Finite Group Databasebeta

← C5×#18149 #11940869

Subgroups — C5×#18149 #11940869

Order 1280.

1074 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
1C2×C5×#538C211yesmaximal, characteristic
2C5×#3095C211yesmaximal, characteristic, complemented
3C5×#3094C211yesmaximal, characteristic, complemented
4C5×#2482C211yesmaximal, characteristic, complemented
5C5×#1618C214yesmaximal, complemented
6C5×#1612C214yesmaximal, complemented
7C5×#1511C211yesmaximal, characteristic, complemented
8C5×#1510C211yesmaximal, characteristic, complemented
9C5×#1462C211yesmaximal, characteristic, complemented
10C5×#538—22no—
11C5×#538—22no—
12C5×#538—22no—
13C5×#538C2214yes—
14C2×C5×#126—21no—
15C2×C5×#124—21no—
16C2×C5×#123—21no—
17C2×C5×C22⋊Q8C2211yescharacteristic
18C2×C5×#121—21no—
19C2×C5×#121C2211yescharacteristic
20C2×C5×#120—21no—
21C2×C4×C5×D4—21no—
22C2×C5×#117C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C5×#485—22no—
25C5×#484C2212yescomplemented
26C5×#483C2212yescomplemented
27C5×#482—22no—
28C5×#481C2212yescomplemented
29C5×#480C2212yescomplemented
30C5×#428—21no—
31C5×#428—21no—
32C5×#419—21no—
33C5×#418—21no—
34C5×#407C2211yescharacteristic
35C5×#407C2211yescharacteristic
36C5×#399C2212yescomplemented
37C5×#397C2212yescomplemented
38C5×#388—22no—
39C5×#385—21no—
40C5×#381C2211yescharacteristic
41C5×#379—21no—
42C5×#328C2214yescomplemented
43C5×#327C2214yescomplemented
44C5×#323C2214yescomplemented
45#18149C511yesmaximal, characteristic, direct product factor, Sylow
46C25×C5D411yescharacteristic
47C22×C5×Q8D411yescharacteristic
48C22×C5×D4—21no—
49C22×C5×D4—21no—
50C22×C5×D4—21no—
51C22×C5×D4D411yescharacteristic
52C23×C4×C5—21no—
53C23×C4×C5D411yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C2×C5×M16—21no—
56C2×C5×M16—21no—
57C5×#126—24no—
58C5×#126—24no—
59C5×#124—24no—
60C5×#124—24no—
61C5×#123—24no—
62C5×#123—24no—
63C5×C22⋊Q8—21no—
64C5×C22⋊Q8—21no—
65C5×C22⋊Q8D412yes—
66C5×C22⋊Q8C2312yes—
67C5×#121—24no—
68C5×#121—24no—
69C5×#121—21no—
70C5×#121—21no—
71C5×#121D412yes—
72C5×#121C2312yes—
73C5×#120—24no—
74C5×#120—24no—
75C4×C5×D4—24no—
76C4×C5×D4—24no—
77C5×#117—21no—
78C5×#117—21no—
79C5×#117—21no—
80C5×#117—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4D411yescharacteristic
85C2×C5×C4⋊C4D411yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4D412yes—
102C2×C5×C22⋊C4C2312yes—
103C2×C42×C5—21no—
104C2×C42×C5—21no—
105C5×#107—22no—
106C5×#107—22no—
107C5×#106—22no—
108C5×#106—22no—
109C5×#103—22no—
110C5×#103—22no—
111C5×#102—22no—
112C5×#102—22no—
113C5×C22⋊C8—21no—
114C5×C22⋊C8—21no—
115C5×C22⋊C8C2312yes—
116C5×C22⋊C8C2312yes—
117C5×#95—21no—
118C5×#95—22no—
119C5×#95C2312yes—
120C2×#538C2×C511yescharacteristic
121#3095C2×C511yescharacteristic, complemented
122#3094C2×C511yescharacteristic, complemented
123#2482C2×C511yescharacteristic, complemented
124#1618C2×C514yescomplemented
125#1612C2×C514yescomplemented
126#1511C2×C511yescharacteristic, complemented
127#1510C2×C511yescharacteristic, complemented
128#1462C2×C511yescharacteristic, complemented
129C24×C5—21no—
130C24×C5—21no—
131C24×C5—21no—
132C24×C5—42no—
133C24×C5—42no—
134C24×C5—81no—
135C24×C5C2×D411yescharacteristic
136C24×C5C2×D412yes—
137C2×C5×Q8—21no—
138C2×C5×Q8—42no—
139C2×C5×Q8C2×D412yes—
140C2×C5×D4—22no—
141C2×C5×D4—22no—
142C2×C5×D4—24no—
143C2×C5×D4—24no—
144C2×C5×D4—21no—
145C2×C5×D4—42no—
146C2×C5×D4—44no—
147C2×C5×D4—82no—
148C2×C5×D4—82no—
149C2×C5×D4C2×D412yes—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—24no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—42no—
160C22×C4×C5—81no—
161C22×C4×C5—82no—
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2411yescharacteristic
