Finite Group Databasebeta

← C5×#18469 #11941189

Subgroups — C5×#18469 #11941189

Order 1280.

814 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3563C211yesmaximal, characteristic
2C5×#3236C211yesmaximal, characteristic, complemented
3C5×#3232C211yesmaximal, characteristic
4C5×#2822C211yesmaximal, characteristic, complemented
5C5×#1617C212yesmaximal, complemented
6C5×#1615C212yesmaximal
7C5×#1611C212yesmaximal, complemented
8C5×#1609C212yesmaximal
9C5×#1518C211yesmaximal, characteristic, complemented
10C5×#1512C211yesmaximal, characteristic
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×C5×#125C2211yescharacteristic
28C5×#501—21no—
29C5×#499—21no—
30C5×#491—21no—
31C5×#488—21no—
32C5×#484C2212yes—
33C5×#484C2211yescharacteristic
34C5×#483C2212yes—
35C5×#483C2211yescharacteristic
36C5×#481C2211yescharacteristic
37C5×#480C2211yescharacteristic
38C5×#479—21no—
39C5×#479—22no—
40C5×#478—21no—
41C5×#432C2211yescharacteristic
42C5×#431C2211yescharacteristic
43C5×#400—21no—
44C5×#400C2212yes—
45C5×#398—22no—
46C5×#398—21no—
47C5×#398C2212yes—
48C5×#382C2211yescharacteristic
49C5×#328C2212yes—
50C5×#328C2212yes—
51C5×#328C2212yes—
52C5×#327C2212yes—
53C5×#324C2212yes—
54C5×#324C2212yes—
55#18469C511yesmaximal, characteristic, direct product factor, Sylow
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8—22no—
58C5×C4⋊Q8—22no—
59C5×C4⋊Q8D411yescharacteristic
60C5×C4⋊Q8D411yescharacteristic
61C5×#126—22no—
62C5×#126—22no—
63C5×#126—22no—
64C5×#126—22no—
65C5×#126—21no—
66C5×#125—22no—
67C5×#125—22no—
68C5×#125—22no—
69C5×#125—22no—
70C5×#125—21no—
71C5×#125—22no—
72C5×#125—22no—
73C5×#125—22no—
74C5×#125—22no—
75C5×#125—21no—
76C5×#125—21no—
77C5×#125—21no—
78C5×#125—21no—
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×Q8D411yescharacteristic
104C4×C5×Q8D412yes—
105C4×C5×D4—21no—
106C4×C5×D4—22no—
107C4×C5×D4D411yescharacteristic
108C5×#117—22no—
109C5×#117—21no—
110C5×#117—21no—
111C5×#117—22no—
112C5×#117—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—22no—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4D412yes—
120C2×C5×C4⋊C4D411yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C4⋊C4C2311yescharacteristic
123C2×C5×C4⋊C4C2312yes—
124C2×C42×C5C2311yescharacteristic
125C5×#107—21no—
126C5×#107—21no—
127C5×#107—22no—
128C5×#106—21no—
129C5×#106—21no—
130C5×#106—22no—
131C5×C4⋊C8—21no—
132C5×C4⋊C8—21no—
133C5×#103—21no—
134C5×#103—22no—
135C5×#103—21no—
136C5×#103—22no—
137C5×#102—21no—
138C5×#102—21no—
139C5×C22⋊C8C2312yes—
140C5×C22⋊C8C2311yescharacteristic
141C5×C22⋊C8C2311yescharacteristic
142C5×#97—21no—
143C4×C5×C8—21no—
144C5×#95—21no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95C2312yes—
149#3563C2×C511yescharacteristic
150#3236C2×C511yescharacteristic, complemented
151#3232C2×C511yescharacteristic
152#2822C2×C511yescharacteristic, complemented
153#1617C2×C512yescomplemented
154#1615C2×C512yes—
155#1611C2×C512yescomplemented
156#1609C2×C512yes—
157#1518C2×C511yescharacteristic, complemented
158#1512C2×C511yescharacteristic
159#1470C2×C511yescharacteristic, complemented
160C2×C5×Q8—22no—
161C2×C5×Q8—21no—
162C2×C5×Q8C2×D412yes—
163C2×C5×Q8C2×D411yescharacteristic
164C2×C5×D4—21no—
165C2×C5×D4C2×D411yescharacteristic
166C22×C4×C5—22no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—22no—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2411yescharacteristic
