Finite Group Databasebeta

← C5×#32747 #11955467

Subgroups — C5×#32747 #11955467

Order 1280.

720 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2854C211yesmaximal, characteristic
2C5×#2851C211yesmaximal, characteristic, complemented
3C5×#2088C211yesmaximal, characteristic, complemented
4C5×#2087C211yesmaximal, characteristic, complemented
5C5×#2085C211yesmaximal, characteristic, complemented
6C5×#2077C211yesmaximal, characteristic, complemented
7C5×#2075C211yesmaximal, characteristic, complemented
8C5×#2073C211yesmaximal, characteristic, complemented
9C5×#2067C211yesmaximal, characteristic, complemented
10C5×#2065C211yesmaximal, characteristic, complemented
11C5×#2059C211yesmaximal, characteristic, complemented
12C5×#2034C211yesmaximal, characteristic
13C5×#2033C211yesmaximal, characteristic
14C5×#2025C211yesmaximal, characteristic, complemented
15C5×#1797C211yesmaximal, characteristic, complemented
16C2×C5×#125C2211yescharacteristic
17C2×C5×#123—21no—
18C2×C5×#121C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C5×#390C2211yescharacteristic
33C5×#390C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#388—21no—
39C5×#388—21no—
40C5×#387—21no—
41C5×#387—21no—
42C5×#386—21no—
43C5×#385—21no—
44C5×#385—21no—
45C5×#382C2211yescharacteristic
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#32747C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4—21no—
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5D411yescharacteristic
63C23×C4×C5D411yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C5×#125—41no—
70C5×#125—41no—
71C5×#123—44no—
72C5×#121—41no—
73C5×#121—41no—
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⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C42×C5—41no—
96C2×C42×C5—41no—
97C2×C42×C5D411yescharacteristic
98C2×C42×C5D411yescharacteristic
99C2×C42×C5C2311yescharacteristic
100C2×C42×C5C2311yescharacteristic
101C5×#107—41no—
102C5×#107—41no—
103C5×#106—41no—
104C5×#106—41no—
105C5×C4⋊C8—41no—
106C5×C4⋊C8—41no—
107C5×#102—41no—
108C5×#102—41no—
109C5×#102—41no—
110C5×#102—41no—
111C5×C22⋊C8—41no—
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—
121C5×#95—21no—
122#2854C2×C511yescharacteristic
123#2851C2×C511yescharacteristic, complemented
124#2088C2×C511yescharacteristic, complemented
125#2087C2×C511yescharacteristic, complemented
126#2085C2×C511yescharacteristic, complemented
127#2077C2×C511yescharacteristic, complemented
128#2075C2×C511yescharacteristic, complemented
129#2073C2×C511yescharacteristic, complemented
130#2067C2×C511yescharacteristic, complemented
131#2065C2×C511yescharacteristic, complemented
132#2059C2×C511yescharacteristic, complemented
133#2034C2×C511yescharacteristic
134#2033C2×C511yescharacteristic
135#2025C2×C511yescharacteristic, complemented
136#1797C2×C511yescharacteristic, complemented
137C24×C5—21no—
138C24×C5C2×D411yescharacteristic
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—42no—
146C2×C5×D4—42no—
147C2×C5×D4—42no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
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—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—41no—
164C22×C4×C5—41no—
165C22×C4×C5—41no—
166C22×C4×C5—41no—
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2411yescharacteristic
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—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—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—21no—
199C5×C4⋊C4—42no—
200C5×C4⋊C4—42no—
201C5×C4⋊C4—42no—
202C5×C4⋊C4—42no—
203C5×C4⋊C4—42no—
204C5×C4⋊C4—42no—
