Finite Group Databasebeta

← C5×#24088 #11946808

Subgroups — C5×#24088 #11946808

Order 1280.

1354 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#547C211yesmaximal, characteristic
2C2×C5×#480C211yesmaximal, characteristic, complemented
3C22×C5×#107C211yesmaximal, characteristic, complemented
4C5×#2486C211yesmaximal, characteristic, complemented
5C5×#2057C212yesmaximal, complemented
6C5×#2033C212yesmaximal, complemented
7C5×#1893C211yesmaximal, characteristic, complemented
8C5×#1869C211yesmaximal, characteristic, complemented
9C5×#1862C212yesmaximal, complemented
10C5×#1852C212yesmaximal, 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×#123—21no—
20C2×C5×C22⋊Q8—21no—
21C2×C5×#121C2211yescharacteristic
22C2×C5×#121C2211yescharacteristic
23C2×C4×C5×D4C2211yescharacteristic
24C2×C4×C5×D4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C5×#480—24no—
29C2×C5×#107—24no—
30C2×C5×#107C2212yes—
31C2×C5×#107C2212yes—
32C2×C5×#107C2212yes—
33C2×C5×#102C2212yes—
34C2×C5×#102C2212yes—
35C2×C5×C22⋊C8C2212yes—
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#398—21no—
38C5×#397—21no—
39C5×#389C2212yes—
40C5×#381—21no—
41C5×#380C2212yes—
42C5×#380C2211yescharacteristic
43C5×#340C2212yes—
44C5×#340C2212yes—
45C5×#340C2212yes—
46C5×#336C2212yes—
47#24088C511yesmaximal, 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×#123—44no—
71C5×C22⋊Q8—28no—
72C5×#121—22no—
73C5×#121—22no—
74C5×#121—22no—
75C5×#121D414yes—
76C4×C5×D4—22no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4D411yescharacteristic
91C2×C5×C4⋊C4D414yes—
92C2×C5×C4⋊C4C2312yes—
93C2×C5×C4⋊C4C2312yes—
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4D411yescharacteristic
103C2×C5×C22⋊C4D411yescharacteristic
104C2×C42×C5C2311yescharacteristic
105C5×#107—24no—
106C5×#107—24no—
107C5×#107—24no—
108C5×#102—24no—
109C5×#102—24no—
110C5×C22⋊C8—22no—
111C5×C22⋊C8—24no—
112C5×#95—22no—
113C5×#95—21no—
114C5×#95—22no—
115C2×#547C2×C511yescharacteristic
116C2×#480C2×C511yescharacteristic, complemented
117C22×#107C2×C511yescharacteristic, complemented
118#2486C2×C511yescharacteristic, complemented
119#2057C2×C512yescomplemented
120#2033C2×C512yescomplemented
121#1893C2×C511yescharacteristic, complemented
122#1869C2×C511yescharacteristic, complemented
123#1862C2×C512yescomplemented
124#1852C2×C512yescomplemented
125#1823C2×C511yescharacteristic, complemented
126C24×C5—21no—
127C24×C5C2×D411yescharacteristic
128C24×C5C2×D411yescharacteristic
129C5×#41—432no—
130C2×C5×Q8—24no—
131C2×C5×Q8—42no—
132C2×C5×Q8—42no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—24no—
136C2×C5×D4—24no—
137C2×C5×D4—21no—
138C2×C5×D4—22no—
139C2×C5×D4—22no—
140C2×C5×D4—42no—
141C2×C5×D4—42no—
142C2×C5×D4—42no—
143C2×C5×D4—42no—
144C2×C5×D4D814yes—
145C2×C5×D4C2×D412yes—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—24no—
149C22×C4×C5—24no—
150C22×C4×C5—24no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
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—42no—
167C22×C4×C5—42no—
168C22×C4×C5—42no—
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2411yescharacteristic
176C2×C5×C8—28no—
177C2×C5×C8—22no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8—22no—
181C2×C5×C8—22no—
182C2×C5×C8#4114yescomplemented
183C5×C4⋊C4—24no—
184C5×C4⋊C4—24no—
185C5×C4⋊C4—24no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—42no—
195C5×C4⋊C4—44no—
196C5×C4⋊C4C2×D412yes—
197C5×C4⋊C4C2×D412yes—
198C5×C4⋊C4C2×D412yes—
