Finite Group Databasebeta

← C5×#19587 #11942307

Subgroups — C5×#19587 #11942307

Order 1280.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3252C211yesmaximal, characteristic
2C5×#3233C211yesmaximal, characteristic
3C5×#3231C211yesmaximal, characteristic, complemented
4C5×#2994C211yesmaximal, characteristic
5C5×#1703C211yesmaximal, characteristic, complemented
6C5×#1700C211yesmaximal, characteristic, complemented
7C5×#1696C211yesmaximal, characteristic, complemented
8C5×#1691C211yesmaximal, characteristic, complemented
9C5×#1684C211yesmaximal, characteristic, complemented
10C5×#1679C211yesmaximal, characteristic, complemented
11C5×#1675C211yesmaximal, characteristic, complemented
12C5×#1672C211yesmaximal, characteristic, complemented
13C5×#1574C211yesmaximal, characteristic, complemented
14C5×#1550C211yesmaximal, characteristic, complemented
15C5×#1542C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C5×#533C2211yescharacteristic
18C5×#529C2211yescharacteristic
19C5×#500C2211yescharacteristic
20C5×#499—21no—
21C5×#498C2211yescharacteristic
22C5×#488—21no—
23C5×#487C2211yescharacteristic
24C5×#487C2211yescharacteristic
25C5×#485—21no—
26C5×#485—21no—
27C5×#485—21no—
28C5×#482—21no—
29C5×#479—21no—
30C5×#479—21no—
31C5×#479—21no—
32C5×#477C2211yescharacteristic
33C5×#477C2211yescharacteristic
34C5×#476C2211yescharacteristic
35C5×#476C2211yescharacteristic
36C5×#475C2211yescharacteristic
37C5×#474C2211yescharacteristic
38C5×#470—21no—
39C5×#468—21no—
40C5×#464—21no—
41C5×#462C2211yescharacteristic
42C5×#461C2211yescharacteristic
43C5×#446C2211yescharacteristic
44C5×C8×Q8C2211yescharacteristic
45C5×#436C2211yescharacteristic
46C5×#435—21no—
47C5×C8×D4—21no—
48C5×C8×D4C2211yescharacteristic
49C5×#433—21no—
50C5×#431C2211yescharacteristic
51C5×#431C2211yescharacteristic
52C5×#424—21no—
53C5×#423C2211yescharacteristic
54C2×C5×C4⋊C8C2211yescharacteristic
55C5×#335C2211yescharacteristic
56C5×#335C2211yescharacteristic
57C5×#334C2211yescharacteristic
58C5×#334C2211yescharacteristic
59C5×#333C2211yescharacteristic
60C5×#333C2211yescharacteristic
61C5×#333C2211yescharacteristic
62C5×#333C2211yescharacteristic
63C5×#332C2211yescharacteristic
64C5×#332C2211yescharacteristic
65C5×#332C2211yescharacteristic
66C5×#332C2211yescharacteristic
67#19587C511yesmaximal, characteristic, direct product factor, Sylow
68C2×C5×Q16—21no—
69C2×C5×SD16—21no—
70C2×C5×M16—21no—
71C2×C5×M16—21no—
72C22×C5×C8—21no—
73C22×C5×C8—21no—
74C5×C4⋊Q8C2311yescharacteristic
75C5×C4⋊Q8C2311yescharacteristic
76C5×C4⋊Q8C2311yescharacteristic
77C5×C4⋊Q8C2311yescharacteristic
78C5×#126—21no—
79C5×#125—21no—
80C5×#125—21no—
81C5×#125D411yescharacteristic
82C5×#124D411yescharacteristic
83C5×#123—21no—
84C5×C22⋊Q8—21no—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—21no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8D411yescharacteristic
89C5×#121D411yescharacteristic
90C4×C5×Q8—21no—
91C4×C5×Q8—21no—
92C4×C5×Q8—21no—
93C4×C5×Q8—21no—
94C4×C5×Q8C2311yescharacteristic
95C4×C5×D4—21no—
96C4×C5×D4C2311yescharacteristic