205C5×C22⋊C4—42no—
206C5×C22⋊C4—42no—
207C5×C22⋊C4—42no—
208C5×C22⋊C4—42no—
209C5×C22⋊C4—42no—
210C5×C22⋊C4—42no—
211C5×C22⋊C4—42no—
212C5×C22⋊C4—42no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5—21no—
216C42×C5—21no—
217C42×C5—41no—
218C42×C5—41no—
219C2×#125C22×C511yescharacteristic
220C2×#123—21no—
221C2×#121C22×C511yescharacteristic
222C22×C42C22×C511yescharacteristic
223C2×#107C22×C511yescharacteristic
224C2×#107C22×C511yescharacteristic
225C2×#106C22×C511yescharacteristic
226C2×#106C22×C511yescharacteristic
227C2×C4⋊C8C22×C511yescharacteristic
228C2×C4⋊C8C22×C511yescharacteristic
229C2×#102C22×C511yescharacteristic
230C2×#102C22×C511yescharacteristic
231C2×#102C22×C511yescharacteristic
232C2×#102C22×C511yescharacteristic
233C2×C22⋊C8C22×C511yescharacteristic
234C2×C22⋊C8C22×C511yescharacteristic
235#390C22×C511yescharacteristic
236#390C22×C511yescharacteristic
237#389C22×C511yescharacteristic
238#389C22×C511yescharacteristic
239#389C22×C511yescharacteristic
240#389C22×C511yescharacteristic
241#388—21no—
242#388—21no—
243#387—21no—
244#387—21no—
245#386—21no—
246#385—21no—
247#385—21no—
248#382C22×C511yescharacteristic
249#380C22×C511yescharacteristic
250#380C22×C511yescharacteristic
251#380C22×C511yescharacteristic
252#340C22×C511yescharacteristic
253#340C22×C511yescharacteristic
254#340C22×C511yescharacteristic
255#340C22×C511yescharacteristic
256#340C22×C511yescharacteristic
257#340C22×C511yescharacteristic
258#340C22×C511yescharacteristic
259#340C22×C511yescharacteristic
260#336C22×C511yescharacteristic
261#336C22×C511yescharacteristic
262C23×C5—21no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—41no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5AGL(1,ℤ/8)12yes—
276C23×C5C22×D411yescharacteristic
277C5×D4—41no—
278C5×D4—41no—
279C5×D4—41no—
280C5×D4—41no—
281C5×D4—84no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—44no—
297C2×C4×C5—44no—
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—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5#13512yes—
324C2×C4×C5H(5,𝔽2)11yescharacteristic
325C2×C4×C5H(5,𝔽2)11yescharacteristic
326C2×C4×C5H(5,𝔽2)11yescharacteristic
327C2×C4×C52−1+411yescharacteristic
328C2×C4×C52−1+411yescharacteristic
329C2×C4×C52−1+411yescharacteristic
330C5×C8—41no—
331C5×C8—41no—
332C5×C8—41no—
333C5×C8—41no—
334C22×D4—21no—
335C22×D4C23×C511yescharacteristic
336C23×C4C5×D411yescharacteristic
337C23×C4C5×D411yescharacteristic
338C23×C4C23×C511yescharacteristic
339C22×C8C23×C511yescharacteristic
340C22×C8C23×C511yescharacteristic
341C22×C8C23×C511yescharacteristic
342C22×C8C23×C511yescharacteristic
343#125—41no—
344#125—41no—
345#123—44no—
346#121—41no—
347#121—41no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
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×C4⋊C4C23×C511yescharacteristic
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⋊C4—21no—
369C2×C42—41no—
370C2×C42—41no—
371C2×C42C5×D411yescharacteristic
372C2×C42C5×D411yescharacteristic
373C2×C42C23×C511yescharacteristic
374C2×C42C23×C511yescharacteristic
375#107—41no—
376#107—41no—
377#106—41no—
378#106—41no—
379C4⋊C8—41no—
380C4⋊C8—41no—
381#102—41no—
382#102—41no—
383#102—41no—
384#102—41no—
385C22⋊C8—41no—
386C22⋊C8—41no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396C22×C5—22no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—81no—
404C22×C5—81no—
405C22×C5—81no—
406C22×C5—81no—
407C22×C5—81no—
408C22×C5—81no—
409C22×C5—81no—
410C22×C5#53411yescharacteristic
411C22×C5#53611yescharacteristic
412C22×C5#53711yescharacteristic
