
70C4×C22⋊D5—22no—
71C4×C22⋊D5—22no—
72C4×C22⋊D5—22no—
73C2×#685C2×C411yescharacteristic
74C2×#685C2×C411yescharacteristic
75C2×C4⋊Dic5—22no—
76C2×C4⋊Dic5C2×C411yescharacteristic
77C2×#683—22no—
78C2×#683—22no—
79C2×#683C2×C411yescharacteristic
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683D414yes—
88C2×#683D414yes—
89C2×C4×Dic5—24no—
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2×C411yescharacteristic
92C2×C4×Dic5C2×C411yescharacteristic
93C2×C4×Dic5C2×C411yescharacteristic
94C2×C4×Dic5C2×C411yescharacteristic
95D5×C4⋊C4—24no—
96#4033—24no—
97#4027—24no—
98#4027—24no—
99#4023—24no—
100#4023—24no—
101#4018—22no—
102#4018—22no—
103C4×Dic10—22no—
104C4×Dic10—22no—
105C5×#99—24no—
106C5×#95—22no—
107#3966—24no—
108#3963—22no—
109#3963—24no—
110#3963—28no—
111#3938—28no—
112C2×#520—51no—
113#2313—52no—
114#1820—52no—
115#1799—52no—
116#1799—51no—
117#1799D511yescharacteristic, complemented
118#1782—52no—
119C4×#99—52no—
120C4×#99—52no—
121C24×C5C22×C411yescharacteristic
122C24×C5C2411yescharacteristic
123C23×D5C22×C411yescharacteristic
124C2×C5×D4—22no—
125C2×C5×D4—22no—
126C2×C5×D4#4112yes—
127C2×C5×D4#4112yes—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—24no—
131C22×C4×C5—81no—
132C22×C4×C5—81no—
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C22×C411yescharacteristic
135C22×C4×C5C22×C411yescharacteristic
136C22×C4×C5C22×C411yescharacteristic
137C22×C4×C5C22×C411yescharacteristic
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×D412yes—
140C2×C22⋊D5—22no—
141C2×C22⋊D5—22no—
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144C2×C22⋊D5—22no—
145C2×C22⋊D5—22no—
146C2×C22⋊D5#4114yes—
147C22×Dic5—22no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—24no—
155C22×Dic5—81no—
156C22×Dic5—81no—
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C2×D414yes—
165C22×Dic5C2×D414yes—
166#711—216no—
167#711—216no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—81no—
174C2×C4×D5—81no—
175C2×Dic10—22no—
176C2×Dic10—22no—
177C2×Dic10—22no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—82no—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—24no—
184C42×C5—21no—
185C42×C5—21no—
186C22⋊Dic5—22no—
187C22⋊Dic5—22no—
188C22⋊Dic5—24no—
189C22⋊Dic5—24no—
190#685—21no—
191#685—21no—
192#685—22no—
193C4⋊Dic5—22no—
194C4⋊Dic5—82no—
195#683—21no—
196#683—21no—
197#683—22no—
198#683—22no—
199#683—22no—
200#683C22⋊C412yes—
201#683C22⋊C412yes—
202#683C22⋊C412yes—
203#683C22⋊C412yes—
204#683C22⋊C414yes—
205#683C22⋊C414yes—
206C4×Dic5—22no—
207C4×Dic5—22no—
208C4×Dic5—22no—
209C4×Dic5—22no—
210C4×Dic5—22no—
211C4×Dic5—84no—
212C22×#41—51no—
213#520—104no—
214#520—104no—
215C2×C4×Q8—51no—
216C2×C4×Q8—51no—
217C2×C4×D4—51no—
218C2×C4×D4—51no—
219C2×C4×D4—51no—
220C2×C4×D4—51no—
221C2×C4×D4—51no—
222C2×C4×D4C2×D511yescharacteristic
223C2×#117—51no—
224C2×#117—51no—
225C2×#117—51no—
226C22×C4⋊C4—51no—
227C22×C4⋊C4—51no—
228C22×C4⋊C4—51no—
229C2×#99—52no—
230C2×#99—54no—
231C2×#99C2×D512yes—
232#387—104no—
233#387—104no—
234#381—54no—
235#380—52no—
236#380C2×D512yes—
237C4×C22⋊C4—54no—
238#342—52no—
239#342—54no—
240#342C2×D512yes—
241C23×C5—21no—
242C23×C5—21no—
243C23×C5—41no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5#11712yes—
248C23×C5C23×C411yescharacteristic
249C23×C5C22×D412yes—
250C23×C5C2×#4111yescharacteristic
