Finite Group Databasebeta

← C5×#18260 #11940980

Subgroups — C5×#18260 #11940980

Order 1280.

1336 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3536C211yesmaximal, characteristic, complemented
2C5×#3003C211yesmaximal, characteristic, complemented
3C2×C5×#447C211yesmaximal, characteristic, complemented
4C5×#2435C211yesmaximal, characteristic, complemented
5C5×#1598C214yesmaximal, complemented
6C5×#1597C214yesmaximal, complemented
7C5×#1507C211yesmaximal, characteristic, complemented
8C5×#1501C211yesmaximal, characteristic, complemented
9C5×#1472C211yesmaximal, characteristic, complemented
10C23×C5×D4C2211yescharacteristic
11C2×C5×AGL(1,ℤ/8)—21no—
12C22×C5×D8—21no—
13C5×#562—22no—
14C5×#554—21no—
15C5×#548—21no—
16C5×#547—21no—
17C5×#546—21no—
18C5×#546—22no—
19C5×#543—21no—
20C5×#542—21no—
21C5×#539C2212yescomplemented
22C5×#538—21no—
23C5×#537—21no—
24C5×#537C2212yescomplemented
25C2×C5×#124—21no—
26C5×#525C2211yescharacteristic
27C2×C5×C22⋊Q8C2211yescharacteristic
28C2×C5×#121C2211yescharacteristic
29C5×#450—21no—
30C5×#450C2212yescomplemented
31C5×#447—22no—
32C5×#447—21no—
33C5×#447C2214yes—
34C5×#447C2212yescomplemented
35C5×#418—21no—
36C2×C5×#102—21no—
37C5×#407C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C5×#394C2214yescomplemented
40C5×#390—21no—
41C5×#379—22no—
42C4×C5×C22⋊C4C2211yescharacteristic
43C5×#328C2212yescomplemented
44C5×#327C2212yescomplemented
45C5×#327C2214yescomplemented
46C5×#324C2214yescomplemented
47#18260C511yesmaximal, characteristic, direct product factor, Sylow
48C25×C5—21no—
49C2×C5×#41—21no—
50C2×C5×#41—22no—
51C2×C5×#41D411yescharacteristic
52C22×C5×Q8D411yescharacteristic
53C22×C5×D4—21no—
54C22×C5×D4—21no—
55C22×C5×D4—21no—
56C22×C5×D4—21no—
57C22×C5×D4—21no—
58C22×C5×D4—21no—
59C22×C5×D4—44no—
60C22×C5×D4D411yescharacteristic
61C22×C5×D4C2312yes—
62C23×C4×C5C2311yescharacteristic
63C5×AGL(1,ℤ/8)—44no—
64C2×C5×SD16—22no—
65C2×C5×D8—24no—
66C2×C5×D8—22no—
67C2×C5×D8—44no—
68C2×C5×M16—21no—
69C22×C5×C8—21no—
70C5×C4⋊Q8—21no—
71C5×#126—22no—
72C5×#125—22no—
73C5×#124—22no—
74C5×#124—21no—
75C5×#124—22no—
76C5×#124—44no—
77C5×#123—22no—
78C5×#123—22no—
79C5×#123—22no—
80C5×#123—21no—
81C5×#123—22no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8D411yescharacteristic
94C5×C22⋊Q8C2311yescharacteristic
95C5×#121—21no—
96C5×#121—22no—
97C5×#121—22no—
98C5×#121—22no—
99C5×#121—22no—
100C5×#121—21no—
101C5×#121—21no—
102C5×#121—22no—
103C5×#121D412yes—
104C5×#121D411yescharacteristic
105C5×#121C2312yes—
106C5×#121C2311yescharacteristic
107C5×#120—22no—
108C5×#120—21no—
109C4×C5×Q8—21no—
110C4×C5×D4—22no—
111C4×C5×D4—21no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—22no—
115C5×#117D411yescharacteristic
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4D411yescharacteristic
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4C2312yes—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—24no—
124C2×C5×C22⋊C4—24no—
125C2×C5×C22⋊C4D412yes—
126C2×C42×C5—21no—
127C5×#102—24no—
128C5×#102—22no—
129C5×#102—22no—
130C5×C22⋊C8—21no—
131C5×C22⋊C8—21no—
132C5×C22⋊C8C2312yes—
133C5×C22⋊C8C2312yes—
134C5×#95C2312yes—
135#3536C2×C511yescharacteristic, complemented
136#3003C2×C511yescharacteristic, complemented
137C2×#447C2×C511yescharacteristic, complemented
