Finite Group Databasebeta

← C5×#19249 #11941969

Subgroups — C5×#19249 #11941969

Order 1280.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3248C211yesmaximal, characteristic
2C5×#3233C211yesmaximal, characteristic
3C5×#3185C211yesmaximal, characteristic, complemented
4C5×#2969C211yesmaximal, characteristic
5C5×#1703C211yesmaximal, characteristic, complemented
6C5×#1699C211yesmaximal, characteristic, complemented
7C5×#1692C211yesmaximal, characteristic, complemented
8C5×#1690C211yesmaximal, characteristic, complemented
9C5×#1684C211yesmaximal, characteristic, complemented
10C5×#1680C211yesmaximal, characteristic, complemented
11C5×#1671C211yesmaximal, characteristic, complemented
12C5×#1669C211yesmaximal, characteristic, complemented
13C5×#1565C211yesmaximal, characteristic, complemented
14C5×#1544C211yesmaximal, characteristic, complemented
15C5×#1542C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C5×#533C2211yescharacteristic
18C5×#529C2211yescharacteristic
19C5×#499—21no—
20C5×#498C2211yescharacteristic
21C5×#494C2211yescharacteristic
22C5×#488—21no—
23C5×#487C2211yescharacteristic
24C5×#487C2211yescharacteristic
25C5×#485—21no—
26C5×#482—21no—
27C5×#479—21no—
28C5×#477C2211yescharacteristic
29C5×#476C2211yescharacteristic
30C5×#475C2211yescharacteristic
31C5×#475C2211yescharacteristic
32C5×#474C2211yescharacteristic
33C5×#474C2211yescharacteristic
34C5×#470—21no—
35C5×#470—21no—
36C5×#467—21no—
37C5×#465—21no—
38C5×#464—21no—
39C5×#462C2211yescharacteristic
40C5×#461C2211yescharacteristic
41C5×#446C2211yescharacteristic
42C5×C8×Q8C2211yescharacteristic
43C5×#441—21no—
44C5×#441—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×#333C2211yescharacteristic
60C5×#333C2211yescharacteristic
61C5×#332C2211yescharacteristic
62C5×#332C2211yescharacteristic
63C5×#332C2211yescharacteristic
64C5×#332C2211yescharacteristic
65C5×#332C2211yescharacteristic
66C5×#332C2211yescharacteristic
67#19249C511yesmaximal, characteristic, direct product factor, Sylow
68C2×C5×Q16—21no—
69C2×C5×Q16—21no—
70C2×C5×Q16—21no—
71C2×C5×SD16—21no—
72C2×C5×M16—21no—
73C2×C5×M16D411yescharacteristic
74C2×C5×M16D411yescharacteristic
75C22×C5×C8—21no—
76C22×C5×C8—21no—
77C5×C4⋊Q8C2311yescharacteristic
78C5×C4⋊Q8C2311yescharacteristic
79C5×C4⋊Q8C2311yescharacteristic
80C5×C4⋊Q8C2311yescharacteristic
81C5×#126—21no—
82C5×#125—21no—
83C5×#125—21no—
84C5×#125D411yescharacteristic
85C5×#124D411yescharacteristic
86C5×#123—21no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8D411yescharacteristic
92C5×#121D411yescharacteristic
93C4×C5×Q8—21no—
94C4×C5×Q8—21no—
95C4×C5×Q8—21no—
96C4×C5×Q8—21no—
97C4×C5×Q8C2311yescharacteristic
98C4×C5×D4—21no—
99C4×C5×D4C2311yescharacteristic
100C5×#117—21no—
101C5×#117—21no—
102C5×#117—21no—
103C2×C42×C5C2311yescharacteristic
104C5×#107—21no—
105C5×#107—21no—
106C5×#107—21no—
107C5×#106—21no—
108C5×#106—21no—
109C5×#106—21no—
110C5×#106—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×#103—21no—
129C5×#103—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
146#3233C2×C511yescharacteristic
147#3185C2×C511yescharacteristic, complemented
148#2969C2×C511yescharacteristic
149#1703C2×C511yescharacteristic, complemented
150#1699C2×C511yescharacteristic, complemented
151#1692C2×C511yescharacteristic, complemented
152#1690C2×C511yescharacteristic, complemented
153#1684C2×C511yescharacteristic, complemented
154#1680C2×C511yescharacteristic, complemented
155#1671C2×C511yescharacteristic, complemented
156#1669C2×C511yescharacteristic, complemented
157#1565C2×C511yescharacteristic, complemented
158#1544C2×C511yescharacteristic, complemented
159#1542C2×C511yescharacteristic, complemented
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8C2×D411yescharacteristic
165C2×C5×D4—21no—
166C2×C5×D4C2×D411yescharacteristic
