Finite Group Databasebeta

← #131×C22⋊D5 #12963264

Subgroups — #131×C22⋊D5 #12963264

Order 1280.

2814 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#131C211yesmaximal, characteristic, complemented
2#41×C22⋊D5C211yesmaximal, characteristic
3C2×D5×#131C211yesmaximal, characteristic, complemented
4#10615806C211yesmaximal, characteristic, complemented
5#10615527C213yesmaximal, complemented
6#10615525C213yesmaximal, complemented
7#10615524C211yesmaximal, characteristic, complemented
8#10615519C213yesmaximal, complemented
9#10615517C213yesmaximal, complemented
10#10615514C211yesmaximal, characteristic, complemented
11Dic5×#131C211yesmaximal, characteristic, complemented
12M16×C22⋊D5C213yesmaximal, complemented
13#10615488C213yesmaximal, complemented
14#10615465C213yesmaximal, complemented
15C2×C8×C22⋊D5C213yesmaximal, complemented
16C22×C5×#41C2211yescharacteristic
17C2×D5×#41C2211yescharacteristic
18C2×C5×#131—28no—
19C2×C5×#131C2211yescharacteristic
20C2×C5×#131C2211yescharacteristic
21C2×C5×#131C2213yescomplemented
22C2×C5×#131C2213yescomplemented
23C22×C5×M16C2213yescomplemented
24C23×C5×C8C2213yescomplemented
25#66168C411yescharacteristic
26#66166C2213yes—
27#66165C411yescharacteristic
28#66163C413yes—
29#66162C2213yes—
30#41×Dic5C2211yescharacteristic
31#66158C413yes—
32C2×#4094C2211yescharacteristic
33C2×#4094C2211yescharacteristic
34#66151C411yescharacteristic
35Q8×C22⋊D5C411yescharacteristic
36#66140C413yes—
37D4×C22⋊D5C413yes—
38#66125C2213yes—
39C2×C4×C22⋊D5C2213yes—
40D5×#131—28no—
41C2×#4053C2213yescomplemented
42C2×D5×M16C2213yescomplemented
43C2×#4047C2213yescomplemented
44C22×C8×D5C2213yescomplemented
45#65523C2213yescomplemented
46#65523C2213yescomplemented
47#65496C2213yescomplemented
48C2×C22⋊#168C2213yescomplemented
49#65418C2213yescomplemented
50#65417C2216yescomplemented
51#65417C2216yescomplemented
52#65416C2216yescomplemented
53#65416C2216yescomplemented
54#65415C2213yescomplemented
55#65411C2213yescomplemented
56#65408C2213yescomplemented
57#65407C2213yescomplemented
58M16×Dic5C2213yescomplemented
59#65400C2216yescomplemented
60#65400C2216yescomplemented
61#65399C2213yescomplemented
62C8×C22⋊D5C2211yescharacteristic
63C8×C22⋊D5C2213yes—
64C8×C22⋊D5C2213yescomplemented
65C8×C22⋊D5C2213yescomplemented
66C8×C22⋊D5C2213yescomplemented
67C8×C22⋊D5C2213yescomplemented
68C8×C22⋊D5C2213yescomplemented
69C8×C22⋊D5C2213yescomplemented
70C8×C22⋊D5C2216yescomplemented
71C2×#3952C2213yescomplemented
72#65391C2213yescomplemented
73#65390C2213yescomplemented