199C5×C22⋊C4—24no—
200C5×C22⋊C4—24no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4—24no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—42no—
205C5×C22⋊C4—44no—
206C42×C5—21no—
207C42×C5—21no—
208C22×#41—21no—
209C23×C8C22×C511yescharacteristic
210#547—24no—
211#547—24no—
212C2×C4⋊Q8C22×C511yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×#121C22×C511yescharacteristic
218C2×#121C22×C511yescharacteristic
219C2×C4×D4C22×C511yescharacteristic
220C2×C4×D4C22×C511yescharacteristic
221C22×C4⋊C4C22×C511yescharacteristic
222C22×C4⋊C4C22×C511yescharacteristic
223C22×C4⋊C4C22×C511yescharacteristic
224#480—24no—
225C2×#107—24no—
226C2×#107C22×C512yes—
227C2×#107C22×C512yes—
228C2×#107C22×C512yes—
229C2×#102C22×C512yes—
230C2×#102C22×C512yes—
231C2×C22⋊C8C22×C511yescharacteristic
232C2×C22⋊C8C22×C512yes—
233#398—21no—
234#397—21no—
235#389C22×C512yes—
236#381—21no—
237#380C22×C511yescharacteristic
238#380C22×C512yes—
239#340C22×C512yes—
240#340C22×C512yes—
241#340C22×C512yes—
242#336C22×C512yes—
243C23×C5—22no—
244C23×C5—22no—
245C23×C5—21no—
246C23×C5—22no—
247C23×C5—21no—
248C23×C5—22no—
249C23×C5—22no—
250C23×C5—42no—
251C23×C5—41no—
252C23×C5—41no—
253C23×C5—42no—
254C23×C5#12012yes—
255C23×C5C2×D812yes—
256C23×C5C2×D812yes—
257C23×C5AGL(1,ℤ/8)12yes—
258C23×C5C22×D411yescharacteristic
259C5×Q8—48no—
260C5×D4—28no—
261C5×D4—24no—
262C5×D4—48no—
263C5×D4—48no—
264C5×D4—41no—
265C5×D4—41no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—21no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—24no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—48no—
280C2×C4×C5—48no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—48no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—84no—
298C2×C4×C5#12012yes—
299C2×C4×C5C2×D812yes—
300C2×C4×C5C22×D411yescharacteristic
301C2×C4×C5C22×D411yescharacteristic
302C2×C4×C5C2×#4112yes—
303C2×C4×C52−1+412yes—
304C5×C8—24no—
305C5×C8—42no—
306C2×#41—28no—
307C2×#41—44no—
308C2×#41—44no—
309C22×Q8—21no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4C5×D411yescharacteristic
313C22×D4C23×C511yescharacteristic
314C23×C4—21no—
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4C23×C511yescharacteristic
319C23×C4C23×C511yescharacteristic
320C22×C8—22no—
321C22×C8—24no—
322C22×C8C23×C512yes—
323C22×C8C23×C512yes—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326#123—28no—
327#123—28no—
328#123—44no—
329C22⋊Q8—28no—
330#121—22no—
331#121—22no—
332#121—22no—
333#121C5×D414yes—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4C5×D411yescharacteristic
349C2×C4⋊C4C5×D414yes—
350C2×C4⋊C4C23×C512yes—
351C2×C4⋊C4C23×C512yes—
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C4⋊C4C23×C511yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4C5×D411yescharacteristic
361C2×C22⋊C4C5×D411yescharacteristic
362C2×C42C23×C511yescharacteristic
363#107—24no—
364#107—24no—
365#107—24no—
366#102—24no—
367#102—24no—
368C22⋊C8—22no—
369C22⋊C8—24no—
370#95—22no—
371#95—21no—
372#95—22no—
373C22×C5—24no—
374C22×C5—24no—
375C22×C5—22no—
376C22×C5—22no—
377C22×C5—24no—
378C22×C5—22no—
379C22×C5—42no—
380C22×C5—41no—
381C22×C5—41no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5—42no—
385C22×C5—82no—
386C22×C5—82no—
387C22×C5#44714yes—
388C22×C5C2×#12011yescharacteristic
389C22×C5#54712yes—
390C22×C5C22×D811yescharacteristic
391C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C5#57812yes—
393C4×C5—22no—
394C4×C5—22no—
