Finite Group Databasebeta

← C5×#18247 #11940967

Subgroups — C5×#18247 #11940967

Order 1280.

852 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3563C211yesmaximal, characteristic
2C5×#3117C211yesmaximal, characteristic
3C5×#3104C211yesmaximal, characteristic, complemented
4C5×#2634C211yesmaximal, characteristic, complemented
5C5×#1617C212yesmaximal, complemented
6C5×#1615C212yesmaximal
7C5×#1605C212yesmaximal, complemented
8C5×#1603C212yesmaximal
9C5×#1521C211yesmaximal, characteristic
10C5×#1515C211yesmaximal, characteristic, complemented
11C5×#1470C211yesmaximal, characteristic, complemented
12C5×#564—21no—
13C5×#563—21no—
14C5×#557—21no—
15C5×#554—21no—
16C5×#552—21no—
17C5×#552—22no—
18C5×#552—21no—
19C5×#544—21no—
20C5×#544C2212yes—
21C5×#541—21no—
22C5×#541—22no—
23C5×#539C2212yes—
24C5×#533C2211yescharacteristic
25C5×#529C2211yescharacteristic
26C2×C5×#125C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C5×#484C2212yes—
29C5×#484C2211yescharacteristic
30C5×#481C2211yescharacteristic
31C5×#479—21no—
32C5×#477—21no—
33C5×#464—21no—
34C5×#462—21no—
35C5×#451C2212yes—
36C5×#451C2211yescharacteristic
37C5×#448C2211yescharacteristic
38C5×#441—21no—
39C5×#440—21no—
40C4×C5×Q16—22no—
41C5×#432C2211yescharacteristic
42C5×#431C2211yescharacteristic
43C5×#400—21no—
44C5×#400C2212yes—
45C5×#398—21no—
46C5×#395C2212yes—
47C5×#387—22no—
48C5×#383C2211yescharacteristic
49C5×#328C2212yes—
50C5×#328C2212yes—
51C5×#328C2212yes—
52C5×#327C2212yes—
53C5×#324C2212yes—
54C5×#324C2212yes—
55#18247C511yesmaximal, characteristic, direct product factor, Sylow
56C22×C5×Q8C2311yescharacteristic
57C2×C5×Q16—22no—
58C2×C5×Q16—21no—
59C2×C5×SD16—21no—
60C5×C4⋊Q8—21no—
61C5×C4⋊Q8—22no—
62C5×C4⋊Q8—22no—
63C5×C4⋊Q8D411yescharacteristic
64C5×C4⋊Q8D411yescharacteristic
65C5×#126—22no—
66C5×#126—22no—
67C5×#126—22no—
68C5×#126—22no—
69C5×#126—21no—
70C5×#125—22no—
71C5×#125—22no—
72C5×#125—22no—
73C5×#125—22no—
74C5×#125—21no—
75C5×#125—22no—
76C5×#125—22no—
77C5×#125—22no—
78C5×#125—22no—
79C5×#125—21no—
80C5×#125—21no—
81C5×#125—21no—
82C5×#125—21no—
83C5×#125—21no—
84C5×#125D411yescharacteristic
85C5×#124D411yescharacteristic
86C5×#123—22no—
87C5×#123—21no—
88C5×#123—22no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8C2311yescharacteristic
97C5×C22⋊Q8C2312yes—
98C5×#121C2311yescharacteristic
99C4×C5×Q8—21no—
100C4×C5×Q8—22no—
101C4×C5×Q8—21no—
102C4×C5×Q8—21no—
103C4×C5×Q8—21no—
104C4×C5×Q8—21no—
105C4×C5×Q8—21no—
106C4×C5×Q8—21no—
107C4×C5×Q8D412yes—
108C4×C5×Q8D411yescharacteristic
109C4×C5×D4—21no—
110C4×C5×D4—22no—
111C4×C5×D4D411yescharacteristic
112C5×#117—22no—
113C5×#117—21no—
114C5×#117—21no—
115C5×#117—22no—
116C5×#117—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4—22no—
119C2×C5×C4⋊C4—21no—
120C2×C5×C4⋊C4D412yes—
121C2×C5×C4⋊C4D411yescharacteristic
122C2×C5×C4⋊C4D411yescharacteristic
123C2×C5×C4⋊C4C2311yescharacteristic
124C2×C5×C4⋊C4C2312yes—
125C2×C42×C5—21no—
126C2×C42×C5C2311yescharacteristic
127C5×#107—22no—
128C5×#107—21no—
129C5×#106—21no—
130C5×C4⋊C8—21no—
131C5×C4⋊C8—21no—
132C5×#103—22no—
133C5×#103—21no—
134C5×#103—22no—
135C5×#103—21no—
136C5×#103—21no—
137C5×#102—21no—
138C5×C22⋊C8C2312yes—
139C5×C22⋊C8C2311yescharacteristic
140C5×C22⋊C8C2311yescharacteristic
141C5×#97—21no—
142C4×C5×C8—21no—
143C5×#95—21no—
144C5×#95—21no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95C2312yes—
149#3563C2×C511yescharacteristic
150#3117C2×C511yescharacteristic
151#3104C2×C511yescharacteristic, complemented
152#2634C2×C511yescharacteristic, complemented
153#1617C2×C512yescomplemented
154#1615C2×C512yes—
155#1605C2×C512yescomplemented
156#1603C2×C512yes—
