Finite Group Databasebeta

← C5×#18439 #11941159

Subgroups — C5×#18439 #11941159

Order 1280.

964 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×#3561C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3230C211yesmaximal, characteristic, complemented
4C5×#2658C211yesmaximal, characteristic, complemented
5C5×#1618C214yesmaximal, complemented
6C5×#1614C214yesmaximal, complemented
7C5×#1506C211yesmaximal, characteristic, complemented
8C5×#1500C211yesmaximal, characteristic, complemented
9C5×#1469C211yesmaximal, characteristic, complemented
10C5×#563—21no—
11C5×#562—21no—
12C5×#556—21no—
13C5×#551—22no—
14C5×D4×Q8—21no—
15C5×#548—21no—
16C5×#546—21no—
17C5×#543C2212yes—
18C5×#542—21no—
19C5×#542—22no—
20C5×#538C2212yes—
21C5×#536—21no—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8—21no—
24C2×C5×C4⋊Q8C2211yescharacteristic
25C5×#529C2211yescharacteristic
26C2×C5×#124—21no—
27C2×C5×#124C2211yescharacteristic
28C5×#501—21no—
29C5×#500—21no—
30C5×#489—21no—
31C5×#487—21no—
32C5×#484C2212yes—
33C5×#484C2214yes—
34C5×#481C2212yes—
35C5×#477—22no—
36C5×#475—21no—
37C5×#474—21no—
38C5×#432C2211yescharacteristic
39C5×#431C2211yescharacteristic
40C5×#399—22no—
41C5×#399C2214yes—
42C5×#376C2211yescharacteristic
43C5×#328C2212yes—
44C5×#328C2214yes—
45C5×#327C2212yes—
46C5×#323C2214yes—
47#18439C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—21no—
49C22×C5×Q8—21no—
50C22×C5×Q8—21no—
51C22×C5×Q8D411yescharacteristic
52C22×C5×D4D411yescharacteristic
53C5×C4⋊Q8—21no—
54C5×C4⋊Q8—22no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8—21no—
58C5×C4⋊Q8—21no—
59C5×C4⋊Q8—44no—
60C5×C4⋊Q8D411yescharacteristic
61C5×C4⋊Q8D411yescharacteristic
62C5×#126—22no—
63C5×#126—22no—
64C5×#126—22no—
65C5×#126—21no—
66C5×#125—21no—
67C5×#125D411yescharacteristic
68C5×#124—21no—
69C5×#124—22no—
70C5×#124—22no—
71C5×#124—21no—
72C5×#124—21no—
73C5×#124—21no—
74C5×#124—21no—
75C5×#124—44no—
76C5×#124D411yescharacteristic
77C5×#123—22no—
78C5×#123—22no—
79C5×#123—22no—
80C5×#123—21no—
81C5×#123—22no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8C2311yescharacteristic
92C5×C22⋊Q8C2312yes—
93C5×#121—21no—
94C5×#121—22no—
95C5×#121—22no—
96C5×#121C2311yescharacteristic
97C5×#120—22no—
98C4×C5×Q8—21no—
99C4×C5×Q8—21no—
100C4×C5×Q8D411yescharacteristic
101C4×C5×Q8D412yes—
102C4×C5×D4—21no—
103C4×C5×D4—22no—
104C4×C5×D4—21no—
105C4×C5×D4—22no—
106C4×C5×D4D411yescharacteristic
107C5×#117—22no—
108C5×#117—21no—
109C5×#117—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4C2312yes—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4D412yes—
116C2×C5×C22⋊C4C2312yes—
117C2×C42×C5—21no—
118C2×C42×C5C2311yescharacteristic
119C5×#107—22no—
120C5×#107—24no—
121C5×#106—22no—
122C5×C4⋊C8—21no—
123C5×C4⋊C8—21no—
124C5×#103—22no—
125C5×#103—24no—
126C5×#102—22no—
127C5×C22⋊C8C2312yes—
128C5×C22⋊C8C2312yes—
129C5×#97—21no—
130C4×C5×C8—21no—
131C5×#95—21no—
132C5×#95C2312yes—
133#3561C2×C511yescharacteristic
134#3239C2×C511yescharacteristic, complemented
135#3230C2×C511yescharacteristic, complemented
136#2658C2×C511yescharacteristic, complemented
137#1618C2×C514yescomplemented
138#1614C2×C514yescomplemented
139#1506C2×C511yescharacteristic, complemented
140#1500C2×C511yescharacteristic, complemented
141#1469C2×C511yescharacteristic, complemented
142C24×C5C2×D412yes—
143C5×#41—82no—
144C2×C5×Q8—22no—
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—42no—
149C2×C5×Q8—42no—
150C2×C5×Q8—42no—
151C2×C5×Q8—41no—
152C2×C5×Q8—41no—
153C2×C5×Q8—82no—
154C2×C5×Q8C2×D411yescharacteristic
155C2×C5×Q8C2×D412yes—
156C2×C5×D4—21no—