74C2×#3946C2213yescomplemented
75C2×C8×Dic5C2213yescomplemented
76D4×#131—51nomaximal, Sylow
77C2×C5×#41—24no—
78C2×C5×#41—24no—
79C2×C5×#41C2×C413yes—
80C2×C5×#41C2×C411yescharacteristic
81C2×C5×#41C2313yes—
82C2×C5×#41C2311yescharacteristic
83C22×C5×Q8C2×C411yescharacteristic
84C22×C5×D4C2×C413yes—
85C23×C4×C5C2313yes—
86C22×C22⋊D5C2×C413yes—
87D5×#41—24no—
88D5×#41—24no—
89C2×#713C2×C411yescharacteristic
90C2×Q8×D5C2×C411yescharacteristic
91C2×#711C2×C413yes—
92C2×D4×D5C2×C413yes—
93C2×#709C2313yes—
94C22×C4×D5C2313yes—
95C5×#131—24no—
96C5×#131—212no—
97C5×#131—212no—
98C5×#131D418yescomplemented
99C2×C5×M16—212no—
100C2×C5×M16C2313yes—
101C2×C5×M16C2316yes—
102C2×C5×M16C2313yes—
103C22×C5×C8—212no—
104C22×C5×C8C2313yes—
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2313yes—
107C22×C5×C8C2313yes—
108C22×C5×C8C2313yes—
109C22×C5×C8C2313yes—
110#4099C2×C416yes—
111C2×C22⋊Dic5C2×C413yes—
112#4094—24no—
113#4094—24no—
114#4093C2×C413yes—
115#4092C2×C413yes—
116#4092C2×C413yes—
117Q8×Dic5C2×C411yescharacteristic
118Q8×Dic5C2×C411yescharacteristic
119#4090C2×C413yes—
120#4086C2×C413yes—
121#4085C2×C416yes—
122#4085C2×C416yes—
123#4084C2×C413yes—
124#4084C2×C413yes—
125#4083C2×C416yes—
126#4082C2×C413yes—
127#4081C2×C416yes—
128D4×Dic5C2×C413yes—
129D4×Dic5C2×C413yes—
130#4076C2×C413yes—
131#4076C2×C413yes—
132#4075C2×C416yes—
133C4×C22⋊D5C2×C413yes—
134C4×C22⋊D5C2×C413yes—
135C4×C22⋊D5C2×C413yes—
136C4×C22⋊D5C2×C413yes—
137C4×C22⋊D5C2311yescharacteristic
138C4×C22⋊D5C2313yes—
139C4×C22⋊D5C2313yes—
140C4×C22⋊D5C2313yes—
141C4×C22⋊D5C2316yes—
142C2×#685C2×C413yes—
143#4072C2313yes—
144#4070C2×C413yes—
145#4070C2×C413yes—
146C2×#683C2×C413yes—
147C2×C4×Dic5C2313yes—
148C2×#681C2313yes—
149C2×#681C2313yes—
150C22×#168C2313yes—
151C22×#168C2313yes—
152#4053—212no—
153D5×M16—212no—
154#4047—212no—
155C2×#676C2316yes—
156C2×C8×D5—212no—
157C2×C8×D5C2311yescharacteristic
158C2×C8×D5C2313yes—
159C2×C8×D5C2313yes—
160C2×C8×D5C2313yes—
161C22⋊#168C2311yescharacteristic
162C22⋊#168C2313yes—
163C22⋊#168C2313yes—
164C22⋊#168C2313yes—
165C22⋊#168C2316yes—
166#3952C2311yescharacteristic
167#3952C2313yes—
168#3952C2313yes—
169#3952C2313yes—
170#3952C2316yes—
171#3947C2316yes—
172#3946C2311yescharacteristic
173#3946C2313yes—
174#3946C2313yes—
175#3946C2313yes—
176#3946C2316yes—
177C8×Dic5C2311yescharacteristic
178C8×Dic5C2313yes—
179C8×Dic5C2313yes—
180C8×Dic5C2313yes—
181C22×#131—51no—
182C22×#131D511yescharacteristic, complemented
183D4×#41—51no—
184#2935—53no—
185D4×M16—53no—
186#2933—53no—
187#2933—53no—
