Finite Group Databasebeta

← C5×#19047 #11941767

Subgroups — C5×#19047 #11941767

Order 1280.

814 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3563C211yesmaximal, characteristic
2C5×#3236C211yesmaximal, characteristic, complemented
3C5×#3181C211yesmaximal, characteristic
4C5×#3162C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1663C212yesmaximal, complemented
7C5×#1663C212yesmaximal, complemented
8C5×#1660C212yesmaximal, complemented
9C5×#1532C211yesmaximal, characteristic
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×#533C2211yescharacteristic
26C5×#529C2211yescharacteristic
27C2×C5×#125C2211yescharacteristic
28C5×#501—21no—
29C5×#501—21no—
30C5×#501C2212yes—
31C5×#501C2212yes—
32C5×#501C2211yescharacteristic
33C5×#501C2212yes—
34C5×#497C2211yescharacteristic
35C5×#491C2211yescharacteristic
36C5×#491C2212yes—
37C5×#489C2211yescharacteristic
38C5×#484—21no—
39C5×#483—21no—
40C5×#479—22no—
41C5×#467—21no—
42C5×#465—21no—
43C5×#441—21no—
44C5×#440—21no—
45C5×#432C2211yescharacteristic
46C5×#427—22no—
47C2×C5×#97C2211yescharacteristic
48C2×C5×#97C2211yescharacteristic
49C5×#330C2212yes—
50C5×#330C2212yes—
51C5×#330C2212yes—
52C5×#330C2212yes—
53C5×#330C2212yes—
54C5×#329C2212yes—
55#19047C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×Q16—21no—
57C2×C5×SD16—21no—
58C22×C5×C8—21no—
59C22×C5×C8—21no—
60C5×C4⋊Q8—22no—
61C5×C4⋊Q8—21no—
62C5×C4⋊Q8—22no—
63C5×C4⋊Q8D411yescharacteristic
64C5×C4⋊Q8D411yescharacteristic
65C5×C4⋊Q8C2311yescharacteristic
66C5×C4⋊Q8C2311yescharacteristic
67C5×#126—22no—
68C5×#126—22no—
69C5×#126—22no—
70C5×#126—22no—
71C5×#126—21no—
72C5×#125—22no—
73C5×#125—22no—
74C5×#125—21no—
75C5×#125—22no—
76C5×#125—22no—
77C5×#125—22no—
78C5×#125—22no—
79C5×#125—22no—
80C5×#125—22no—
81C5×#125—21no—
82C5×#125—21no—
83C5×#125—21no—
84C5×#125D412yes—
85C5×#125C2312yes—
86C5×#125C2311yescharacteristic
87C5×#125C2312yes—
88C5×#124C2311yescharacteristic
89C5×#123—22no—
90C5×#123—22no—
91C5×#123—21no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—21no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8—21no—
97C5×C22⋊Q8—21no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—21no—
101C5×C22⋊Q8—21no—
102C5×C22⋊Q8D411yescharacteristic
103C5×#121D411yescharacteristic
104C4×C5×Q8—21no—
105C4×C5×Q8—22no—
106C4×C5×Q8—21no—
107C4×C5×Q8—21no—
108C4×C5×Q8—21no—
109C4×C5×Q8—21no—
110C4×C5×Q8—21no—
111C4×C5×Q8D411yescharacteristic
112C4×C5×D4—22no—
113C4×C5×D4—21no—
114C4×C5×D4D411yescharacteristic
115C5×#117—22no—
116C5×#117—21no—
117C5×#117—22no—
118C5×#117—21no—
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—22no—
128C5×#107—22no—
129C5×#107—21no—
130C5×#107—22no—
131C5×#106—22no—
132C5×#106—22no—
133C5×#106—21no—
134C5×#106—22no—
135C5×C4⋊C8—21no—
136C5×#103—21no—
137C5×#103—21no—
138C5×#103—21no—
139C5×#103—22no—
140C5×#103—22no—
141C5×#102—21no—
142C5×C22⋊C8—21no—
143C5×#97—21no—
144C5×#97—21no—
145C5×#97C2312yes—
146C5×#97C2312yes—
147C5×#97C2311yescharacteristic
148C5×#97C2311yescharacteristic
149#3563C2×C511yescharacteristic
150#3236C2×C511yescharacteristic, complemented
151#3181C2×C511yescharacteristic
152#3162C2×C511yescharacteristic, complemented
153#1664C2×C512yescomplemented
154#1663C2×C512yescomplemented
155#1663C2×C512yescomplemented
156#1660C2×C512yescomplemented
157#1532C2×C511yescharacteristic
158#1531C2×C511yescharacteristic, complemented
159C2×#330C2×C511yescharacteristic, complemented
