Finite Group Databasebeta

← C5×#19046 #11941766

Subgroups — C5×#19046 #11941766

Order 1280.

836 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, complemented
2C5×#3234C211yesmaximal, characteristic, complemented
3C5×#3180C211yesmaximal, characteristic
4C5×#3135C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1663C212yesmaximal, complemented
7C5×#1658C212yesmaximal, complemented
8C5×#1657C212yesmaximal, complemented
9C5×#1532C211yesmaximal, characteristic, complemented
10C5×#1531C211yesmaximal, characteristic, complemented
11C2×C5×#330C211yesmaximal, characteristic, complemented
12C5×#564C2212yes—
13C5×#563C2212yes—
14C5×#557—21no—
15C5×#554—21no—
16C5×#552—21no—
17C5×#552—22no—
18C5×#552—21no—
19C5×#544—21no—
20C5×#544—21no—
21C5×#541—21no—
22C5×#541—22no—
23C5×#539—21no—
24C5×#533C2211yescharacteristic
25C5×#532C2211yescharacteristic
26C5×#529C2211yescharacteristic
27C2×C5×#125C2211yescharacteristic
28C5×#501C2211yescharacteristic
29C5×#501C2212yes—
30C5×#496C2211yescharacteristic
31C5×#491C2212yes—
32C5×#490C2212yes—
33C5×#490C2212yes—
34C5×#490C2211yescharacteristic
35C5×#489—21no—
36C5×#489—21no—
37C5×#489C2211yescharacteristic
38C5×#481—21no—
39C5×#480—21no—
40C5×#478—22no—
41C5×#466—21no—
42C5×#465—21no—
43C5×#442—21no—
44C5×#440—21no—
45C5×#432C2211yescharacteristic
46C5×#416—22no—
47C2×C5×#97C2211yescharacteristic
48C2×C5×#97C2211yescharacteristic
49C5×#330C2212yes—
50C5×#330C2212yes—
51C5×#330C2212yes—
52C5×#330C2212yes—
53C5×#330C2212yes—
54C5×#329C2212yes—
55#19046C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C2×C5×SD16—21no—
58C2×C5×D8—21no—
59C22×C5×C8—21no—
60C22×C5×C8—21no—
61C5×C4⋊Q8—22no—
62C5×C4⋊Q8—21no—
63C5×C4⋊Q8—22no—
64C5×C4⋊Q8D411yescharacteristic
65C5×C4⋊Q8D411yescharacteristic
66C5×C4⋊Q8C2311yescharacteristic
67C5×#127C2311yescharacteristic
68C5×#126—22no—
69C5×#126—22no—
70C5×#126—22no—
71C5×#126—22no—
72C5×#126—21no—
73C5×#125—22no—
74C5×#125—22no—
75C5×#125—21no—
76C5×#125—22no—
77C5×#125—22no—
78C5×#125—22no—
79C5×#125—22no—
80C5×#125—22no—
81C5×#125—22no—
82C5×#125—21no—
83C5×#125—21no—
84C5×#125D412yes—
85C5×#125C2312yes—
86C5×#125C2312yes—
87C5×#125C2311yescharacteristic
88C5×#124—21no—
89C5×#124C2311yescharacteristic
90C5×#123—22no—
91C5×#123—22no—
92C5×#123—21no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—21no—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—21no—
98C5×C22⋊Q8—21no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8D411yescharacteristic
102C5×#121—21no—
103C5×#121—21no—
104C5×#121D411yescharacteristic
105C4×C5×Q8—21no—
106C4×C5×Q8—22no—
107C4×C5×Q8—21no—
108C4×C5×Q8—21no—
109C4×C5×Q8—21no—
110C4×C5×Q8D411yescharacteristic
111C4×C5×D4—22no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4D411yescharacteristic
116C5×#117—22no—
117C5×#117—21no—
118C5×#117—22no—
119C5×#117—21no—
120C5×#117D412yes—
121C2×C5×C4⋊C4—21no—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4D411yescharacteristic
125C2×C5×C4⋊C4D411yescharacteristic
126C2×C42×C5C2311yescharacteristic
127C5×#107—21no—
128C5×#107—22no—
129C5×#106—21no—
130C5×#106—22no—
131C5×C4⋊C8—21no—
132C5×#103—21no—
133C5×#103—22no—
134C5×#103—22no—
135C5×#102—21no—
136C5×#102—22no—
137C5×#102—22no—
138C5×#102—21no—
139C5×#102—21no—
140C5×#102—22no—
141C5×#102—22no—
142C5×C22⋊C8—21no—
143C5×#97—21no—
144C5×#97—21no—
145C5×#97C2312yes—
146C5×#97C2312yes—
147C5×#97C2311yescharacteristic
148C5×#97C2311yescharacteristic
149#3563C2×C511yescharacteristic, complemented
150#3234C2×C511yescharacteristic, complemented
151#3180C2×C511yescharacteristic
152#3135C2×C511yescharacteristic, complemented
153#1664C2×C512yescomplemented
154#1663C2×C512yescomplemented
