Finite Group Databasebeta

← C5×#18468 #11941188

Subgroups — C5×#18468 #11941188

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic
2C5×#3234C211yesmaximal, characteristic, complemented
3C5×#3232C211yesmaximal, characteristic, complemented
4C5×#2822C211yesmaximal, characteristic, complemented
5C5×#1616C212yesmaximal, complemented
6C5×#1615C212yesmaximal, complemented
7C5×#1610C212yesmaximal, complemented
8C5×#1609C212yesmaximal, complemented
9C5×#1517C211yesmaximal, characteristic, complemented
10C5×#1512C211yesmaximal, 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×C5×#125C2211yescharacteristic
28C5×#501—21no—
29C5×#499—21no—
30C5×#490—21no—
31C5×#488—21no—
32C5×#484C2211yescharacteristic
33C5×#483C2211yescharacteristic
34C5×#481C2212yes—
35C5×#481C2211yescharacteristic
36C5×#480C2212yes—
37C5×#480C2211yescharacteristic
38C5×#479—21no—
39C5×#478—21no—
40C5×#478—22no—
41C5×#432C2211yescharacteristic
42C5×#431C2211yescharacteristic
43C5×#400—21no—
44C5×#400C2212yes—
45C5×#398—22no—
46C5×#398—21no—
47C5×#398C2212yes—
48C5×#382C2211yescharacteristic
49C5×#328C2212yes—
50C5×#327C2212yes—
51C5×#327C2212yes—
52C5×#327C2212yes—
53C5×#324C2212yes—
54C5×#324C2212yes—
55#18468C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C2×C5×#41—22no—
58C5×C4⋊Q8—21no—
59C5×C4⋊Q8—22no—
60C5×C4⋊Q8D411yescharacteristic
61C5×#127D411yescharacteristic
62C5×#126—22no—
63C5×#126—22no—
64C5×#126—21no—
65C5×#125—21no—
66C5×#125—22no—
67C5×#125—21no—
68C5×#125—21no—
69C5×#125—21no—
70C5×#125—21no—
71C5×#125—21no—
72C5×#125—21no—
73C5×#125—21no—
74C5×#125—21no—
75C5×#125D411yescharacteristic
76C5×#124—21no—
77C5×#124D411yescharacteristic
78C5×#123—22no—
79C5×#123—22no—
80C5×#123—22no—
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—21no—
84C5×#123—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8C2311yescharacteristic
92C5×#121—21no—
93C5×#121—22no—
94C5×#121—21no—
95C5×#121—22no—
96C5×#121—22no—
97C5×#121—21no—
98C5×#121—22no—
99C5×#121C2311yescharacteristic
100C5×#121C2312yes—
101C4×C5×Q8D411yescharacteristic
102C4×C5×D4—22no—
103C4×C5×D4—21no—
104C4×C5×D4—21no—
105C4×C5×D4—21no—
106C4×C5×D4—22no—
107C4×C5×D4—21no—
108C4×C5×D4D411yescharacteristic
109C4×C5×D4D412yes—
110C5×#117—21no—
111C5×#117—21no—
112C2×C5×C4⋊C4—22no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—22no—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4D412yes—
120C2×C5×C4⋊C4D411yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C4⋊C4C2311yescharacteristic
123C2×C5×C4⋊C4C2312yes—
124C2×C42×C5C2311yescharacteristic
125C5×#107—22no—
126C5×#107—21no—
127C5×#107—21no—
128C5×#106—22no—
129C5×#106—21no—
130C5×#106—21no—
131C5×C4⋊C8—21no—
132C5×C4⋊C8—21no—
133C5×#103—21no—
134C5×#103—21no—
135C5×#102—21no—
136C5×#102—22no—
137C5×#102—21no—
138C5×#102—22no—
139C5×C22⋊C8C2311yescharacteristic
140C5×C22⋊C8C2311yescharacteristic
141C5×C22⋊C8C2312yes—
142C5×#97—21no—
143C4×C5×C8—21no—
144C5×#95—21no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95C2312yes—
149#3559C2×C511yescharacteristic
150#3234C2×C511yescharacteristic, complemented
151#3232C2×C511yescharacteristic, complemented
152#2822C2×C511yescharacteristic, complemented
153#1616C2×C512yescomplemented
154#1615C2×C512yescomplemented
155#1610C2×C512yescomplemented
156#1609C2×C512yescomplemented
157#1517C2×C511yescharacteristic, complemented
158#1512C2×C511yescharacteristic, complemented
159#1470C2×C511yescharacteristic, complemented
160C5×#41—81no—
161C5×#41—81no—
162C5×#41—82no—
163C5×#41—82no—
164C2×C5×Q8—22no—
165C2×C5×Q8—21no—
166C2×C5×Q8C2×D411yescharacteristic
167C2×C5×D4—21no—
