Finite Group Databasebeta

← C5×#18276 #11940996

Subgroups — C5×#18276 #11940996

Order 1280.

966 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic, complemented
2C5×#3109C211yesmaximal, characteristic, complemented
3C5×#3105C211yesmaximal, characteristic, complemented
4C5×#2562C211yesmaximal, characteristic, complemented
5C5×#1616C212yesmaximal, complemented
6C5×#1615C212yesmaximal, complemented
7C5×#1598C212yesmaximal, complemented
8C5×#1597C212yesmaximal, complemented
9C5×#1509C211yesmaximal, characteristic, complemented
10C5×#1502C211yesmaximal, characteristic, complemented
11C5×#1470C211yesmaximal, characteristic, complemented
12C5×#563—21no—
13C5×#562—21no—
14C5×#554—21no—
15C5×#553—21no—
16C5×#553—21no—
17C5×#547—22no—
18C5×#547—21no—
19C5×#544—21no—
20C5×#540—21no—
21C5×#539—22no—
22C5×#539C2212yes—
23C5×#537C2212yes—
24C5×#532C2211yescharacteristic
25C5×#529C2211yescharacteristic
26C2×C5×#125C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C5×#484C2211yescharacteristic
29C5×#481C2212yes—
30C5×#481C2211yescharacteristic
31C5×#478—21no—
32C5×#476—21no—
33C5×#463—21no—
34C5×#459—21no—
35C5×#450C2211yescharacteristic
36C5×#447C2212yes—
37C5×#447C2211yescharacteristic
38C5×#442—22no—
39C4×C5×SD16—21no—
40C4×C5×D8—21no—
41C5×#432C2211yescharacteristic
42C5×#431C2211yescharacteristic
43C5×#400C2212yes—
44C5×#394C2212yes—
45C5×#388—22no—
46C5×#380—21no—
47C5×#380—21no—
48C4×C5×C4⋊C4C2211yescharacteristic
49C5×#328C2212yes—
50C5×#327C2212yes—
51C5×#327C2212yes—
52C5×#327C2212yes—
53C5×#324C2212yes—
54C5×#324C2212yes—
55#18276C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C2×C5×#41—22no—
58C22×C5×D4C2311yescharacteristic
59C23×C4×C5—21no—
60C2×C5×SD16—21no—
61C2×C5×D8—21no—
62C2×C5×D8—22no—
63C5×C4⋊Q8—21no—
64C5×C4⋊Q8—22no—
65C5×C4⋊Q8D411yescharacteristic
66C5×#127D411yescharacteristic
67C5×#126—22no—
68C5×#126—22no—
69C5×#126—21no—
70C5×#125—21no—
71C5×#125—22no—
72C5×#125—21no—
73C5×#125—21no—
74C5×#125—21no—
75C5×#125—21no—
76C5×#125D411yescharacteristic
77C5×#124—21no—
78C5×#124D411yescharacteristic
79C5×#123—22no—
80C5×#123—22no—
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—22no—
84C5×#123—21no—
85C5×#123—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8C2311yescharacteristic
93C5×#121—21no—
94C5×#121—22no—
95C5×#121—21no—
96C5×#121—22no—
97C5×#121—22no—
98C5×#121—21no—
99C5×#121—22no—
100C5×#121C2311yescharacteristic
101C5×#121C2312yes—
102C4×C5×Q8D411yescharacteristic
103C4×C5×D4—22no—
104C4×C5×D4—21no—
105C4×C5×D4—21no—
106C4×C5×D4—21no—
107C4×C5×D4—22no—
108C4×C5×D4—21no—
109C4×C5×D4—21no—
110C4×C5×D4—21no—
111C4×C5×D4—21no—
112C4×C5×D4—21no—
113C4×C5×D4D411yescharacteristic
114C4×C5×D4D412yes—
115C5×#117—21no—
116C5×#117—21no—
117C2×C5×C4⋊C4—22no—
118C2×C5×C4⋊C4—21no—
119C2×C5×C4⋊C4—21no—
120C2×C5×C4⋊C4D411yescharacteristic
121C2×C5×C4⋊C4D411yescharacteristic
122C2×C5×C4⋊C4D412yes—
123C2×C5×C4⋊C4C2311yescharacteristic
124C2×C5×C4⋊C4C2312yes—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—21no—
127C2×C5×C22⋊C4—22no—
128C2×C42×C5—21no—
129C2×C42×C5C2311yescharacteristic
130C5×#107—21no—
131C5×#106—21no—
132C5×#106—22no—
133C5×C4⋊C8—21no—
134C5×C4⋊C8—21no—
135C5×#103—21no—
136C5×#102—21no—
137C5×#102—22no—
138C5×#102—21no—
139C5×#102—21no—
140C5×#102—22no—
141C5×C22⋊C8C2311yescharacteristic
142C5×C22⋊C8C2311yescharacteristic
143C5×C22⋊C8C2312yes—
144C5×#97—21no—
145C4×C5×C8—21no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95C2312yes—
149#3559C2×C511yescharacteristic, complemented
150#3109C2×C511yescharacteristic, complemented
151#3105C2×C511yescharacteristic, complemented
152#2562C2×C511yescharacteristic, complemented
153#1616C2×C512yescomplemented
154#1615C2×C512yescomplemented
155#1598C2×C512yescomplemented
156#1597C2×C512yescomplemented
157#1509C2×C511yescharacteristic, complemented
158#1502C2×C511yescharacteristic, complemented
159#1470C2×C511yescharacteristic, complemented
160C24×C5—21no—
161C5×#41—81no—
162C5×#41—81no—
163C5×#41—82no—
164C5×#41—82no—
165C2×C5×Q8—22no—
166C2×C5×Q8—21no—
167C2×C5×Q8C2×D411yescharacteristic
