Finite Group Databasebeta

← C5×#18467 #11941187

Subgroups — C5×#18467 #11941187

Order 1280.

890 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3561C211yesmaximal, characteristic
2C5×#3236C211yesmaximal, characteristic, complemented
3C5×#3232C211yesmaximal, characteristic, complemented
4C5×#2820C211yesmaximal, characteristic, complemented
5C5×#1618C212yesmaximal, complemented
6C5×#1614C212yesmaximal, complemented
7C5×#1612C212yesmaximal, complemented
8C5×#1608C212yesmaximal, complemented
9C5×#1518C211yesmaximal, characteristic, complemented
10C5×#1512C211yesmaximal, characteristic, complemented
11C5×#1469C211yesmaximal, characteristic, complemented
12C5×#563—21no—
13C5×#562—21no—
14C5×#556—21no—
15C5×#551—22no—
16C5×D4×Q8—21no—
17C5×#548—21no—
18C5×#546—21no—
19C5×#543C2212yes—
20C5×#542—21no—
21C5×#542—22no—
22C5×#538C2212yes—
23C5×#536—21no—
24C5×#533C2211yescharacteristic
25C5×#529C2211yescharacteristic
26C2×C5×#125C2211yescharacteristic
27C2×C5×#124C2211yescharacteristic
28C5×#501—21no—
29C5×#499—21no—
30C5×#491—21no—
31C5×#488—21no—
32C5×#484C2211yescharacteristic
33C5×#484C2212yes—
34C5×#483C2211yescharacteristic
35C5×#483C2212yes—
36C5×#481C2211yescharacteristic
37C5×#480C2211yescharacteristic
38C5×#479—21no—
39C5×#479—22no—
40C5×#478—21no—
41C5×#432C2211yescharacteristic
42C5×#431C2211yescharacteristic
43C5×#399C2212yes—
44C5×#397C2212yes—
45C5×#396—22no—
46C5×#395—21no—
47C5×#394—21no—
48C5×#382C2211yescharacteristic
49C5×#328C2212yes—
50C5×#328C2212yes—
51C5×#328C2212yes—
52C5×#327C2212yes—
53C5×#323C2212yes—
54C5×#323C2212yes—
55#18467C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8D411yescharacteristic
59C22×C5×D4D411yescharacteristic
60C5×C4⋊Q8—21no—
61C5×C4⋊Q8—22no—
62C5×C4⋊Q8D411yescharacteristic
63C5×C4⋊Q8D411yescharacteristic
64C5×#126—22no—
65C5×#126—22no—
66C5×#126—22no—
67C5×#126—21no—
68C5×#125—21no—
69C5×#125—21no—
70C5×#125—21no—
71C5×#125—21no—
72C5×#125—21no—
73C5×#125D411yescharacteristic
74C5×#124—21no—
75C5×#124—22no—
76C5×#124—22no—
77C5×#124—21no—
78C5×#124—21no—
79C5×#124—21no—
80C5×#124—21no—
81C5×#124D411yescharacteristic
82C5×#123—22no—
83C5×#123—22no—
84C5×#123—22no—
85C5×#123—21no—
86C5×#123—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—21no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8C2311yescharacteristic
97C5×C22⋊Q8C2312yes—
98C5×#121—21no—
99C5×#121—22no—
100C5×#121—22no—
101C5×#121C2311yescharacteristic
102C5×#120—22no—
103C4×C5×Q8—21no—
104C4×C5×Q8—21no—
105C4×C5×Q8D411yescharacteristic
106C4×C5×Q8D412yes—
107C4×C5×D4—21no—
108C4×C5×D4—22no—
109C4×C5×D4—21no—
110C4×C5×D4—22no—
111C4×C5×D4D411yescharacteristic
112C5×#117—22no—
113C5×#117—21no—
114C5×#117—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4—22no—
119C2×C5×C4⋊C4C2311yescharacteristic
120C2×C5×C4⋊C4C2311yescharacteristic
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4D412yes—
125C2×C5×C22⋊C4C2312yes—
126C2×C42×C5C2311yescharacteristic
127C5×#107—21no—
128C5×#107—21no—
129C5×#107—22no—
130C5×#106—21no—
131C5×#106—21no—
132C5×#106—22no—
133C5×C4⋊C8—21no—
134C5×C4⋊C8—21no—
135C5×#103—21no—
136C5×#103—22no—
137C5×#103—21no—
138C5×#103—22no—
139C5×#102—21no—
140C5×#102—21no—
141C5×C22⋊C8C2312yes—
142C5×C22⋊C8C2311yescharacteristic
143C5×C22⋊C8C2311yescharacteristic
144C5×#97—21no—
145C4×C5×C8—21no—
146C5×#95—21no—
147C5×#95—22no—
148C5×#95C2312yes—
149#3561C2×C511yescharacteristic
150#3236C2×C511yescharacteristic, complemented
151#3232C2×C511yescharacteristic, complemented
152#2820C2×C511yescharacteristic, complemented
153#1618C2×C512yescomplemented
154#1614C2×C512yescomplemented
155#1612C2×C512yescomplemented
156#1608C2×C512yescomplemented
157#1518C2×C511yescharacteristic, complemented
158#1512C2×C511yescharacteristic, complemented
159#1469C2×C511yescharacteristic, complemented