251C23×C5C2×#4111yescharacteristic
252C23×C5C2×#4112yes—
253C22×D5—21no—
254C22×D5—21no—
255C22×D5—41no—
256C22×D5—41no—
257C22×D5#11712yes—
258C5×D4—24no—
259C5×D4—24no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—44no—
271C2×C4×C5—44no—
272C2×C4×C5—44no—
273C2×C4×C5—81no—
274C2×C4×C5—81no—
275C2×C4×C5C2×C22⋊C412yes—
276C2×C4×C5C2×C22⋊C411yescharacteristic
277C2×C4×C5C2×C22⋊C411yescharacteristic
278C2×C4×C5#11712yes—
279C22⋊D5—28no—
280C22⋊D5—24no—
281C22⋊D5—24no—
282C2×Dic5—28no—
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—24no—
290C2×Dic5—24no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—44no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—44no—
299C2×Dic5—44no—
300C2×Dic5—44no—
301C2×Dic5—82no—
302C2×Dic5C2×C22⋊C412yes—
303C2×Dic5C2×C22⋊C412yes—
304C2×Dic5C2×C22⋊C412yes—
305C2×Dic5C2×C22⋊C412yes—
306C2×Dic5#11712yes—
307C4×D5—28no—
308C4×D5—82no—
309C4×D5—82no—
310Dic10—28no—
311C2×#41—104no—
312C2×#41—104no—
313C2×#41—102no—
314C2×#41—102no—
315C22×Q8—51no—
316C22×D4—51no—
317C22×D4—51no—
318C22×D4C22×D511yescharacteristic
319C23×C4—51no—
320C23×C4—51no—
321C23×C4—51no—
322C23×C4—51no—
323C23×C4—51no—
324C23×C4—51no—
325C23×C4—51no—
326C23×C4C4×D511yescharacteristic
327C23×C4C22×D511yescharacteristic
328C4×Q8—102no—
329C4×Q8—102no—
330C4×Q8—104no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—104no—
334C4×D4—104no—
335C4×D4—102no—
336C4×D4—102no—
337C4×D4—104no—
338C4×D4—102no—
339C4×D4—102no—
340#117—102no—
341#117—102no—
342#117—104no—
343#117—104no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—54no—
350C2×C4⋊C4—54no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—104no—
357C2×C4⋊C4—102no—
358C2×C4⋊C4—102no—
359C2×C4⋊C4—102no—
360C2×C4⋊C4C4×D511yescharacteristic
361C2×C22⋊C4—51no—
362C2×C22⋊C4—51no—
363C2×C22⋊C4—51no—
364C2×C22⋊C4—51no—
365C2×C22⋊C4—54no—
366C2×C22⋊C4C4×D511yescharacteristic
367C2×C22⋊C4C22×D514yes—
368C2×C22⋊C4C22×D511yescharacteristic
369C2×C42—51no—
370C2×C42—51no—
371C2×C42—51no—
372C2×C42—51no—
373C2×C42—51no—
374C2×C42—104no—
375C2×C42C4×D511yescharacteristic
376#99—24no—
377#99—108no—
378#99—104no—
379#95—22no—
380#95—104no—
381#95—108no—
382#95—102no—
383C22×C5—22no—
384C22×C5—21no—
385C22×C5—22no—
386C22×C5—21no—
387C22×C5—22no—
388C22×C5—41no—
389C22×C5—41no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5C22×C22⋊C411yescharacteristic
396C22×C5C2×#11711yescharacteristic
397C22×C5C2×#11711yescharacteristic
398C22×C5#52512yes—
399C22×C5#52512yes—
400C2×D5—22no—
401C2×D5—42no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—42no—
405C4×C5—22no—
406C4×C5—21no—
407C4×C5—21no—
408C4×C5—22no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—84no—
412Dic5—22no—
413Dic5—22no—
414Dic5—22no—
415Dic5—22no—
416Dic5—22no—
417Dic5—41no—
418Dic5—41no—
419Dic5—84no—
420C24—51no—
421C24C2×C4×D511yescharacteristic
422C24C23×D511yescharacteristic
423#41—1016no—
424#41—1016no—
425C2×Q8—102no—
426C2×Q8—102no—
427C2×Q8—102no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—54no—
431C2×D4—102no—
432C2×D4—102no—
433C2×D4—102no—
434C2×D4—101no—
435C2×D4—101no—
436C2×D4—102no—
437C2×D4#71112yes—
438C2×D4#71312yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—51no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—54no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—54no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—104no—