168C2×C5×D4—22no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4C2×D411yescharacteristic
174C2×C5×D4C2×D412yes—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—21no—
179C22×C4×C5—22no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—22no—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D412yes—
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2411yescharacteristic
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—41no—
213C5×C4⋊C4—41no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4—41no—
216C5×C4⋊C4—81no—
217C5×C4⋊C4—82no—
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—21no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—21no—
232C5×C22⋊C4—22no—
233C42×C5—22no—
234C42×C5—21no—
235C42×C5C2×D411yescharacteristic
236C42×C5C2×D411yescharacteristic
237C42×C5C2×D411yescharacteristic
238C42×C5C2×D411yescharacteristic
239#563—21no—
240#562—21no—
241#554—21no—
242#553—21no—
243#553—21no—
244#547—22no—
245#547—21no—
246#544—21no—
247#540—21no—
248#539—22no—
249#539C22×C512yes—
250#537C22×C512yes—
251#532C22×C511yescharacteristic
252#529C22×C511yescharacteristic
253C2×#125C22×C511yescharacteristic
254C2×#125C22×C511yescharacteristic
255#501—21no—
256#499—21no—
257#490—21no—
258#488—21no—
259#484C22×C511yescharacteristic
260#483C22×C511yescharacteristic
261#481C22×C512yes—
262#481C22×C511yescharacteristic
263#480C22×C512yes—
264#480C22×C511yescharacteristic
265#479—21no—
266#478—21no—
267#478—22no—
268#432C22×C511yescharacteristic
269#431C22×C511yescharacteristic
270#400—21no—
271#400C22×C512yes—
272#398—21no—
273#398—22no—
274#398C22×C512yes—
275#382C22×C511yescharacteristic
276#328C22×C512yes—
277#327C22×C512yes—
278#327C22×C512yes—
279#327C22×C512yes—
280#324C22×C512yes—
281#324C22×C512yes—
282C23×C5—21no—
283C23×C5—22no—
284C23×C5C22×D411yescharacteristic
285C5×Q8—41no—
286C5×Q8—81no—
287C5×Q8—82no—
288C5×D4—42no—
289C5×D4—41no—
290C5×D4—42no—
291C5×D4—42no—
292C5×D4—41no—
293C5×D4—42no—
294C5×D4—41no—
295C5×D4—81no—
296C5×D4—82no—
297C5×D4—82no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—21no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—42no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—82no—
321C2×C4×C5—82no—
322C2×C4×C5—82no—
323C2×C4×C5—82no—
324C2×C4×C5#12011yescharacteristic
325C2×C4×C5#12011yescharacteristic
326C2×C4×C5#12011yescharacteristic
327C2×C4×C5#12011yescharacteristic
328C2×C4×C5C22×D411yescharacteristic
329C2×C4×C5C22×D411yescharacteristic
330C5×C8—42no—
331C5×C8—41no—
332C5×C8—41no—
333C2×#41—21no—
334C2×#41—22no—
335C4⋊Q8—21no—
336C4⋊Q8—22no—
337C4⋊Q8C5×D411yescharacteristic
338#127C5×D411yescharacteristic
339#126—22no—
340#126—22no—
341#126—21no—
342#125—21no—
343#125—22no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125—21no—
348#125—21no—
349#125—21no—
350#125—21no—
351#125—21no—
352#125C5×D411yescharacteristic
353#124—21no—
354#124C5×D411yescharacteristic
355#123—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359#123—22no—
360#123—21no—
361#123—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8C23×C511yescharacteristic
369#121—21no—
370#121—22no—
371#121—21no—
372#121—22no—
373#121—22no—
374#121—21no—
375#121—22no—
376#121C23×C511yescharacteristic
377#121C23×C512yes—
378C4×Q8C5×D411yescharacteristic
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4C5×D411yescharacteristic
386C4×D4C5×D412yes—
387#117—21no—
388#117—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4C5×D411yescharacteristic
396C2×C4⋊C4C5×D412yes—
397C2×C4⋊C4C5×D411yescharacteristic
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C4⋊C4C23×C512yes—
