Finite Group Databasebeta

← C5×#19832 #11942552

Subgroups — C5×#19832 #11942552

Order 1280.

580 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3364C211yesmaximal, characteristic, complemented
2C5×#3359C211yesmaximal, characteristic, complemented
3C5×#3340C211yesmaximal, characteristic
4C5×#3329C211yesmaximal, characteristic
5C5×#1718C211yesmaximal, characteristic, complemented
6C5×#1699C211yesmaximal, characteristic, complemented
7C5×#1684C211yesmaximal, characteristic, complemented
8C5×#1679C211yesmaximal, characteristic, complemented
9C5×#1672C211yesmaximal, characteristic, complemented
10C5×#1650C211yesmaximal, characteristic, complemented
11C5×#1649C211yesmaximal, characteristic, complemented
12C5×#1646C211yesmaximal, characteristic
13C5×#1636C211yesmaximal, characteristic, complemented
14C5×#1583C211yesmaximal, characteristic, complemented
15C5×SD16⋊C8C211yesmaximal, characteristic, complemented
16C5×#557C2211yescharacteristic
17C5×#556C2211yescharacteristic
18C5×#555C2211yescharacteristic
19C5×D4×Q8C2211yescharacteristic
20C5×#500C2211yescharacteristic
21C5×#498C2211yescharacteristic
22C5×#488—21no—
23C5×#487—21no—
24C5×#487C2211yescharacteristic
25C5×#487C2211yescharacteristic
26C5×#487C2211yescharacteristic
27C5×#487C2211yescharacteristic
28C5×#485—21no—
29C5×#485—21no—
30C5×#482—21no—
31C5×#479—21no—
32C5×#477C2211yescharacteristic
33C5×#477C2211yescharacteristic
34C5×#475—21no—
35C5×#475C2211yescharacteristic
36C5×#474C2211yescharacteristic
37C5×#474C2211yescharacteristic
38C5×#468—21no—
39C5×#465—21no—
40C5×#464—21no—
41C5×#462C2211yescharacteristic
42C5×#461—21no—
43C5×#461C2211yescharacteristic
44C5×#461C2211yescharacteristic
45C5×#448—21no—
46C5×C8×Q8C2211yescharacteristic
47C5×C8×Q8C2211yescharacteristic
48C4×C5×Q16—21no—
49C4×C5×SD16—21no—
50C4×C5×SD16C2211yescharacteristic
51C4×C5×SD16C2211yescharacteristic
52C5×#436C2211yescharacteristic
53C5×C8×D4C2211yescharacteristic
54C5×#427—21no—
55C5×#419—21no—
56C5×#335C2211yescharacteristic
57C5×#334C2211yescharacteristic
58C5×#333C2211yescharacteristic
59C5×#332C2211yescharacteristic
60C5×#332C2211yescharacteristic
61C5×#332C2211yescharacteristic
62C5×Q8⋊C8C2211yescharacteristic
63C5×Q8⋊C8C2211yescharacteristic
64C5×D4⋊C8C2211yescharacteristic
65C5×D4⋊C8C2211yescharacteristic
66C5×#322C2211yescharacteristic
67#19832C511yesmaximal, characteristic, direct product factor, Sylow
68C22×C5×Q8—21no—
69C2×C5×Q16—21no—
70C2×C5×SD16—21no—
71C2×C5×SD16—21no—
72C2×C5×SD16D411yescharacteristic
73C2×C5×SD16D411yescharacteristic
74C2×C5×M16—21no—
75C22×C5×C8—21no—
76C5×C4⋊Q8—21no—
77C5×C4⋊Q8—21no—
78C5×C4⋊Q8C2311yescharacteristic
79C5×C4⋊Q8C2311yescharacteristic
80C5×C4⋊Q8C2311yescharacteristic
81C5×C4⋊Q8C2311yescharacteristic
82C5×#126—41no—
83C5×#125—21no—
84C5×#125—41no—
85C5×#124—21no—
86C5×#124—41no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—41no—
90C5×#121—21no—
91C5×#121—21no—
92C4×C5×Q8—21no—
93C4×C5×Q8—21no—
94C4×C5×Q8—21no—
95C4×C5×Q8C2311yescharacteristic
96C4×C5×Q8C2311yescharacteristic
97C4×C5×D4—21no—
98C4×C5×D4C2311yescharacteristic
99C4×C5×D4C2311yescharacteristic
100C5×#117—21no—