97C5×#117—21no—
98C5×#117—21no—
99C5×#117—21no—
100C2×C42×C5C2311yescharacteristic
101C5×#107—21no—
102C5×#107—21no—
103C5×#107—21no—
104C5×#107—21no—
105C5×#107—21no—
106C5×#106—21no—
107C5×#106—21no—
108C5×#106—21no—
109C5×#106—21no—
110C5×#106—21no—
111C5×C4⋊C8—21no—
112C5×C4⋊C8—21no—
113C5×C4⋊C8—21no—
114C5×C4⋊C8—21no—
115C5×C4⋊C8D411yescharacteristic
116C5×C4⋊C8D411yescharacteristic
117C5×C4⋊C8C2311yescharacteristic
118C5×C4⋊C8C2311yescharacteristic
119C5×C4⋊C8C2311yescharacteristic
120C5×C4⋊C8C2311yescharacteristic
121C5×C4⋊C8C2311yescharacteristic
122C5×C4⋊C8C2311yescharacteristic
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—21no—
132C5×#102—21no—
133C5×#102—21no—
134C5×#102—21no—
135C5×C22⋊C8—21no—
136C5×C22⋊C8—21no—
137C5×C22⋊C8—21no—
138C5×C22⋊C8D411yescharacteristic
139C5×C22⋊C8D411yescharacteristic
140C5×#97—21no—
141C4×C5×C8—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3252C2×C511yescharacteristic
146#3233C2×C511yescharacteristic
147#3231C2×C511yescharacteristic, complemented
148#2994C2×C511yescharacteristic
149#1703C2×C511yescharacteristic, complemented
150#1700C2×C511yescharacteristic, complemented
151#1696C2×C511yescharacteristic, complemented
152#1691C2×C511yescharacteristic, complemented
153#1684C2×C511yescharacteristic, complemented
154#1679C2×C511yescharacteristic, complemented
155#1675C2×C511yescharacteristic, complemented
156#1672C2×C511yescharacteristic, complemented
157#1574C2×C511yescharacteristic, complemented
158#1550C2×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—81no—
172C5×SD16—81no—
173C5×M16—81no—
174C5×M16—81no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—81no—
182C2×C5×C8—81no—
183C2×C5×C8C2×D411yescharacteristic
184C2×C5×C8C2×D411yescharacteristic
185C2×C5×C8C2×D411yescharacteristic
186C2×C5×C8C2×D411yescharacteristic
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
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—41no—
200C5×C4⋊C4—41no—
201C5×C4⋊C4—41no—
202C5×C4⋊C4—41no—
203C5×C4⋊C4C2×D411yescharacteristic
204C5×C4⋊C4C2×D411yescharacteristic
205C5×C22⋊C4—21no—
206C5×C22⋊C4—21no—
207C5×C22⋊C4—21no—
208C5×C22⋊C4—21no—
209C5×C22⋊C4—21no—
210C5×C22⋊C4—41no—
211C5×C22⋊C4—41no—
212C42×C5—21no—
213C42×C5—41no—
214C42×C5—41no—
215C42×C5C2×D411yescharacteristic
216C42×C5C2×D411yescharacteristic
217C42×C5#4111yescharacteristic
218C42×C5C2411yescharacteristic
219#533C22×C511yescharacteristic
220#533C22×C511yescharacteristic
221#529C22×C511yescharacteristic
222#500C22×C511yescharacteristic
223#499—21no—
224#498C22×C511yescharacteristic
225#488—21no—
226#487C22×C511yescharacteristic
227#487C22×C511yescharacteristic
228#485—21no—
229#485—21no—
230#485—21no—
231#482—21no—
232#479—21no—
233#479—21no—
234#479—21no—
235#477C22×C511yescharacteristic
236#477C22×C511yescharacteristic
237#476C22×C511yescharacteristic
238#476C22×C511yescharacteristic
239#475C22×C511yescharacteristic
240#474C22×C511yescharacteristic
241#470—21no—
242#468—21no—
243#464—21no—
244#462C22×C511yescharacteristic
245#461C22×C511yescharacteristic
246#446C22×C511yescharacteristic