401C2×C42C23×C511yescharacteristic
402#107—22no—
403#107—21no—
404#107—21no—
405#106—22no—
406#106—21no—
407#106—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—22no—
414#102—21no—
415#102—22no—
416C22⋊C8C23×C511yescharacteristic
417C22⋊C8C23×C511yescharacteristic
418C22⋊C8C23×C512yes—
419#97—21no—
420C4×C8—21no—
421#95—21no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95C23×C512yes—
426C22×C5—21no—
427C22×C5—21no—
428C22×C5—42no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—42no—
432C22×C5—42no—
433C22×C5—41no—
434C22×C5C2×#12011yescharacteristic
435C22×C5#57611yescharacteristic
436C22×C5#57711yescharacteristic
437C4×C5—21no—
438C4×C5—21no—
439C4×C5—21no—
440C4×C5—21no—
441C4×C5—21no—
442C4×C5—21no—
443C4×C5—42no—
444C4×C5—42no—
445C4×C5—41no—
446C4×C5—41no—
447C4×C5—42no—
448C4×C5—41no—
449C4×C5—82no—
450C4×C5—81no—
451C4×C5—81no—
452#41—81no—
453#41—81no—
454#41—82no—
455#41—82no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8C2×C5×D411yescharacteristic
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4C2×C5×D411yescharacteristic
466C2×D4C2×C5×D412yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4C2×C5×D412yes—
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D412yes—
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C24×C511yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—81no—
509C4⋊C4—82no—
510C4⋊C4C2×C5×D412yes—
511C4⋊C4C2×C5×D411yescharacteristic
512C4⋊C4C2×C5×D411yescharacteristic
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C42—22no—
526C42—21no—
527C42C2×C5×D411yescharacteristic
528C42C2×C5×D411yescharacteristic
529C42C2×C5×D411yescharacteristic
530C42C2×C5×D411yescharacteristic
531C2×C5—21no—
532C2×C5—21no—
533C2×C5—81no—
534C2×C5—82no—
535C2×C5#301211yescharacteristic
536C2×C5#302011yescharacteristic
537C2×C5#302811yescharacteristic
538C23—21no—
539C23—22no—
540C23C22×C5×D411yescharacteristic
541Q8—41no—
542Q8—81no—
543Q8—82no—
544D4—42no—
545D4—41no—
546D4—42no—
547D4—42no—
548D4—41no—
549D4—42no—
550D4—41no—
551D4—81no—
552D4—82no—
553D4—82no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4C5×#12011yescharacteristic
581C2×C4C5×#12011yescharacteristic
582C2×C4C5×#12011yescharacteristic
583C2×C4C5×#12011yescharacteristic
584C2×C4C22×C5×D411yescharacteristic
585C2×C4C22×C5×D411yescharacteristic
586C8—42no—
587C8—41no—
588C8—41no—
589C5#1846811yescharacteristic, direct product factor, Sylow
590C22—21no—
591C22—21no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22C2×C5×#12011yescharacteristic
599C22C5×#57611yescharacteristic
600C22C5×#57711yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—82no—
614C4—81no—
615C4—81no—
616C2—21no—
617C2—21no—
618C2—81no—
619C2—82no—
620C2C5×#301211yescharacteristic
621C2C5×#302011yescharacteristic
622C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3559C2
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
2. C5×#3234C2semidirect
3. C5×#3232C2semidirect
4. C5×#2822C2semidirect
5. C5×#1616C2semidirect
6. C5×#1615C2semidirect
7. C5×#1610C2semidirect
8. C5×#1609C2semidirect
9. C5×#1517C2semidirect
10. C5×#1512C2semidirect
11. C5×#1470C2semidirect
55. #18468C5direct (N × H)
150. #3234C2×C5semidirect
151. #3232C2×C5semidirect
152. #2822C2×C5semidirect
153. #1616C2×C5semidirect
154. #1615C2×C5semidirect
155. #1610C2×C5semidirect
156. #1609C2×C5semidirect
157. #1517C2×C5semidirect
158. #1512C2×C5semidirect
159. #1470C2×C5semidirect
589. C5#18468direct (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×#32342
C5×#32322
C5×#28222
C5×#16162
C5×#16152
C5×#16102
C5×#16092
C5×#15172
C5×#15122
C5×#14702
#184685