169C5×M16—42no—
170C5×M16—42no—
171C2×C5×C8—22no—
172C2×C5×C8—22no—
173C5×C4⋊C4—24no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—82no—
183C5×C4⋊C4C2×D412yes—
184C5×C4⋊C4C2×D412yes—
185C5×C22⋊C4—24no—
186C5×C22⋊C4—24no—
187C5×C22⋊C4—24no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—22no—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—42no—
197C5×C22⋊C4—44no—
198C5×C22⋊C4—41no—
199C5×C22⋊C4—41no—
200C5×C22⋊C4—82no—
201C42×C5—24no—
202C42×C5—41no—
203C42×C5—41no—
204#538—22no—
205#538—22no—
206#538—22no—
207#538C22×C514yes—
208C2×#126—21no—
209C2×#124—21no—
210C2×#123—21no—
211C2×C22⋊Q8C22×C511yescharacteristic
212C2×#121—21no—
213C2×#121C22×C511yescharacteristic
214C2×#120—21no—
215C2×C4×D4—21no—
216C2×#117C22×C511yescharacteristic
217C22×C22⋊C4C22×C511yescharacteristic
218#485—22no—
219#484C22×C512yescomplemented
220#483C22×C512yescomplemented
221#482—22no—
222#481C22×C512yescomplemented
223#480C22×C512yescomplemented
224#428—21no—
225#428—21no—
226#419—21no—
227#418—21no—
228#407C22×C511yescharacteristic
229#407C22×C511yescharacteristic
230#399C22×C512yescomplemented
231#397C22×C512yescomplemented
232#388—22no—
233#385—21no—
234#381C22×C511yescharacteristic
235#379—21no—
236#328C22×C514yescomplemented
237#327C22×C514yescomplemented
238#323C22×C514yescomplemented
239C23×C5—22no—
240C23×C5—22no—
241C23×C5—22no—
242C23×C5—22no—
243C23×C5—22no—
244C23×C5—22no—
245C23×C5—41no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—42no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5—42no—
255C23×C5—81no—
256C23×C5—81no—
257C23×C5—88no—
258C23×C5#12011yescharacteristic
259C23×C5#12011yescharacteristic
260C23×C5C22×D411yescharacteristic
261C5×Q8—42no—
262C5×Q8—81no—
263C5×D4—42no—
264C5×D4—44no—
265C5×D4—44no—
266C5×D4—81no—
267C5×D4—84no—
268C5×D4—84no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—42no—
290C2×C4×C5—42no—
291C2×C4×C5—81no—
292C2×C4×C5—84no—
293C2×C4×C5#12011yescharacteristic
294C2×C4×C5#12011yescharacteristic
295C2×C4×C5C22×D411yescharacteristic
296C2×C4×C5C22×D411yescharacteristic
297C5×C8—42no—
298C5×C8—42no—
299C25C5×D411yescharacteristic
300C22×Q8C5×D411yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C5×D411yescharacteristic
305C23×C4—21no—
306C23×C4C5×D411yescharacteristic
307C23×C4C23×C511yescharacteristic
308C2×M16—21no—
309C2×M16—21no—
310#126—24no—
311#126—24no—
312#124—24no—
313#124—24no—
314#123—24no—
315#123—24no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8C5×D412yes—
319C22⋊Q8C23×C512yes—
320#121—24no—
321#121—24no—
322#121—21no—
323#121—21no—
324#121C5×D412yes—
325#121C23×C512yes—
326#120—24no—
327#120—24no—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331#117—21no—
332#117—21no—
333#117—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4C5×D411yescharacteristic
338C2×C4⋊C4C5×D411yescharacteristic
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4C5×D412yes—
355C2×C22⋊C4C23×C512yes—
356C2×C42—21no—
357C2×C42—21no—
358#107—22no—
359#107—22no—
360#106—22no—
361#106—22no—
362#103—22no—
363#103—22no—
364#102—22no—
365#102—22no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8C23×C512yes—
369C22⋊C8C23×C512yes—
370#95—21no—
371#95—22no—
372#95C23×C512yes—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—21no—
376C22×C5—21no—
377C22×C5—21no—
378C22×C5—21no—
379C22×C5—21no—
380C22×C5—44no—
381C22×C5—44no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5—42no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5—42no—
388C22×C5—82no—
389C22×C5—84no—
390C22×C5—84no—
391C22×C5—84no—
392C22×C5#45812yes—
393C22×C5C2×#12011yescharacteristic
394C22×C5#57512yes—
395C4×C5—21no—
396C4×C5—21no—