466C22×C4—401no—
467C22×C4—401no—
468C22×C4—401no—
469C22×C4—401no—
470C22×C4C2×C4×D511yescharacteristic
471C22×C4C2×C4×D511yescharacteristic
472C22×C4C2×C4×D511yescharacteristic
473C22×C4C2×C4×D511yescharacteristic
474C22×C4C2×C4×D511yescharacteristic
475C22×C4D4×D512yes—
476C22×C4D4×D512yes—
477C4⋊C4—22no—
478C4⋊C4—52no—
479C4⋊C4—52no—
480C4⋊C4—54no—
481C4⋊C4—52no—
482C4⋊C4—52no—
483C4⋊C4—54no—
484C4⋊C4—82no—
485C4⋊C4—102no—
486C4⋊C4—102no—
487C4⋊C4—102no—
488C4⋊C4—102no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—402no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—102no—
497C22⋊C4—102no—
498C22⋊C4—102no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—104no—
502C22⋊C4—104no—
503C42—21no—
504C42—21no—
505C42—102no—
506C42—102no—
507C42—102no—
508C42—102no—
509C42—102no—
510C42—404no—
511C2×C5—22no—
512C2×C5—22no—
513C2×C5—21no—
514C2×C5—21no—
515C2×C5—42no—
516C2×C5#228011yescharacteristic
517C2×C5#288311yescharacteristic
518C2×C5#288411yescharacteristic
519D5—42no—
520C23—21no—
521C23—21no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—52no—
527C23—101no—
528C23—101no—
529C23—201no—
530C23—201no—
531C23#403812yes—
532C23C22×C4×D511yescharacteristic
533C23C2×D4×D512yes—
534C23C2×#71111yescharacteristic
535C23C2×#71311yescharacteristic
536C23D5×#4112yes—
537Q8—108no—
538D4—24no—
539D4—24no—
540D4—108no—
541D4—104no—
542D4—104no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—108no—
564C2×C4—108no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—104no—
572C2×C4—104no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—204no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—204no—
581C2×C4—204no—
582C2×C4—204no—
583C2×C4—402no—
584C2×C4—402no—
585C2×C4—402no—
586C2×C4D5×C22⋊C411yescharacteristic
587C2×C4D5×C22⋊C411yescharacteristic
588C2×C4D5×C22⋊C412yes—
589C2×C4#403812yes—
590C5#2072511yescharacteristic, complemented, Sylow
591C22—22no—
592C22—21no—
593C22—22no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—41no—
603C22—102no—
604C22—202no—
605C22—202no—
606C22—201no—
607C22—201no—
608C22C2×D5×C22⋊C411yescharacteristic
609C22C2×#403811yescharacteristic
610C22D5×#11711yescharacteristic
611C22#6594012yes—
612C22#6596112yes—
613C4—22no—
614C4—21no—
615C4—21no—
616C4—22no—
617C4—41no—
618C4—41no—
619C4—84no—
620C4—102no—
621C4—102no—
622C4—102no—
623C4—102no—
624C4—102no—
625C4—201no—
626C4—201no—
627C4—404no—
628C2—22no—
629C2—22no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—202no—
634C2#1060559311yescharacteristic
635C2#1061041911yescharacteristic
636C2#1061042011yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC5×#1799C2
socleC22×C5C22×C22⋊C4
prime radicalC22×#711C22
cosocleC24×C5C24
hypercenter#1799D5
hypocenterC5#20725
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #10605598C2semidirect
3. C5×#1799C2semidirect
4. #10602412C2semidirect
6. Dic5×#99C2semidirect
7. #10600323C2semidirect
8. #10599746C2semidirect
9. #10599745C2semidirect
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
117. #1799D5semidirect
590. C5#20725semidirect

Maximal subgroups

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

subgroupindex
C2×#658802
#106055982
C5×#17992
#106024122
#106008202
Dic5×#992
#106003232
#105997462
#105997452
#207255