160C2×C5×Q8—22no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4C2×D411yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—22no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C5×Q16—42no—
176C5×SD16—42no—
177C2×C5×C8—24no—
178C2×C5×C8—21no—
179C2×C5×C8—22no—
180C2×C5×C8—21no—
181C2×C5×C8—22no—
182C2×C5×C8—42no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—22no—
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—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
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—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—41no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4C2×D412yes—
212C5×C4⋊C4C2×D412yes—
213C5×C4⋊C4C2×D412yes—
214C5×C4⋊C4C2×D412yes—
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—21no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—21no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—41no—
227C42×C5—22no—
228C42×C5—22no—
229C42×C5—22no—
230C42×C5—22no—
231C42×C5—21no—
232C42×C5—41no—
233C42×C5C2×D411yescharacteristic
234C42×C5C2×D411yescharacteristic
235C42×C5C2×D411yescharacteristic
236C42×C5C2411yescharacteristic
237#564C22×C512yes—
238#563C22×C512yes—
239#557—21no—
240#554—21no—
241#552—21no—
242#552—22no—
243#552—21no—
244#544—21no—
245#544—21no—
246#541—21no—
247#541—22no—
248#539—21no—
249#533C22×C511yescharacteristic
250#533C22×C511yescharacteristic
251#529C22×C511yescharacteristic
252C2×#125C22×C511yescharacteristic
253#501—21no—
254#501—21no—
255#501C22×C512yes—
256#501C22×C512yes—
257#501C22×C511yescharacteristic
258#501C22×C512yes—
259#497C22×C511yescharacteristic
260#491C22×C511yescharacteristic
261#491C22×C512yes—
262#489C22×C511yescharacteristic
263#484—21no—
264#483—21no—
265#479—22no—
266#467—21no—
267#465—21no—
268#441—21no—
269#440—21no—
270#432C22×C511yescharacteristic
271#427—22no—
272C2×#97C22×C511yescharacteristic
273C2×#97C22×C511yescharacteristic
274#330C22×C512yes—
275#330C22×C512yes—
276#330C22×C512yes—
277#330C22×C512yes—
278#330C22×C512yes—
279#329C22×C512yes—
280C23×C5—21no—
281C23×C5#12011yescharacteristic
282C5×Q8—41no—
283C5×Q8—42no—
284C5×Q8—41no—
285C5×Q8—41no—
286C5×Q8—42no—
287C5×Q8—81no—
288C5×Q8—82no—
289C5×D4—41no—
290C5×D4—42no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—22no—
296C2×C4×C5—21no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—81no—
306C2×C4×C5—82no—
307C2×C4×C5#12011yescharacteristic
308C2×C4×C5#12011yescharacteristic
309C2×C4×C5#12011yescharacteristic
310C2×C4×C5C22×D411yescharacteristic
311C2×C4×C5C22×D411yescharacteristic
312C2×C4×C5C22×D411yescharacteristic
313C5×C8—24no—
314C5×C8—22no—
315C5×C8—42no—
316C5×C8—41no—
317C2×Q16—21no—
318C2×SD16—21no—
319C22×C8—21no—
320C22×C8—21no—
321C4⋊Q8—22no—
322C4⋊Q8—21no—
323C4⋊Q8—22no—
324C4⋊Q8C5×D411yescharacteristic
325C4⋊Q8C5×D411yescharacteristic
326C4⋊Q8C23×C511yescharacteristic
327C4⋊Q8C23×C511yescharacteristic
328#126—22no—
329#126—22no—
330#126—22no—
331#126—22no—
332#126—21no—
333#125—22no—
334#125—22no—
335#125—21no—
336#125—22no—
337#125—22no—
338#125—22no—
339#125—22no—
340#125—22no—
341#125—22no—
342#125—21no—
343#125—21no—
344#125—21no—
345#125C5×D412yes—
346#125C23×C512yes—
347#125C23×C511yescharacteristic
348#125C23×C512yes—
349#124C23×C511yescharacteristic
350#123—22no—
351#123—22no—
352#123—21no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—22no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8C5×D411yescharacteristic
364#121C5×D411yescharacteristic
365C4×Q8—21no—