138#2435C2×C511yescharacteristic, complemented
139#1598C2×C514yescomplemented
140#1597C2×C514yescomplemented
141#1507C2×C511yescharacteristic, complemented
142#1501C2×C511yescharacteristic, complemented
143#1472C2×C511yescharacteristic, complemented
144C24×C5—22no—
145C24×C5—21no—
146C24×C5—44no—
147C24×C5—44no—
148C24×C5—41no—
149C24×C5—41no—
150C24×C5—82no—
151C24×C5C2×D411yescharacteristic
152C5×#41—42no—
153C5×#41—84no—
154C5×#41—82no—
155C2×C5×Q8—22no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—42no—
159C2×C5×Q8C2×D411yescharacteristic
160C2×C5×D4—24no—
161C2×C5×D4—24no—
162C2×C5×D4—24no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—22no—
166C2×C5×D4—22no—
167C2×C5×D4—22no—
168C2×C5×D4—21no—
169C2×C5×D4—22no—
170C2×C5×D4—21no—
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4—42no—
174C2×C5×D4—42no—
175C2×C5×D4—42no—
176C2×C5×D4—42no—
177C2×C5×D4—44no—
178C2×C5×D4—44no—
179C2×C5×D4—44no—
180C2×C5×D4—41no—
181C2×C5×D4—41no—
182C2×C5×D4—82no—
183C2×C5×D4C2×D411yescharacteristic
184C2×C5×D4C2×D412yes—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—22no—
191C22×C4×C5—42no—
192C22×C4×C5C2×D412yes—
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D412yes—
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2411yescharacteristic
200C5×SD16—44no—
201C5×D8—48no—
202C5×D8—44no—
203C5×M16—42no—
204C2×C5×C8—22no—
205C2×C5×C8—22no—
206C2×C5×C8—42no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—22no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—22no—
216C5×C4⋊C4—22no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4C2×D412yes—
219C5×C4⋊C4C2×D411yescharacteristic
220C5×C4⋊C4C2×D411yescharacteristic
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4—21no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—48no—
237C5×C22⋊C4—84no—
238C42×C5—22no—
239C42×C5—21no—
240C42×C5—42no—
241C23×D4C22×C511yescharacteristic
242C2×AGL(1,ℤ/8)—21no—
243C22×D8—21no—
244#562—22no—
245#554—21no—
246#548—21no—
247#547—21no—
248#546—21no—
249#546—22no—
250#543—21no—
251#542—21no—
252#539C22×C512yescomplemented
253#538—21no—
254#537—21no—
255#537C22×C512yescomplemented
256C2×#124—21no—
257#525C22×C511yescharacteristic
258C2×C22⋊Q8C22×C511yescharacteristic
259C2×#121C22×C511yescharacteristic
260#450—21no—
261#450C22×C512yescomplemented
262#447—22no—
263#447—21no—
264#447C22×C514yes—
265#447C22×C512yescomplemented
266#418—21no—
267C2×#102—21no—
268#407C22×C511yescharacteristic
269C2×C22⋊C8C22×C511yescharacteristic
270#394C22×C514yescomplemented
271#390—21no—
272#379—22no—
273C4×C22⋊C4C22×C511yescharacteristic
274#328C22×C512yescomplemented
275#327C22×C514yescomplemented
276#327C22×C512yescomplemented
277#324C22×C514yescomplemented
278C23×C5—22no—
279C23×C5—22no—
280C23×C5—24no—
281C23×C5—22no—
282C23×C5—21no—
283C23×C5—41no—
284C23×C5—44no—
285C23×C5—44no—
286C23×C5—42no—
287C23×C5—44no—
288C23×C5—42no—
289C23×C5—44no—
290C23×C5—42no—
291C23×C5—81no—
292C23×C5—81no—
293C23×C5—82no—
294C23×C5—82no—
295C23×C5—82no—
296C23×C5—816no—
297C23×C5—82no—
298C23×C5#12011yescharacteristic
299C23×C5#12011yescharacteristic
300C23×C5C22×D411yescharacteristic
301C5×Q8—41no—
302C5×Q8—42no—
303C5×Q8—81no—
304C5×Q8—82no—
305C5×D4—24no—
306C5×D4—24no—
307C5×D4—42no—
