Finite Group Databasebeta

← C5×#19449 #11942169

Subgroups — C5×#19449 #11942169

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3210C211yesmaximal, characteristic, complemented
2C5×#3115C211yesmaximal, characteristic
3C5×#3107C211yesmaximal, characteristic, complemented
4C5×#2989C211yesmaximal, characteristic, complemented
5C5×#1702C211yesmaximal, characteristic, complemented
6C5×#1701C211yesmaximal, characteristic, complemented
7C5×#1700C211yesmaximal, characteristic, complemented
8C5×#1699C211yesmaximal, characteristic, complemented
9C5×#1690C211yesmaximal, characteristic, complemented
10C5×#1689C211yesmaximal, characteristic, complemented
11C5×#1686C211yesmaximal, characteristic, complemented
12C5×#1685C211yesmaximal, characteristic, complemented
13C5×#1572C211yesmaximal, characteristic, complemented
14C5×#1552C211yesmaximal, characteristic, complemented
15C5×#1540C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C5×#532C2211yescharacteristic
18C4×C5×#41C2211yescharacteristic
19C5×#494C2211yescharacteristic
20C5×#492C2211yescharacteristic
21C5×#487C2211yescharacteristic
22C5×#486C2211yescharacteristic
23C5×#485—21no—
24C5×#482—21no—
25C5×#475C2211yescharacteristic
26C5×#475C2211yescharacteristic
27C5×#474C2211yescharacteristic
28C5×#474C2211yescharacteristic
29C5×#464—21no—
30C5×#464—21no—
31C5×#462C2211yescharacteristic
32C5×#461C2211yescharacteristic
33C5×#460C2211yescharacteristic
34C5×#459C2211yescharacteristic
35C5×#452—21no—
36C5×#452—21no—
37C5×#452—21no—
38C5×#449—21no—
39C5×#446C2211yescharacteristic
40C5×#446C2211yescharacteristic
41C5×#442—21no—
42C5×#440—21no—
43C4×C5×Q16—21no—
44C4×C5×SD16—21no—
45C5×#436C2211yescharacteristic
46C5×#436C2211yescharacteristic
47C5×#435—21no—
48C5×#435—21no—
49C5×#432—21no—
50C5×#432C2211yescharacteristic
51C5×#431C2211yescharacteristic
52C5×#431C2211yescharacteristic
53C5×#423—21no—
54C2×C5×C4⋊C8C2211yescharacteristic
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#19449C511yesmaximal, characteristic, direct product factor, Sylow
68C2×C5×#41—21no—
69C2×C5×#41D411yescharacteristic
70C2×C5×Q16—21no—
71C2×C5×Q16—21no—
72C2×C5×Q16—21no—
73C2×C5×SD16—21no—
74C2×C5×SD16—21no—
75C2×C5×SD16—21no—
76C2×C5×SD16—21no—
77C2×C5×D8—21no—
78C2×C5×M16—21no—
79C2×C5×M16—21no—
80C22×C5×C8—21no—
81C5×C4⋊Q8C2311yescharacteristic
82C5×C4⋊Q8C2311yescharacteristic
83C5×C4⋊Q8C2311yescharacteristic
84C5×#127C2311yescharacteristic
85C5×#125—21no—
86C5×#124—21no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—21no—
89C5×#121—21no—
90C5×#121—21no—
91C4×C5×Q8—21no—
92C4×C5×Q8—21no—
93C4×C5×Q8D411yescharacteristic
94C4×C5×Q8C2311yescharacteristic
95C4×C5×D4—21no—
96C4×C5×D4—21no—
97C4×C5×D4—21no—
98C4×C5×D4—21no—
99C4×C5×D4D411yescharacteristic
100C4×C5×D4C2311yescharacteristic
101C5×#117—21no—
102C5×#117—21no—
103C5×#117D411yescharacteristic
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C5×#107—21no—
107C5×#107—21no—
108C5×#106—21no—
109C5×#106—21no—
110C5×C4⋊C8—21no—
111C5×C4⋊C8—21no—
112C5×C4⋊C8—21no—
113C5×C4⋊C8D411yescharacteristic
114C5×C4⋊C8D411yescharacteristic
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×#102—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×C22⋊C8D411yescharacteristic
138C5×C22⋊C8D411yescharacteristic
139C5×#97—21no—
140C5×#97—21no—
141C5×#97—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3210C2×C511yescharacteristic, complemented
146#3115C2×C511yescharacteristic
147#3107C2×C511yescharacteristic, complemented
148#2989C2×C511yescharacteristic, complemented
149#1702C2×C511yescharacteristic, complemented
150#1701C2×C511yescharacteristic, complemented
151#1700C2×C511yescharacteristic, complemented
152#1699C2×C511yescharacteristic, complemented
153#1690C2×C511yescharacteristic, complemented
154#1689C2×C511yescharacteristic, complemented
155#1686C2×C511yescharacteristic, complemented
156#1685C2×C511yescharacteristic, complemented