188#2931—53no—
189#2929—53no—
190#2929—53no—
191C2×C8×D4—53no—
192#2906—51no—
193#2880—51no—
194#2880—51no—
195C4×#131—51no—
196C24×C5C22×C413yes—
197C23×D5C22×C413yes—
198C5×#41—24no—
199C5×#41—212no—
200C5×#41—26no—
201C5×#41—26no—
202C5×#41C2×D414yes—
203C5×#41#4114yes—
204C2×C5×Q8—24no—
205C2×C5×Q8C22×C413yes—
206C2×C5×Q8C22×C411yescharacteristic
207C2×C5×D4—212no—
208C2×C5×D4C22×C416yes—
209C2×C5×D4C22×C413yes—
210C2×C5×D4C22×C413yes—
211C22×C4×C5—26no—
212C22×C4×C5—26no—
213C22×C4×C5C22×C413yes—
214C22×C4×C5C22×C413yes—
215C22×C4×C5C22×C413yes—
216C22×C4×C5C2411yescharacteristic
217C22×C4×C5C2413yes—
218C22×C4×C5C2413yes—
219C2×C22⋊D5—212no—
220C2×C22⋊D5C22×C413yes—
221C2×C22⋊D5C22×C416yes—
222C2×C22⋊D5C22×C413yes—
223C2×C22⋊D5C22×C413yes—
224C2×C22⋊D5C22×C416yes—
225C2×C22⋊D5C22×C411yescharacteristic
226C22×Dic5C22×C413yes—
227C22×Dic5C22×C413yes—
228C22×Dic5C22×C413yes—
229#713—24no—
230Q8×D5—24no—
231#711—212no—
232D4×D5—212no—
233#709—26no—
234#709—26no—
235C2×D20C22×C413yes—
236C2×C4×D5—26no—
237C2×C4×D5—26no—
238C2×C4×D5C22×C413yes—
239C2×C4×D5C22×C413yes—
240C2×C4×D5C2411yescharacteristic
241C2×C4×D5C2413yes—
242C2×Dic10C22×C413yes—
243C5×M16—26no—
244C5×M16—212no—
245C5×M16C2×D4112yescomplemented
246C2×C5×C8—26no—
247C2×C5×C8—22no—
248C2×C5×C8—26no—
249C2×C5×C8—26no—
250C2×C5×C8—26no—
251C2×C5×C8C2×D4112yescomplemented
252C2×C5×C8C2411yescharacteristic
253C2×C5×C8C2413yes—
254C2×C5×C8C2413yes—
255C2×C5×C8C2411yescharacteristic
256C22⋊Dic5C22×C411yescharacteristic
257C22⋊Dic5C22×C413yes—
258C22⋊Dic5C22×C413yes—
259C22⋊Dic5C22×C413yes—
260C22⋊Dic5C22×C416yes—
261C22⋊Dic5C22×C416yes—
262#685C22×C411yescharacteristic
263#685C22×C413yes—
264#685C22×C413yes—
265#685C22×C413yes—
266#685C22×C416yes—
267C4⋊Dic5C22×C413yes—
268C4⋊Dic5C22×C413yes—
269#683C22×C411yescharacteristic
270#683C22×C413yes—
271#683C22×C413yes—
272#683C22×C413yes—
273#683C22×C416yes—
274C4×Dic5C22×C413yes—
275C4×Dic5C22×C413yes—
276C4×Dic5C2411yescharacteristic
277C4×Dic5C2413yes—
278#681—26no—
279#681—26no—
280C2×#168—26no—
281C2×#168—26no—
282C2×#168C2411yescharacteristic
283C2×#168C2413yes—
284C2×#168C2411yescharacteristic
285C2×#168C2413yes—
286#676—212no—
287C8×D5—22no—
288C8×D5—26no—
289C8×D5—26no—
290C8×D5—26no—
291C22×#41—51no—
292C22×#41C2×D511yescharacteristic
293C2×#131—28no—
294C2×#131—51no—
295C2×#131—51no—
296C2×#131—53no—
297C2×#131—53no—
298C2×#131—108no—
299C2×#131C2×D511yescharacteristic
300C2×#131C2×D511yescharacteristic
301C2×#131C2×D513yescomplemented
302C2×#131C2×D513yescomplemented
