Finite Group Databasebeta

← C5×#19574 #11942294

Subgroups — C5×#19574 #11942294

Order 1280.

534 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3249C211yesmaximal, characteristic
2C5×#3237C211yesmaximal, characteristic
3C5×#3231C211yesmaximal, characteristic
4C5×#2986C211yesmaximal, characteristic
5C5×#1704C211yesmaximal, characteristic, complemented
6C5×#1700C211yesmaximal, characteristic, complemented
7C5×#1696C211yesmaximal, characteristic, complemented
8C5×#1692C211yesmaximal, characteristic, complemented
9C5×#1684C211yesmaximal, characteristic, complemented
10C5×#1680C211yesmaximal, characteristic, complemented
11C5×#1676C211yesmaximal, characteristic, complemented
12C5×#1672C211yesmaximal, characteristic, complemented
13C5×#1573C211yesmaximal, characteristic
14C5×#1554C211yesmaximal, characteristic
15C5×#1542C211yesmaximal, characteristic
16C5×#533C2211yescharacteristic
17C5×#533C2211yescharacteristic
18C5×#533C2211yescharacteristic
19C5×#501—21no—
20C5×#500C2211yescharacteristic
21C5×#498C2211yescharacteristic
22C5×#491—21no—
23C5×#487C2211yescharacteristic
24C5×#487C2211yescharacteristic
25C5×#485—21no—
26C5×#485—21no—
27C5×#485—21no—
28C5×#485—21no—
29C5×#479—21no—
30C5×#479—21no—
31C5×#477—21no—
32C5×#477C2211yescharacteristic
33C5×#477C2211yescharacteristic
34C5×#477C2211yescharacteristic
35C5×#477C2211yescharacteristic
36C5×#475C2211yescharacteristic
37C5×#475C2211yescharacteristic
38C5×#467—21no—
39C5×#467—21no—
40C5×#462—21no—
41C5×#462C2211yescharacteristic
42C5×#462C2211yescharacteristic
43C5×#446—21no—
44C5×#446C2211yescharacteristic
45C5×#446C2211yescharacteristic
46C5×C8×Q8—21no—
47C5×C8×Q8C2211yescharacteristic
48C5×C8×Q8C2211yescharacteristic
49C5×#433—21no—
50C5×#433—21no—
51C5×#432C2211yescharacteristic
52C5×#431C2211yescharacteristic
53C5×#431C2211yescharacteristic
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#19574C511yesmaximal, characteristic, direct product factor, Sylow
68C2×C5×Q16—21no—
69C2×C5×Q16—21no—
70C22×C5×C8—21no—
71C5×C4⋊Q8D411yescharacteristic
72C5×C4⋊Q8D411yescharacteristic
73C5×C4⋊Q8C2311yescharacteristic
74C5×C4⋊Q8C2311yescharacteristic
75C5×C4⋊Q8C2311yescharacteristic
76C5×C4⋊Q8C2311yescharacteristic
77C5×#125—21no—
78C5×#125—21no—
79C5×#125—21no—
80C5×C22⋊Q8—21no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—21no—
85C5×C22⋊Q8D411yescharacteristic
86C5×C22⋊Q8D411yescharacteristic
87C4×C5×Q8—21no—
88C4×C5×Q8—21no—
89C4×C5×Q8—21no—
90C4×C5×Q8—21no—
91C4×C5×Q8—21no—
92C4×C5×Q8C2311yescharacteristic
93C4×C5×Q8C2311yescharacteristic
94C5×#117—21no—
95C5×#117—21no—
96C5×#117—21no—
97C2×C42×C5C2311yescharacteristic
98C5×#107—21no—
99C5×#107—21no—
100C5×#107—21no—
101C5×#107—21no—
102C5×#107—21no—
103C5×#107—21no—
104C5×#106—21no—
105C5×#106—21no—
106C5×#106—21no—
107C5×#106—21no—
108C5×C4⋊C8—21no—
109C5×C4⋊C8—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×#103—21no—
128C5×#103—21no—
129C5×#103—21no—
130C5×#103—21no—
131C5×#103—21no—
132C5×#103—21no—
133C5×C22⋊C8—21no—
134C5×C22⋊C8—21no—
135C5×C22⋊C8D411yescharacteristic
136C5×C22⋊C8D411yescharacteristic
137C5×#97—21no—
138C5×#97—21no—
139C5×#97—21no—
140C4×C5×C8—21no—
141C4×C5×C8—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3249C2×C511yescharacteristic
146#3237C2×C511yescharacteristic
147#3231C2×C511yescharacteristic
148#2986C2×C511yescharacteristic
149#1704C2×C511yescharacteristic, complemented
150#1700C2×C511yescharacteristic, complemented
151#1696C2×C511yescharacteristic, complemented
152#1692C2×C511yescharacteristic, complemented
153#1684C2×C511yescharacteristic, complemented
154#1680C2×C511yescharacteristic, complemented
155#1676C2×C511yescharacteristic, complemented
156#1672C2×C511yescharacteristic, complemented
157#1573C2×C511yescharacteristic