247C8×Q8C22×C511yescharacteristic
248#436C22×C511yescharacteristic
249#435—21no—
250C8×D4—21no—
251C8×D4C22×C511yescharacteristic
252#433—21no—
253#431C22×C511yescharacteristic
254#431C22×C511yescharacteristic
255#424—21no—
256#423C22×C511yescharacteristic
257C2×C4⋊C8C22×C511yescharacteristic
258#335C22×C511yescharacteristic
259#335C22×C511yescharacteristic
260#334C22×C511yescharacteristic
261#334C22×C511yescharacteristic
262#333C22×C511yescharacteristic
263#333C22×C511yescharacteristic
264#333C22×C511yescharacteristic
265#333C22×C511yescharacteristic
266#332C22×C511yescharacteristic
267#332C22×C511yescharacteristic
268#332C22×C511yescharacteristic
269#332C22×C511yescharacteristic
270C23×C5—21no—
271C23×C5#12111yescharacteristic
272C5×Q8—21no—
273C5×Q8—21no—
274C5×Q8—41no—
275C5×Q8—41no—
276C5×Q8—41no—
277C5×Q8—41no—
278C5×Q8—81no—
279C5×Q8—81no—
280C5×D4—21no—
281C5×D4—21no—
282C5×D4—42no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5#12111yescharacteristic
298C2×C4×C5#12111yescharacteristic
299C2×C4×C5#12111yescharacteristic
300C2×C4×C5C22×D411yescharacteristic
301C2×C4×C5C22×D411yescharacteristic
302C2×C4×C5C2×#4111yescharacteristic
303C5×C8—21no—
304C5×C8—21no—
305C5×C8—21no—
306C5×C8—21no—
307C5×C8—41no—
308C5×C8—41no—
309C5×C8—41no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—41no—
313C2×Q16—21no—
314C2×SD16—21no—
315C2×M16—21no—
316C2×M16—21no—
317C22×C8—21no—
318C22×C8—21no—
319C4⋊Q8C23×C511yescharacteristic
320C4⋊Q8C23×C511yescharacteristic
321C4⋊Q8C23×C511yescharacteristic
322C4⋊Q8C23×C511yescharacteristic
323#126—21no—
324#125—21no—
325#125—21no—
326#125C5×D411yescharacteristic
327#124C5×D411yescharacteristic
328#123—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8C5×D411yescharacteristic
334#121C5×D411yescharacteristic
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8C23×C511yescharacteristic
340C4×D4—21no—
341C4×D4C23×C511yescharacteristic
342#117—21no—
343#117—21no—
344#117—21no—
345C2×C42C23×C511yescharacteristic
346#107—21no—
347#107—21no—
348#107—21no—
349#107—21no—
350#107—21no—
351#106—21no—
352#106—21no—
353#106—21no—
354#106—21no—
355#106—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8C5×D411yescharacteristic
361C4⋊C8C5×D411yescharacteristic
362C4⋊C8C23×C511yescharacteristic
363C4⋊C8C23×C511yescharacteristic
364C4⋊C8C23×C511yescharacteristic
365C4⋊C8C23×C511yescharacteristic
366C4⋊C8C23×C511yescharacteristic
367C4⋊C8C23×C511yescharacteristic
368#103—21no—
369#103—21no—
370#103—21no—
371#103—21no—
372#103—21no—
373#103—21no—
374#103—21no—
375#103—21no—
376#103—21no—
377#102—21no—
378#102—21no—
379#102—21no—
380C22⋊C8—21no—
381C22⋊C8—21no—
382C22⋊C8—21no—
383C22⋊C8C5×D411yescharacteristic
384C22⋊C8C5×D411yescharacteristic
385#97—21no—
386C4×C8—21no—
387C4×C8—21no—
388C4×C8C23×C511yescharacteristic
389C4×C8C23×C511yescharacteristic
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—21no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5C2×#12111yescharacteristic
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—21no—