303C22×M16—53no—
304C22×M16C2×D513yescomplemented
305C23×C8—53no—
306C23×C8C2×D513yescomplemented
307#550—51no—
308D4×Q8—51no—
309#548—51no—
310#548—51no—
311#547—53no—
312#546—53no—
313#546—53no—
314D42—53no—
315#532—53no—
316#525—53no—
317#525—53no—
318C4×#41—51no—
319C2×C4×D4—53no—
320#436—56no—
321#436—56no—
322#435—56no—
323#435—56no—
324#435—56no—
325#435—56no—
326C8×D4—51no—
327C8×D4—53no—
328C8×D4—53no—
329C8×D4—53no—
330C8×D4—53no—
331C8×D4—53no—
332C8×D4—53no—
333C8×D4—53no—
334C8×D4—56no—
335#424—53no—
336#424—53no—
337#423—53no—
338C2×C4⋊C8—53no—
339#408—53no—
340#408—53no—
341#408—53no—
342#408—53no—
343#407—53no—
344#407—53no—
345C2×C22⋊C8—53no—
346C2×C22⋊C8—53no—
347#405—53no—
348#405—53no—
349C4×M16—53no—
350C2×C4×C8—53no—
351C23×C5—26no—
352C23×C5—26no—
353C23×C5—43no—
354C23×C5C23×C413yes—
355C23×C5C23×C413yes—
356C23×C5C23×C411yescharacteristic
357C22×D5—26no—
358C22×D5—26no—
359C22×D5—43no—
360C22×D5C23×C413yes—
361C22×D5C23×C411yescharacteristic
362C5×Q8—26no—
363C5×Q8C4×D414yes—
364C5×D4—212no—
365C5×D4—26no—
366C5×D4C4×D4112yes—
367C2×C4×C5—26no—
368C2×C4×C5—26no—
369C2×C4×C5—26no—
370C2×C4×C5—21no—
371C2×C4×C5—23no—
372C2×C4×C5—21no—
373C2×C4×C5—23no—
374C2×C4×C5C23×C411yescharacteristic
375C2×C4×C5C23×C413yes—
376C2×C4×C5C23×C413yes—
377C2×C4×C5C22×D416yes—
378C2×C4×C5C2×#4116yes—
379C2×C4×C5C2511yescharacteristic
380C22⋊D5—212no—
381C22⋊D5—26no—
382C22⋊D5—26no—
383C22⋊D5—26no—
384C22⋊D5—46no—
385C22⋊D5#13114yesdirect product factor
386C2×Dic5—26no—
387C2×Dic5—26no—
388C2×Dic5—43no—
389C2×Dic5C23×C411yescharacteristic
390C2×Dic5C23×C413yes—
391C2×Dic5C23×C413yes—
392C2×Dic5C23×C413yes—
393C2×Dic5C23×C411yescharacteristic
394C2×Dic5C23×C411yescharacteristic
395D20—26no—
396C4×D5—26no—
397C4×D5—26no—
398C4×D5—21no—
399C4×D5—23no—
400C4×D5—21no—
401C4×D5—23no—
402Dic10—26no—
403C5×C8—21no—
404C5×C8—23no—
405C5×C8C22×D412yes—
406C5×C8C22×D416yes—
407#168—21no—
408#168—23no—
409#168—21no—
410#168—23no—
411C2×#41—24no—
412C2×#41—24no—
413C2×#41—51no—
414C2×#41—53no—
415C2×#41—53no—
416C2×#41—104no—
417C2×#41—104no—
418C2×#41C4×D513yes—
419C2×#41C4×D511yescharacteristic
420C2×#41C22×D513yes—
421C2×#41C22×D511yescharacteristic
422C22×Q8—51no—
423C22×Q8C4×D511yescharacteristic
424C22×D4—53no—
425C22×D4—53no—
426C22×D4C4×D513yes—
427C23×C4—53no—
428C23×C4C22×D513yes—
429#131—24no—
430#131—212no—
431#131—212no—
432#131—104no—
433#131—104no—
434#131—1012no—
435#131—1012no—
436#131C22⋊D518yesdirect product factor
437C2×M16—212no—
438C2×M16—53no—
439C2×M16—53no—
440C2×M16—56no—