160C24×C5C2×D412yes—
161C5×#41—82no—
162C2×C5×Q8—22no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—81no—
167C2×C5×Q8—82no—
168C2×C5×Q8C2×D411yescharacteristic
169C2×C5×Q8C2×D412yes—
170C2×C5×D4—21no—
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—81no—
176C2×C5×D4C2×D411yescharacteristic
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—22no—
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—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—41no—
209C5×C4⋊C4—41no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4—81no—
213C5×C4⋊C4—82no—
214C5×C4⋊C4C2×D411yescharacteristic
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D412yes—
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—21no—
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—22no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—21no—
232C5×C22⋊C4—82no—
233C5×C22⋊C4—82no—
234C42×C5—22no—
235C42×C5—22no—
236C42×C5—21no—
237C42×C5C2×D411yescharacteristic
238C42×C5C2×D411yescharacteristic
239C42×C5C2×D411yescharacteristic
240C42×C5C2×D411yescharacteristic
241#563—21no—
242#562—21no—
243#556—21no—
244#551—22no—
245D4×Q8—21no—
246#548—21no—
247#546—21no—
248#543C22×C512yes—
249#542—21no—
250#542—22no—
251#538C22×C512yes—
252#536—21no—
253#533C22×C511yescharacteristic
254#529C22×C511yescharacteristic
255C2×#125C22×C511yescharacteristic
256C2×#124C22×C511yescharacteristic
257#501—21no—
258#499—21no—
259#491—21no—
260#488—21no—
261#484C22×C511yescharacteristic
262#484C22×C512yes—
263#483C22×C511yescharacteristic
264#483C22×C512yes—
265#481C22×C511yescharacteristic
266#480C22×C511yescharacteristic
267#479—21no—
268#479—22no—
269#478—21no—
270#432C22×C511yescharacteristic
271#431C22×C511yescharacteristic
272#399C22×C512yes—
273#397C22×C512yes—
274#396—22no—
275#395—21no—
276#394—21no—
277#382C22×C511yescharacteristic
278#328C22×C512yes—
279#328C22×C512yes—
280#328C22×C512yes—
281#327C22×C512yes—
282#323C22×C512yes—
283#323C22×C512yes—
284C23×C5—22no—
285C23×C5—21no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—42no—
289C23×C5—42no—
290C23×C5C22×D411yescharacteristic
291C5×Q8—41no—
292C5×Q8—42no—
293C5×Q8—42no—
294C5×Q8—42no—
295C5×Q8—81no—
296C5×Q8—82no—
297C5×D4—41no—
298C5×D4—42no—
299C5×D4—41no—
300C5×D4—41no—
301C5×D4—81no—
302C5×D4—82no—
303C5×D4—82no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—42no—
323C2×C4×C5—41no—
324C2×C4×C5—82no—
325C2×C4×C5—82no—
326C2×C4×C5—82no—
327C2×C4×C5#12011yescharacteristic
328C2×C4×C5#12011yescharacteristic
329C2×C4×C5#12011yescharacteristic
330C2×C4×C5#12011yescharacteristic
331C2×C4×C5C22×D411yescharacteristic
332C2×C4×C5C22×D411yescharacteristic
333C5×C8—41no—
334C5×C8—41no—
335C5×C8—42no—
336C2×#41—21no—
337C22×Q8—21no—
338C22×Q8C5×D411yescharacteristic
339C22×D4C5×D411yescharacteristic
340C4⋊Q8—21no—
341C4⋊Q8—22no—
342C4⋊Q8C5×D411yescharacteristic
343C4⋊Q8C5×D411yescharacteristic
344#126—22no—
345#126—22no—
346#126—22no—
347#126—21no—
348#125—21no—
349#125—21no—
350#125—21no—
351#125—21no—
352#125—21no—
353#125C5×D411yescharacteristic
354#124—21no—
355#124—22no—
356#124—22no—
357#124—21no—
358#124—21no—
359#124—21no—
360#124—21no—
361#124C5×D411yescharacteristic
362#123—22no—
363#123—22no—
364#123—22no—
365#123—21no—
366#123—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8C23×C511yescharacteristic
377C22⋊Q8C23×C512yes—
378#121—21no—
379#121—22no—
380#121—22no—
381#121C23×C511yescharacteristic
382#120—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C5×D411yescharacteristic
386C4×Q8C5×D412yes—
387C4×D4—21no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—22no—
391C4×D4C5×D411yescharacteristic
392#117—22no—
393#117—21no—
394#117—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4C5×D412yes—
405C2×C22⋊C4C23×C512yes—
406C2×C42C23×C511yescharacteristic