157#1572C2×C511yescharacteristic, complemented
158#1552C2×C511yescharacteristic, complemented
159#1540C2×C511yescharacteristic, complemented
160C5×#41—41no—
161C5×#41—41no—
162C5×#41—81no—
163C5×#41—81no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8C2×D411yescharacteristic
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—41no—
173C2×C5×D4C2×D411yescharacteristic
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—41no—
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5#4111yescharacteristic
181C5×Q16—42no—
182C5×Q16—81no—
183C5×Q16—81no—
184C5×SD16—42no—
185C5×SD16—42no—
186C5×SD16—81no—
187C5×SD16—81no—
188C5×D8—42no—
189C5×M16—81no—
190C5×M16—81no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—81no—
198C2×C5×C8C2×D411yescharacteristic
199C2×C5×C8C2×D411yescharacteristic
200C2×C5×C8C2×D411yescharacteristic
201C2×C5×C8C2×D411yescharacteristic
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—41no—
218C5×C22⋊C4—41no—
219C5×C22⋊C4—41no—
220C42×C5—21no—
221C42×C5—21no—
222C42×C5—21no—
223C42×C5—41no—
224C42×C5C2×D411yescharacteristic
225C42×C5C2×D411yescharacteristic
226C42×C5#4111yescharacteristic
227C42×C5C2411yescharacteristic
228#533C22×C511yescharacteristic
229#532C22×C511yescharacteristic
230C4×#41C22×C511yescharacteristic
231#494C22×C511yescharacteristic
232#492C22×C511yescharacteristic
233#487C22×C511yescharacteristic
234#486C22×C511yescharacteristic
235#485—21no—
236#482—21no—
237#475C22×C511yescharacteristic
238#475C22×C511yescharacteristic
239#474C22×C511yescharacteristic
240#474C22×C511yescharacteristic
241#464—21no—
242#464—21no—
243#462C22×C511yescharacteristic
244#461C22×C511yescharacteristic
245#460C22×C511yescharacteristic
246#459C22×C511yescharacteristic
247#452—21no—
248#452—21no—
249#452—21no—
250#449—21no—
251#446C22×C511yescharacteristic
252#446C22×C511yescharacteristic
253#442—21no—
254#440—21no—
255C4×Q16—21no—
256C4×SD16—21no—
257#436C22×C511yescharacteristic
258#436C22×C511yescharacteristic
259#435—21no—
260#435—21no—
261#432—21no—
262#432C22×C511yescharacteristic
263#431C22×C511yescharacteristic
264#431C22×C511yescharacteristic
265#423—21no—
266C2×C4⋊C8C22×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—42no—
293C5×D4—41no—
294C5×D4—41no—
295C5×D4—41no—
296C5×D4—41no—
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—42no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—81no—
314C2×C4×C5—82no—
315C2×C4×C5#12111yescharacteristic
316C2×C4×C5#12111yescharacteristic
317C2×C4×C5#12111yescharacteristic
318C2×C4×C5C22×D411yescharacteristic
319C2×C4×C5C22×D411yescharacteristic
320C2×C4×C5C2×#4111yescharacteristic
321C5×C8—21no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—41no—
326C5×C8—41no—
327C5×C8—41no—
328C5×C8—41no—
329C5×C8—41no—
330C5×C8—41no—
331C2×#41—21no—
332C2×#41C5×D411yescharacteristic
333C2×Q16—21no—
334C2×Q16—21no—
335C2×Q16—21no—
336C2×SD16—21no—
337C2×SD16—21no—
338C2×SD16—21no—
339C2×SD16—21no—
340C2×D8—21no—
341C2×M16—21no—
342C2×M16—21no—
343C22×C8—21no—
344C4⋊Q8C23×C511yescharacteristic
345C4⋊Q8C23×C511yescharacteristic
346C4⋊Q8C23×C511yescharacteristic
347#127C23×C511yescharacteristic
348#125—21no—
349#124—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352#121—21no—
353#121—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8C5×D411yescharacteristic
357C4×Q8C23×C511yescharacteristic
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C5×D411yescharacteristic
363C4×D4C23×C511yescharacteristic
364#117—21no—
365#117—21no—
366#117C5×D411yescharacteristic
367C2×C42—21no—
368C2×C42C23×C511yescharacteristic
369#107—21no—
370#107—21no—
371#106—21no—
372#106—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8C5×D411yescharacteristic
377C4⋊C8C5×D411yescharacteristic
378C4⋊C8C23×C511yescharacteristic
379C4⋊C8C23×C511yescharacteristic
380C4⋊C8C23×C511yescharacteristic
381C4⋊C8C23×C511yescharacteristic
