Finite Group Databasebeta

← C5×#24944 #11947664

Subgroups — C5×#24944 #11947664

Order 1280.

740 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2485C211yesmaximal, characteristic
2C5×#2354C211yesmaximal, characteristic
3C5×#2099C211yesmaximal, characteristic, complemented
4C5×#2084C211yesmaximal, characteristic, complemented
5C5×#2077C211yesmaximal, characteristic, complemented
6C5×#2077C211yesmaximal, characteristic, complemented
7C5×#1921C211yesmaximal, characteristic, complemented
8C5×#1919C211yesmaximal, characteristic, complemented
9C5×#1869C211yesmaximal, characteristic
10C5×#1854C211yesmaximal, characteristic, complemented
11C5×#1854C211yesmaximal, characteristic, complemented
12C5×#1825C211yesmaximal, characteristic, complemented
13C5×#1825C211yesmaximal, characteristic, complemented
14C5×#1807C211yesmaximal, characteristic, complemented
15C5×#1735C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C5×#117C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C22⋊C8C2211yescharacteristic
26C2×C5×C22⋊C8C2211yescharacteristic
27C2×C5×C22⋊C8C2211yescharacteristic
28C5×#397—21no—
29C5×#394—21no—
30C5×#390—21no—
31C5×#389C2211yescharacteristic
32C5×#389C2211yescharacteristic
33C5×#388—21no—
34C5×#388—21no—
35C5×#388—21no—
36C5×#387—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#24944C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4D411yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C22×C5×C8—22no—
64C22×C5×C8—22no—
65C22×C5×C8—41no—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C4×C5×D4—22no—
71C4×C5×D4—22no—
72C5×#117—22no—
73C5×#117—22no—
74C5×#117—22no—
75C5×#117—22no—
76C5×#117—41no—
77C5×#117—41no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4D411yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
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×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⋊C4D411yescharacteristic
100C2×C5×C22⋊C4D411yescharacteristic
101C2×C42×C5—21no—
102C2×C42×C5—21no—
103C2×C42×C5—21no—
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C5×#107—22no—
107C5×#106—22no—
108C5×#106—41no—
109C5×#106—41no—
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#2485C2×C511yescharacteristic
122#2354C2×C511yescharacteristic
123#2099C2×C511yescharacteristic, complemented
124#2084C2×C511yescharacteristic, complemented
125#2077C2×C511yescharacteristic, complemented
126#2077C2×C511yescharacteristic, complemented
127#1921C2×C511yescharacteristic, complemented
128#1919C2×C511yescharacteristic, complemented
129#1869C2×C511yescharacteristic
130#1854C2×C511yescharacteristic, complemented
131#1854C2×C511yescharacteristic, complemented
132#1825C2×C511yescharacteristic, complemented
133#1825C2×C511yescharacteristic, complemented
134#1807C2×C511yescharacteristic, complemented
135#1735C2×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×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5#4112yes—
164C22×C4×C5#4112yes—
165C22×C4×C5C2411yescharacteristic
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
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—44no—
178C2×C5×C8#4112yes—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
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—42no—
196C5×C4⋊C4—42no—
197C5×C4⋊C4—81no—
198C5×C4⋊C4—81no—
199C5×C4⋊C4#4112yes—
200C5×C22⋊C4—22no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4—42no—
203C5×C22⋊C4—42no—
204C5×C22⋊C4—42no—
205C5×C22⋊C4—42no—
206C5×C22⋊C4—81no—
207C5×C22⋊C4—81no—
208C5×C22⋊C4—81no—
209C5×C22⋊C4—81no—
210C42×C5—21no—
211C42×C5—21no—
212C42×C5—42no—
213C42×C5—42no—
214C42×C5—42no—
215C42×C5—42no—
216C23×C8C22×C511yescharacteristic
217C2×C4×D4C22×C511yescharacteristic
218C2×#117C22×C511yescharacteristic
219C2×#117C22×C511yescharacteristic
220C2×#117C22×C511yescharacteristic
221C2×#107C22×C511yescharacteristic
222C2×#106C22×C511yescharacteristic
223C2×#106C22×C511yescharacteristic
224C2×#106C22×C511yescharacteristic
225C2×C22⋊C8C22×C511yescharacteristic
226C2×C22⋊C8C22×C511yescharacteristic
227C2×C22⋊C8C22×C511yescharacteristic
228#397—21no—
229#394—21no—
230#390—21no—
231#389C22×C511yescharacteristic
232#389C22×C511yescharacteristic
233#388—21no—
234#388—21no—
235#388—21no—
236#387—21no—
237#384C22×C511yescharacteristic
238#380C22×C511yescharacteristic
239#380C22×C511yescharacteristic
240#380C22×C511yescharacteristic
241#380C22×C511yescharacteristic
242#380C22×C511yescharacteristic
243C4×C4⋊C4—21no—
244C4×C4⋊C4C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×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#336C22×C511yescharacteristic
258#336C22×C511yescharacteristic
259C23×C5—21no—
260C23×C5—21no—
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#12312yes—
273C23×C5C22×D411yescharacteristic
274C5×D4—44no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
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#12312yes—
318C2×C4×C5#13512yes—
319C2×C4×C5C2×#4111yescharacteristic
320C2×C4×C5C2×#4111yescharacteristic
321C2×C4×C5C2×#4111yescharacteristic
322C2×C4×C5C2×#4111yescharacteristic
323C2×C4×C5H(5,𝔽2)11yescharacteristic