157#1521C2×C511yescharacteristic
158#1515C2×C511yescharacteristic, complemented
159#1470C2×C511yescharacteristic, complemented
160C2×C5×Q8—22no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—42no—
165C2×C5×Q8C2×D412yes—
166C2×C5×Q8C2×D411yescharacteristic
167C2×C5×D4—21no—
168C2×C5×D4C2×D411yescharacteristic
169C22×C4×C5—21no—
170C22×C4×C5—22no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—22no—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5C2×D412yes—
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2411yescharacteristic
179C5×Q16—42no—
180C5×Q16—44no—
181C5×SD16—42no—
182C2×C5×C8—21no—
183C2×C5×C8—22no—
184C2×C5×C8—21no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—44no—
213C5×C4⋊C4—41no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D412yes—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—21no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C42×C5—22no—
228C42×C5—22no—
229C42×C5—22no—
230C42×C5—22no—
231C42×C5—21no—
232C42×C5—41no—
233C42×C5—41no—
234C42×C5C2×D411yescharacteristic
235C42×C5C2×D411yescharacteristic
236C42×C5C2×D411yescharacteristic
237C42×C5C2×D411yescharacteristic
238#564—21no—
239#563—21no—
240#557—21no—
241#554—21no—
242#552—21no—
243#552—22no—
244#552—21no—
245#544—21no—
246#544C22×C512yes—
247#541—21no—
248#541—22no—
249#539C22×C512yes—
250#533C22×C511yescharacteristic
251#529C22×C511yescharacteristic
252C2×#125C22×C511yescharacteristic
253C2×C4×Q8C22×C511yescharacteristic
254#484C22×C512yes—
255#484C22×C511yescharacteristic
256#481C22×C511yescharacteristic
257#479—21no—
258#477—21no—
259#464—21no—
260#462—21no—
261#451C22×C512yes—
262#451C22×C511yescharacteristic
263#448C22×C511yescharacteristic
264#441—21no—
265#440—21no—
266C4×Q16—22no—
267#432C22×C511yescharacteristic
268#431C22×C511yescharacteristic
269#400—21no—
270#400C22×C512yes—
271#398—21no—
272#395C22×C512yes—
273#387—22no—
274#383C22×C511yescharacteristic
275#328C22×C512yes—
276#328C22×C512yes—
277#328C22×C512yes—
278#327C22×C512yes—
279#324C22×C512yes—
280#324C22×C512yes—
281C23×C5—21no—
282C23×C5C22×D411yescharacteristic
283C5×Q8—22no—
284C5×Q8—22no—
285C5×Q8—41no—
286C5×Q8—42no—
287C5×Q8—42no—
288C5×Q8—41no—
289C5×Q8—41no—
290C5×Q8—82no—
291C5×D4—41no—
292C5×D4—42no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—21no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—24no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—42no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—41no—
313C2×C4×C5—42no—
314C2×C4×C5—82no—
315C2×C4×C5#12011yescharacteristic
316C2×C4×C5#12011yescharacteristic
317C2×C4×C5#12011yescharacteristic
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5C22×D411yescharacteristic
320C2×C4×C5C22×D411yescharacteristic
321C5×C8—41no—
322C5×C8—41no—
323C5×C8—42no—
324C22×Q8C23×C511yescharacteristic
325C2×Q16—22no—
326C2×Q16—21no—
327C2×SD16—21no—
328C4⋊Q8—21no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8C5×D411yescharacteristic
332C4⋊Q8C5×D411yescharacteristic
333#126—22no—
334#126—22no—
335#126—22no—
336#126—22no—
337#126—21no—
338#125—22no—
339#125—22no—
340#125—22no—
341#125—22no—
342#125—21no—
343#125—22no—
344#125—22no—
345#125—22no—
346#125—22no—
347#125—21no—
348#125—21no—
349#125—21no—
350#125—21no—
351#125—21no—
352#125C5×D411yescharacteristic
353#124C5×D411yescharacteristic
354#123—22no—
355#123—21no—
356#123—22no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—22no—
364C22⋊Q8C23×C511yescharacteristic
365C22⋊Q8C23×C512yes—
366#121C23×C511yescharacteristic
367C4×Q8—21no—
368C4×Q8—22no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C5×D411yescharacteristic
376C4×Q8C5×D412yes—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4C5×D411yescharacteristic
