Finite Group Databasebeta

← C5×#24089 #11946809

Subgroups — C5×#24089 #11946809

Order 1280.

1334 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#547C211yesmaximal, characteristic
2C2×C5×#481C211yesmaximal, characteristic, complemented
3C22×C5×#106C211yesmaximal, characteristic, complemented
4C5×#2487C211yesmaximal, characteristic, complemented
5C5×#2058C212yesmaximal, complemented
6C5×#2034C212yesmaximal, complemented
7C5×#1893C211yesmaximal, characteristic, complemented
8C5×#1869C211yesmaximal, characteristic, complemented
9C5×#1864C212yesmaximal, complemented
10C5×#1853C212yesmaximal, complemented
11C5×#1823C211yesmaximal, characteristic, complemented
12C22×C5×#41—21no—
13C23×C5×C8C2211yescharacteristic
14C5×#547—24no—
15C5×#547—24no—
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C5×#123—21no—
18C2×C5×#123—21no—
19C2×C5×C22⋊Q8—21no—
20C2×C5×#121C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C2×C4×C5×D4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C5×#481—24no—
28C2×C5×#106—24no—
29C2×C5×#106C2212yes—
30C2×C5×#106C2212yes—
31C2×C5×#106C2212yes—
32C2×C5×#102C2212yes—
33C2×C5×#102C2212yes—
34C2×C5×C22⋊C8C2212yes—
35C2×C5×C22⋊C8C2211yescharacteristic
36C5×#400—21no—
37C5×#399—21no—
38C5×#389C2212yes—
39C5×#386—21no—
40C5×#385—21no—
41C5×#380C2212yes—
42C5×#380C2211yescharacteristic
43C5×#340C2212yes—
44C5×#340C2212yes—
45C5×#340C2212yes—
46C5×#336C2212yes—
47#24089C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—28no—
49C2×C5×#41—44no—
50C2×C5×#41—44no—
51C22×C5×Q8—21no—
52C22×C5×D4—21no—
53C22×C5×D4—21no—
54C22×C5×D4D411yescharacteristic
55C22×C5×D4C2311yescharacteristic
56C23×C4×C5—21no—
57C23×C4×C5—21no—
58C23×C4×C5—21no—
59C23×C4×C5—21no—
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C22×C5×C8—22no—
63C22×C5×C8—24no—
64C22×C5×C8C2312yes—
65C22×C5×C8C2312yes—
66C5×C4⋊Q8—22no—
67C5×C4⋊Q8—22no—
68C5×#123—28no—
69C5×#123—28no—
70C5×C22⋊Q8—28no—
71C5×#121—22no—
72C5×#121—22no—
73C5×#121—22no—
74C5×#121D414yes—
75C4×C5×D4—22no—
76C4×C5×D4—22no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4D411yescharacteristic
90C2×C5×C4⋊C4D414yes—
91C2×C5×C4⋊C4C2312yes—
92C2×C5×C4⋊C4C2312yes—
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4D411yescharacteristic
102C2×C5×C22⋊C4D411yescharacteristic
103C2×C42×C5C2311yescharacteristic
104C5×#106—24no—
105C5×#106—24no—
106C5×#106—24no—
107C5×#102—24no—
108C5×#102—24no—
109C5×C22⋊C8—22no—
110C5×C22⋊C8—24no—
111C5×#95—22no—
112C5×#95—21no—
113C5×#95—22no—
114C2×#547C2×C511yescharacteristic
115C2×#481C2×C511yescharacteristic, complemented
116C22×#106C2×C511yescharacteristic, complemented
117#2487C2×C511yescharacteristic, complemented
118#2058C2×C512yescomplemented
119#2034C2×C512yescomplemented
120#1893C2×C511yescharacteristic, complemented
121#1869C2×C511yescharacteristic, complemented
122#1864C2×C512yescomplemented
123#1853C2×C512yescomplemented
124#1823C2×C511yescharacteristic, complemented
125C24×C5—21no—
126C24×C5C2×D411yescharacteristic
127C24×C5C2×D411yescharacteristic
128C5×#41—432no—
129C2×C5×Q8—24no—
130C2×C5×Q8—42no—
131C2×C5×Q8—42no—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—24no—
135C2×C5×D4—24no—
136C2×C5×D4—21no—
137C2×C5×D4—22no—
138C2×C5×D4—22no—
139C2×C5×D4—42no—
140C2×C5×D4—42no—
141C2×C5×D4—42no—
142C2×C5×D4—42no—
143C2×C5×D4SD1614yes—
144C2×C5×D4C2×D412yes—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—24no—
148C22×C4×C5—24no—
149C22×C4×C5—24no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—42no—
160C22×C4×C5—42no—
161C22×C4×C5—42no—
162C22×C4×C5—42no—
163C22×C4×C5—42no—
164C22×C4×C5—42no—
165C22×C4×C5—42no—
