Finite Group Databasebeta

← C5×#32749 #11955469

Subgroups — C5×#32749 #11955469

Order 1280.

658 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2855C211yesmaximal, characteristic
2C5×#2851C211yesmaximal, characteristic
3C5×#2088C211yesmaximal, characteristic, complemented
4C5×#2086C211yesmaximal, characteristic, complemented
5C5×#2085C211yesmaximal, characteristic, complemented
6C5×#2077C211yesmaximal, characteristic
7C5×#2076C211yesmaximal, characteristic
8C5×#2074C211yesmaximal, characteristic, complemented
9C5×#2068C211yesmaximal, characteristic, complemented
10C5×#2066C211yesmaximal, characteristic, complemented
11C5×#2059C211yesmaximal, characteristic, complemented
12C5×#2036C211yesmaximal, characteristic
13C5×#2035C211yesmaximal, characteristic
14C5×#2026C211yesmaximal, characteristic, complemented
15C5×#1797C211yesmaximal, characteristic
16C2×C5×#125C2211yescharacteristic
17C2×C5×C22⋊Q8C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×#103C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×C22⋊C8C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C5×#391C2211yescharacteristic
32C5×#391C2211yescharacteristic
33C5×#389C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#387—21no—
38C5×#387—21no—
39C5×#387—21no—
40C5×#387—21no—
41C5×#385—21no—
42C5×#385—21no—
43C5×#385—21no—
44C5×#382C2211yescharacteristic
45C5×#381—21no—
46C5×#380C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#32749C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C23×C4×C5D411yescharacteristic
62C23×C4×C5D411yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C5×#125—41no—
69C5×#125—41no—
70C5×C22⋊Q8—41no—
71C5×C22⋊Q8—41no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C42×C5—41no—
91C2×C42×C5—41no—
92C2×C42×C5D411yescharacteristic
93C2×C42×C5D411yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C5×#107—41no—
97C5×#107—41no—
98C5×#106—41no—
99C5×#106—41no—
100C5×C4⋊C8—41no—
101C5×C4⋊C8—41no—
102C5×#103—41no—
103C5×#103—41no—
104C5×#103—41no—
105C5×#103—41no—
106C5×C22⋊C8—41no—
107C5×C22⋊C8—41no—
108C5×#95—21no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95—21no—
112C5×#95—21no—
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#2855C2×C511yescharacteristic
122#2851C2×C511yescharacteristic
123#2088C2×C511yescharacteristic, complemented
124#2086C2×C511yescharacteristic, complemented
125#2085C2×C511yescharacteristic, complemented
126#2077C2×C511yescharacteristic
127#2076C2×C511yescharacteristic
128#2074C2×C511yescharacteristic, complemented
129#2068C2×C511yescharacteristic, complemented
130#2066C2×C511yescharacteristic, complemented
131#2059C2×C511yescharacteristic, complemented
132#2036C2×C511yescharacteristic
133#2035C2×C511yescharacteristic
134#2026C2×C511yescharacteristic, complemented
135#1797C2×C511yescharacteristic
136C24×C5C2×D411yescharacteristic
137C2×C5×Q8—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
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—41no—
160C22×C4×C5—41no—
161C22×C4×C5—41no—
162C22×C4×C5—41no—
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2411yescharacteristic
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—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—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—42no—
198C5×C4⋊C4—42no—
199C5×C4⋊C4—42no—
200C5×C4⋊C4—42no—
201C5×C4⋊C4—42no—
202C5×C22⋊C4—42no—
203C5×C22⋊C4—42no—
204C5×C22⋊C4—42no—
205C5×C22⋊C4—42no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5—41no—
211C42×C5—41no—
212C2×#125C22×C511yescharacteristic
213C2×C22⋊Q8C22×C511yescharacteristic
214C22×C42C22×C511yescharacteristic
215C2×#107C22×C511yescharacteristic
216C2×#107C22×C511yescharacteristic
217C2×#106C22×C511yescharacteristic
218C2×#106C22×C511yescharacteristic
219C2×C4⋊C8C22×C511yescharacteristic
220C2×C4⋊C8C22×C511yescharacteristic
221C2×#103C22×C511yescharacteristic
222C2×#103C22×C511yescharacteristic
223C2×#103C22×C511yescharacteristic
224C2×#103C22×C511yescharacteristic
225C2×C22⋊C8C22×C511yescharacteristic
226C2×C22⋊C8C22×C511yescharacteristic
227#391C22×C511yescharacteristic
228#391C22×C511yescharacteristic
229#389C22×C511yescharacteristic
230#389C22×C511yescharacteristic
231#389C22×C511yescharacteristic
232#389C22×C511yescharacteristic
233#387—21no—
234#387—21no—
235#387—21no—
236#387—21no—
237#385—21no—
238#385—21no—
239#385—21no—
240#382C22×C511yescharacteristic
241#381—21no—
242#380C22×C511yescharacteristic
243#380C22×C511yescharacteristic
244#380C22×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#336C22×C511yescharacteristic
254#336C22×C511yescharacteristic
255C23×C5—21no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5#13712yes—
262C23×C5C22×D411yescharacteristic
263C5×Q8—41no—
264C5×Q8—41no—
265C5×Q8—41no—
266C5×Q8—41no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