158#1554C2×C511yescharacteristic
159#1542C2×C511yescharacteristic
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×Q8C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5#4111yescharacteristic
170C5×Q16—81no—
171C5×Q16—81no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—81no—
179C2×C5×C8C2×D411yescharacteristic
180C2×C5×C8C2×D411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
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—41no—
199C5×C4⋊C4—41no—
200C5×C4⋊C4—41no—
201C5×C4⋊C4—41no—
202C5×C4⋊C4C2×D411yescharacteristic
203C5×C4⋊C4C2×D411yescharacteristic
204C5×C22⋊C4—21no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—41no—
207C5×C22⋊C4—41no—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5—41no—
211C42×C5—41no—
212C42×C5C2×D411yescharacteristic
213C42×C5C2×D411yescharacteristic
214C42×C5#4111yescharacteristic
215C42×C5C2411yescharacteristic
216#533C22×C511yescharacteristic
217#533C22×C511yescharacteristic
218#533C22×C511yescharacteristic
219#501—21no—
220#500C22×C511yescharacteristic
221#498C22×C511yescharacteristic
222#491—21no—
223#487C22×C511yescharacteristic
224#487C22×C511yescharacteristic
225#485—21no—
226#485—21no—
227#485—21no—
228#485—21no—
229#479—21no—
230#479—21no—
231#477—21no—
232#477C22×C511yescharacteristic
233#477C22×C511yescharacteristic
234#477C22×C511yescharacteristic
235#477C22×C511yescharacteristic
236#475C22×C511yescharacteristic
237#475C22×C511yescharacteristic
238#467—21no—
239#467—21no—
240#462—21no—
241#462C22×C511yescharacteristic
242#462C22×C511yescharacteristic
243#446—21no—
244#446C22×C511yescharacteristic
245#446C22×C511yescharacteristic
246C8×Q8—21no—
247C8×Q8C22×C511yescharacteristic
248C8×Q8C22×C511yescharacteristic
249#433—21no—
250#433—21no—
251#432C22×C511yescharacteristic
252#431C22×C511yescharacteristic
253#431C22×C511yescharacteristic
254C2×C4⋊C8C22×C511yescharacteristic
255#335C22×C511yescharacteristic
256#335C22×C511yescharacteristic
257#334C22×C511yescharacteristic
258#334C22×C511yescharacteristic
259#333C22×C511yescharacteristic
260#333C22×C511yescharacteristic
261#333C22×C511yescharacteristic
262#333C22×C511yescharacteristic
263#332C22×C511yescharacteristic
264#332C22×C511yescharacteristic
265#332C22×C511yescharacteristic
266#332C22×C511yescharacteristic
267C23×C5#12111yescharacteristic
268C5×Q8—21no—
269C5×Q8—21no—
270C5×Q8—21no—
271C5×Q8—21no—
272C5×Q8—42no—
273C5×Q8—41no—
274C5×Q8—41no—
275C5×Q8—41no—
276C5×Q8—41no—
277C5×Q8—81no—
278C5×Q8—81no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5#12111yescharacteristic
293C2×C4×C5#12111yescharacteristic
294C2×C4×C5#12111yescharacteristic
295C2×C4×C5C22×D411yescharacteristic
296C2×C4×C5C22×D411yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C5×C8—21no—
299C5×C8—21no—
300C5×C8—21no—
301C5×C8—21no—
302C5×C8—41no—
303C5×C8—41no—
304C5×C8—41no—
305C5×C8—41no—
306C5×C8—41no—
307C5×C8—41no—
308C2×Q16—21no—
309C2×Q16—21no—
310C22×C8—21no—
311C4⋊Q8C5×D411yescharacteristic
312C4⋊Q8C5×D411yescharacteristic
313C4⋊Q8C23×C511yescharacteristic
314C4⋊Q8C23×C511yescharacteristic
315C4⋊Q8C23×C511yescharacteristic
316C4⋊Q8C23×C511yescharacteristic
317#125—21no—
318#125—21no—
319#125—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8C5×D411yescharacteristic
326C22⋊Q8C5×D411yescharacteristic
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8C23×C511yescharacteristic
333C4×Q8C23×C511yescharacteristic
334#117—21no—
335#117—21no—
336#117—21no—
337C2×C42C23×C511yescharacteristic
338#107—21no—
339#107—21no—
340#107—21no—
341#107—21no—
342#107—21no—
343#107—21no—
344#106—21no—
345#106—21no—
346#106—21no—
347#106—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8C5×D411yescharacteristic
354C4⋊C8C5×D411yescharacteristic
