Finite Group Databasebeta

← C5×#19246 #11941966

Subgroups — C5×#19246 #11941966

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3248C211yesmaximal, characteristic, complemented
2C5×#3212C211yesmaximal, characteristic
3C5×#3182C211yesmaximal, characteristic, complemented
4C5×#2969C211yesmaximal, characteristic, complemented
5C5×#1701C211yesmaximal, characteristic, complemented
6C5×#1699C211yesmaximal, characteristic, complemented
7C5×#1694C211yesmaximal, characteristic, complemented
8C5×#1686C211yesmaximal, characteristic, complemented
9C5×#1682C211yesmaximal, characteristic, complemented
10C5×#1680C211yesmaximal, characteristic, complemented
11C5×#1673C211yesmaximal, characteristic, complemented
12C5×#1665C211yesmaximal, characteristic, complemented
13C5×#1565C211yesmaximal, characteristic, complemented
14C5×#1544C211yesmaximal, characteristic, complemented
15C5×#1540C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C5×#532C2211yescharacteristic
18C5×#529C2211yescharacteristic
19C5×#500C2211yescharacteristic
20C5×#495—21no—
21C5×#492C2211yescharacteristic
22C5×#488—21no—
23C5×#487C2211yescharacteristic
24C5×#486C2211yescharacteristic
25C5×#479—21no—
26C5×#475C2211yescharacteristic
27C5×#474C2211yescharacteristic
28C5×#468—21no—
29C5×#468—21no—
30C5×#467—21no—
31C5×#465—21no—
32C5×#464—21no—
33C5×#462C2211yescharacteristic
34C5×#462C2211yescharacteristic
35C5×#461C2211yescharacteristic
36C5×#461C2211yescharacteristic
37C5×#460C2211yescharacteristic
38C5×#459C2211yescharacteristic
39C5×#452—21no—
40C5×#449—21no—
41C5×#446C2211yescharacteristic
42C5×C8×Q8C2211yescharacteristic
43C5×#440—21no—
44C5×#440—21no—
45C5×#436—21no—
46C5×#436C2211yescharacteristic
47C5×#435—21no—
48C5×C8×D4C2211yescharacteristic
49C5×#433—21no—
50C5×#431C2211yescharacteristic
51C5×#431C2211yescharacteristic
52C2×C5×C4⋊C8C2211yescharacteristic
53C5×#405—21no—
54C4×C5×M16C2211yescharacteristic
55C5×#335C2211yescharacteristic
56C5×#335C2211yescharacteristic
57C5×#334C2211yescharacteristic
58C5×#334C2211yescharacteristic
59C5×#332C2211yescharacteristic
60C5×#332C2211yescharacteristic
61C5×#332C2211yescharacteristic
62C5×#332C2211yescharacteristic
63C5×#332C2211yescharacteristic
64C5×#332C2211yescharacteristic
65C5×#331C2211yescharacteristic
66C5×#331C2211yescharacteristic
67#19246C511yesmaximal, characteristic, direct product factor, Sylow
68C2×C5×#41—21no—
69C2×C5×Q16—21no—
70C2×C5×Q16—21no—
71C2×C5×SD16—21no—
72C2×C5×SD16—21no—
73C2×C5×SD16—21no—
74C2×C5×SD16—21no—
75C2×C5×SD16—21no—
76C2×C5×D8—21no—
77C2×C5×M16—21no—
78C2×C5×M16D411yescharacteristic
79C2×C5×M16D411yescharacteristic
80C22×C5×C8—21no—
81C22×C5×C8—21no—
82C5×C4⋊Q8C2311yescharacteristic
83C5×C4⋊Q8C2311yescharacteristic
84C5×C4⋊Q8C2311yescharacteristic
85C5×#127C2311yescharacteristic
86C5×#126—21no—
87C5×#125—21no—
88C5×#125D411yescharacteristic
89C5×#124—21no—
90C5×#124D411yescharacteristic
91C5×#123—21no—
92C5×C22⋊Q8—21no—
93C5×C22⋊Q8—21no—
94C5×C22⋊Q8D411yescharacteristic
95C5×#121—21no—
96C5×#121—21no—
97C5×#121D411yescharacteristic
98C4×C5×Q8—21no—
99C4×C5×Q8—21no—
100C4×C5×Q8C2311yescharacteristic
101C4×C5×D4—21no—
102C4×C5×D4—21no—
103C4×C5×D4—21no—
104C4×C5×D4C2311yescharacteristic
105C5×#117—21no—
106C5×#117—21no—
