Finite Group Databasebeta

← C5×#18267 #11940987

Subgroups — C5×#18267 #11940987

Order 1280.

1056 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3536C211yesmaximal, characteristic
2C5×#3092C211yesmaximal, characteristic, complemented
3C2×C5×#484C211yesmaximal, characteristic, complemented
4C5×#2501C211yesmaximal, characteristic, complemented
5C5×#1618C214yesmaximal, complemented
6C5×#1614C214yesmaximal, complemented
7C5×#1508C211yesmaximal, characteristic, complemented
8C5×#1501C211yesmaximal, characteristic, complemented
9C5×#1471C211yesmaximal, characteristic, complemented
10C5×#562—22no—
11C5×#554—21no—
12C5×#548—21no—
13C5×#547—21no—
14C5×#546—22no—
15C5×#546—21no—
16C5×#543C2212yes—
17C5×#542—21no—
18C5×#539—21no—
19C5×#538C2212yes—
20C5×#537—21no—
21C5×#537—21no—
22C5×#525C2211yescharacteristic
23C2×C5×#123—22no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C5×#484—22no—
28C5×#484C2214yes—
29C5×#484C2212yes—
30C5×#483—21no—
31C5×#481C2212yes—
32C5×#480—21no—
33C5×#428—21no—
34C2×C5×#107—21no—
35C5×#417—21no—
36C2×C5×#103—21no—
37C5×#407C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C5×#399C2214yes—
40C5×#390—21no—
41C5×#384—21no—
42C4×C5×C22⋊C4C2211yescharacteristic
43C5×#328C2212yes—
44C5×#328C2214yes—
45C5×#327C2212yes—
46C5×#323C2214yes—
47#18267C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—22no—
49C2×C5×#41—21no—
50C2×C5×#41D411yescharacteristic
51C22×C5×Q8D411yescharacteristic
52C22×C5×D4D411yescharacteristic
53C22×C5×D4D412yes—
54C23×C4×C5—21no—
55C23×C4×C5C2311yescharacteristic
56C2×C5×M16—21no—
57C22×C5×C8—21no—
58C5×C4⋊Q8—21no—
59C5×#126—22no—
60C5×#125—22no—
61C5×#124—21no—
62C5×#124—22no—
63C5×#124—22no—
64C5×#123—22no—
65C5×#123—22no—
66C5×#123—22no—
67C5×#123—21no—
68C5×#123—22no—
69C5×#123—48no—
70C5×C22⋊Q8—21no—
71C5×C22⋊Q8—22no—
72C5×C22⋊Q8—22no—
73C5×C22⋊Q8—22no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—22no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8D411yescharacteristic
80C5×C22⋊Q8D412yes—
81C5×C22⋊Q8C2312yes—
82C5×C22⋊Q8C2311yescharacteristic
83C5×#121—21no—
84C5×#121—22no—
85C5×#121—22no—
86C5×#121—22no—
87C5×#121—22no—
88C5×#121—22no—
89C5×#121—21no—
90C5×#121—21no—
91C5×#121—21no—
92C5×#121—21no—
93C5×#121D411yescharacteristic
94C5×#121C2311yescharacteristic
95C5×#120—21no—
96C5×#120—22no—
97C4×C5×Q8—21no—
98C4×C5×D4—22no—
99C4×C5×D4—21no—
100C4×C5×D4—21no—
101C4×C5×D4—21no—
102C4×C5×D4—22no—
103C5×#117D411yescharacteristic
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4C2312yes—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4C2312yes—
120C2×C42×C5—21no—
121C5×#107—24no—
122C5×#107—22no—
123C5×#106—22no—
124C5×#103—24no—
125C5×#103—22no—
126C5×#102—22no—
127C5×C22⋊C8—21no—
128C5×C22⋊C8—21no—
129C5×C22⋊C8C2312yes—
130C5×C22⋊C8C2312yes—
131C5×#95C2312yes—
132#3536C2×C511yescharacteristic
133#3092C2×C511yescharacteristic, complemented
134C2×#484C2×C511yescharacteristic, complemented
135#2501C2×C511yescharacteristic, complemented
136#1618C2×C514yescomplemented
137#1614C2×C514yescomplemented
138#1508C2×C511yescharacteristic, complemented
139#1501C2×C511yescharacteristic, complemented
140#1471C2×C511yescharacteristic, complemented
141C24×C5C2×D411yescharacteristic
142C24×C5C2×D412yes—
143C5×#41—42no—
144C5×#41—84no—
145C5×#41—82no—
146C2×C5×Q8—22no—
147C2×C5×Q8—21no—
148C2×C5×Q8—42no—
149C2×C5×Q8C2×D411yescharacteristic
150C2×C5×Q8C2×D412yes—
151C2×C5×D4—21no—
152C2×C5×D4—22no—
153C2×C5×D4—21no—
154C2×C5×D4—22no—
155C2×C5×D4—22no—
156C2×C5×D4—21no—
157C2×C5×D4—22no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—42no—
161C2×C5×D4—44no—
162C2×C5×D4C2×D411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—22no—
171C22×C4×C5—42no—
172C22×C4×C5—44no—
173C22×C4×C5—41no—