400C4×C5—21no—
401C4×C5—41no—
402C4×C5—41no—
403C4×C5—41no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5—81no—
407C4×C5—81no—
408C4×C5#57711yescharacteristic
409C4×C5#57711yescharacteristic
410C4×C5#57811yescharacteristic
411C4×C5#57811yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8C2×C5×D411yescharacteristic
417C2×D4—21no—
418C2×D4C2×C5×D411yescharacteristic
419C22×C4—21no—
420C22×C4C2×C5×D411yescharacteristic
421C22×C4C2×C5×D411yescharacteristic
422C22×C4C5×#4111yescharacteristic
423Q16—81no—
424SD16—81no—
425M16—81no—
426M16—81no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—81no—
434C2×C8—81no—
435C2×C8C2×C5×D411yescharacteristic
436C2×C8C2×C5×D411yescharacteristic
437C2×C8C2×C5×D411yescharacteristic
438C2×C8C2×C5×D411yescharacteristic
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4C2×C5×D411yescharacteristic
456C4⋊C4C2×C5×D411yescharacteristic
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C42—21no—
465C42—41no—
466C42—41no—
467C42C2×C5×D411yescharacteristic
468C42C2×C5×D411yescharacteristic
469C42C5×#4111yescharacteristic
470C42C24×C511yescharacteristic
471C2×C5—41no—
472C2×C5—81no—
473C2×C5#304611yescharacteristic
474C2×C5#306311yescharacteristic
475C2×C5#306711yescharacteristic
476C23—21no—
477C23C5×#12111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—41no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—81no—
485Q8—81no—
486D4—21no—
487D4—21no—
488D4—42no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4C5×#12111yescharacteristic
504C2×C4C5×#12111yescharacteristic
505C2×C4C5×#12111yescharacteristic
506C2×C4C22×C5×D411yescharacteristic
507C2×C4C22×C5×D411yescharacteristic
508C2×C4C2×C5×#4111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C5#1958711yescharacteristic, direct product factor, Sylow
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×C5×#12111yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4C5×#57711yescharacteristic
539C4C5×#57711yescharacteristic
540C4C5×#57811yescharacteristic
541C4C5×#57811yescharacteristic
542C2—41no—
543C2—81no—
544C2C5×#304611yescharacteristic
545C2C5×#306311yescharacteristic
546C2C5×#306711yescharacteristic
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×#3231C2semidirect
5. C5×#1703C2semidirect
6. C5×#1700C2semidirect
7. C5×#1696C2semidirect
8. C5×#1691C2semidirect
9. C5×#1684C2semidirect
10. C5×#1679C2semidirect
11. C5×#1675C2semidirect
12. C5×#1672C2semidirect
13. C5×#1574C2semidirect
14. C5×#1550C2semidirect
15. C5×#1542C2semidirect
67. #19587C5direct (N × H)
147. #3231C2×C5semidirect
149. #1703C2×C5semidirect
150. #1700C2×C5semidirect
151. #1696C2×C5semidirect
152. #1691C2×C5semidirect
153. #1684C2×C5semidirect
154. #1679C2×C5semidirect
155. #1675C2×C5semidirect
156. #1672C2×C5semidirect
157. #1574C2×C5semidirect
158. #1550C2×C5semidirect
159. #1542C2×C5semidirect
519. C5#19587direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32522
C5×#32332
C5×#32312
C5×#29942
C5×#17032
C5×#17002
C5×#16962
C5×#16912
C5×#16842
C5×#16792
C5×#16752
C5×#16722
C5×#15742
C5×#15502
C5×#15422
#195875