166C22×C4×C5—82no—
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2411yescharacteristic
174C2×C5×C8—28no—
175C2×C5×C8—22no—
176C2×C5×C8—22no—
177C2×C5×C8—22no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8#4114yescomplemented
181C5×C4⋊C4—24no—
182C5×C4⋊C4—24no—
183C5×C4⋊C4—24no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4—82no—
194C5×C4⋊C4C2×D412yes—
195C5×C4⋊C4C2×D412yes—
196C5×C4⋊C4C2×D412yes—
197C5×C22⋊C4—24no—
198C5×C22⋊C4—24no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—24no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4—42no—
203C5×C22⋊C4—82no—
204C42×C5—21no—
205C42×C5—21no—
206C22×#41—21no—
207C23×C8C22×C511yescharacteristic
208#547—24no—
209#547—24no—
210C2×C4⋊Q8C22×C511yescharacteristic
211C2×#123—21no—
212C2×#123—21no—
213C2×C22⋊Q8—21no—
214C2×#121C22×C511yescharacteristic
215C2×#121C22×C511yescharacteristic
216C2×C4×D4C22×C511yescharacteristic
217C2×C4×D4C22×C511yescharacteristic
218C22×C4⋊C4C22×C511yescharacteristic
219C22×C4⋊C4C22×C511yescharacteristic
220C22×C4⋊C4C22×C511yescharacteristic
221#481—24no—
222C2×#106—24no—
223C2×#106C22×C512yes—
224C2×#106C22×C512yes—
225C2×#106C22×C512yes—
226C2×#102C22×C512yes—
227C2×#102C22×C512yes—
228C2×C22⋊C8C22×C511yescharacteristic
229C2×C22⋊C8C22×C512yes—
230#400—21no—
231#399—21no—
232#389C22×C512yes—
233#386—21no—
234#385—21no—
235#380C22×C511yescharacteristic
236#380C22×C512yes—
237#340C22×C512yes—
238#340C22×C512yes—
239#340C22×C512yes—
240#336C22×C512yes—
241C23×C5—22no—
242C23×C5—22no—
243C23×C5—21no—
244C23×C5—22no—
245C23×C5—21no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—42no—
249C23×C5—41no—
250C23×C5—41no—
251C23×C5—42no—
252C23×C5#12012yes—
253C23×C5C2×SD1612yes—
254C23×C5C2×SD1612yes—
255C23×C5AGL(1,ℤ/8)12yes—
256C23×C5C22×D411yescharacteristic
257C5×Q8—48no—
258C5×D4—28no—
259C5×D4—24no—
260C5×D4—48no—
261C5×D4—48no—
262C5×D4—41no—
263C5×D4—41no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—48no—
278C2×C4×C5—48no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—48no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
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—42no—
295C2×C4×C5—84no—
296C2×C4×C5#12012yes—
297C2×C4×C5C2×SD1612yes—
298C2×C4×C5C22×D411yescharacteristic
299C2×C4×C5C22×D411yescharacteristic
300C2×C4×C5C2×#4112yes—
301C2×C4×C52−1+412yes—
302C5×C8—24no—
303C5×C8—42no—
304C2×#41—28no—
305C2×#41—44no—
306C2×#41—44no—
307C22×Q8—21no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C5×D411yescharacteristic
311C22×D4C23×C511yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4C23×C511yescharacteristic
317C23×C4C23×C511yescharacteristic
318C22×C8—22no—
319C22×C8—24no—
320C22×C8C23×C512yes—
321C22×C8C23×C512yes—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324#123—28no—
325#123—28no—
326C22⋊Q8—28no—
327#121—22no—
328#121—22no—
329#121—22no—
330#121C5×D414yes—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4C5×D411yescharacteristic
346C2×C4⋊C4C5×D414yes—
347C2×C4⋊C4C23×C512yes—
348C2×C4⋊C4C23×C512yes—
349C2×C4⋊C4C23×C511yescharacteristic
350C2×C4⋊C4C23×C511yescharacteristic
351C2×C4⋊C4C23×C511yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4C5×D411yescharacteristic
358C2×C22⋊C4C5×D411yescharacteristic
359C2×C42C23×C511yescharacteristic
360#106—24no—
361#106—24no—
362#106—24no—
363#102—24no—
364#102—24no—
365C22⋊C8—22no—
366C22⋊C8—24no—
367#95—22no—
368#95—21no—
369#95—22no—
370C22×C5—24no—
371C22×C5—24no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—24no—
375C22×C5—22no—
376C22×C5—42no—
377C22×C5—41no—
378C22×C5—41no—
379C22×C5—42no—
380C22×C5—42no—
381C22×C5—42no—