308C5×D4—41no—
309C5×D4—42no—
310C5×D4—42no—
311C5×D4—44no—
312C5×D4—44no—
313C5×D4—42no—
314C5×D4—42no—
315C5×D4—44no—
316C5×D4—42no—
317C5×D4—82no—
318C5×D4—81no—
319C5×D4—82no—
320C5×D4—82no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—22no—
326C2×C4×C5—21no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—22no—
330C2×C4×C5—24no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5—81no—
340C2×C4×C5—82no—
341C2×C4×C5—82no—
342C2×C4×C5—82no—
343C2×C4×C5#12011yescharacteristic
344C2×C4×C5#12011yescharacteristic
345C2×C4×C5C22×D411yescharacteristic
346C2×C4×C5C22×D411yescharacteristic
347C5×C8—42no—
348C5×C8—42no—
349C25—21no—
350C2×#41—21no—
351C2×#41—22no—
352C2×#41C5×D411yescharacteristic
353C22×Q8C5×D411yescharacteristic
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—44no—
361C22×D4C5×D411yescharacteristic
362C22×D4C23×C512yes—
363C23×C4C23×C511yescharacteristic
364AGL(1,ℤ/8)—44no—
365C2×SD16—22no—
366C2×D8—24no—
367C2×D8—22no—
368C2×D8—44no—
369C2×M16—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372#126—22no—
373#125—22no—
374#124—22no—
375#124—21no—
376#124—22no—
377#124—44no—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—21no—
382#123—22no—
383C22⋊Q8—21no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8C5×D411yescharacteristic
395C22⋊Q8C23×C511yescharacteristic
396#121—21no—
397#121—22no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121—22no—
404#121C5×D412yes—
405#121C5×D411yescharacteristic
406#121C23×C512yes—
407#121C23×C511yescharacteristic
408#120—22no—
409#120—21no—
410C4×Q8—21no—
411C4×D4—22no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—22no—
416#117C5×D411yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4C5×D411yescharacteristic
419C2×C4⋊C4C5×D411yescharacteristic
420C2×C4⋊C4C23×C512yes—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4C5×D412yes—
427C2×C42—21no—
428#102—24no—
429#102—22no—
430#102—22no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8C23×C512yes—
434C22⋊C8C23×C512yes—
435#95C23×C512yes—
436C22×C5—21no—
437C22×C5—21no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5—21no—
443C22×C5—44no—
444C22×C5—48no—
445C22×C5—41no—
446C22×C5—42no—
447C22×C5—41no—
448C22×C5—42no—
449C22×C5—41no—
450C22×C5—42no—
451C22×C5—44no—
452C22×C5—84no—
453C22×C5—88no—
454C22×C5—88no—
455C22×C5—82no—
456C22×C5—82no—
457C22×C5—162no—
458C22×C5#45412yes—
459C22×C5C2×#12011yescharacteristic
460C22×C5#57612yes—
461C4×C5—21no—
462C4×C5—21no—
463C4×C5—21no—
464C4×C5—42no—
465C4×C5—42no—
466C4×C5—41no—
467C4×C5—41no—
468C4×C5—41no—
469C4×C5—42no—
470C4×C5—82no—
471C4×C5B(4,𝔽2)12yes—
472C24—22no—
473C24—21no—
474C24—44no—
475C24—44no—
476C24—41no—
477C24—41no—
478C24—82no—
479C24C2×C5×D411yescharacteristic
480#41—42no—
481#41—84no—
482#41—82no—
483C2×Q8—22no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—42no—
487C2×Q8C2×C5×D411yescharacteristic
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—82no—
511C2×D4C2×C5×D411yescharacteristic
512C2×D4C2×C5×D412yes—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4C2×C5×D412yes—
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D412yes—
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C24×C511yescharacteristic
528SD16—44no—
529D8—48no—
530D8—44no—
