Finite Group Databasebeta

← C5×#24960 #11947680

Subgroups — C5×#24960 #11947680

Order 1280.

750 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2487C211yesmaximal, characteristic
2C5×#2354C211yesmaximal, characteristic
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2083C211yesmaximal, characteristic, complemented
5C5×#2077C211yesmaximal, characteristic, complemented
6C5×#2075C211yesmaximal, characteristic, complemented
7C5×#1920C211yesmaximal, characteristic, complemented
8C5×#1920C211yesmaximal, characteristic, complemented
9C5×#1870C211yesmaximal, characteristic
10C5×#1854C211yesmaximal, characteristic, complemented
11C5×#1854C211yesmaximal, characteristic, complemented
12C5×#1825C211yesmaximal, characteristic, complemented
13C5×#1823C211yesmaximal, characteristic, complemented
14C5×#1809C211yesmaximal, characteristic, complemented
15C5×#1736C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C5×#117C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#107C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C22⋊C8C2211yescharacteristic
26C2×C5×C22⋊C8C2211yescharacteristic
27C2×C5×C22⋊C8C2211yescharacteristic
28C5×#400—21no—
29C5×#399—21no—
30C5×#390—21no—
31C5×#389C2211yescharacteristic
32C5×#389C2211yescharacteristic
33C5×#388—21no—
34C5×#388—21no—
35C5×#386—21no—
36C5×#385—21no—
37C5×#384C2211yescharacteristic
38C5×#380C2211yescharacteristic
39C5×#380C2211yescharacteristic
40C5×#380C2211yescharacteristic
41C5×#380C2211yescharacteristic
42C5×#380C2211yescharacteristic
43C4×C5×C4⋊C4—21no—
44C4×C5×C4⋊C4C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#24960C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4D411yescharacteristic
61C23×C4×C5—21no—
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C2×C5×M16—22no—
65C2×C5×M16—22no—
66C2×C5×M16—41no—
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C4×C5×D4—22no—
72C4×C5×D4—22no—
73C5×#117—22no—
74C5×#117—22no—
75C5×#117—41no—
76C5×#117—41no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4D411yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
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—21no—
100C2×C5×C22⋊C4D411yescharacteristic
101C2×C5×C22⋊C4D411yescharacteristic
102C2×C42×C5—21no—
103C2×C42×C5—21no—
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C5×#107—41no—
107C5×#107—41no—
108C5×#106—22no—
109C5×#106—22no—
110C5×C22⋊C8—22no—
111C5×C22⋊C8—22no—
112C5×C22⋊C8—41no—
113C5×#95—21no—
114C5×#95—21no—
115C5×#95—21no—
116C5×#95—21no—
117C5×#95—21no—
118C5×#95—21no—
119C5×#95—21no—
120C5×#95—21no—
121#2487C2×C511yescharacteristic
122#2354C2×C511yescharacteristic
123#2100C2×C511yescharacteristic, complemented
124#2083C2×C511yescharacteristic, complemented
125#2077C2×C511yescharacteristic, complemented
126#2075C2×C511yescharacteristic, complemented
127#1920C2×C511yescharacteristic, complemented
128#1920C2×C511yescharacteristic, complemented
129#1870C2×C511yescharacteristic
130#1854C2×C511yescharacteristic, complemented
131#1854C2×C511yescharacteristic, complemented
132#1825C2×C511yescharacteristic, complemented
133#1823C2×C511yescharacteristic, complemented
134#1809C2×C511yescharacteristic, complemented
135#1736C2×C511yescharacteristic, complemented
136C24×C5C2×D411yescharacteristic
137C24×C5C2×D411yescharacteristic
138C2×C5×D4—22no—
139C2×C5×D4—22no—
140C2×C5×D4—41no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—42no—
160C22×C4×C5—81no—
161C22×C4×C5—81no—
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5#4112yes—
167C22×C4×C5#4112yes—
168C22×C4×C5C2411yescharacteristic