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—42no—
400C4×C5—42no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—82no—
404C4×C5—81no—
405C4×C5—81no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—42no—
410C24—42no—
411C24—81no—
412C24C2×C5×D411yescharacteristic
413C24C2×C5×D412yes—
414C2×Q8—21no—
415C2×Q8—42no—
416C2×Q8C2×C5×D412yes—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—21no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—82no—
425C2×D4—82no—
426C2×D4C2×C5×D412yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—81no—
438C22×C4—82no—
439C22×C4C2×C5×D411yescharacteristic
440C22×C4C2×C5×D411yescharacteristic
441C22×C4C2×C5×D412yes—
442C22×C4C2×C5×D411yescharacteristic
443C22×C4C2×C5×D411yescharacteristic
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C24×C511yescharacteristic
446M16—42no—
447M16—42no—
448C2×C8—22no—
449C2×C8—22no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—82no—
460C4⋊C4C2×C5×D412yes—
461C4⋊C4C2×C5×D412yes—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—44no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—82no—
478C42—24no—
479C42—41no—
480C42—41no—
481C2×C5—22no—
482C2×C5—22no—
483C2×C5—41no—
484C2×C5—82no—
485C2×C5—82no—
486C2×C5#300511yescharacteristic
487C2×C5#301911yescharacteristic
488C2×C5C2×#45811yescharacteristic
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—41no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—81no—
506C23—81no—
507C23—88no—
508C23C5×#12011yescharacteristic
509C23C5×#12011yescharacteristic
510C23C22×C5×D411yescharacteristic
511Q8—42no—
512Q8—81no—
513D4—42no—
514D4—44no—
515D4—44no—
516D4—81no—
517D4—84no—
518D4—84no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
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—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—81no—
542C2×C4—84no—
543C2×C4C5×#12011yescharacteristic
544C2×C4C5×#12011yescharacteristic
545C2×C4C22×C5×D411yescharacteristic
546C2×C4C22×C5×D411yescharacteristic
547C8—42no—
548C8—42no—
549C5#1814911yescharacteristic, direct product factor, Sylow
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—44no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—82no—
566C22—84no—
567C22—84no—
568C22—84no—
569C22C5×#45812yes—
570C22C2×C5×#12011yescharacteristic
571C22C5×#57512yes—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—82no—
581C4—81no—
582C4—81no—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—82no—
587C2—82no—
588C2C5×#300511yescharacteristic
589C2C5×#301911yescharacteristic
590C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#538C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C5×#3095C2semidirect
3. C5×#3094C2semidirect
4. C5×#2482C2semidirect
5. C5×#1618C2semidirect
6. C5×#1612C2semidirect
7. C5×#1511C2semidirect
8. C5×#1510C2semidirect
9. C5×#1462C2semidirect
25. C5×#484C22semidirect
26. C5×#483C22semidirect
28. C5×#481C22semidirect
29. C5×#480C22semidirect
36. C5×#399C22semidirect
37. C5×#397C22semidirect
42. C5×#328C22semidirect
43. C5×#327C22semidirect
44. C5×#323C22semidirect
45. #18149C5direct (N × H)
121. #3095C2×C5semidirect
122. #3094C2×C5semidirect
123. #2482C2×C5semidirect
124. #1618C2×C5semidirect
125. #1612C2×C5semidirect
126. #1511C2×C5semidirect
127. #1510C2×C5semidirect
128. #1462C2×C5semidirect
219. #484C22×C5semidirect
220. #483C22×C5semidirect
222. #481C22×C5semidirect
223. #480C22×C5semidirect
230. #399C22×C5semidirect
231. #397C22×C5semidirect
236. #328C22×C5semidirect
237. #327C22×C5semidirect
238. #323C22×C5semidirect
549. C5#18149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5382
C5×#30952
C5×#30942
C5×#24822
C5×#16182
C5×#16122
C5×#15112
C5×#15102
C5×#14622
#181495