Finite Group Databasebeta

← C5×#24066 #11946786

Subgroups — C5×#24066 #11946786

Order 1280.

1176 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#529C211yesmaximal, characteristic
2C2×C5×#483C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic, complemented
5C5×#2059C212yesmaximal, complemented
6C5×#2042C212yesmaximal, complemented
7C5×#1874C211yesmaximal, characteristic
8C5×#1872C211yesmaximal, characteristic, complemented
9C5×#1864C212yesmaximal, complemented
10C5×#1863C212yesmaximal, complemented
11C5×#1817C211yesmaximal, characteristic, complemented
12C5×#529—24no—
13C5×#529—24no—
14C2×C5×#126—21no—
15C2×C5×#125C2211yescharacteristic
16C2×C5×#124C2211yescharacteristic
17C2×C5×#123—21no—
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×D4—21no—
22C2×C4×C5×D4C2211yescharacteristic
23C2×C5×#117—21no—
24C22×C5×C4⋊C4—21no—
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C5×#483—24no—
29C5×#480—24no—
30C2×C5×#107C2212yes—
31C2×C5×#106C2212yes—
32C2×C5×#103C2212yes—
33C2×C5×#103C2212yes—
34C2×C5×#102C2212yes—
35C2×C5×#102C2212yes—
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C5×#389—21no—
39C5×#389—21no—
40C5×#389C2212yes—
41C5×#389C2212yes—
42C2×C5×#95—21no—
43C5×#340C2212yes—
44C5×#340C2212yes—
45C5×#336C2212yes—
46C5×#336C2212yes—
47#24066C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8C2311yescharacteristic
49C22×C5×D4—21no—
50C22×C5×D4C2311yescharacteristic
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C23×C4×C5D411yescharacteristic
55C23×C4×C5D411yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C22×C5×C8C2312yes—
58C22×C5×C8C2312yes—
59C5×#126—28no—
60C5×#125—22no—
61C5×#125—22no—
62C5×#124—22no—
63C5×#124—22no—
64C5×#123—28no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8D414yes—
67C5×#121—22no—
68C5×#121D414yes—
69C4×C5×Q8—22no—
70C4×C5×Q8—22no—
71C4×C5×D4—28no—
72C4×C5×D4—22no—
73C4×C5×D4—22no—
74C5×#117—28no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—24no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—44no—
87C2×C5×C4⋊C4C2312yes—
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2312yes—
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×C42×C5—22no—
97C2×C42×C5—22no—
98C2×C42×C5—21no—
99C2×C42×C5D411yescharacteristic
100C2×C42×C5D411yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C2×C42×C5C2311yescharacteristic
103C5×#107—24no—
104C5×#106—24no—
105C5×#103—24no—
106C5×#103—24no—
107C5×#102—24no—
108C5×#102—24no—
109C5×C22⋊C8—22no—
110C5×C22⋊C8—22no—
111C5×#95—22no—
112C5×#95—22no—
113C2×#529C2×C511yescharacteristic
114C2×#483C2×C511yescharacteristic, complemented
115C2×#480C2×C511yescharacteristic
116C2×#389C2×C511yescharacteristic, complemented
117#2059C2×C512yescomplemented
118#2042C2×C512yescomplemented
119#1874C2×C511yescharacteristic
120#1872C2×C511yescharacteristic, complemented
121#1864C2×C512yescomplemented
122#1863C2×C512yescomplemented
123#1817C2×C511yescharacteristic, complemented
124C24×C5—21no—
125C24×C5C2×D411yescharacteristic
126C2×C5×Q8—21no—
127C2×C5×Q8—22no—
128C2×C5×Q8—22no—
129C2×C5×Q8C2×D412yes—
130C2×C5×D4—24no—
131C2×C5×D4—21no—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—42no—
135C2×C5×D4—42no—
136C2×C5×D4C2×D412yes—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—24no—
140C22×C4×C5—24no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—41no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5—42no—
155C22×C4×C5—42no—
156C22×C4×C5—42no—
157C22×C4×C5—42no—
158C22×C4×C5—42no—
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D412yes—