169C5×M16—44no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8#4112yes—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—42no—
199C5×C4⋊C4—42no—
200C5×C4⋊C4—81no—
201C5×C4⋊C4—81no—
202C5×C4⋊C4—81no—
203C5×C4⋊C4#4112yes—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—22no—
206C5×C22⋊C4—42no—
207C5×C22⋊C4—42no—
208C5×C22⋊C4—42no—
209C5×C22⋊C4—81no—
210C5×C22⋊C4—81no—
211C5×C22⋊C4—81no—
212C5×C22⋊C4—81no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5—42no—
216C42×C5—42no—
217C42×C5—42no—
218C22×M16C22×C511yescharacteristic
219C2×C4×D4C22×C511yescharacteristic
220C2×#117C22×C511yescharacteristic
221C2×#117C22×C511yescharacteristic
222C22×C4⋊C4C22×C511yescharacteristic
223C2×#107C22×C511yescharacteristic
224C2×#107C22×C511yescharacteristic
225C2×#106C22×C511yescharacteristic
226C2×#106C22×C511yescharacteristic
227C2×C22⋊C8C22×C511yescharacteristic
228C2×C22⋊C8C22×C511yescharacteristic
229C2×C22⋊C8C22×C511yescharacteristic
230#400—21no—
231#399—21no—
232#390—21no—
233#389C22×C511yescharacteristic
234#389C22×C511yescharacteristic
235#388—21no—
236#388—21no—
237#386—21no—
238#385—21no—
239#384C22×C511yescharacteristic
240#380C22×C511yescharacteristic
241#380C22×C511yescharacteristic
242#380C22×C511yescharacteristic
243#380C22×C511yescharacteristic
244#380C22×C511yescharacteristic
245C4×C4⋊C4—21no—
246C4×C4⋊C4C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249#340C22×C511yescharacteristic
250#340C22×C511yescharacteristic
251#340C22×C511yescharacteristic
252#340C22×C511yescharacteristic
253#340C22×C511yescharacteristic
254#340C22×C511yescharacteristic
255#340C22×C511yescharacteristic
256#340C22×C511yescharacteristic
257#340C22×C511yescharacteristic
258#340C22×C511yescharacteristic
259#336C22×C511yescharacteristic
260#336C22×C511yescharacteristic
261C23×C5—21no—
262C23×C5—21no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5—21no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5#12312yes—
275C23×C5C22×D411yescharacteristic
276C5×D4—44no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—84no—
320C2×C4×C5#12312yes—
321C2×C4×C5#13712yes—
322C2×C4×C5C2×#4111yescharacteristic
323C2×C4×C5C2×#4111yescharacteristic
324C2×C4×C5C2×#4111yescharacteristic
325C2×C4×C5C2×#4111yescharacteristic
326C2×C4×C5H(5,𝔽2)11yescharacteristic
327C2×C4×C52−1+411yescharacteristic
328C5×C8—22no—
329C5×C8—41no—
330C5×C8—41no—
331C5×C8—41no—
332C22×D4C5×D411yescharacteristic
333C23×C4—21no—
334C23×C4C23×C511yescharacteristic
335C23×C4C23×C511yescharacteristic
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—41no—
339C22×C8C23×C511yescharacteristic
340C22×C8C23×C511yescharacteristic
341C22×C8C23×C511yescharacteristic
342C22×C8C23×C511yescharacteristic
343C4×D4—22no—
344C4×D4—22no—
345#117—22no—
346#117—22no—
347#117—41no—
348#117—41no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C5×D411yescharacteristic
357C2×C4⋊C4C23×C511yescharacteristic
358C2×C4⋊C4C23×C511yescharacteristic
359C2×C4⋊C4C23×C511yescharacteristic
360C2×C4⋊C4C23×C511yescharacteristic
361C2×C4⋊C4C23×C511yescharacteristic
362C2×C4⋊C4C23×C511yescharacteristic
363C2×C4⋊C4C23×C511yescharacteristic
364C2×C4⋊C4C23×C511yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4C5×D411yescharacteristic
373C2×C22⋊C4C5×D411yescharacteristic
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42C23×C511yescharacteristic
378#107—41no—
379#107—41no—
380#106—22no—
381#106—22no—
382C22⋊C8—22no—
383C22⋊C8—22no—
384C22⋊C8—41no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393C22×C5—22no—
394C22×C5—22no—
395C22×C5—22no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5C2×#12311yescharacteristic
408C22×C5#54611yescharacteristic