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—22no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—22no—
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—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—41no—
209C5×C4⋊C4—41no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4—81no—
213C5×C4⋊C4—82no—
214C5×C4⋊C4C2×D411yescharacteristic
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D412yes—
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—21no—
222C5×C22⋊C4—21no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C42×C5—22no—
227C42×C5—22no—
228C42×C5—22no—
229C42×C5—22no—
230C42×C5—21no—
231C42×C5C2×D411yescharacteristic
232C42×C5C2×D411yescharacteristic
233C42×C5C2×D411yescharacteristic
234C42×C5C2×D411yescharacteristic
235#564—21no—
236#563—21no—
237#557—21no—
238#554—21no—
239#552—21no—
240#552—22no—
241#552—21no—
242#544—21no—
243#544C22×C512yes—
244#541—21no—
245#541—22no—
246#539C22×C512yes—
247#533C22×C511yescharacteristic
248#529C22×C511yescharacteristic
249C2×#125C22×C511yescharacteristic
250C2×#125C22×C511yescharacteristic
251#501—21no—
252#499—21no—
253#491—21no—
254#488—21no—
255#484C22×C512yes—
256#484C22×C511yescharacteristic
257#483C22×C512yes—
258#483C22×C511yescharacteristic
259#481C22×C511yescharacteristic
260#480C22×C511yescharacteristic
261#479—21no—
262#479—22no—
263#478—21no—
264#432C22×C511yescharacteristic
265#431C22×C511yescharacteristic
266#400—21no—
267#400C22×C512yes—
268#398—21no—
269#398—22no—
270#398C22×C512yes—
271#382C22×C511yescharacteristic
272#328C22×C512yes—
273#328C22×C512yes—
274#328C22×C512yes—
275#327C22×C512yes—
276#324C22×C512yes—
277#324C22×C512yes—
278C23×C5—21no—
279C23×C5C22×D411yescharacteristic
280C5×Q8—41no—
281C5×Q8—42no—
282C5×Q8—42no—
283C5×Q8—82no—
284C5×D4—41no—
285C5×D4—41no—
286C5×D4—41no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—22no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—42no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—82no—
311C2×C4×C5#12011yescharacteristic
312C2×C4×C5#12011yescharacteristic
313C2×C4×C5#12011yescharacteristic
314C2×C4×C5#12011yescharacteristic
315C2×C4×C5C22×D411yescharacteristic
316C2×C4×C5C22×D411yescharacteristic
317C5×C8—41no—
318C5×C8—41no—
319C5×C8—42no—
320C4⋊Q8—21no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8C5×D411yescharacteristic
324C4⋊Q8C5×D411yescharacteristic
325#126—22no—
326#126—22no—
327#126—22no—
328#126—22no—
329#126—21no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125—22no—
334#125—21no—
335#125—22no—
336#125—22no—
337#125—22no—
338#125—22no—
339#125—21no—
340#125—21no—
341#125—21no—
342#125—21no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125—21no—
348#125C5×D411yescharacteristic
349#124C5×D411yescharacteristic
350#123—22no—
351#123—21no—
352#123—22no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8C23×C511yescharacteristic
361C22⋊Q8C23×C512yes—
362#121C23×C511yescharacteristic
363C4×Q8—21no—
364C4×Q8—22no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C5×D411yescharacteristic
368C4×Q8C5×D412yes—
369C4×D4—21no—
370C4×D4—22no—
371C4×D4C5×D411yescharacteristic
372#117—22no—
373#117—21no—
374#117—21no—
375#117—22no—
376#117—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4C5×D411yescharacteristic