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—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—44no—
282C2×C4×C5—44no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
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#13512yes—
312C2×C4×C5H(5,𝔽2)11yescharacteristic
313C2×C4×C5H(5,𝔽2)11yescharacteristic
314C2×C4×C5H(5,𝔽2)11yescharacteristic
315C2×C4×C52−1+411yescharacteristic
316C2×C4×C52−1+411yescharacteristic
317C2×C4×C52−1+411yescharacteristic
318C5×C8—41no—
319C5×C8—41no—
320C5×C8—41no—
321C5×C8—41no—
322C22×Q8C23×C511yescharacteristic
323C23×C4C5×D411yescharacteristic
324C23×C4C5×D411yescharacteristic
325C23×C4C23×C511yescharacteristic
326C22×C8C23×C511yescharacteristic
327C22×C8C23×C511yescharacteristic
328C22×C8C23×C511yescharacteristic
329C22×C8C23×C511yescharacteristic
330#125—41no—
331#125—41no—
332C22⋊Q8—41no—
333C22⋊Q8—41no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C23×C511yescharacteristic
342C2×C4⋊C4C23×C511yescharacteristic
343C2×C4⋊C4C23×C511yescharacteristic
344C2×C4⋊C4C23×C511yescharacteristic
345C2×C4⋊C4C23×C511yescharacteristic
346C2×C4⋊C4C23×C511yescharacteristic
347C2×C4⋊C4C23×C511yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—41no—
353C2×C42—41no—
354C2×C42C5×D411yescharacteristic
355C2×C42C5×D411yescharacteristic
356C2×C42C23×C511yescharacteristic
357C2×C42C23×C511yescharacteristic
358#107—41no—
359#107—41no—
360#106—41no—
361#106—41no—
362C4⋊C8—41no—
363C4⋊C8—41no—
364#103—41no—
365#103—41no—
366#103—41no—
367#103—41no—
368C22⋊C8—41no—
369C22⋊C8—41no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—41no—
387C22×C5—41no—
388C22×C5—41no—
389C22×C5—41no—
390C22×C5#53411yescharacteristic
391C22×C5#53611yescharacteristic
392C22×C5#53711yescharacteristic
393C22×C5C2×#13511yescharacteristic
394C22×C5C2×#13711yescharacteristic
395C22×C5#57511yescharacteristic
396C22×C5#57511yescharacteristic
397C4×C5—22no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5—41no—
402C4×C5—81no—
403C4×C5—81no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5—81no—
407C4×C5—81no—
408C4×C5—81no—
409C4×C5—81no—
410C4×C5#56211yescharacteristic
411C4×C5#56211yescharacteristic
412C4×C5#56311yescharacteristic
413C4×C5#56311yescharacteristic
414C24C2×C5×D411yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4C2×C5×D411yescharacteristic
442C22×C4C2×C5×D411yescharacteristic
443C22×C4C2×C5×D411yescharacteristic
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C24×C511yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42—41no—
490C2×C5—42no—
491C2×C5#281411yescharacteristic
492C2×C5#319111yescharacteristic
493C2×C5#319611yescharacteristic
494C2×C5#323311yescharacteristic
495C2×C5#323611yescharacteristic
496C2×C5#324811yescharacteristic
497C2×C5#325611yescharacteristic
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C5×#13712yes—
505C23C22×C5×D411yescharacteristic
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
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—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4C5×#13512yes—
555C2×C4C5×H(5,𝔽2)11yescharacteristic
556C2×C4C5×H(5,𝔽2)11yescharacteristic
557C2×C4C5×H(5,𝔽2)11yescharacteristic
558C2×C4C5×2−1+411yescharacteristic
559C2×C4C5×2−1+411yescharacteristic
560C2×C4C5×2−1+411yescharacteristic
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C5#3274911yescharacteristic, direct product factor, Sylow
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C5×#53411yescharacteristic
574C22C5×#53611yescharacteristic
575C22C5×#53711yescharacteristic
576C22C2×C5×#13511yescharacteristic
577C22C2×C5×#13711yescharacteristic
578C22C5×#57511yescharacteristic
579C22C5×#57511yescharacteristic
580C4—22no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C5×#56211yescharacteristic
594C4C5×#56211yescharacteristic
595C4C5×#56311yescharacteristic
596C4C5×#56311yescharacteristic
597C2—42no—
598C2C5×#281411yescharacteristic
599C2C5×#319111yescharacteristic
600C2C5×#319611yescharacteristic
601C2C5×#323311yescharacteristic
602C2C5×#323611yescharacteristic
603C2C5×#324811yescharacteristic
604C2C5×#325611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
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
3. C5×#2088C2semidirect
4. C5×#2086C2semidirect
5. C5×#2085C2semidirect
8. C5×#2074C2semidirect
9. C5×#2068C2semidirect
10. C5×#2066C2semidirect
11. C5×#2059C2semidirect
14. C5×#2026C2semidirect
59. #32749C5direct (N × H)
123. #2088C2×C5semidirect
124. #2086C2×C5semidirect
125. #2085C2×C5semidirect
128. #2074C2×C5semidirect
129. #2068C2×C5semidirect
130. #2066C2×C5semidirect
131. #2059C2×C5semidirect
134. #2026C2×C5semidirect
565. C5#32749direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28552
C5×#28512
C5×#20882
C5×#20862
C5×#20852
C5×#20772
C5×#20762
C5×#20742
C5×#20682
C5×#20662
C5×#20592
C5×#20362
C5×#20352
C5×#20262
C5×#17972
#327495