174C22×C4×C5—41no—
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5C2×D411yescharacteristic
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D412yes—
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2411yescharacteristic
182C5×M16—42no—
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—42no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—48no—
200C5×C4⋊C4—41no—
201C5×C4⋊C4—41no—
202C5×C4⋊C4C2×D412yes—
203C5×C4⋊C4C2×D411yescharacteristic
204C5×C4⋊C4C2×D411yescharacteristic
205C5×C22⋊C4—22no—
206C5×C22⋊C4—22no—
207C5×C22⋊C4—24no—
208C5×C22⋊C4—22no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—22no—
211C5×C22⋊C4—22no—
212C5×C22⋊C4—21no—
213C5×C22⋊C4—21no—
214C5×C22⋊C4—22no—
215C5×C22⋊C4—21no—
216C5×C22⋊C4—21no—
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—21no—
220C5×C22⋊C4—48no—
221C42×C5—22no—
222C42×C5—21no—
223C42×C5—42no—
224#562—22no—
225#554—21no—
226#548—21no—
227#547—21no—
228#546—22no—
229#546—21no—
230#543C22×C512yes—
231#542—21no—
232#539—21no—
233#538C22×C512yes—
234#537—21no—
235#537—21no—
236#525C22×C511yescharacteristic
237C2×#123—22no—
238C2×C22⋊Q8C22×C511yescharacteristic
239C2×#121C22×C511yescharacteristic
240C22×C4⋊C4C22×C511yescharacteristic
241#484—22no—
242#484C22×C514yes—
243#484C22×C512yes—
244#483—21no—
245#481C22×C512yes—
246#480—21no—
247#428—21no—
248C2×#107—21no—
249#417—21no—
250C2×#103—21no—
251#407C22×C511yescharacteristic
252C2×C22⋊C8C22×C511yescharacteristic
253#399C22×C514yes—
254#390—21no—
255#384—21no—
256C4×C22⋊C4C22×C511yescharacteristic
257#328C22×C512yes—
258#328C22×C514yes—
259#327C22×C512yes—
260#323C22×C514yes—
261C23×C5—22no—
262C23×C5—22no—
263C23×C5—22no—
264C23×C5—21no—
265C23×C5—24no—
266C23×C5—41no—
267C23×C5—42no—
268C23×C5—42no—
269C23×C5#12011yescharacteristic
270C23×C5#12011yescharacteristic
271C23×C5C22×D411yescharacteristic
272C5×Q8—42no—
273C5×Q8—41no—
274C5×Q8—42no—
275C5×Q8—82no—
276C5×D4—41no—
277C5×D4—42no—
278C5×D4—44no—
279C5×D4—42no—
280C5×D4—42no—
281C5×D4—81no—
282C5×D4—82no—
283C5×D4—81no—
284C5×D4—82no—
285C5×D4—82no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—24no—
290C2×C4×C5—21no—
291C2×C4×C5—22no—
292C2×C4×C5—21no—
293C2×C4×C5—22no—
294C2×C4×C5—21no—
295C2×C4×C5—22no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—44no—
305C2×C4×C5—42no—
306C2×C4×C5—81no—
307C2×C4×C5—82no—
308C2×C4×C5—82no—
309C2×C4×C5—82no—
310C2×C4×C5—82no—
311C2×C4×C5—82no—
312C2×C4×C5#12011yescharacteristic
313C2×C4×C5#12011yescharacteristic
314C2×C4×C5C22×D411yescharacteristic
315C2×C4×C5C22×D411yescharacteristic
316C5×C8—42no—
317C5×C8—42no—
318C2×#41—22no—
319C2×#41—21no—
320C2×#41C5×D411yescharacteristic
321C22×Q8C5×D411yescharacteristic
322C22×D4C5×D412yes—
323C22×D4C5×D411yescharacteristic
324C23×C4—21no—
325C23×C4C23×C511yescharacteristic
326C2×M16—21no—
327C22×C8—21no—
328C4⋊Q8—21no—
329#126—22no—
330#125—22no—
331#124—21no—
332#124—22no—
333#124—22no—
334#123—22no—
335#123—22no—
336#123—22no—
337#123—21no—
338#123—22no—
339#123—48no—
340C22⋊Q8—21no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8C5×D412yes—
350C22⋊Q8C5×D411yescharacteristic
351C22⋊Q8C23×C512yes—
352C22⋊Q8C23×C511yescharacteristic
353#121—21no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121C5×D411yescharacteristic
364#121C23×C511yescharacteristic
365#120—21no—
366#120—22no—
367C4×Q8—21no—
368C4×D4—22no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—22no—
373#117C5×D411yescharacteristic
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4C5×D411yescharacteristic
383C2×C4⋊C4C5×D411yescharacteristic
384C2×C4⋊C4C23×C512yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C23×C512yes—
390C2×C42—21no—
391#107—24no—
392#107—22no—
393#106—22no—
394#103—24no—
395#103—22no—