531M16—42no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—42no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4C2×C5×D412yes—
547C4⋊C4C2×C5×D411yescharacteristic
548C4⋊C4C2×C5×D411yescharacteristic
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—21no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—48no—
564C22⋊C4—42no—
565C22⋊C4—84no—
566C42—22no—
567C42—21no—
568C42—42no—
569C2×C5—22no—
570C2×C5—22no—
571C2×C5—41no—
572C2×C5—81no—
573C2×C5—84no—
574C2×C5—82no—
575C2×C5#300811yescharacteristic
576C2×C5C2×#45411yescharacteristic
577C2×C5C2×B(4,𝔽2)11yescharacteristic
578C23—22no—
579C23—22no—
580C23—24no—
581C23—22no—
582C23—21no—
583C23—41no—
584C23—44no—
585C23—44no—
586C23—42no—
587C23—44no—
588C23—42no—
589C23—44no—
590C23—42no—
591C23—81no—
592C23—81no—
593C23—82no—
594C23—82no—
595C23—82no—
596C23—816no—
597C23—82no—
598C23C5×#12011yescharacteristic
599C23C5×#12011yescharacteristic
600C23C22×C5×D411yescharacteristic
601Q8—41no—
602Q8—42no—
603Q8—81no—
604Q8—82no—
605D4—24no—
606D4—24no—
607D4—42no—
608D4—41no—
609D4—42no—
610D4—42no—
611D4—44no—
612D4—42no—
613D4—44no—
614D4—42no—
615D4—44no—
616D4—42no—
617D4—82no—
618D4—81no—
619D4—82no—
620D4—82no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—81no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4C5×#12011yescharacteristic
644C2×C4C5×#12011yescharacteristic
645C2×C4C22×C5×D411yescharacteristic
646C2×C4C22×C5×D411yescharacteristic
647C8—42no—
648C8—42no—
649C5#1826011yescharacteristic, direct product factor, Sylow
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—44no—
658C22—48no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—42no—
665C22—44no—
666C22—84no—
667C22—88no—
668C22—88no—
669C22—82no—
670C22—82no—
671C22—162no—
672C22C5×#45412yes—
673C22C2×C5×#12011yescharacteristic
674C22C5×#57612yes—
675C4—21no—
676C4—21no—
677C4—21no—
678C4—42no—
679C4—42no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—82no—
685C4C5×B(4,𝔽2)12yes—
686C2—22no—
687C2—22no—
688C2—41no—
689C2—84no—
690C2—82no—
691C2—81no—
692C2C5×#300811yescharacteristic
693C2C2×C5×#45411yescharacteristic
694C2C2×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3536C2semidirect
2. C5×#3003C2semidirect
3. C2×C5×#447C2semidirect
4. C5×#2435C2semidirect
5. C5×#1598C2semidirect
6. C5×#1597C2semidirect
7. C5×#1507C2semidirect
8. C5×#1501C2semidirect
9. C5×#1472C2semidirect
21. C5×#539C22semidirect
24. C5×#537C22semidirect
30. C5×#450C22semidirect
34. C5×#447C22semidirect
39. C5×#394C22semidirect
43. C5×#328C22semidirect
44. C5×#327C22semidirect
45. C5×#327C22semidirect
46. C5×#324C22semidirect
47. #18260C5direct (N × H)
135. #3536C2×C5semidirect
136. #3003C2×C5semidirect
137. C2×#447C2×C5semidirect
138. #2435C2×C5semidirect
139. #1598C2×C5semidirect
140. #1597C2×C5semidirect
141. #1507C2×C5semidirect
142. #1501C2×C5semidirect
143. #1472C2×C5semidirect
252. #539C22×C5semidirect
255. #537C22×C5semidirect
261. #450C22×C5semidirect
265. #447C22×C5semidirect
270. #394C22×C5semidirect
274. #328C22×C5semidirect
275. #327C22×C5semidirect
276. #327C22×C5semidirect
277. #324C22×C5semidirect
649. C5#18260direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35362
C5×#30032
C2×C5×#4472
C5×#24352
C5×#15982
C5×#15972
C5×#15072
C5×#15012
C5×#14722
#182605