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2411yescharacteristic
167C2×C5×C8—22no—
168C2×C5×C8—22no—
169C2×C5×C8—22no—
170C2×C5×C8—22no—
171C2×C5×C8—22no—
172C2×C5×C8—22no—
173C5×C4⋊C4—24no—
174C5×C4⋊C4—24no—
175C5×C4⋊C4—24no—
176C5×C4⋊C4—24no—
177C5×C4⋊C4—24no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—44no—
184C5×C4⋊C4—44no—
185C5×C4⋊C4—42no—
186C5×C4⋊C4C2×D412yes—
187C5×C4⋊C4C2×D412yes—
188C5×C4⋊C4#4114yes—
189C5×C22⋊C4—24no—
190C5×C22⋊C4—24no—
191C5×C22⋊C4—24no—
192C5×C22⋊C4—24no—
193C5×C22⋊C4—24no—
194C42×C5—24no—
195C42×C5—22no—
196C42×C5—22no—
197C42×C5—21no—
198C42×C5—21no—
199C42×C5—21no—
200C42×C5—21no—
201#529—24no—
202#529—24no—
203C2×#126—21no—
204C2×#125C22×C511yescharacteristic
205C2×#124C22×C511yescharacteristic
206C2×#123—21no—
207C2×C22⋊Q8C22×C511yescharacteristic
208C2×#121C22×C511yescharacteristic
209C2×C4×Q8C22×C511yescharacteristic
210C2×C4×D4—21no—
211C2×C4×D4C22×C511yescharacteristic
212C2×#117—21no—
213C22×C4⋊C4—21no—
214C22×C4⋊C4C22×C511yescharacteristic
215C22×C4⋊C4C22×C511yescharacteristic
216C22×C42C22×C511yescharacteristic
217#483—24no—
218#480—24no—
219C2×#107C22×C512yes—
220C2×#106C22×C512yes—
221C2×#103C22×C512yes—
222C2×#103C22×C512yes—
223C2×#102C22×C512yes—
224C2×#102C22×C512yes—
225C2×C22⋊C8C22×C511yescharacteristic
226C2×C22⋊C8C22×C511yescharacteristic
227#389—21no—
228#389—21no—
229#389C22×C512yes—
230#389C22×C512yes—
231C2×#95—21no—
232#340C22×C512yes—
233#340C22×C512yes—
234#336C22×C512yes—
235#336C22×C512yes—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—22no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5—41no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5#12012yes—
248C23×C5#13512yes—
249C23×C5AGL(1,ℤ/8)12yes—
250C23×C5C22×D411yescharacteristic
251C5×Q8—24no—
252C5×Q8—42no—
253C5×D4—24no—
254C5×D4—48no—
255C5×D4—42no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—24no—
261C2×C4×C5—24no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—24no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—44no—
276C2×C4×C5—48no—
277C2×C4×C5—48no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—42no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—42no—
285C2×C4×C5—41no—
286C2×C4×C5—44no—
287C2×C4×C5—42no—
288C2×C4×C5—42no—
289C2×C4×C5—42no—
290C2×C4×C5—84no—
291C2×C4×C5#12012yes—
292C2×C4×C5#13712yes—
293C2×C4×C5C22×D411yescharacteristic
294C2×C4×C5C22×D411yescharacteristic
295C2×C4×C5C2×#4112yes—
296C2×C4×C52−1+412yes—
297C5×C8—42no—
298C5×C8—42no—
299C22×Q8C23×C511yescharacteristic
300C22×D4—21no—
301C22×D4C23×C511yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4C5×D411yescharacteristic
306C23×C4C5×D411yescharacteristic
307C23×C4C23×C511yescharacteristic
308C22×C8C23×C512yes—
309C22×C8C23×C512yes—
310#126—28no—
311#125—22no—
312#125—22no—
313#124—22no—
314#124—22no—
315#123—28no—
316C22⋊Q8—22no—
317C22⋊Q8C5×D414yes—
318#121—22no—
319#121C5×D414yes—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×D4—28no—
323C4×D4—22no—
324C4×D4—22no—
325#117—28no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4C23×C512yes—
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C4⋊C4C23×C512yes—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42C5×D411yescharacteristic
351C2×C42C5×D411yescharacteristic
352C2×C42C23×C511yescharacteristic
353C2×C42C23×C511yescharacteristic
354#107—24no—
355#106—24no—
356#103—24no—
357#103—24no—
358#102—24no—
359#102—24no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362#95—22no—
363#95—22no—
364C22×C5—22no—
365C22×C5—22no—
366C22×C5—22no—
367C22×C5—22no—
368C22×C5—22no—
369C22×C5—22no—
370C22×C5—42no—
371C22×C5—42no—