382C4⋊C8C23×C511yescharacteristic
383C4⋊C8C23×C511yescharacteristic
384#103—21no—
385#103—21no—
386#103—21no—
387#103—21no—
388#103—21no—
389#103—21no—
390#102—21no—
391#102—21no—
392#102—21no—
393#102—21no—
394#102—21no—
395#102—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8C5×D411yescharacteristic
401C22⋊C8C5×D411yescharacteristic
402#97—21no—
403#97—21no—
404#97—21no—
405C4×C8—21no—
406C4×C8C23×C511yescharacteristic
407C4×C8C23×C511yescharacteristic
408C22×C5—21no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—81no—
415C22×C5—81no—
416C22×C5—81no—
417C22×C5C2×#12111yescharacteristic
418C4×C5—21no—
419C4×C5—21no—
420C4×C5—21no—
421C4×C5—21no—
422C4×C5—41no—
423C4×C5—41no—
424C4×C5—41no—
425C4×C5—81no—
426C4×C5—81no—
427C4×C5—81no—
428C4×C5#57511yescharacteristic
429C4×C5#57511yescharacteristic
430C4×C5#57611yescharacteristic
431C4×C5#57711yescharacteristic
432#41—41no—
433#41—41no—
434#41—81no—
435#41—81no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×C5×D411yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×C5×D411yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4C2×C5×D411yescharacteristic
451C22×C4C2×C5×D411yescharacteristic
452C22×C4C5×#4111yescharacteristic
453Q16—42no—
454Q16—81no—
455Q16—81no—
456SD16—42no—
457SD16—42no—
458SD16—81no—
459SD16—81no—
460D8—42no—
461M16—81no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8C2×C5×D411yescharacteristic
471C2×C8C2×C5×D411yescharacteristic
472C2×C8C2×C5×D411yescharacteristic
473C2×C8C2×C5×D411yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×C5×D411yescharacteristic
485C4⋊C4C2×C5×D411yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C2×C5×D411yescharacteristic
497C42C2×C5×D411yescharacteristic
498C42C5×#4111yescharacteristic
499C42C24×C511yescharacteristic
500C2×C5—41no—
501C2×C5—81no—
502C2×C5—161no—
503C2×C5#304511yescharacteristic
504C2×C5#305411yescharacteristic
505C2×C5#306911yescharacteristic
506C23—21no—
507C23—41no—
508C23C5×#12111yescharacteristic
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517D4—21no—
518D4—21no—
519D4—42no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—81no—
541C2×C4—82no—
542C2×C4C5×#12111yescharacteristic
543C2×C4C5×#12111yescharacteristic
544C2×C4C5×#12111yescharacteristic
545C2×C4C22×C5×D411yescharacteristic
546C2×C4C22×C5×D411yescharacteristic
547C2×C4C2×C5×#4111yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C5#1944911yescharacteristic, direct product factor, Sylow
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×C5×#12111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C5×#57511yescharacteristic
580C4C5×#57511yescharacteristic
581C4C5×#57611yescharacteristic
582C4C5×#57711yescharacteristic
583C2—41no—
584C2—81no—
585C2—161no—
586C2C5×#304511yescharacteristic
587C2C5×#305411yescharacteristic
588C2C5×#306911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3115C2
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×#3210C2semidirect
3. C5×#3107C2semidirect
4. C5×#2989C2semidirect
5. C5×#1702C2semidirect
6. C5×#1701C2semidirect
7. C5×#1700C2semidirect
8. C5×#1699C2semidirect
9. C5×#1690C2semidirect
10. C5×#1689C2semidirect
11. C5×#1686C2semidirect
12. C5×#1685C2semidirect
13. C5×#1572C2semidirect
14. C5×#1552C2semidirect
15. C5×#1540C2semidirect
67. #19449C5direct (N × H)
145. #3210C2×C5semidirect
147. #3107C2×C5semidirect
148. #2989C2×C5semidirect
149. #1702C2×C5semidirect
150. #1701C2×C5semidirect
151. #1700C2×C5semidirect
152. #1699C2×C5semidirect
153. #1690C2×C5semidirect
154. #1689C2×C5semidirect
155. #1686C2×C5semidirect
156. #1685C2×C5semidirect
157. #1572C2×C5semidirect
158. #1552C2×C5semidirect
159. #1540C2×C5semidirect
558. C5#19449direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32102
C5×#31152
C5×#31072
C5×#29892
C5×#17022
C5×#17012
C5×#17002
C5×#16992
C5×#16902
C5×#16892
C5×#16862
C5×#16852
C5×#15722
C5×#15522
C5×#15402
#194495