167C22×C4×C5—21no—
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5#4111yescharacteristic
171C5×Q16—42no—
172C5×Q16—42no—
173C5×Q16—81no—
174C5×SD16—81no—
175C5×M16—22no—
176C5×M16—41no—
177C5×M16—42no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—42no—
185C2×C5×C8—81no—
186C2×C5×C8C2×D411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C5×C4⋊C4—21no—
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—21no—
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×C22⋊C4—21no—
209C5×C22⋊C4—21no—
210C5×C22⋊C4—21no—
211C5×C22⋊C4—21no—
212C5×C22⋊C4—21no—
213C5×C22⋊C4—41no—
214C5×C22⋊C4—41no—
215C42×C5—21no—
216C42×C5—41no—
217C42×C5—41no—
218C42×C5C2×D411yescharacteristic
219C42×C5C2×D411yescharacteristic
220C42×C5#4111yescharacteristic
221C42×C5C2411yescharacteristic
222#533C22×C511yescharacteristic
223#533C22×C511yescharacteristic
224#529C22×C511yescharacteristic
225#499—21no—
226#498C22×C511yescharacteristic
227#494C22×C511yescharacteristic
228#488—21no—
229#487C22×C511yescharacteristic
230#487C22×C511yescharacteristic
231#485—21no—
232#482—21no—
233#479—21no—
234#477C22×C511yescharacteristic
235#476C22×C511yescharacteristic
236#475C22×C511yescharacteristic
237#475C22×C511yescharacteristic
238#474C22×C511yescharacteristic
239#474C22×C511yescharacteristic
240#470—21no—
241#470—21no—
242#467—21no—
243#465—21no—
244#464—21no—
245#462C22×C511yescharacteristic
246#461C22×C511yescharacteristic
247#446C22×C511yescharacteristic
248C8×Q8C22×C511yescharacteristic
249#441—21no—
250#441—21no—
251#436—21no—
252#436C22×C511yescharacteristic
253#435—21no—
254C8×D4C22×C511yescharacteristic
255#433—21no—
256#431C22×C511yescharacteristic
257#431C22×C511yescharacteristic
258C2×C4⋊C8C22×C511yescharacteristic
259#405—21no—
260C4×M16C22×C511yescharacteristic
261#335C22×C511yescharacteristic
262#335C22×C511yescharacteristic
263#334C22×C511yescharacteristic
264#334C22×C511yescharacteristic
265#333C22×C511yescharacteristic
266#333C22×C511yescharacteristic
267#332C22×C511yescharacteristic
268#332C22×C511yescharacteristic
269#332C22×C511yescharacteristic
270#332C22×C511yescharacteristic
271#332C22×C511yescharacteristic
272#332C22×C511yescharacteristic
273C23×C5—21no—
274C23×C5#12111yescharacteristic
275C5×Q8—21no—
276C5×Q8—21no—
277C5×Q8—41no—
278C5×Q8—41no—
279C5×Q8—41no—
280C5×Q8—41no—
281C5×Q8—41no—
282C5×Q8—41no—
283C5×Q8—81no—
284C5×D4—21no—
285C5×D4—21no—
286C5×D4—81no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5#12111yescharacteristic
302C2×C4×C5#12111yescharacteristic
303C2×C4×C5#12111yescharacteristic
304C2×C4×C5C22×D411yescharacteristic
305C2×C4×C5C22×D411yescharacteristic
306C2×C4×C5C2×#4111yescharacteristic
307C5×C8—21no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8#13512yes—
317C2×Q16—21no—
318C2×Q16—21no—
319C2×Q16—21no—
320C2×SD16—21no—
321C2×M16—21no—
322C2×M16C5×D411yescharacteristic
323C2×M16C5×D411yescharacteristic
324C22×C8—21no—
325C22×C8—21no—
326C4⋊Q8C23×C511yescharacteristic
327C4⋊Q8C23×C511yescharacteristic
328C4⋊Q8C23×C511yescharacteristic
329C4⋊Q8C23×C511yescharacteristic
330#126—21no—
331#125—21no—
332#125—21no—
333#125C5×D411yescharacteristic
334#124C5×D411yescharacteristic
335#123—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8C5×D411yescharacteristic
341#121C5×D411yescharacteristic
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8C23×C511yescharacteristic
347C4×D4—21no—
348C4×D4C23×C511yescharacteristic
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C42C23×C511yescharacteristic
353#107—21no—
354#107—21no—
355#107—21no—
356#106—21no—
357#106—21no—
358#106—21no—
359#106—21no—
360#106—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8C23×C511yescharacteristic
365C4⋊C8C23×C511yescharacteristic
366C4⋊C8C23×C511yescharacteristic