407#107—21no—
408#107—21no—
409#107—22no—
410#106—21no—
411#106—21no—
412#106—22no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415#103—21no—
416#103—22no—
417#103—21no—
418#103—22no—
419#102—21no—
420#102—21no—
421C22⋊C8C23×C512yes—
422C22⋊C8C23×C511yescharacteristic
423C22⋊C8C23×C511yescharacteristic
424#97—21no—
425C4×C8—21no—
426#95—21no—
427#95—22no—
428#95C23×C512yes—
429C22×C5—21no—
430C22×C5—21no—
431C22×C5—41no—
432C22×C5—42no—
433C22×C5—41no—
434C22×C5—42no—
435C22×C5—42no—
436C22×C5—41no—
437C22×C5—82no—
438C22×C5—82no—
439C22×C5C2×#12011yescharacteristic
440C22×C5#57711yescharacteristic
441C22×C5#57811yescharacteristic
442C4×C5—21no—
443C4×C5—21no—
444C4×C5—21no—
445C4×C5—21no—
446C4×C5—21no—
447C4×C5—21no—
448C4×C5—41no—
449C4×C5—41no—
450C4×C5—42no—
451C4×C5—42no—
452C4×C5—41no—
453C4×C5—42no—
454C4×C5—82no—
455C4×C5—81no—
456C4×C5—81no—
457C24C2×C5×D412yes—
458#41—82no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—81no—
464C2×Q8—82no—
465C2×Q8C2×C5×D411yescharacteristic
466C2×Q8C2×C5×D412yes—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—81no—
473C2×D4C2×C5×D411yescharacteristic
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4C2×C5×D411yescharacteristic
482C22×C4C2×C5×D412yes—
483C22×C4C2×C5×D411yescharacteristic
484C22×C4C24×C511yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—81no—
510C4⋊C4—82no—
511C4⋊C4C2×C5×D411yescharacteristic
512C4⋊C4C2×C5×D411yescharacteristic
513C4⋊C4C2×C5×D412yes—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4—82no—
530C22⋊C4—82no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42C2×C5×D411yescharacteristic
535C42C2×C5×D411yescharacteristic
536C42C2×C5×D411yescharacteristic
537C42C2×C5×D411yescharacteristic
538C2×C5—21no—
539C2×C5—21no—
540C2×C5—81no—
541C2×C5—82no—
542C2×C5#301311yescharacteristic
543C2×C5#301911yescharacteristic
544C2×C5#302811yescharacteristic
545C23—22no—
546C23—21no—
547C23—22no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23C22×C5×D411yescharacteristic
552Q8—41no—
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—81no—
557Q8—82no—
558D4—41no—
559D4—42no—
560D4—41no—
561D4—41no—
562D4—81no—
563D4—82no—
564D4—82no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4C5×#12011yescharacteristic
589C2×C4C5×#12011yescharacteristic
590C2×C4C5×#12011yescharacteristic
591C2×C4C5×#12011yescharacteristic
592C2×C4C22×C5×D411yescharacteristic
593C2×C4C22×C5×D411yescharacteristic
594C8—41no—
595C8—41no—
596C8—42no—
597C5#1846711yescharacteristic, direct product factor, Sylow
598C22—21no—
599C22—21no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—41no—
606C22—82no—
607C22—82no—
608C22C2×C5×#12011yescharacteristic
609C22C5×#57711yescharacteristic
610C22C5×#57811yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—42no—
620C4—42no—
621C4—41no—
622C4—42no—
623C4—82no—
624C4—81no—
625C4—81no—
626C2—21no—
627C2—21no—
628C2—82no—
629C2—81no—
630C2C5×#301311yescharacteristic
631C2C5×#301911yescharacteristic
632C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3561C2
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×#3236C2semidirect
3. C5×#3232C2semidirect
4. C5×#2820C2semidirect
5. C5×#1618C2semidirect
6. C5×#1614C2semidirect
7. C5×#1612C2semidirect
8. C5×#1608C2semidirect
9. C5×#1518C2semidirect
10. C5×#1512C2semidirect
11. C5×#1469C2semidirect
55. #18467C5direct (N × H)
150. #3236C2×C5semidirect
151. #3232C2×C5semidirect
152. #2820C2×C5semidirect
153. #1618C2×C5semidirect
154. #1614C2×C5semidirect
155. #1612C2×C5semidirect
156. #1608C2×C5semidirect
157. #1518C2×C5semidirect
158. #1512C2×C5semidirect
159. #1469C2×C5semidirect
597. C5#18467direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35612
C5×#32362
C5×#32322
C5×#28202
C5×#16182
C5×#16142
C5×#16122
C5×#16082
C5×#15182
C5×#15122
C5×#14692
#184675