366C4×Q8—22no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C5×D411yescharacteristic
373C4×D4—22no—
374C4×D4—21no—
375C4×D4C5×D411yescharacteristic
376#117—22no—
377#117—21no—
378#117—22no—
379#117—21no—
380#117—21no—
381#117C5×D412yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C5×D411yescharacteristic
386C2×C4⋊C4C5×D411yescharacteristic
387C2×C42C23×C511yescharacteristic
388#107—22no—
389#107—22no—
390#107—21no—
391#107—22no—
392#106—22no—
393#106—22no—
394#106—21no—
395#106—22no—
396C4⋊C8—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—22no—
401#103—22no—
402#102—21no—
403C22⋊C8—21no—
404#97—21no—
405#97—21no—
406#97C23×C512yes—
407#97C23×C512yes—
408#97C23×C511yescharacteristic
409#97C23×C511yescharacteristic
410C22×C5—21no—
411C22×C5—21no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5#45612yes—
416C22×C5C2×#12011yescharacteristic
417C4×C5—21no—
418C4×C5—21no—
419C4×C5—21no—
420C4×C5—21no—
421C4×C5—21no—
422C4×C5—21no—
423C4×C5—42no—
424C4×C5—41no—
425C4×C5—42no—
426C4×C5—42no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5—42no—
430C4×C5—81no—
431C4×C5—81no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×C5×D411yescharacteristic
438C2×D4—21no—
439C2×D4C2×C5×D411yescharacteristic
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C2×C5×D411yescharacteristic
447Q16—42no—
448SD16—42no—
449C2×C8—24no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—42no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4C2×C5×D412yes—
484C4⋊C4C2×C5×D411yescharacteristic
485C4⋊C4C2×C5×D412yes—
486C4⋊C4C2×C5×D411yescharacteristic
487C4⋊C4C2×C5×D412yes—
488C4⋊C4C2×C5×D412yes—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C42—22no—
500C42—22no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—41no—
505C42C2×C5×D411yescharacteristic
506C42C2×C5×D411yescharacteristic
507C42C2×C5×D411yescharacteristic
508C42C24×C511yescharacteristic
509C2×C5—22no—
510C2×C5—81no—
511C2×C5C2×#45611yescharacteristic
512C2×C5#301811yescharacteristic
513C2×C5#302011yescharacteristic
514C23—21no—
515C23C5×#12011yescharacteristic
516Q8—41no—
517Q8—42no—
518Q8—41no—
519Q8—41no—
520Q8—42no—
521Q8—81no—
522Q8—82no—
523D4—41no—
524D4—42no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4C5×#12011yescharacteristic
542C2×C4C5×#12011yescharacteristic
543C2×C4C5×#12011yescharacteristic
544C2×C4C22×C5×D411yescharacteristic
545C2×C4C22×C5×D411yescharacteristic
546C2×C4C22×C5×D411yescharacteristic
547C8—24no—
548C8—22no—
549C8—41no—
550C8—42no—
551C5#1904711yescharacteristic, direct product factor, Sylow
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C5×#45612yes—
558C22C2×C5×#12011yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—81no—
573C4—81no—
574C2—22no—
575C2—81no—
576C2C2×C5×#45611yescharacteristic
577C2C5×#301811yescharacteristic
578C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
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
2. C5×#3236C2semidirect
4. C5×#3162C2semidirect
5. C5×#1664C2semidirect
6. C5×#1663C2semidirect
7. C5×#1663C2semidirect
8. C5×#1660C2semidirect
10. C5×#1531C2semidirect
11. C2×C5×#330C2semidirect
55. #19047C5direct (N × H)
150. #3236C2×C5semidirect
152. #3162C2×C5semidirect
153. #1664C2×C5semidirect
154. #1663C2×C5semidirect
155. #1663C2×C5semidirect
156. #1660C2×C5semidirect
158. #1531C2×C5semidirect
159. C2×#330C2×C5semidirect
551. C5#19047direct (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×#31812
C5×#31622
C5×#16642
C5×#16632
C5×#16602
C5×#15322
C5×#15312
C2×C5×#3302
#190475