383C2×C4⋊C4C5×D412yes—
384C2×C4⋊C4C5×D411yescharacteristic
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C512yes—
388C2×C42C23×C511yescharacteristic
389#107—21no—
390#107—21no—
391#107—22no—
392#106—21no—
393#106—21no—
394#106—22no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397#103—21no—
398#103—22no—
399#103—21no—
400#103—22no—
401#102—21no—
402#102—21no—
403C22⋊C8C23×C512yes—
404C22⋊C8C23×C511yescharacteristic
405C22⋊C8C23×C511yescharacteristic
406#97—21no—
407C4×C8—21no—
408#95—21no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95C23×C512yes—
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—41no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5C2×#12011yescharacteristic
419C22×C5#57711yescharacteristic
420C22×C5#57811yescharacteristic
421C4×C5—21no—
422C4×C5—21no—
423C4×C5—21no—
424C4×C5—21no—
425C4×C5—21no—
426C4×C5—21no—
427C4×C5—42no—
428C4×C5—41no—
429C4×C5—41no—
430C4×C5—42no—
431C4×C5—42no—
432C4×C5—42no—
433C4×C5—41no—
434C4×C5—82no—
435C4×C5—81no—
436C4×C5—81no—
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8C2×C5×D412yes—
440C2×Q8C2×C5×D411yescharacteristic
441C2×D4—21no—
442C2×D4C2×C5×D411yescharacteristic
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4C2×C5×D412yes—
449C22×C4C2×C5×D411yescharacteristic
450C22×C4C2×C5×D412yes—
451C22×C4C2×C5×D411yescharacteristic
452C22×C4C24×C511yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—81no—
490C4⋊C4—82no—
491C4⋊C4C2×C5×D411yescharacteristic
492C4⋊C4C2×C5×D411yescharacteristic
493C4⋊C4C2×C5×D412yes—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—21no—
508C42C2×C5×D411yescharacteristic
509C42C2×C5×D411yescharacteristic
510C42C2×C5×D411yescharacteristic
511C42C2×C5×D411yescharacteristic
512C2×C5—21no—
513C2×C5—21no—
514C2×C5—81no—
515C2×C5#301311yescharacteristic
516C2×C5#302011yescharacteristic
517C2×C5#302811yescharacteristic
518C23—21no—
519C23C22×C5×D411yescharacteristic
520Q8—41no—
521Q8—42no—
522Q8—42no—
523Q8—82no—
524D4—41no—
525D4—41no—
526D4—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4C5×#12011yescharacteristic
552C2×C4C5×#12011yescharacteristic
553C2×C4C5×#12011yescharacteristic
554C2×C4C5×#12011yescharacteristic
555C2×C4C22×C5×D411yescharacteristic
556C2×C4C22×C5×D411yescharacteristic
557C8—41no—
558C8—41no—
559C8—42no—
560C5#1846911yescharacteristic, direct product factor, Sylow
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×C5×#12011yescharacteristic
567C22C5×#57711yescharacteristic
568C22C5×#57811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—82no—
583C4—81no—
584C4—81no—
585C2—21no—
586C2—21no—
587C2—81no—
588C2C5×#301311yescharacteristic
589C2C5×#302011yescharacteristic
590C2C5×#302811yescharacteristic
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
2. C5×#3236C2semidirect
4. C5×#2822C2semidirect
5. C5×#1617C2semidirect
7. C5×#1611C2semidirect
9. C5×#1518C2semidirect
11. C5×#1470C2semidirect
55. #18469C5direct (N × H)
150. #3236C2×C5semidirect
152. #2822C2×C5semidirect
153. #1617C2×C5semidirect
155. #1611C2×C5semidirect
157. #1518C2×C5semidirect
159. #1470C2×C5semidirect
560. C5#18469direct (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×#32362
C5×#32322
C5×#28222
C5×#16172
C5×#16152
C5×#16112
C5×#16092
C5×#15182
C5×#15122
C5×#14702
#184695