409C22×C5#54711yescharacteristic
410C22×C5C2×#13711yescharacteristic
411C22×C5#57511yescharacteristic
412C22×C5#57611yescharacteristic
413C22×C5#57711yescharacteristic
414C4×C5—22no—
415C4×C5—22no—
416C4×C5—42no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5—81no—
420C4×C5—81no—
421C4×C5—81no—
422C4×C5—81no—
423C4×C5—81no—
424C4×C5—81no—
425C4×C5—81no—
426C4×C5#52911yescharacteristic
427C4×C5#53911yescharacteristic
428C4×C5#55111yescharacteristic
429C4×C5#55211yescharacteristic
430C24C2×C5×D411yescharacteristic
431C24C2×C5×D411yescharacteristic
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—41no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4C2×C5×D411yescharacteristic
457C22×C4C2×C5×D411yescharacteristic
458C22×C4C2×C5×D411yescharacteristic
459C22×C4C2×C5×D411yescharacteristic
460C22×C4C5×#4112yes—
461C22×C4C5×#4112yes—
462C22×C4C24×C511yescharacteristic
463M16—44no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C5×#4112yes—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4C5×#4112yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—42no—
511C42—42no—
512C2×C5—42no—
513C2×C5—81no—
514C2×C5#241911yescharacteristic
515C2×C5#309511yescharacteristic
516C2×C5#309611yescharacteristic
517C2×C5#330911yescharacteristic
518C2×C5#333111yescharacteristic
519C2×C5#335011yescharacteristic
520C2×C5#335711yescharacteristic
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23C5×#12312yes—
535C23C22×C5×D411yescharacteristic
536D4—44no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—84no—
580C2×C4C5×#12312yes—
581C2×C4C5×#13712yes—
582C2×C4C2×C5×#4111yescharacteristic
583C2×C4C2×C5×#4111yescharacteristic
584C2×C4C2×C5×#4111yescharacteristic
585C2×C4C2×C5×#4111yescharacteristic
586C2×C4C5×H(5,𝔽2)11yescharacteristic
587C2×C4C5×2−1+411yescharacteristic
588C8—22no—
589C8—41no—
590C8—41no—
591C8—41no—
592C5#2496011yescharacteristic, direct product factor, Sylow
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22C2×C5×#12311yescharacteristic
608C22C5×#54611yescharacteristic
609C22C5×#54711yescharacteristic
610C22C2×C5×#13711yescharacteristic
611C22C5×#57511yescharacteristic
612C22C5×#57611yescharacteristic
613C22C5×#57711yescharacteristic
614C4—22no—
615C4—22no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4C5×#52911yescharacteristic
627C4C5×#53911yescharacteristic
628C4C5×#55111yescharacteristic
629C4C5×#55211yescharacteristic
630C2—42no—
631C2—81no—
632C2C5×#241911yescharacteristic
633C2C5×#309511yescharacteristic
634C2C5×#309611yescharacteristic
635C2C5×#330911yescharacteristic
636C2C5×#333111yescharacteristic
637C2C5×#335011yescharacteristic
638C2C5×#335711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
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
3. C5×#2100C2semidirect
4. C5×#2083C2semidirect
5. C5×#2077C2semidirect
6. C5×#2075C2semidirect
7. C5×#1920C2semidirect
8. C5×#1920C2semidirect
10. C5×#1854C2semidirect
11. C5×#1854C2semidirect
12. C5×#1825C2semidirect
13. C5×#1823C2semidirect
14. C5×#1809C2semidirect
15. C5×#1736C2semidirect
59. #24960C5direct (N × H)
123. #2100C2×C5semidirect
124. #2083C2×C5semidirect
125. #2077C2×C5semidirect
126. #2075C2×C5semidirect
127. #1920C2×C5semidirect
128. #1920C2×C5semidirect
130. #1854C2×C5semidirect
131. #1854C2×C5semidirect
132. #1825C2×C5semidirect
133. #1823C2×C5semidirect
134. #1809C2×C5semidirect
135. #1736C2×C5semidirect
592. C5#24960direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24872
C5×#23542
C5×#21002
C5×#20832
C5×#20772
C5×#20752
C5×#19202
C5×#18702
C5×#18542
C5×#18252
C5×#18232
C5×#18092
C5×#17362
#249605