395C4×C5—41no—
396C4×C5—42no—
397C4×C5—42no—
398C4×C5—42no—
399C4×C5—41no—
400C4×C5—82no—
401C4×C5—82no—
402C4×C5#52511yescharacteristic
403C4×C5#53611yescharacteristic
404C4×C5#54712yes—
405C24—21no—
406C24C2×C5×D411yescharacteristic
407C24C2×C5×D411yescharacteristic
408#41—432no—
409C2×Q8—24no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4C5×D814yes—
424C2×D4C2×C5×D412yes—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4C2×C5×D411yescharacteristic
449C22×C4C2×C5×D411yescharacteristic
450C22×C4C2×C5×D411yescharacteristic
451C22×C4C2×C5×D412yes—
452C22×C4C2×C5×D412yes—
453C22×C4C2×C5×D411yescharacteristic
454C22×C4C24×C511yescharacteristic
455C2×C8—28no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8C5×#4114yescomplemented
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—42no—
474C4⋊C4—44no—
475C4⋊C4C2×C5×D412yes—
476C4⋊C4C2×C5×D412yes—
477C4⋊C4C2×C5×D412yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—42no—
484C22⋊C4—44no—
485C42—21no—
486C42—21no—
487C2×C5—24no—
488C2×C5—42no—
489C2×C5—82no—
490C2×C5#240611yescharacteristic
491C2×C5C2×#44711yescharacteristic
492C2×C5#301111yescharacteristic
493C2×C5#333412yes—
494C2×C5#334312yes—
495C23—22no—
496C23—22no—
497C23—21no—
498C23—22no—
499C23—21no—
500C23—22no—
501C23—22no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23C5×#12012yes—
507C23C2×C5×D812yes—
508C23C2×C5×D812yes—
509C23C5×AGL(1,ℤ/8)12yes—
510C23C22×C5×D411yescharacteristic
511Q8—48no—
512D4—28no—
513D4—24no—
514D4—48no—
515D4—48no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—48no—
532C2×C4—48no—
533C2×C4—48no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—84no—
550C2×C4C5×#12012yes—
551C2×C4C2×C5×D812yes—
552C2×C4C22×C5×D411yescharacteristic
553C2×C4C22×C5×D411yescharacteristic
554C2×C4C2×C5×#4112yes—
555C2×C4C5×2−1+412yes—
556C8—24no—
557C8—42no—
558C5#2408811yescharacteristic, direct product factor, Sylow
559C22—22no—
560C22—24no—
561C22—24no—
562C22—22no—
563C22—22no—
564C22—24no—
565C22—41no—
566C22—42no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22C5×#44714yes—
574C22C2×C5×#12011yescharacteristic
575C22C5×#54712yes—
576C22C22×C5×D811yescharacteristic
577C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
578C22C5×#57812yes—
579C4—22no—
580C4—22no—
581C4—42no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—41no—
586C4—82no—
587C4—82no—
588C4C5×#52511yescharacteristic
589C4C5×#53611yescharacteristic
590C4C5×#54712yes—
591C2—24no—
592C2—42no—
593C2—82no—
594C2C5×#240611yescharacteristic
595C2C2×C5×#44711yescharacteristic
596C2C5×#301111yescharacteristic
597C2C5×#333412yes—
598C2C5×#334312yes—
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×#480C2semidirect
3. C22×C5×#107C2semidirect
4. C5×#2486C2semidirect
5. C5×#2057C2semidirect
6. C5×#2033C2semidirect
7. C5×#1893C2semidirect
8. C5×#1869C2semidirect
9. C5×#1862C2semidirect
10. C5×#1852C2semidirect
11. C5×#1823C2semidirect
47. #24088C5direct (N × H)
116. C2×#480C2×C5semidirect
117. C22×#107C2×C5semidirect
118. #2486C2×C5semidirect
119. #2057C2×C5semidirect
120. #2033C2×C5semidirect
121. #1893C2×C5semidirect
122. #1869C2×C5semidirect
123. #1862C2×C5semidirect
124. #1852C2×C5semidirect
125. #1823C2×C5semidirect
182. C2×C5×C8#41semidirect
461. C2×C8C5×#41semidirect
558. C5#24088direct (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×#4802
C22×C5×#1072
C5×#24862
C5×#20572
C5×#20332
C5×#18932
C5×#18692
C5×#18622
C5×#18522
C5×#18232
#240885