107C2×C42×C5C2311yescharacteristic
108C5×#107—21no—
109C5×#107—21no—
110C5×#107—21no—
111C5×#106—21no—
112C5×C4⋊C8—21no—
113C5×C4⋊C8—21no—
114C5×C4⋊C8—21no—
115C5×C4⋊C8C2311yescharacteristic
116C5×C4⋊C8C2311yescharacteristic
117C5×C4⋊C8C2311yescharacteristic
118C5×C4⋊C8C2311yescharacteristic
119C5×C4⋊C8C2311yescharacteristic
120C5×C4⋊C8C2311yescharacteristic
121C5×#103—21no—
122C5×#103—21no—
123C5×#103—21no—
124C5×#103—21no—
125C5×#103—21no—
126C5×#103—21no—
127C5×#103—21no—
128C5×#102—21no—
129C5×#102—21no—
130C5×#102—21no—
131C5×#102—21no—
132C5×#102—21no—
133C5×C22⋊C8—21no—
134C5×C22⋊C8—21no—
135C5×C22⋊C8—21no—
136C5×C22⋊C8—21no—
137C5×#97—21no—
138C5×#97D411yescharacteristic
139C5×#97D411yescharacteristic
140C4×C5×C8—21no—
141C4×C5×C8—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3248C2×C511yescharacteristic, complemented
146#3212C2×C511yescharacteristic
147#3182C2×C511yescharacteristic, complemented
148#2969C2×C511yescharacteristic, complemented
149#1701C2×C511yescharacteristic, complemented
150#1699C2×C511yescharacteristic, complemented
151#1694C2×C511yescharacteristic, complemented
152#1686C2×C511yescharacteristic, complemented
153#1682C2×C511yescharacteristic, complemented
154#1680C2×C511yescharacteristic, complemented
155#1673C2×C511yescharacteristic, complemented
156#1665C2×C511yescharacteristic, complemented
157#1565C2×C511yescharacteristic, complemented
158#1544C2×C511yescharacteristic, complemented
159#1540C2×C511yescharacteristic, complemented
160C5×#41—81no—
161C5×#41—81no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—41no—
171C2×C5×D4C2×D411yescharacteristic
172C22×C4×C5—21no—
173C22×C4×C5—41no—
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5#4111yescharacteristic
177C5×Q16—81no—
178C5×Q16—81no—
179C5×SD16—42no—
180C5×SD16—42no—
181C5×SD16—81no—
182C5×SD16—81no—
183C5×SD16—81no—
184C5×D8—81no—
185C5×M16—22no—
186C5×M16—41no—
187C5×M16—42no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—42no—
195C2×C5×C8—81no—
196C2×C5×C8C2×D411yescharacteristic
197C2×C5×C8C2×D411yescharacteristic
198C2×C5×C8C2×D411yescharacteristic
199C2×C5×C8C2×D411yescharacteristic
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4C2×D411yescharacteristic
213C5×C4⋊C4C2×D411yescharacteristic
214C5×C22⋊C4—21no—
215C5×C22⋊C4—21no—
216C5×C22⋊C4—21no—
217C5×C22⋊C4—21no—
218C5×C22⋊C4—21no—
219C5×C22⋊C4—41no—
220C5×C22⋊C4—41no—
221C5×C22⋊C4—41no—
222C42×C5—21no—
223C42×C5—41no—
224C42×C5C2×D411yescharacteristic
225C42×C5C2×D411yescharacteristic
226C42×C5#4111yescharacteristic
227C42×C5C2411yescharacteristic
228#533C22×C511yescharacteristic
229#532C22×C511yescharacteristic
230#529C22×C511yescharacteristic
231#500C22×C511yescharacteristic
232#495—21no—
233#492C22×C511yescharacteristic
234#488—21no—
235#487C22×C511yescharacteristic
236#486C22×C511yescharacteristic
237#479—21no—
238#475C22×C511yescharacteristic
239#474C22×C511yescharacteristic
240#468—21no—
241#468—21no—
242#467—21no—
243#465—21no—
244#464—21no—
245#462C22×C511yescharacteristic
246#462C22×C511yescharacteristic
247#461C22×C511yescharacteristic
248#461C22×C511yescharacteristic
249#460C22×C511yescharacteristic
250#459C22×C511yescharacteristic
251#452—21no—
252#449—21no—
253#446C22×C511yescharacteristic
254C8×Q8C22×C511yescharacteristic