441C2×M16—1012no—
442C2×M16C22×D513yes—
443C2×M16C22×D516yes—
444C2×M16C22×D513yes—
445C22×C8—212no—
446C22×C8—53no—
447C22×C8—53no—
448C22×C8—53no—
449C22×C8—53no—
450C22×C8—51no—
451C22×C8—53no—
452C22×C8—1012no—
453C22×C8C22×D513yes—
454C22×C8C22×D513yes—
455C22×C8C22×D513yes—
456C22×C8C22×D511yescharacteristic
457C22×C8C22×D513yes—
458C22×C8C22×D513yes—
459C4⋊Q8—53no—
460#127—53no—
461#124—53no—
462#124—53no—
463#123—56no—
464#123—56no—
465C22⋊Q8—53no—
466C22⋊Q8—53no—
467C22⋊Q8—53no—
468C22⋊Q8—53no—
469#121—53no—
470#121—53no—
471#121—56no—
472#121—56no—
473#121—53no—
474#121—53no—
475#120—56no—
476#120—56no—
477C4×Q8—51no—
478C4×Q8—51no—
479C4×D4—53no—
480C4×D4—53no—
481C4×D4—53no—
482C4×D4—53no—
483C4×D4—53no—
484C4×D4—53no—
485C4×D4—51no—
486C4×D4—53no—
487C4×D4—53no—
488C4×D4—53no—
489C4×D4—56no—
490#117—53no—
491C2×C4⋊C4—53no—
492C2×C22⋊C4—53no—
493C2×C22⋊C4—53no—
494C2×C42—53no—
495C4⋊C8—51no—
496C4⋊C8—53no—
497C4⋊C8—53no—
498C4⋊C8—53no—
499C4⋊C8—56no—
500C22⋊C8—51no—
501C22⋊C8—53no—
502C22⋊C8—53no—
503C22⋊C8—53no—
504C22⋊C8—56no—
505C22⋊C8—51no—
506C22⋊C8—53no—
507C22⋊C8—53no—
508C22⋊C8—53no—
509C22⋊C8—56no—
510#97—56no—
511C4×C8—53no—
512C4×C8—53no—
513C4×C8—51no—
514C4×C8—53no—
515C22×C5—21no—
516C22×C5—23no—
517C22×C5—23no—
518C22×C5—21no—
519C22×C5—23no—
520C22×C5—23no—
521C22×C5—23no—
522C22×C5—412no—
523C22×C5C2×C4×D416yes—
524C22×C5C2×#13112yescomplemented
525C22×C5C24×C411yescharacteristic
526C2×D5—21no—
527C2×D5—21no—
528C2×D5—23no—
529C2×D5—23no—
530C2×D5—23no—
531C2×D5—412no—
532C2×D5C2×#13112yescomplemented
533C4×C5—21no—
534C4×C5—23no—
535C4×C5C2×C4×D416yes—
536C4×C5C23×D411yescharacteristic
537C4×C5C22×#4111yescharacteristic
538Dic5—23no—
539Dic5—21no—
540Dic5—23no—
541Dic5—21no—
542Dic5—23no—
543Dic5C2×#13112yescomplemented
544C24—53no—
545C24C2×C4×D513yes—
546#41—24no—
547#41—212no—
548#41—26no—
549#41—26no—
550#41—104no—
551#41—1012no—
552#41—106no—
553#41—106no—
554#41#70914yes—
555#41C2×C22⋊D514yes—
556C2×Q8—24no—
557C2×Q8—53no—
558C2×Q8—104no—
559C2×Q8C2×C4×D513yes—
560C2×Q8C2×C4×D511yescharacteristic
561C2×D4—212no—
562C2×D4—51no—
563C2×D4—53no—
564C2×D4—53no—
565C2×D4—53no—
566C2×D4—56no—
567C2×D4—56no—
568C2×D4—53no—
569C2×D4—1012no—
570C2×D4—1012no—
571C2×D4C2×C4×D516yes—
572C2×D4C2×C4×D513yes—
573C2×D4C2×C4×D513yes—
574C22×C4—26no—
575C22×C4—26no—
576C22×C4—53no—
577C22×C4—53no—
578C22×C4—53no—
579C22×C4—53no—
580C22×C4—53no—
581C22×C4—51no—
582C22×C4—53no—
583C22×C4—106no—
584C22×C4—106no—
585C22×C4C2×C4×D513yes—
586C22×C4C2×C4×D513yes—