367C4⋊C8C23×C511yescharacteristic
368C4⋊C8C23×C511yescharacteristic
369C4⋊C8C23×C511yescharacteristic
370#103—21no—
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#102—21no—
380#102—21no—
381#102—21no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386#97—21no—
387#97C5×D411yescharacteristic
388#97C5×D411yescharacteristic
389C4×C8—21no—
390C4×C8—21no—
391C4×C8—21no—
392C4×C8C23×C511yescharacteristic
393C4×C8C23×C511yescharacteristic
394C22×C5—21no—
395C22×C5—21no—
396C22×C5—21no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×#12111yescharacteristic
401C4×C5—21no—
402C4×C5—21no—
403C4×C5—21no—
404C4×C5—21no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5—41no—
408C4×C5—81no—
409C4×C5—81no—
410C4×C5—81no—
411C4×C5—81no—
412C4×C5C2×#13511yescharacteristic
413C4×C5#57511yescharacteristic
414C4×C5#57711yescharacteristic
415C4×C5#57811yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C2×C5×D411yescharacteristic
421C2×D4—21no—
422C2×D4C2×C5×D411yescharacteristic
423C22×C4—21no—
424C22×C4C2×C5×D411yescharacteristic
425C22×C4C2×C5×D411yescharacteristic
426C22×C4C5×#4111yescharacteristic
427Q16—42no—
428Q16—42no—
429Q16—81no—
430SD16—81no—
431M16—22no—
432M16—41no—
433M16—42no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—42no—
441C2×C8—81no—
442C2×C8C2×C5×D411yescharacteristic
443C2×C8C2×C5×D411yescharacteristic
444C2×C8C2×C5×D411yescharacteristic
445C2×C8C2×C5×D411yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
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—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×C5×D411yescharacteristic
463C4⋊C4C2×C5×D411yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—21no—
472C42—41no—
473C42—41no—
474C42C2×C5×D411yescharacteristic
475C42C2×C5×D411yescharacteristic
476C42C5×#4111yescharacteristic
477C42C24×C511yescharacteristic
478C2×C5—41no—
479C2×C5—81no—
480C2×C5#303511yescharacteristic
481C2×C5#306311yescharacteristic
482C2×C5#306911yescharacteristic
483C23—21no—
484C23C5×#12111yescharacteristic
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—81no—
494D4—21no—
495D4—21no—
496D4—81no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4C5×#12111yescharacteristic
512C2×C4C5×#12111yescharacteristic
513C2×C4C5×#12111yescharacteristic
514C2×C4C22×C5×D411yescharacteristic
515C2×C4C22×C5×D411yescharacteristic
516C2×C4C2×C5×#4111yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8C5×#13512yes—
527C5#1924911yescharacteristic, direct product factor, Sylow
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×C5×#12111yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×C5×#13511yescharacteristic
547C4C5×#57511yescharacteristic
548C4C5×#57711yescharacteristic
549C4C5×#57811yescharacteristic
550C2—41no—
551C2—81no—
552C2C5×#303511yescharacteristic
553C2C5×#306311yescharacteristic
554C2C5×#306911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#121D4
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
3. C5×#3185C2semidirect
5. C5×#1703C2semidirect
6. C5×#1699C2semidirect
7. C5×#1692C2semidirect
8. C5×#1690C2semidirect
9. C5×#1684C2semidirect
10. C5×#1680C2semidirect
11. C5×#1671C2semidirect
12. C5×#1669C2semidirect
13. C5×#1565C2semidirect
14. C5×#1544C2semidirect
15. C5×#1542C2semidirect
67. #19249C5direct (N × H)
147. #3185C2×C5semidirect
149. #1703C2×C5semidirect
150. #1699C2×C5semidirect
151. #1692C2×C5semidirect
152. #1690C2×C5semidirect
153. #1684C2×C5semidirect
154. #1680C2×C5semidirect
155. #1671C2×C5semidirect
156. #1669C2×C5semidirect
157. #1565C2×C5semidirect
158. #1544C2×C5semidirect
159. #1542C2×C5semidirect
527. C5#19249direct (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×#32332
C5×#31852
C5×#29692
C5×#17032
C5×#16992
C5×#16922
C5×#16902
C5×#16842
C5×#16802
C5×#16712
C5×#16692
C5×#15652
C5×#15442
C5×#15422
#192495