380#117—22no—
381#117—21no—
382#117—21no—
383#117—22no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4C5×D412yes—
389C2×C4⋊C4C5×D411yescharacteristic
390C2×C4⋊C4C5×D411yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C512yes—
393C2×C42—21no—
394C2×C42C23×C511yescharacteristic
395#107—22no—
396#107—21no—
397#106—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400#103—22no—
401#103—21no—
402#103—22no—
403#103—21no—
404#103—21no—
405#102—21no—
406C22⋊C8C23×C512yes—
407C22⋊C8C23×C511yescharacteristic
408C22⋊C8C23×C511yescharacteristic
409#97—21no—
410C4×C8—21no—
411#95—21no—
412#95—21no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95C23×C512yes—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5C2×#12011yescharacteristic
423C22×C5#57812yes—
424C4×C5—21no—
425C4×C5—21no—
426C4×C5—21no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—42no—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5—42no—
435C4×C5—42no—
436C4×C5—42no—
437C4×C5—41no—
438C4×C5—82no—
439C4×C5—81no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C2×C5×D412yes—
446C2×Q8C2×C5×D411yescharacteristic
447C2×D4—21no—
448C2×D4C2×C5×D411yescharacteristic
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4C2×C5×D412yes—
455C22×C4C2×C5×D411yescharacteristic
456C22×C4C2×C5×D412yes—
457C22×C4C2×C5×D411yescharacteristic
458C22×C4C24×C511yescharacteristic
459Q16—42no—
460Q16—44no—
461SD16—42no—
462C2×C8—22no—
463C2×C8—21no—
464C2×C8—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—44no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C2×C5×D411yescharacteristic
496C4⋊C4C2×C5×D411yescharacteristic
497C4⋊C4C2×C5×D412yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C42—22no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—21no—
512C42—41no—
513C42—41no—
514C42C2×C5×D411yescharacteristic
515C42C2×C5×D411yescharacteristic
516C42C2×C5×D411yescharacteristic
517C42C2×C5×D411yescharacteristic
518C2×C5—22no—
519C2×C5—81no—
520C2×C5#301111yescharacteristic
521C2×C5#302011yescharacteristic
522C2×C5#302511yescharacteristic
523C23—21no—
524C23C22×C5×D411yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—42no—
529Q8—41no—
530Q8—41no—
531Q8—42no—
532Q8—82no—
533D4—41no—
534D4—42no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—82no—
557C2×C4C5×#12011yescharacteristic
558C2×C4C5×#12011yescharacteristic
559C2×C4C5×#12011yescharacteristic
560C2×C4C5×#12011yescharacteristic
561C2×C4C22×C5×D411yescharacteristic
562C2×C4C22×C5×D411yescharacteristic
563C8—41no—
564C8—41no—
565C8—42no—
566C5#1824711yescharacteristic, direct product factor, Sylow
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22C2×C5×#12011yescharacteristic
573C22C5×#57812yes—
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—42no—
581C4—41no—
582C4—41no—
583C4—42no—
584C4—42no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—82no—
589C4—81no—
590C2—22no—
591C2—81no—
592C2C5×#301111yescharacteristic
593C2C5×#302011yescharacteristic
594C2C5×#302511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#121C23
LCSG ▷ C22×C4 ▷ 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×#3104C2semidirect
4. C5×#2634C2semidirect
5. C5×#1617C2semidirect
7. C5×#1605C2semidirect
10. C5×#1515C2semidirect
11. C5×#1470C2semidirect
55. #18247C5direct (N × H)
151. #3104C2×C5semidirect
152. #2634C2×C5semidirect
153. #1617C2×C5semidirect
155. #1605C2×C5semidirect
158. #1515C2×C5semidirect
159. #1470C2×C5semidirect
566. C5#18247direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35632
C5×#31172
C5×#31042
C5×#26342
C5×#16172
C5×#16152
C5×#16052
C5×#16032
C5×#15212
C5×#15152
C5×#14702
#182475