101C5×#117—21no—
102C5×#117—21no—
103C5×#107—21no—
104C5×#107—21no—
105C5×#107—21no—
106C5×#107—21no—
107C5×#107—41no—
108C5×#106—21no—
109C5×#106—21no—
110C5×#106—21no—
111C5×#106D411yescharacteristic
112C5×#106D411yescharacteristic
113C5×C4⋊C8—21no—
114C5×C4⋊C8—21no—
115C5×C4⋊C8C2311yescharacteristic
116C5×C4⋊C8C2311yescharacteristic
117C5×C4⋊C8C2311yescharacteristic
118C5×C4⋊C8C2311yescharacteristic
119C5×#103—21no—
120C5×#103—21no—
121C5×#103—21no—
122C5×#103—21no—
123C5×#103—21no—
124C5×#103—21no—
125C5×#103—21no—
126C5×#103—21no—
127C5×#103—21no—
128C5×#103—21no—
129C5×#103—21no—
130C5×#103—21no—
131C5×#103—41no—
132C5×#103D411yescharacteristic
133C5×#103D411yescharacteristic
134C5×#102—21no—
135C5×#102—21no—
136C5×#102D411yescharacteristic
137C5×#102D411yescharacteristic
138C5×C22⋊C8—21no—
139C5×C22⋊C8—21no—
140C4×C5×C8—21no—
141C4×C5×C8—21no—
142C4×C5×C8C2311yescharacteristic
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3364C2×C511yescharacteristic, complemented
146#3359C2×C511yescharacteristic, complemented
147#3340C2×C511yescharacteristic
148#3329C2×C511yescharacteristic
149#1718C2×C511yescharacteristic, complemented
150#1699C2×C511yescharacteristic, complemented
151#1684C2×C511yescharacteristic, complemented
152#1679C2×C511yescharacteristic, complemented
153#1672C2×C511yescharacteristic, complemented
154#1650C2×C511yescharacteristic, complemented
155#1649C2×C511yescharacteristic, complemented
156#1646C2×C511yescharacteristic
157#1636C2×C511yescharacteristic, complemented
158#1583C2×C511yescharacteristic, complemented
159SD16⋊C8C2×C511yescharacteristic, complemented
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—41no—
165C2×C5×Q8—42no—
166C2×C5×Q8—81no—
167C2×C5×Q8C2×D411yescharacteristic
168C2×C5×Q8C2×D411yescharacteristic
169C2×C5×D4—41no—
170C2×C5×D4C2×D411yescharacteristic
171C2×C5×D4C2×D411yescharacteristic
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—41no—
175C5×Q16—42no—
176C5×SD16—22no—
177C5×SD16—41no—
178C5×SD16—42no—
179C5×SD16—81no—
180C5×M16—81no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—42no—
187C2×C5×C8C2×D411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C2×C5×C8C2×D411yescharacteristic
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
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—41no—
202C5×C4⋊C4—41no—
203C5×C4⋊C4—41no—
204C5×C4⋊C4—41no—
205C5×C4⋊C4—41no—
206C5×C4⋊C4C2×D411yescharacteristic
207C5×C4⋊C4C2×D411yescharacteristic
208C5×C4⋊C4C2×D411yescharacteristic
209C5×C4⋊C4C2×D411yescharacteristic
210C5×C22⋊C4—21no—
211C5×C22⋊C4—21no—
212C5×C22⋊C4—41no—
213C5×C22⋊C4—41no—
214C5×C22⋊C4—41no—
215C5×C22⋊C4—41no—
216C5×C22⋊C4—41no—
217C42×C5—21no—
218C42×C5—21no—
219C42×C5—41no—
220C42×C5—41no—
221C42×C5—41no—
222C42×C5C2411yescharacteristic
223#557C22×C511yescharacteristic
224#556C22×C511yescharacteristic
225#555C22×C511yescharacteristic
226D4×Q8C22×C511yescharacteristic
227#500C22×C511yescharacteristic
228#498C22×C511yescharacteristic
229#488—21no—
230#487—21no—
231#487C22×C511yescharacteristic
232#487C22×C511yescharacteristic
233#487C22×C511yescharacteristic
234#487C22×C511yescharacteristic
235#485—21no—