587C22×C4C2×C4×D513yes—
588C22×C4C23×D511yescharacteristic
589C22×C4C23×D513yes—
590C22×C4C23×D513yes—
591M16—26no—
592M16—212no—
593M16—106no—
594M16—106no—
595M16—1012no—
596M16C2×C22⋊D5112yescomplemented
597C2×C8—26no—
598C2×C8—22no—
599C2×C8—26no—
600C2×C8—26no—
601C2×C8—26no—
602C2×C8—51no—
603C2×C8—53no—
604C2×C8—51no—
605C2×C8—53no—
606C2×C8—106no—
607C2×C8—106no—
608C2×C8—102no—
609C2×C8—106no—
610C2×C8—106no—
611C2×C8—106no—
612C2×C8C2×C22⋊D5112yescomplemented
613C2×C8C23×D511yescharacteristic
614C2×C8C23×D513yes—
615C2×C8C23×D513yes—
616C2×C8C23×D511yescharacteristic
617C4⋊C4—51no—
618C4⋊C4—53no—
619C4⋊C4—53no—
620C4⋊C4—53no—
621C4⋊C4—53no—
622C4⋊C4—53no—
623C4⋊C4—56no—
624C22⋊C4—51no—
625C22⋊C4—53no—
626C22⋊C4—53no—
627C22⋊C4—53no—
628C22⋊C4—56no—
629C22⋊C4—56no—
630C22⋊C4—51no—
631C22⋊C4—53no—
632C22⋊C4—53no—
633C22⋊C4—53no—
634C22⋊C4—56no—
635C42—53no—
636C42—53no—
637C42—51no—
638C42—53no—
639C2×C5—26no—
640C2×C5—22no—
641C2×C5—43no—
642C2×C5C22×C4×D411yescharacteristic
643C2×C5C22×#13111yescharacteristic
644C2×C5#357311yescharacteristic
645D5—22no—
646D5—43no—
647C23—26no—
648C23—26no—
649C23—43no—
650C23—51no—
651C23—53no—
652C23—106no—
653C23—106no—
654C23—203no—
655C23C22×C4×D513yes—
656C23C22×C4×D511yescharacteristic
657C23C22×C4×D513yes—
658Q8—26no—
659Q8—106no—
660Q8C4×C22⋊D514yes—
661D4—212no—
662D4—26no—
663D4—54no—
664D4—106no—
665D4—106no—
666D4—106no—
667D4—1012no—
668D4—106no—
669D4—206no—
670D4C4×C22⋊D5112yes—
671C2×C4—26no—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—21no—
675C2×C4—23no—
676C2×C4—21no—
677C2×C4—23no—
678C2×C4—51no—
679C2×C4—51no—
680C2×C4—53no—
681C2×C4—53no—
682C2×C4—51no—
683C2×C4—53no—
684C2×C4—106no—
685C2×C4—106no—
686C2×C4—106no—
687C2×C4—106no—
688C2×C4—101no—
689C2×C4—103no—
690C2×C4—101no—
691C2×C4—103no—
692C2×C4—203no—
693C2×C4C22×C4×D511yescharacteristic
694C2×C4C22×C4×D513yes—
695C2×C4C22×C4×D513yes—
696C2×C4C2×#70916yes—
697C2×C4C22×C22⋊D516yes—
698C2×C4C24×D511yescharacteristic
699C8—21no—
700C8—23no—
701C8—101no—
702C8—103no—
703C8—101no—
704C8—103no—
705C8C22×C22⋊D512yes—
706C8C22×C22⋊D516yes—
707C5D4×#13111yescharacteristic, complemented, Sylow
708C22—23no—
709C22—23no—
710C22—21no—
711C22—21no—
712C22—23no—
713C22—23no—
714C22—23no—
715C22—412no—
716C22—52no—
717C22—101no—
718C22—101no—
719C22—103no—
720C22—103no—
721C22—103no—
722C22—2012no—
723C22D5×#13112yescomplemented
724C22C2×C4×C22⋊D516yes—
725C22C23×C4×D511yescharacteristic
726C4—21no—
727C4—23no—
728C4—52no—
729C4—103no—
730C4—101no—
731C4—103no—
732C4—101no—