168C2×C5×D4—21no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—22no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—42no—
177C2×C5×D4C2×D411yescharacteristic
178C2×C5×D4C2×D412yes—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—21no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—21no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—41no—
189C22×C4×C5—41no—
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D412yes—
194C22×C4×C5C2411yescharacteristic
195C5×SD16—42no—
196C5×D8—44no—
197C5×D8—42no—
198C2×C5×C8—21no—
199C2×C5×C8—22no—
200C2×C5×C8—21no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
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⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4C2×D412yes—
222C5×C4⋊C4C2×D411yescharacteristic
223C5×C4⋊C4C2×D411yescharacteristic
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—21no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4—21no—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—44no—
237C5×C22⋊C4—41no—
238C5×C22⋊C4—41no—
239C5×C22⋊C4—82no—
240C42×C5—22no—
241C42×C5—21no—
242C42×C5—81no—
243C42×C5C2×D411yescharacteristic
244C42×C5C2×D411yescharacteristic
245C42×C5C2×D411yescharacteristic
246C42×C5C2×D411yescharacteristic
247#563—21no—
248#562—21no—
249#554—21no—
250#553—21no—
251#553—21no—
252#547—22no—
253#547—21no—
254#544—21no—
255#540—21no—
256#539—22no—
257#539C22×C512yes—
258#537C22×C512yes—
259#532C22×C511yescharacteristic
260#529C22×C511yescharacteristic
261C2×#125C22×C511yescharacteristic
262C2×C4×D4C22×C511yescharacteristic
263#484C22×C511yescharacteristic
264#481C22×C511yescharacteristic
265#481C22×C512yes—
266#478—21no—
267#476—21no—
268#463—21no—
269#459—21no—
270#450C22×C511yescharacteristic
271#447C22×C511yescharacteristic
272#447C22×C512yes—
273#442—22no—
274C4×SD16—21no—
275C4×D8—21no—
276#432C22×C511yescharacteristic
277#431C22×C511yescharacteristic
278#400C22×C512yes—
279#394C22×C512yes—
280#388—22no—
281#380—21no—
282#380—21no—
283C4×C4⋊C4C22×C511yescharacteristic
284#328C22×C512yes—
285#327C22×C512yes—
286#327C22×C512yes—
287#327C22×C512yes—
288#324C22×C512yes—
289#324C22×C512yes—
290C23×C5—22no—
291C23×C5—21no—
292C23×C5—22no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5C22×D411yescharacteristic
300C5×Q8—41no—
301C5×Q8—81no—
302C5×Q8—82no—
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—42no—
306C5×D4—41no—
307C5×D4—41no—
308C5×D4—41no—
309C5×D4—42no—
310C5×D4—41no—
311C5×D4—42no—
312C5×D4—41no—
313C5×D4—42no—
314C5×D4—81no—
315C5×D4—82no—
316C5×D4—82no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—41no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—42no—
337C2×C4×C5—82no—
338C2×C4×C5—82no—
339C2×C4×C5—82no—
340C2×C4×C5—82no—
341C2×C4×C5—82no—
342C2×C4×C5—82no—
343C2×C4×C5#12011yescharacteristic
344C2×C4×C5#12011yescharacteristic
345C2×C4×C5#12011yescharacteristic
346C2×C4×C5#12011yescharacteristic
347C2×C4×C5C22×D411yescharacteristic
348C2×C4×C5C22×D411yescharacteristic
349C5×C8—42no—
350C5×C8—41no—
351C5×C8—41no—
352C2×#41—21no—
353C2×#41—22no—
354C22×D4C23×C511yescharacteristic
355C23×C4—21no—
356C2×SD16—21no—
357C2×D8—21no—
358C2×D8—22no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8C5×D411yescharacteristic
362#127C5×D411yescharacteristic
363#126—22no—
364#126—22no—
365#126—21no—
366#125—21no—
367#125—22no—
368#125—21no—
369#125—21no—
370#125—21no—
371#125—21no—
372#125C5×D411yescharacteristic
373#124—21no—
374#124C5×D411yescharacteristic
375#123—22no—
376#123—22no—
377#123—22no—
378#123—22no—
379#123—22no—
380#123—21no—
381#123—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8C23×C511yescharacteristic
389#121—21no—
390#121—22no—
391#121—21no—
392#121—22no—
393#121—22no—
394#121—21no—
395#121—22no—
396#121C23×C511yescharacteristic
397#121C23×C512yes—
398C4×Q8C5×D411yescharacteristic
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C5×D411yescharacteristic
410C4×D4C5×D412yes—
411#117—21no—
412#117—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C5×D411yescharacteristic
417C2×C4⋊C4C5×D412yes—
418C2×C4⋊C4C5×D411yescharacteristic