382C22×C5—82no—
383C22×C5—82no—
384C22×C5#45014yes—
385C22×C5C2×#12011yescharacteristic
386C22×C5#54712yes—
387C22×C5C22×SD1611yescharacteristic
388C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C5#57712yes—
390C4×C5—22no—
391C4×C5—22no—
392C4×C5—41no—
393C4×C5—42no—
394C4×C5—42no—
395C4×C5—42no—
396C4×C5—41no—
397C4×C5—82no—
398C4×C5—82no—
399C4×C5#52511yescharacteristic
400C4×C5#53611yescharacteristic
401C4×C5#54712yes—
402C24—21no—
403C24C2×C5×D411yescharacteristic
404C24C2×C5×D411yescharacteristic
405#41—432no—
406C2×Q8—24no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4C5×SD1614yes—
421C2×D4C2×C5×D412yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—82no—
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C2×C5×D411yescharacteristic
447C22×C4C2×C5×D412yes—
448C22×C4C2×C5×D412yes—
449C22×C4C2×C5×D411yescharacteristic
450C22×C4C24×C511yescharacteristic
451C2×C8—28no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8C5×#4114yescomplemented
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C4⋊C4—82no—
471C4⋊C4C2×C5×D412yes—
472C4⋊C4C2×C5×D412yes—
473C4⋊C4C2×C5×D412yes—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—42no—
480C22⋊C4—82no—
481C42—21no—
482C42—21no—
483C2×C5—24no—
484C2×C5—42no—
485C2×C5—82no—
486C2×C5#240611yescharacteristic
487C2×C5C2×#45011yescharacteristic
488C2×C5#301011yescharacteristic
489C2×C5#333512yes—
490C2×C5#334512yes—
491C23—22no—
492C23—22no—
493C23—21no—
494C23—22no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23C5×#12012yes—
503C23C2×C5×SD1612yes—
504C23C2×C5×SD1612yes—
505C23C5×AGL(1,ℤ/8)12yes—
506C23C22×C5×D411yescharacteristic
507Q8—48no—
508D4—28no—
509D4—24no—
510D4—48no—
511D4—48no—
512D4—41no—
513D4—41no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—48no—
528C2×C4—48no—
529C2×C4—48no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4C5×#12012yes—
547C2×C4C2×C5×SD1612yes—
548C2×C4C22×C5×D411yescharacteristic
549C2×C4C22×C5×D411yescharacteristic
550C2×C4C2×C5×#4112yes—
551C2×C4C5×2−1+412yes—
552C8—24no—
553C8—42no—
554C5#2408911yescharacteristic, direct product factor, Sylow
555C22—22no—
556C22—24no—
557C22—24no—
558C22—22no—
559C22—22no—
560C22—24no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—82no—
568C22—82no—
569C22C5×#45014yes—
570C22C2×C5×#12011yescharacteristic
571C22C5×#54712yes—
572C22C22×C5×SD1611yescharacteristic
573C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
574C22C5×#57712yes—
575C4—22no—
576C4—22no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—82no—
583C4—82no—
584C4C5×#52511yescharacteristic
585C4C5×#53611yescharacteristic
586C4C5×#54712yes—
587C2—24no—
588C2—42no—
589C2—82no—
590C2C5×#240611yescharacteristic
591C2C2×C5×#45011yescharacteristic
592C2C5×#301011yescharacteristic
593C2C5×#333512yes—
594C2C5×#334512yes—
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#481C2semidirect
3. C22×C5×#106C2semidirect
4. C5×#2487C2semidirect
5. C5×#2058C2semidirect
6. C5×#2034C2semidirect
7. C5×#1893C2semidirect
8. C5×#1869C2semidirect
9. C5×#1864C2semidirect
10. C5×#1853C2semidirect
11. C5×#1823C2semidirect
47. #24089C5direct (N × H)
115. C2×#481C2×C5semidirect
116. C22×#106C2×C5semidirect
117. #2487C2×C5semidirect
118. #2058C2×C5semidirect
119. #2034C2×C5semidirect
120. #1893C2×C5semidirect
121. #1869C2×C5semidirect
122. #1864C2×C5semidirect
123. #1853C2×C5semidirect
124. #1823C2×C5semidirect
180. C2×C5×C8#41semidirect
457. C2×C8C5×#41semidirect
554. C5#24089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5472
C2×C5×#4812
C22×C5×#1062
C5×#24872
C5×#20582
C5×#20342
C5×#18932
C5×#18692
C5×#18642
C5×#18532
C5×#18232
#240895