372C22×C5—42no—
373C22×C5—81no—
374C22×C5—81no—
375C22×C5—81no—
376C22×C5—81no—
377C22×C5#44914yes—
378C22×C5C2×#12011yescharacteristic
379C22×C5#52511yescharacteristic
380C22×C5#53611yescharacteristic
381C22×C5C2×#13511yescharacteristic
382C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C5C2×#13711yescharacteristic
384C22×C5#57511yescharacteristic
385C4×C5—22no—
386C4×C5—22no—
387C4×C5—44no—
388C4×C5—42no—
389C4×C5—41no—
390C4×C5—41no—
391C4×C5—42no—
392C4×C5—41no—
393C4×C5—42no—
394C4×C5—82no—
395C4×C5#54712yes—
396C4×C5#54712yes—
397C24—21no—
398C24C2×C5×D411yescharacteristic
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8C2×C5×D412yes—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4C2×C5×D412yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4C2×C5×D411yescharacteristic
433C22×C4C2×C5×D411yescharacteristic
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D412yes—
437C22×C4C2×C5×D412yes—
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C24×C511yescharacteristic
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—44no—
457C4⋊C4—44no—
458C4⋊C4—42no—
459C4⋊C4C2×C5×D412yes—
460C4⋊C4C2×C5×D412yes—
461C4⋊C4C5×#4114yes—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C42—24no—
468C42—22no—
469C42—22no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C2×C5—24no—
475C2×C5—82no—
476C2×C5#240611yescharacteristic
477C2×C5C2×#44911yescharacteristic
478C2×C5#300711yescharacteristic
479C2×C5#310811yescharacteristic
480C2×C5#311411yescharacteristic
481C2×C5#323211yescharacteristic
482C2×C5#323811yescharacteristic
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C5×#12012yes—
495C23C5×#13512yes—
496C23C5×AGL(1,ℤ/8)12yes—
497C23C22×C5×D411yescharacteristic
498Q8—24no—
499Q8—42no—
500D4—24no—
501D4—48no—
502D4—42no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4—48no—
524C2×C4—48no—
525C2×C4—44no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—84no—
538C2×C4C5×#12012yes—
539C2×C4C5×#13712yes—
540C2×C4C22×C5×D411yescharacteristic
541C2×C4C22×C5×D411yescharacteristic
542C2×C4C2×C5×#4112yes—
543C2×C4C5×2−1+412yes—
544C8—42no—
545C8—42no—
546C5#2406611yescharacteristic, direct product factor, Sylow
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C5×#44914yes—
561C22C2×C5×#12011yescharacteristic
562C22C5×#52511yescharacteristic
563C22C5×#53611yescharacteristic
564C22C2×C5×#13511yescharacteristic
565C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
566C22C2×C5×#13711yescharacteristic
567C22C5×#57511yescharacteristic
568C4—22no—
569C4—22no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—42no—
575C4—44no—
576C4—42no—
577C4—82no—
578C4C5×#54712yes—
579C4C5×#54712yes—
580C2—24no—
581C2—82no—
582C2C5×#240611yescharacteristic
583C2C2×C5×#44911yescharacteristic
584C2C5×#300711yescharacteristic
585C2C5×#310811yescharacteristic
586C2C5×#311411yescharacteristic
587C2C5×#323211yescharacteristic
588C2C5×#323811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#483C2semidirect
4. C2×C5×#389C2semidirect
5. C5×#2059C2semidirect
6. C5×#2042C2semidirect
8. C5×#1872C2semidirect
9. C5×#1864C2semidirect
10. C5×#1863C2semidirect
11. C5×#1817C2semidirect
47. #24066C5direct (N × H)
114. C2×#483C2×C5semidirect
116. C2×#389C2×C5semidirect
117. #2059C2×C5semidirect
118. #2042C2×C5semidirect
120. #1872C2×C5semidirect
121. #1864C2×C5semidirect
122. #1863C2×C5semidirect
123. #1817C2×C5semidirect
546. C5#24066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5292
C2×C5×#4832
C2×C5×#4802
C2×C5×#3892
C5×#20592
C5×#20422
C5×#18742
C5×#18722
C5×#18642
C5×#18632
C5×#18172
#240665