413C22×C5C2×#13511yescharacteristic
414C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C5#57511yescharacteristic
416C22×C5#57511yescharacteristic
417C4×C5—22no—
418C4×C5—41no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5—81no—
423C4×C5—81no—
424C4×C5—81no—
425C4×C5—81no—
426C4×C5—81no—
427C4×C5—81no—
428C4×C5—81no—
429C4×C5#56211yescharacteristic
430C4×C5#56211yescharacteristic
431C4×C5#56311yescharacteristic
432C4×C5#56311yescharacteristic
433C24—21no—
434C24C2×C5×D411yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4C2×C5×D411yescharacteristic
464C22×C4C2×C5×D411yescharacteristic
465C22×C4C2×C5×D411yescharacteristic
466C22×C4C2×C5×D411yescharacteristic
467C22×C4C2×C5×D411yescharacteristic
468C22×C4C24×C511yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—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—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42—41no—
515C2×C5—42no—
516C2×C5—161no—
517C2×C5#281411yescharacteristic
518C2×C5#319111yescharacteristic
519C2×C5#319411yescharacteristic
520C2×C5#323311yescharacteristic
521C2×C5#323411yescharacteristic
522C2×C5#324711yescharacteristic
523C2×C5#325611yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23C5×AGL(1,ℤ/8)12yes—
538C23C22×C5×D411yescharacteristic
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—84no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—44no—
559C2×C4—44no—
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—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4C5×#13512yes—
586C2×C4C5×H(5,𝔽2)11yescharacteristic
587C2×C4C5×H(5,𝔽2)11yescharacteristic
588C2×C4C5×H(5,𝔽2)11yescharacteristic
589C2×C4C5×2−1+411yescharacteristic
590C2×C4C5×2−1+411yescharacteristic
591C2×C4C5×2−1+411yescharacteristic
592C8—41no—
593C8—41no—
594C8—41no—
595C8—41no—
596C5#3274711yescharacteristic, direct product factor, Sylow
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C5×#53411yescharacteristic
612C22C5×#53611yescharacteristic
613C22C5×#53711yescharacteristic
614C22C2×C5×#13511yescharacteristic
615C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
616C22C5×#57511yescharacteristic
617C22C5×#57511yescharacteristic
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4C5×#56211yescharacteristic
631C4C5×#56211yescharacteristic
632C4C5×#56311yescharacteristic
633C4C5×#56311yescharacteristic
634C2—42no—
635C2—161no—
636C2C5×#281411yescharacteristic
637C2C5×#319111yescharacteristic
638C2C5×#319411yescharacteristic
639C2C5×#323311yescharacteristic
640C2C5×#323411yescharacteristic
641C2C5×#324711yescharacteristic
642C2C5×#325611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
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
2. C5×#2851C2semidirect
3. C5×#2088C2semidirect
4. C5×#2087C2semidirect
5. C5×#2085C2semidirect
6. C5×#2077C2semidirect
7. C5×#2075C2semidirect
8. C5×#2073C2semidirect
9. C5×#2067C2semidirect
10. C5×#2065C2semidirect
11. C5×#2059C2semidirect
14. C5×#2025C2semidirect
15. C5×#1797C2semidirect
59. #32747C5direct (N × H)
123. #2851C2×C5semidirect
124. #2088C2×C5semidirect
125. #2087C2×C5semidirect
126. #2085C2×C5semidirect
127. #2077C2×C5semidirect
128. #2075C2×C5semidirect
129. #2073C2×C5semidirect
130. #2067C2×C5semidirect
131. #2065C2×C5semidirect
132. #2059C2×C5semidirect
135. #2025C2×C5semidirect
136. #1797C2×C5semidirect
596. C5#32747direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28542
C5×#28512
C5×#20882
C5×#20872
C5×#20852
C5×#20772
C5×#20752
C5×#20732
C5×#20672
C5×#20652
C5×#20592
C5×#20342
C5×#20332
C5×#20252
C5×#17972
#327475