236#485—21no—
237#482—21no—
238#479—21no—
239#477C22×C511yescharacteristic
240#477C22×C511yescharacteristic
241#475—21no—
242#475C22×C511yescharacteristic
243#474C22×C511yescharacteristic
244#474C22×C511yescharacteristic
245#468—21no—
246#465—21no—
247#464—21no—
248#462C22×C511yescharacteristic
249#461—21no—
250#461C22×C511yescharacteristic
251#461C22×C511yescharacteristic
252#448—21no—
253C8×Q8C22×C511yescharacteristic
254C8×Q8C22×C511yescharacteristic
255C4×Q16—21no—
256C4×SD16—21no—
257C4×SD16C22×C511yescharacteristic
258C4×SD16C22×C511yescharacteristic
259#436C22×C511yescharacteristic
260C8×D4C22×C511yescharacteristic
261#427—21no—
262#419—21no—
263#335C22×C511yescharacteristic
264#334C22×C511yescharacteristic
265#333C22×C511yescharacteristic
266#332C22×C511yescharacteristic
267#332C22×C511yescharacteristic
268#332C22×C511yescharacteristic
269Q8⋊C8C22×C511yescharacteristic
270Q8⋊C8C22×C511yescharacteristic
271D4⋊C8C22×C511yescharacteristic
272D4⋊C8C22×C511yescharacteristic
273#322C22×C511yescharacteristic
274C23×C5—21no—
275C23×C5—21no—
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—41no—
280C5×Q8—41no—
281C5×Q8—41no—
282C5×Q8—41no—
283C5×Q8—41no—
284C5×Q8—41no—
285C5×Q8—82no—
286C5×Q8—81no—
287C5×Q8#13512yes—
288C5×D4—21no—
289C5×D4—21no—
290C5×D4—21no—
291C5×D4—21no—
292C5×D4—161no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—82no—
308C2×C4×C5C22×D411yescharacteristic
309C2×C4×C5C22×D411yescharacteristic
310C2×C4×C5H(5,𝔽2)11yescharacteristic
311C5×C8—21no—
312C5×C8—21no—
313C5×C8—21no—
314C5×C8—21no—
315C5×C8—41no—
316C5×C8—41no—
317C5×C8—41no—
318C5×C8—41no—
319C5×C8—41no—
320C22×Q8—21no—
321C2×Q16—21no—
322C2×SD16—21no—
323C2×SD16—21no—
324C2×SD16C5×D411yescharacteristic
325C2×SD16C5×D411yescharacteristic
326C2×M16—21no—
327C22×C8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8C23×C511yescharacteristic
331C4⋊Q8C23×C511yescharacteristic
332C4⋊Q8C23×C511yescharacteristic
333C4⋊Q8C23×C511yescharacteristic
334#126—41no—
335#125—21no—
336#125—41no—
337#124—21no—
338#124—41no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—41no—
342#121—21no—
343#121—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C23×C511yescharacteristic
348C4×Q8C23×C511yescharacteristic
349C4×D4—21no—
350C4×D4C23×C511yescharacteristic
351C4×D4C23×C511yescharacteristic
352#117—21no—
353#117—21no—
354#117—21no—
355#107—21no—
356#107—21no—
357#107—21no—
358#107—21no—
359#107—41no—
360#106—21no—
361#106—21no—
362#106—21no—
363#106C5×D411yescharacteristic
364#106C5×D411yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8C23×C511yescharacteristic
368C4⋊C8C23×C511yescharacteristic
369C4⋊C8C23×C511yescharacteristic
370C4⋊C8C23×C511yescharacteristic
371#103—21no—
372#103—21no—
373#103—21no—
374#103—21no—
375#103—21no—
376#103—21no—
377#103—21no—
378#103—21no—
379#103—21no—
380#103—21no—
381#103—21no—
382#103—21no—
383#103—41no—
384#103C5×D411yescharacteristic
385#103C5×D411yescharacteristic
386#102—21no—
387#102—21no—
388#102C5×D411yescharacteristic
389#102C5×D411yescharacteristic
390C22⋊C8—21no—
391C22⋊C8—21no—
392C4×C8—21no—
393C4×C8—21no—
394C4×C8C23×C511yescharacteristic