157C2×C5×D4—22no—
158C2×C5×D4—22no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—42no—
162C2×C5×D4C2×D411yescharacteristic
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—21no—
168C22×C4×C5—22no—
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2411yescharacteristic
173C2×C5×C8—22no—
174C2×C5×C8—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—48no—
191C5×C4⋊C4—41no—
192C5×C4⋊C4—41no—
193C5×C4⋊C4C2×D411yescharacteristic
194C5×C4⋊C4C2×D411yescharacteristic
195C5×C4⋊C4C2×D412yes—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—22no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—22no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—22no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—21no—
207C5×C22⋊C4—21no—
208C5×C22⋊C4—22no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—21no—
211C5×C22⋊C4—48no—
212C42×C5—24no—
213C42×C5—22no—
214C42×C5—22no—
215C42×C5—21no—
216C42×C5C2×D411yescharacteristic
217C42×C5C2×D411yescharacteristic
218C42×C5C2×D411yescharacteristic
219C42×C5C2×D411yescharacteristic
220#563—21no—
221#562—21no—
222#556—21no—
223#551—22no—
224D4×Q8—21no—
225#548—21no—
226#546—21no—
227#543C22×C512yes—
228#542—21no—
229#542—22no—
230#538C22×C512yes—
231#536—21no—
232#533C22×C511yescharacteristic
233C2×C4⋊Q8—21no—
234C2×C4⋊Q8C22×C511yescharacteristic
235#529C22×C511yescharacteristic
236C2×#124—21no—
237C2×#124C22×C511yescharacteristic
238#501—21no—
239#500—21no—
240#489—21no—
241#487—21no—
242#484C22×C512yes—
243#484C22×C514yes—
244#481C22×C512yes—
245#477—22no—
246#475—21no—
247#474—21no—
248#432C22×C511yescharacteristic
249#431C22×C511yescharacteristic
250#399—22no—
251#399C22×C514yes—
252#376C22×C511yescharacteristic
253#328C22×C512yes—
254#328C22×C514yes—
255#327C22×C512yes—
256#323C22×C514yes—
257C23×C5—22no—
258C23×C5—21no—
259C23×C5—24no—
260C23×C5—42no—
261C23×C5—42no—
262C23×C5C22×D411yescharacteristic
263C5×Q8—41no—
264C5×Q8—42no—
265C5×Q8—42no—
266C5×Q8—42no—
267C5×Q8—81no—
268C5×Q8—82no—
269C5×Q8—82no—
270C5×Q8—82no—
271C5×D4—41no—
272C5×D4—42no—
273C5×D4—42no—
274C5×D4—81no—
275C5×D4—82no—
276C5×D4—82no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—21no—
286C2×C4×C5—41no—
287C2×C4×C5—42no—
288C2×C4×C5—42no—
289C2×C4×C5—42no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—82no—
295C2×C4×C5—82no—
296C2×C4×C5—82no—
297C2×C4×C5#12011yescharacteristic
298C2×C4×C5#12011yescharacteristic
299C2×C4×C5#12011yescharacteristic
300C2×C4×C5#12011yescharacteristic
301C2×C4×C5C22×D411yescharacteristic
302C2×C4×C5C22×D411yescharacteristic
303C5×C8—42no—
304C5×C8—42no—
305C2×#41—21no—
306C22×Q8—21no—
307C22×Q8—21no—
308C22×Q8C5×D411yescharacteristic
309C22×D4C5×D411yescharacteristic
310C4⋊Q8—21no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—44no—
317C4⋊Q8C5×D411yescharacteristic
318C4⋊Q8C5×D411yescharacteristic
319#126—22no—
320#126—22no—
321#126—22no—
322#126—21no—
323#125—21no—
324#125C5×D411yescharacteristic
325#124—21no—
326#124—22no—
327#124—22no—
328#124—21no—
329#124—21no—
330#124—21no—
331#124—21no—
332#124—44no—
333#124C5×D411yescharacteristic
334#123—22no—
335#123—22no—
336#123—22no—
337#123—21no—
338#123—22no—
339C22⋊Q8—22no—
340C22⋊Q8—21no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8C23×C511yescharacteristic
349C22⋊Q8C23×C512yes—
350#121—21no—
351#121—22no—
352#121—22no—
353#121C23×C511yescharacteristic
354#120—22no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8C5×D411yescharacteristic
358C4×Q8C5×D412yes—
359C4×D4—21no—
360C4×D4—22no—
361C4×D4—21no—
362C4×D4—22no—
363C4×D4C5×D411yescharacteristic