324C2×C4×C52−1+411yescharacteristic
325C5×C8—22no—
326C5×C8—41no—
327C5×C8—41no—
328C5×C8—41no—
329C22×D4C5×D411yescharacteristic
330C23×C4C23×C511yescharacteristic
331C23×C4C23×C511yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—41no—
335C22×C8C23×C511yescharacteristic
336C22×C8C23×C511yescharacteristic
337C22×C8C23×C511yescharacteristic
338C22×C8C23×C511yescharacteristic
339C4×D4—22no—
340C4×D4—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—41no—
346#117—41no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4C5×D411yescharacteristic
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C4⋊C4C23×C511yescharacteristic
355C2×C4⋊C4C23×C511yescharacteristic
356C2×C4⋊C4C23×C511yescharacteristic
357C2×C4⋊C4C23×C511yescharacteristic
358C2×C4⋊C4C23×C511yescharacteristic
359C2×C4⋊C4C23×C511yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4C5×D411yescharacteristic
369C2×C22⋊C4C5×D411yescharacteristic
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C511yescharacteristic
375#107—22no—
376#106—22no—
377#106—41no—
378#106—41no—
379C22⋊C8—22no—
380C22⋊C8—22no—
381C22⋊C8—41no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5—22no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
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×C5C2×#12311yescharacteristic
405C22×C5#54611yescharacteristic
406C22×C5#54711yescharacteristic
407C22×C5C2×#13511yescharacteristic
408C22×C5#57511yescharacteristic
409C22×C5#57711yescharacteristic
410C22×C5#57711yescharacteristic
411C4×C5—22no—
412C4×C5—22no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5—42no—
416C4×C5—81no—
417C4×C5—81no—
418C4×C5—81no—
419C4×C5—81no—
420C4×C5—81no—
421C4×C5—81no—
422C4×C5—81no—
423C4×C5#52911yescharacteristic
424C4×C5#53911yescharacteristic
425C4×C5#55111yescharacteristic
426C4×C5#55211yescharacteristic
427C24C2×C5×D411yescharacteristic
428C24C2×C5×D411yescharacteristic
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—41no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
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×C4C2×C5×D411yescharacteristic
451C22×C4C2×C5×D411yescharacteristic
452C22×C4C2×C5×D411yescharacteristic
453C22×C4C2×C5×D411yescharacteristic
454C22×C4C5×#4112yes—
455C22×C4C5×#4112yes—
456C22×C4C24×C511yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—44no—
469C2×C8C5×#4112yes—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
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—42no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4C5×#4112yes—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C42—21no—
502C42—21no—
503C42—42no—
504C42—42no—
505C42—42no—
506C42—42no—
507C2×C5—42no—
508C2×C5—81no—
509C2×C5#241911yescharacteristic
510C2×C5#309111yescharacteristic
511C2×C5#309911yescharacteristic
512C2×C5#330411yescharacteristic
513C2×C5#330711yescharacteristic
514C2×C5#334011yescharacteristic
515C2×C5#334811yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23C5×#12312yes—
530C23C22×C5×D411yescharacteristic
531D4—44no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
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×C4C5×#12312yes—
575C2×C4C5×#13512yes—
576C2×C4C2×C5×#4111yescharacteristic
577C2×C4C2×C5×#4111yescharacteristic
578C2×C4C2×C5×#4111yescharacteristic
579C2×C4C2×C5×#4111yescharacteristic
580C2×C4C5×H(5,𝔽2)11yescharacteristic
581C2×C4C5×2−1+411yescharacteristic
582C8—22no—
583C8—41no—
584C8—41no—
585C8—41no—
586C5#2494411yescharacteristic, direct product factor, Sylow
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22C2×C5×#12311yescharacteristic
602C22C5×#54611yescharacteristic
603C22C5×#54711yescharacteristic
604C22C2×C5×#13511yescharacteristic
605C22C5×#57511yescharacteristic
606C22C5×#57711yescharacteristic
607C22C5×#57711yescharacteristic
608C4—22no—
609C4—22no—
610C4—42no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4C5×#52911yescharacteristic
621C4C5×#53911yescharacteristic
622C4C5×#55111yescharacteristic
623C4C5×#55211yescharacteristic
624C2—42no—
625C2—81no—
626C2C5×#241911yescharacteristic
627C2C5×#309111yescharacteristic
628C2C5×#309911yescharacteristic
629C2C5×#330411yescharacteristic
630C2C5×#330711yescharacteristic
631C2C5×#334011yescharacteristic
632C2C5×#334811yescharacteristic
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×#2099C2semidirect
4. C5×#2084C2semidirect
5. C5×#2077C2semidirect
6. C5×#2077C2semidirect
7. C5×#1921C2semidirect
8. C5×#1919C2semidirect
10. C5×#1854C2semidirect
11. C5×#1854C2semidirect
12. C5×#1825C2semidirect
13. C5×#1825C2semidirect
14. C5×#1807C2semidirect
15. C5×#1735C2semidirect
59. #24944C5direct (N × H)
123. #2099C2×C5semidirect
124. #2084C2×C5semidirect
125. #2077C2×C5semidirect
126. #2077C2×C5semidirect
127. #1921C2×C5semidirect
128. #1919C2×C5semidirect
130. #1854C2×C5semidirect
131. #1854C2×C5semidirect
132. #1825C2×C5semidirect
133. #1825C2×C5semidirect
134. #1807C2×C5semidirect
135. #1735C2×C5semidirect
586. C5#24944direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24852
C5×#23542
C5×#20992
C5×#20842
C5×#20772
C5×#19212
C5×#19192
C5×#18692
C5×#18542
C5×#18252
C5×#18072
C5×#17352
#249445