155#1658C2×C512yescomplemented
156#1657C2×C512yescomplemented
157#1532C2×C511yescharacteristic, complemented
158#1531C2×C511yescharacteristic, complemented
159C2×#330C2×C511yescharacteristic, complemented
160C5×#41—44no—
161C2×C5×Q8—22no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—41no—
171C2×C5×D4C2×D411yescharacteristic
172C22×C4×C5—21no—
173C22×C4×C5—22no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—41no—
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C5×SD16—42no—
181C5×D8—42no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—42no—
187C2×C5×C8—42no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4C2×D412yes—
213C5×C4⋊C4C2×D412yes—
214C5×C4⋊C4C2×D412yes—
215C5×C4⋊C4C2×D412yes—
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—21no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—41no—
228C5×C22⋊C4—41no—
229C42×C5—22no—
230C42×C5—22no—
231C42×C5—22no—
232C42×C5—22no—
233C42×C5—21no—
234C42×C5C2×D411yescharacteristic
235C42×C5C2×D411yescharacteristic
236C42×C5C2×D411yescharacteristic
237C42×C5C2411yescharacteristic
238#564C22×C512yes—
239#563C22×C512yes—
240#557—21no—
241#554—21no—
242#552—21no—
243#552—22no—
244#552—21no—
245#544—21no—
246#544—21no—
247#541—21no—
248#541—22no—
249#539—21no—
250#533C22×C511yescharacteristic
251#532C22×C511yescharacteristic
252#529C22×C511yescharacteristic
253C2×#125C22×C511yescharacteristic
254#501C22×C511yescharacteristic
255#501C22×C512yes—
256#496C22×C511yescharacteristic
257#491C22×C512yes—
258#490C22×C512yes—
259#490C22×C511yescharacteristic
260#490C22×C512yes—
261#489—21no—
262#489—21no—
263#489C22×C511yescharacteristic
264#481—21no—
265#480—21no—
266#478—22no—
267#466—21no—
268#465—21no—
269#442—21no—
270#440—21no—
271#432C22×C511yescharacteristic
272#416—22no—
273C2×#97C22×C511yescharacteristic
274C2×#97C22×C511yescharacteristic
275#330C22×C512yes—
276#330C22×C512yes—
277#330C22×C512yes—
278#330C22×C512yes—
279#330C22×C512yes—
280#329C22×C512yes—
281C23×C5—21no—
282C23×C5—41no—
283C23×C5#12011yescharacteristic
284C5×Q8—41no—
285C5×Q8—42no—
286C5×Q8—42no—
287C5×Q8—81no—
288C5×Q8—82no—
289C5×D4—41no—
290C5×D4—41no—
291C5×D4—41no—
292C5×D4—42no—
293C5×D4—42no—
294C5×D4—42no—
295C5×D4—82no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—22no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—42no—
307C2×C4×C5—42no—
308C2×C4×C5—41no—
309C2×C4×C5—82no—
310C2×C4×C5—81no—
311C2×C4×C5—82no—
312C2×C4×C5#12011yescharacteristic
313C2×C4×C5#12011yescharacteristic
314C2×C4×C5#12011yescharacteristic
315C2×C4×C5C22×D411yescharacteristic
316C2×C4×C5C22×D411yescharacteristic
317C2×C4×C5C22×D411yescharacteristic
318C5×C8—22no—
319C5×C8—42no—
320C5×C8—42no—
321C5×C8—41no—
322C2×#41—21no—
323C2×SD16—21no—
324C2×D8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C4⋊Q8—22no—
328C4⋊Q8—21no—
329C4⋊Q8—22no—
330C4⋊Q8C5×D411yescharacteristic
331C4⋊Q8C5×D411yescharacteristic
332C4⋊Q8C23×C511yescharacteristic
333#127C23×C511yescharacteristic
334#126—22no—
335#126—22no—
336#126—22no—
337#126—22no—
338#126—21no—
339#125—22no—
340#125—22no—
341#125—21no—
342#125—22no—
343#125—22no—
344#125—22no—
345#125—22no—
346#125—22no—
347#125—22no—
348#125—21no—
349#125—21no—
350#125C5×D412yes—
351#125C23×C512yes—
352#125C23×C511yescharacteristic
353#125C23×C512yes—
354#124—21no—
355#124C23×C511yescharacteristic
356#123—22no—
357#123—22no—
358#123—21no—
359C22⋊Q8—22no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8C5×D411yescharacteristic
368#121—21no—
369#121—21no—
370#121C5×D411yescharacteristic
371C4×Q8—21no—
372C4×Q8—22no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C5×D411yescharacteristic