733C4—103no—
734C4C2×C4×C22⋊D516yes—
735C4C22×#70911yescharacteristic
736C4C23×C22⋊D511yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—102no—
741C2—203no—
742C2C2×D5×#13111yescharacteristic
743C2#1061906111yescharacteristic
744C2C22×C4×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C8C23×D5
commutator, socleC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC22×C5×#131C2
prime radical#41×C22⋊D5C2
cosocleC2×C4×C5C25
hypercenterC22×#131D5
hypocenterC5D4×#131
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C22×C5×#131C2semidirect
3. C2×D5×#131C2semidirect
4. #10615806C2semidirect
5. #10615527C2semidirect
6. #10615525C2semidirect
7. #10615524C2semidirect
8. #10615519C2semidirect
9. #10615517C2semidirect
10. #10615514C2semidirect
11. Dic5×#131C2semidirect
12. M16×C22⋊D5C2semidirect
13. #10615488C2semidirect
14. #10615465C2semidirect
15. C2×C8×C22⋊D5C2semidirect
21. C2×C5×#131C22semidirect
22. C2×C5×#131C22semidirect
23. C22×C5×M16C22semidirect
24. C23×C5×C8C22semidirect
41. C2×#4053C22semidirect
42. C2×D5×M16C22semidirect
43. C2×#4047C22semidirect
44. C22×C8×D5C22semidirect
45. #65523C22semidirect
46. #65523C22semidirect
47. #65496C22semidirect
48. C2×C22⋊#168C22semidirect
49. #65418C22semidirect
50. #65417C22semidirect
51. #65417C22semidirect
52. #65416C22semidirect
53. #65416C22semidirect
54. #65415C22semidirect
55. #65411C22semidirect
56. #65408C22semidirect
57. #65407C22semidirect
58. M16×Dic5C22semidirect
59. #65400C22semidirect
60. #65400C22semidirect
61. #65399C22semidirect
64. C8×C22⋊D5C22semidirect
65. C8×C22⋊D5C22semidirect
66. C8×C22⋊D5C22semidirect
67. C8×C22⋊D5C22semidirect
68. C8×C22⋊D5C22semidirect
69. C8×C22⋊D5C22semidirect
70. C8×C22⋊D5C22semidirect
71. C2×#3952C22semidirect
72. #65391C22semidirect
73. #65390C22semidirect
74. C2×#3946C22semidirect
75. C2×C8×Dic5C22semidirect
98. C5×#131D4semidirect
182. C22×#131D5semidirect
245. C5×M16C2×D4semidirect
251. C2×C5×C8C2×D4semidirect
301. C2×#131C2×D5semidirect
302. C2×#131C2×D5semidirect
304. C22×M16C2×D5semidirect
306. C23×C8C2×D5semidirect
385. C22⋊D5#131direct (N × H)
436. #131C22⋊D5direct (N × H)
524. C22×C5C2×#131semidirect
532. C2×D5C2×#131semidirect
543. Dic5C2×#131semidirect
596. M16C2×C22⋊D5semidirect
612. C2×C8C2×C22⋊D5semidirect
707. C5D4×#131semidirect
723. C22D5×#131semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#1312
#41×C22⋊D52
C2×D5×#1312
#106158062
#106155272
#106155252
#106155242
#106155192
#106155172
#106155142
Dic5×#1312
M16×C22⋊D52
#106154882
#106154652
C2×C8×C22⋊D52
D4×#1315