364#117—22no—
365#117—21no—
366#117—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C23×C512yes—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4C5×D412yes—
373C2×C22⋊C4C23×C512yes—
374C2×C42—21no—
375C2×C42C23×C511yescharacteristic
376#107—22no—
377#107—24no—
378#106—22no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381#103—22no—
382#103—24no—
383#102—22no—
384C22⋊C8C23×C512yes—
385C22⋊C8C23×C512yes—
386#97—21no—
387C4×C8—21no—
388#95—21no—
389#95C23×C512yes—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—42no—
394C22×C5—41no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—41no—
398C22×C5—84no—
399C22×C5C2×#12011yescharacteristic
400C22×C5#57812yes—
401C4×C5—21no—
402C4×C5—21no—
403C4×C5—21no—
404C4×C5—21no—
405C4×C5—21no—
406C4×C5—44no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—42no—
410C4×C5—42no—
411C4×C5—41no—
412C4×C5—42no—
413C4×C5—82no—
414C4×C5#45312yes—
415C24C2×C5×D412yes—
416#41—82no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×C5×D411yescharacteristic
428C2×Q8C2×C5×D412yes—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—42no—
435C2×D4C2×C5×D411yescharacteristic
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4C2×C5×D411yescharacteristic
443C22×C4C2×C5×D411yescharacteristic
444C22×C4C2×C5×D412yes—
445C22×C4C24×C511yescharacteristic
446C2×C8—22no—
447C2×C8—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—48no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×C5×D411yescharacteristic
467C4⋊C4C2×C5×D411yescharacteristic
468C4⋊C4C2×C5×D412yes—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—48no—
485C42—24no—
486C42—22no—
487C42—22no—
488C42—21no—
489C42C2×C5×D411yescharacteristic
490C42C2×C5×D411yescharacteristic
491C42C2×C5×D411yescharacteristic
492C42C2×C5×D411yescharacteristic
493C2×C5—22no—
494C2×C5—81no—
495C2×C5—82no—
496C2×C5#301111yescharacteristic
497C2×C5C2×#45311yescharacteristic
498C2×C5#302811yescharacteristic
499C23—22no—
500C23—21no—
501C23—24no—
502C23—42no—
503C23—42no—
504C23C22×C5×D411yescharacteristic
505Q8—41no—
506Q8—42no—
507Q8—42no—
508Q8—42no—
509Q8—81no—
510Q8—82no—
511Q8—82no—
512Q8—82no—
513D4—41no—
514D4—42no—
515D4—42no—
516D4—81no—
517D4—82no—
518D4—82no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4C5×#12011yescharacteristic
540C2×C4C5×#12011yescharacteristic
541C2×C4C5×#12011yescharacteristic
542C2×C4C5×#12011yescharacteristic
543C2×C4C22×C5×D411yescharacteristic
544C2×C4C22×C5×D411yescharacteristic
545C8—42no—
546C8—42no—
547C5#1843911yescharacteristic, direct product factor, Sylow
548C22—21no—
549C22—21no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—84no—
557C22C2×C5×#12011yescharacteristic
558C22C5×#57812yes—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—82no—
572C4C5×#45312yes—
573C2—22no—
574C2—82no—
575C2—81no—
576C2C5×#301111yescharacteristic
577C2C2×C5×#45311yescharacteristic
578C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3561C2
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×#3239C2semidirect
3. C5×#3230C2semidirect
4. C5×#2658C2semidirect
5. C5×#1618C2semidirect
6. C5×#1614C2semidirect
7. C5×#1506C2semidirect
8. C5×#1500C2semidirect
9. C5×#1469C2semidirect
47. #18439C5direct (N × H)
134. #3239C2×C5semidirect
135. #3230C2×C5semidirect
136. #2658C2×C5semidirect
137. #1618C2×C5semidirect
138. #1614C2×C5semidirect
139. #1506C2×C5semidirect
140. #1500C2×C5semidirect
141. #1469C2×C5semidirect
547. C5#18439direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35612
C5×#32392
C5×#32302
C5×#26582
C5×#16182
C5×#16142
C5×#15062
C5×#15002
C5×#14692
#184395