255#440—21no—
256#440—21no—
257#436—21no—
258#436C22×C511yescharacteristic
259#435—21no—
260C8×D4C22×C511yescharacteristic
261#433—21no—
262#431C22×C511yescharacteristic
263#431C22×C511yescharacteristic
264C2×C4⋊C8C22×C511yescharacteristic
265#405—21no—
266C4×M16C22×C511yescharacteristic
267#335C22×C511yescharacteristic
268#335C22×C511yescharacteristic
269#334C22×C511yescharacteristic
270#334C22×C511yescharacteristic
271#332C22×C511yescharacteristic
272#332C22×C511yescharacteristic
273#332C22×C511yescharacteristic
274#332C22×C511yescharacteristic
275#332C22×C511yescharacteristic
276#332C22×C511yescharacteristic
277#331C22×C511yescharacteristic
278#331C22×C511yescharacteristic
279C23×C5—21no—
280C23×C5—41no—
281C23×C5#12111yescharacteristic
282C5×Q8—21no—
283C5×Q8—21no—
284C5×Q8—41no—
285C5×Q8—41no—
286C5×Q8—41no—
287C5×Q8—41no—
288C5×Q8—41no—
289C5×Q8—41no—
290C5×D4—21no—
291C5×D4—21no—
292C5×D4—41no—
293C5×D4—41no—
294C5×D4—41no—
295C5×D4—41no—
296C5×D4—81no—
297C5×D4—81no—
298C5×D4—82no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—82no—
313C2×C4×C5#12111yescharacteristic
314C2×C4×C5#12111yescharacteristic
315C2×C4×C5#12111yescharacteristic
316C2×C4×C5C22×D411yescharacteristic
317C2×C4×C5C22×D411yescharacteristic
318C2×C4×C5C2×#4111yescharacteristic
319C5×C8—21no—
320C5×C8—21no—
321C5×C8—21no—
322C5×C8—41no—
323C5×C8—41no—
324C5×C8—41no—
325C5×C8—41no—
326C5×C8—41no—
327C5×C8—41no—
328C5×C8#13512yes—
329C2×#41—21no—
330C2×Q16—21no—
331C2×Q16—21no—
332C2×SD16—21no—
333C2×SD16—21no—
334C2×SD16—21no—
335C2×SD16—21no—
336C2×SD16—21no—
337C2×D8—21no—
338C2×M16—21no—
339C2×M16C5×D411yescharacteristic
340C2×M16C5×D411yescharacteristic
341C22×C8—21no—
342C22×C8—21no—
343C4⋊Q8C23×C511yescharacteristic
344C4⋊Q8C23×C511yescharacteristic
345C4⋊Q8C23×C511yescharacteristic
346#127C23×C511yescharacteristic
347#126—21no—
348#125—21no—
349#125C5×D411yescharacteristic
350#124—21no—
351#124C5×D411yescharacteristic
352#123—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8C5×D411yescharacteristic
356#121—21no—
357#121—21no—
358#121C5×D411yescharacteristic
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C23×C511yescharacteristic
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C23×C511yescharacteristic
366#117—21no—
367#117—21no—
368C2×C42C23×C511yescharacteristic
369#107—21no—
370#107—21no—
371#107—21no—
372#106—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8C23×C511yescharacteristic
377C4⋊C8C23×C511yescharacteristic
378C4⋊C8C23×C511yescharacteristic
379C4⋊C8C23×C511yescharacteristic
380C4⋊C8C23×C511yescharacteristic
381C4⋊C8C23×C511yescharacteristic
382#103—21no—
383#103—21no—
384#103—21no—
385#103—21no—
386#103—21no—
387#103—21no—
388#103—21no—
389#102—21no—
390#102—21no—
391#102—21no—
392#102—21no—
393#102—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398#97—21no—
399#97C5×D411yescharacteristic
400#97C5×D411yescharacteristic
401C4×C8—21no—
402C4×C8—21no—
403C4×C8—21no—
404C4×C8C23×C511yescharacteristic
405C4×C8C23×C511yescharacteristic
406C22×C5—21no—
407C22×C5—21no—
408C22×C5—21no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—81no—
413C22×C5—81no—
414C22×C5—81no—
415C22×C5C2×#12111yescharacteristic
416C4×C5—21no—
417C4×C5—21no—
418C4×C5—21no—