355C4⋊C8C23×C511yescharacteristic
356C4⋊C8C23×C511yescharacteristic
357C4⋊C8C23×C511yescharacteristic
358C4⋊C8C23×C511yescharacteristic
359C4⋊C8C23×C511yescharacteristic
360C4⋊C8C23×C511yescharacteristic
361#103—21no—
362#103—21no—
363#103—21no—
364#103—21no—
365#103—21no—
366#103—21no—
367#103—21no—
368#103—21no—
369#103—21no—
370#103—21no—
371#103—21no—
372#103—21no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8C5×D411yescharacteristic
376C22⋊C8C5×D411yescharacteristic
377#97—21no—
378#97—21no—
379#97—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8C23×C511yescharacteristic
384C4×C8C23×C511yescharacteristic
385C22×C5—21no—
386C22×C5—21no—
387C22×C5—21no—
388C22×C5C2×#12111yescharacteristic
389C4×C5—21no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—41no—
394C4×C5—41no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—81no—
398C4×C5—81no—
399C4×C5—81no—
400C4×C5—81no—
401C4×C5#57711yescharacteristic
402C4×C5#57811yescharacteristic
403C4×C5#57811yescharacteristic
404C4×C5#57811yescharacteristic
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C2×C5×D411yescharacteristic
411C2×Q8C2×C5×D411yescharacteristic
412C22×C4C2×C5×D411yescharacteristic
413C22×C4C2×C5×D411yescharacteristic
414C22×C4C5×#4111yescharacteristic
415Q16—81no—
416Q16—81no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—81no—
424C2×C8C2×C5×D411yescharacteristic
425C2×C8C2×C5×D411yescharacteristic
426C2×C8C2×C5×D411yescharacteristic
427C2×C8C2×C5×D411yescharacteristic
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4C2×C5×D411yescharacteristic
448C4⋊C4C2×C5×D411yescharacteristic
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C42—21no—
454C42—21no—
455C42—41no—
456C42—41no—
457C42C2×C5×D411yescharacteristic
458C42C2×C5×D411yescharacteristic
459C42C5×#4111yescharacteristic
460C42C24×C511yescharacteristic
461C2×C5—41no—
462C2×C5#304411yescharacteristic
463C2×C5#306311yescharacteristic
464C2×C5#306711yescharacteristic
465C23C5×#12111yescharacteristic
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—21no—
470Q8—42no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—81no—
476Q8—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4C5×#12111yescharacteristic
491C2×C4C5×#12111yescharacteristic
492C2×C4C5×#12111yescharacteristic
493C2×C4C22×C5×D411yescharacteristic
494C2×C4C22×C5×D411yescharacteristic
495C2×C4C2×C5×#4111yescharacteristic
496C8—21no—
497C8—21no—
498C8—21no—
499C8—21no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—41no—
504C8—41no—
505C8—41no—
506C5#1957411yescharacteristic, direct product factor, Sylow
507C22—21no—
508C22—21no—
509C22—21no—
510C22C2×C5×#12111yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—41no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4C5×#57711yescharacteristic
524C4C5×#57811yescharacteristic
525C4C5×#57811yescharacteristic
526C4C5×#57811yescharacteristic
527C2—41no—
528C2C5×#304411yescharacteristic
529C2C5×#306311yescharacteristic
530C2C5×#306711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC23×C5#121
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
5. C5×#1704C2semidirect
6. C5×#1700C2semidirect
7. C5×#1696C2semidirect
8. C5×#1692C2semidirect
9. C5×#1684C2semidirect
10. C5×#1680C2semidirect
11. C5×#1676C2semidirect
12. C5×#1672C2semidirect
67. #19574C5direct (N × H)
149. #1704C2×C5semidirect
150. #1700C2×C5semidirect
151. #1696C2×C5semidirect
152. #1692C2×C5semidirect
153. #1684C2×C5semidirect
154. #1680C2×C5semidirect
155. #1676C2×C5semidirect
156. #1672C2×C5semidirect
506. C5#19574direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32492
C5×#32372
C5×#32312
C5×#29862
C5×#17042
C5×#17002
C5×#16962
C5×#16922
C5×#16842
C5×#16802
C5×#16762
C5×#16722
C5×#15732
C5×#15542
C5×#15422
#195745