419C2×C4⋊C4C23×C511yescharacteristic
420C2×C4⋊C4C23×C512yes—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C42—21no—
425C2×C42C23×C511yescharacteristic
426#107—21no—
427#106—21no—
428#106—22no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431#103—21no—
432#102—21no—
433#102—22no—
434#102—21no—
435#102—21no—
436#102—22no—
437C22⋊C8C23×C511yescharacteristic
438C22⋊C8C23×C511yescharacteristic
439C22⋊C8C23×C512yes—
440#97—21no—
441C4×C8—21no—
442#95—22no—
443#95—22no—
444#95C23×C512yes—
445C22×C5—21no—
446C22×C5—21no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—42no—
453C22×C5—42no—
454C22×C5—42no—
455C22×C5—41no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5C2×#12011yescharacteristic
461C22×C5#57611yescharacteristic
462C22×C5#57711yescharacteristic
463C4×C5—21no—
464C4×C5—21no—
465C4×C5—21no—
466C4×C5—21no—
467C4×C5—21no—
468C4×C5—42no—
469C4×C5—42no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—41no—
474C4×C5—82no—
475C4×C5—81no—
476C4×C5#45412yes—
477C24—21no—
478#41—81no—
479#41—81no—
480#41—82no—
481#41—82no—
482C2×Q8—22no—
483C2×Q8—21no—
484C2×Q8C2×C5×D411yescharacteristic
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4C2×C5×D411yescharacteristic
495C2×D4C2×C5×D412yes—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4C2×C5×D412yes—
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C2×C5×D412yes—
511C22×C4C24×C511yescharacteristic
512SD16—42no—
513D8—44no—
514D8—42no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4C2×C5×D412yes—
539C4⋊C4C2×C5×D411yescharacteristic
540C4⋊C4C2×C5×D411yescharacteristic
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—21no—
552C22⋊C4—22no—
553C22⋊C4—44no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—82no—
557C42—22no—
558C42—21no—
559C42—81no—
560C42C2×C5×D411yescharacteristic
561C42C2×C5×D411yescharacteristic
562C42C2×C5×D411yescharacteristic
563C42C2×C5×D411yescharacteristic
564C2×C5—21no—
565C2×C5—21no—
566C2×C5—81no—
567C2×C5—82no—
568C2×C5—82no—
569C2×C5#301211yescharacteristic
570C2×C5C2×#45411yescharacteristic
571C2×C5#302511yescharacteristic
572C23—22no—
573C23—21no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23C22×C5×D411yescharacteristic
582Q8—41no—
583Q8—81no—
584Q8—82no—
585D4—22no—
586D4—22no—
587D4—42no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—42no—
592D4—41no—
593D4—42no—
594D4—41no—
595D4—42no—
596D4—81no—
597D4—82no—
598D4—82no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—82no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4C5×#12011yescharacteristic
626C2×C4C5×#12011yescharacteristic
627C2×C4C5×#12011yescharacteristic
628C2×C4C5×#12011yescharacteristic
629C2×C4C22×C5×D411yescharacteristic
630C2×C4C22×C5×D411yescharacteristic
631C8—42no—
632C8—41no—
633C8—41no—
634C5#1827611yescharacteristic, direct product factor, Sylow
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—41no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22C2×C5×#12011yescharacteristic
651C22C5×#57611yescharacteristic
652C22C5×#57711yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—82no—
665C4—81no—
666C4C5×#45412yes—
667C2—21no—
668C2—21no—
669C2—82no—
670C2—81no—
671C2—82no—
672C2C5×#301211yescharacteristic
673C2C2×C5×#45411yescharacteristic
674C2C5×#302511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3559C2semidirect
2. C5×#3109C2semidirect
3. C5×#3105C2semidirect
4. C5×#2562C2semidirect
5. C5×#1616C2semidirect
6. C5×#1615C2semidirect
7. C5×#1598C2semidirect
8. C5×#1597C2semidirect
9. C5×#1509C2semidirect
10. C5×#1502C2semidirect
11. C5×#1470C2semidirect
55. #18276C5direct (N × H)
149. #3559C2×C5semidirect
150. #3109C2×C5semidirect
151. #3105C2×C5semidirect
152. #2562C2×C5semidirect
153. #1616C2×C5semidirect
154. #1615C2×C5semidirect
155. #1598C2×C5semidirect
156. #1597C2×C5semidirect
157. #1509C2×C5semidirect
158. #1502C2×C5semidirect
159. #1470C2×C5semidirect
634. C5#18276direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35592
C5×#31092
C5×#31052
C5×#25622
C5×#16162
C5×#16152
C5×#15982
C5×#15972
C5×#15092
C5×#15022
C5×#14702
#182765