395C4×C8C23×C511yescharacteristic
396C4×C8C23×C511yescharacteristic
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5D4211yescharacteristic
404C4×C5—22no—
405C4×C5—21no—
406C4×C5—41no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—81no—
412C4×C5—81no—
413C4×C5—81no—
414C4×C5—81no—
415C4×C5C2×#13511yescharacteristic
416C4×C5#57511yescharacteristic
417C4×C5#57711yescharacteristic
418C4×C5#57811yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8C2×C5×D411yescharacteristic
427C2×Q8C2×C5×D411yescharacteristic
428C2×D4—41no—
429C2×D4C2×C5×D411yescharacteristic
430C2×D4C2×C5×D411yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434Q16—42no—
435SD16—22no—
436SD16—41no—
437SD16—42no—
438SD16—81no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8C2×C5×D411yescharacteristic
447C2×C8C2×C5×D411yescharacteristic
448C2×C8C2×C5×D411yescharacteristic
449C2×C8C2×C5×D411yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4C2×C5×D411yescharacteristic
466C4⋊C4C2×C5×D411yescharacteristic
467C4⋊C4C2×C5×D411yescharacteristic
468C4⋊C4C2×C5×D411yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42—41no—
481C42C24×C511yescharacteristic
482C2×C5—81no—
483C2×C5—81no—
484C2×C5#326911yescharacteristic
485C2×C5#328211yescharacteristic
486C2×C5#328911yescharacteristic
487C23—21no—
488C23—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—82no—
499Q8—81no—
500Q8C5×#13512yes—
501D4—21no—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—161no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—82no—
521C2×C4C22×C5×D411yescharacteristic
522C2×C4C22×C5×D411yescharacteristic
523C2×C4C5×H(5,𝔽2)11yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C5#1983211yescharacteristic, direct product factor, Sylow
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C5×D4211yescharacteristic
541C4—22no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×C5×#13511yescharacteristic
553C4C5×#57511yescharacteristic
554C4C5×#57711yescharacteristic
555C4C5×#57811yescharacteristic
556C2—81no—
557C2—81no—
558C2C5×#326911yescharacteristic
559C2C5×#328211yescharacteristic
560C2C5×#328911yescharacteristic
subgroupG/H
center, socleC22×C5D42
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#555C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3364C2semidirect
2. C5×#3359C2semidirect
5. C5×#1718C2semidirect
6. C5×#1699C2semidirect
7. C5×#1684C2semidirect
8. C5×#1679C2semidirect
9. C5×#1672C2semidirect
10. C5×#1650C2semidirect
11. C5×#1649C2semidirect
13. C5×#1636C2semidirect
14. C5×#1583C2semidirect
15. C5×SD16⋊C8C2semidirect
67. #19832C5direct (N × H)
145. #3364C2×C5semidirect
146. #3359C2×C5semidirect
149. #1718C2×C5semidirect
150. #1699C2×C5semidirect
151. #1684C2×C5semidirect
152. #1679C2×C5semidirect
153. #1672C2×C5semidirect
154. #1650C2×C5semidirect
155. #1649C2×C5semidirect
157. #1636C2×C5semidirect
158. #1583C2×C5semidirect
159. SD16⋊C8C2×C5semidirect
533. C5#19832direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#33642
C5×#33592
C5×#33402
C5×#33292
C5×#17182
C5×#16992
C5×#16842
C5×#16792
C5×#16722
C5×#16502
C5×#16492
C5×#16462
C5×#16362
C5×#15832
C5×SD16⋊C82
#198325