377C4×D4—22no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C5×D411yescharacteristic
382#117—22no—
383#117—21no—
384#117—22no—
385#117—21no—
386#117C5×D412yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C5×D411yescharacteristic
391C2×C4⋊C4C5×D411yescharacteristic
392C2×C42C23×C511yescharacteristic
393#107—21no—
394#107—22no—
395#106—21no—
396#106—22no—
397C4⋊C8—21no—
398#103—21no—
399#103—22no—
400#103—22no—
401#102—21no—
402#102—22no—
403#102—22no—
404#102—21no—
405#102—21no—
406#102—22no—
407#102—22no—
408C22⋊C8—21no—
409#97—21no—
410#97—21no—
411#97C23×C512yes—
412#97C23×C512yes—
413#97C23×C511yescharacteristic
414#97C23×C511yescharacteristic
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—81no—
421C22×C5—81no—
422C22×C5—81no—
423C22×C5#45412yes—
424C22×C5C2×#12011yescharacteristic
425C4×C5—21no—
426C4×C5—21no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—42no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5—42no—
435C4×C5—41no—
436C4×C5—41no—
437C4×C5—42no—
438C4×C5—81no—
439#41—44no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×C5×D411yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4C2×C5×D411yescharacteristic
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4C2×C5×D411yescharacteristic
457C22×C4C2×C5×D411yescharacteristic
458C22×C4C2×C5×D411yescharacteristic
459SD16—42no—
460D8—42no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—42no—
466C2×C8—42no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4C2×C5×D412yes—
492C4⋊C4C2×C5×D412yes—
493C4⋊C4C2×C5×D412yes—
494C4⋊C4C2×C5×D411yescharacteristic
495C4⋊C4C2×C5×D412yes—
496C4⋊C4C2×C5×D411yescharacteristic
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42C2×C5×D411yescharacteristic
514C42C2×C5×D411yescharacteristic
515C42C2×C5×D411yescharacteristic
516C42C24×C511yescharacteristic
517C2×C5—22no—
518C2×C5—81no—
519C2×C5—161no—
520C2×C5C2×#45411yescharacteristic
521C2×C5#301811yescharacteristic
522C2×C5#302011yescharacteristic
523C23—21no—
524C23—41no—
525C23C5×#12011yescharacteristic
526Q8—41no—
527Q8—42no—
528Q8—42no—
529Q8—81no—
530Q8—82no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—82no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4—81no—
553C2×C4—82no—
554C2×C4C5×#12011yescharacteristic
555C2×C4C5×#12011yescharacteristic
556C2×C4C5×#12011yescharacteristic
557C2×C4C22×C5×D411yescharacteristic
558C2×C4C22×C5×D411yescharacteristic
559C2×C4C22×C5×D411yescharacteristic
560C8—22no—
561C8—42no—
562C8—41no—
563C8—42no—
564C5#1904611yescharacteristic, direct product factor, Sylow
565C22—21no—
566C22—21no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C5×#45412yes—
574C22C2×C5×#12011yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—42no—
588C4—81no—
589C2—22no—
590C2—81no—
591C2—161no—
592C2C2×C5×#45411yescharacteristic
593C2C5×#301811yescharacteristic
594C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3180C2
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
1. C5×#3563C2semidirect
2. C5×#3234C2semidirect
4. C5×#3135C2semidirect
5. C5×#1664C2semidirect
6. C5×#1663C2semidirect
7. C5×#1658C2semidirect
8. C5×#1657C2semidirect
9. C5×#1532C2semidirect
10. C5×#1531C2semidirect
11. C2×C5×#330C2semidirect
55. #19046C5direct (N × H)
149. #3563C2×C5semidirect
150. #3234C2×C5semidirect
152. #3135C2×C5semidirect
153. #1664C2×C5semidirect
154. #1663C2×C5semidirect
155. #1658C2×C5semidirect
156. #1657C2×C5semidirect
157. #1532C2×C5semidirect
158. #1531C2×C5semidirect
159. C2×#330C2×C5semidirect
564. C5#19046direct (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×#32342
C5×#31802
C5×#31352
C5×#16642
C5×#16632
C5×#16582
C5×#16572
C5×#15322
C5×#15312
C2×C5×#3302
#190465