419C4×C5—21no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—81no—
424C4×C5—81no—
425C4×C5—81no—
426C4×C5C2×#13511yescharacteristic
427C4×C5#57511yescharacteristic
428C4×C5#57611yescharacteristic
429C4×C5#57711yescharacteristic
430#41—81no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×C5×D411yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4C2×C5×D411yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C5×#4111yescharacteristic
447Q16—81no—
448Q16—81no—
449SD16—42no—
450SD16—42no—
451SD16—81no—
452SD16—81no—
453SD16—81no—
454D8—81no—
455M16—22no—
456M16—41no—
457M16—42no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8—81no—
466C2×C8C2×C5×D411yescharacteristic
467C2×C8C2×C5×D411yescharacteristic
468C2×C8C2×C5×D411yescharacteristic
469C2×C8C2×C5×D411yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×C5×D411yescharacteristic
483C4⋊C4C2×C5×D411yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—41no—
494C42C2×C5×D411yescharacteristic
495C42C2×C5×D411yescharacteristic
496C42C5×#4111yescharacteristic
497C42C24×C511yescharacteristic
498C2×C5—41no—
499C2×C5—81no—
500C2×C5—161no—
501C2×C5#303511yescharacteristic
502C2×C5#306211yescharacteristic
503C2×C5#306911yescharacteristic
504C23—21no—
505C23—41no—
506C23C5×#12111yescharacteristic
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515D4—21no—
516D4—21no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—81no—
522D4—81no—
523D4—82no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4C5×#12111yescharacteristic
539C2×C4C5×#12111yescharacteristic
540C2×C4C5×#12111yescharacteristic
541C2×C4C22×C5×D411yescharacteristic
542C2×C4C22×C5×D411yescharacteristic
543C2×C4C2×C5×#4111yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8C5×#13512yes—
554C5#1924611yescharacteristic, direct product factor, Sylow
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×C5×#12111yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×C5×#13511yescharacteristic
576C4C5×#57511yescharacteristic
577C4C5×#57611yescharacteristic
578C4C5×#57711yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2C5×#303511yescharacteristic
583C2C5×#306211yescharacteristic
584C2C5×#306911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3212C2
LCSG ▷ C42 ▷ 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×#3248C2semidirect
3. C5×#3182C2semidirect
4. C5×#2969C2semidirect
5. C5×#1701C2semidirect
6. C5×#1699C2semidirect
7. C5×#1694C2semidirect
8. C5×#1686C2semidirect
9. C5×#1682C2semidirect
10. C5×#1680C2semidirect
11. C5×#1673C2semidirect
12. C5×#1665C2semidirect
13. C5×#1565C2semidirect
14. C5×#1544C2semidirect
15. C5×#1540C2semidirect
67. #19246C5direct (N × H)
145. #3248C2×C5semidirect
147. #3182C2×C5semidirect
148. #2969C2×C5semidirect
149. #1701C2×C5semidirect
150. #1699C2×C5semidirect
151. #1694C2×C5semidirect
152. #1686C2×C5semidirect
153. #1682C2×C5semidirect
154. #1680C2×C5semidirect
155. #1673C2×C5semidirect
156. #1665C2×C5semidirect
157. #1565C2×C5semidirect
158. #1544C2×C5semidirect
159. #1540C2×C5semidirect
554. C5#19246direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32482
C5×#32122
C5×#31822
C5×#29692
C5×#17012
C5×#16992
C5×#16942
C5×#16862
C5×#16822
C5×#16802
C5×#16732
C5×#16652
C5×#15652
C5×#15442
C5×#15402
#192465