396#102—22no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8C23×C512yes—
400C22⋊C8C23×C512yes—
401#95C23×C512yes—
402C22×C5—21no—
403C22×C5—21no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—21no—
407C22×C5—21no—
408C22×C5—21no—
409C22×C5—44no—
410C22×C5—41no—
411C22×C5—42no—
412C22×C5—41no—
413C22×C5—42no—
414C22×C5—41no—
415C22×C5—42no—
416C22×C5—84no—
417C22×C5#45312yes—
418C22×C5C2×#12011yescharacteristic
419C22×C5#57812yes—
420C4×C5—21no—
421C4×C5—21no—
422C4×C5—21no—
423C4×C5—44no—
424C4×C5—41no—
425C4×C5—42no—
426C4×C5—42no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5—42no—
430C4×C5—82no—
431C4×C5#45812yes—
432C24C2×C5×D411yescharacteristic
433C24C2×C5×D412yes—
434#41—42no—
435#41—84no—
436#41—82no—
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8—42no—
440C2×Q8C2×C5×D411yescharacteristic
441C2×Q8C2×C5×D412yes—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—44no—
453C2×D4C2×C5×D411yescharacteristic
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—42no—
463C22×C4—44no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4C2×C5×D411yescharacteristic
467C22×C4C2×C5×D411yescharacteristic
468C22×C4C2×C5×D411yescharacteristic
469C22×C4C2×C5×D412yes—
470C22×C4C2×C5×D411yescharacteristic
471C22×C4C2×C5×D411yescharacteristic
472C22×C4C24×C511yescharacteristic
473M16—42no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—42no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—48no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×C5×D411yescharacteristic
494C4⋊C4C2×C5×D412yes—
495C4⋊C4C2×C5×D411yescharacteristic
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—48no—
512C42—22no—
513C42—21no—
514C42—42no—
515C2×C5—22no—
516C2×C5—22no—
517C2×C5—41no—
518C2×C5—81no—
519C2×C5—82no—
520C2×C5#301111yescharacteristic
521C2×C5C2×#45311yescharacteristic
522C2×C5C2×#45811yescharacteristic
523C23—22no—
524C23—22no—
525C23—22no—
526C23—21no—
527C23—24no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23C5×#12011yescharacteristic
532C23C5×#12011yescharacteristic
533C23C22×C5×D411yescharacteristic
534Q8—42no—
535Q8—41no—
536Q8—42no—
537Q8—82no—
538D4—41no—
539D4—44no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—81no—
544D4—82no—
545D4—81no—
546D4—82no—
547D4—82no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—81no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C5×#12011yescharacteristic
575C2×C4C5×#12011yescharacteristic
576C2×C4C22×C5×D411yescharacteristic
577C2×C4C22×C5×D411yescharacteristic
578C8—42no—
579C8—42no—
580C5#1826711yescharacteristic, direct product factor, Sylow
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—44no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—84no—
596C22C5×#45312yes—
597C22C2×C5×#12011yescharacteristic
598C22C5×#57812yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—44no—
603C4—41no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—82no—
610C4C5×#45812yes—
611C2—22no—
612C2—22no—
613C2—41no—
614C2—82no—
615C2—81no—
616C2C5×#301111yescharacteristic
617C2C2×C5×#45311yescharacteristic
618C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3536C2
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
2. C5×#3092C2semidirect
3. C2×C5×#484C2semidirect
4. C5×#2501C2semidirect
5. C5×#1618C2semidirect
6. C5×#1614C2semidirect
7. C5×#1508C2semidirect
8. C5×#1501C2semidirect
9. C5×#1471C2semidirect
47. #18267C5direct (N × H)
133. #3092C2×C5semidirect
134. C2×#484C2×C5semidirect
135. #2501C2×C5semidirect
136. #1618C2×C5semidirect
137. #1614C2×C5semidirect
138. #1508C2×C5semidirect
139. #1501C2×C5semidirect
140. #1471C2×C5semidirect
580. C5#18267direct (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×#30922
C2×C5×#4842
C5×#25012
C5×#16182
C5×#16142
C5×#15082
C5×#15012
C5×#14712
#182675