Finite Group Databasebeta

← C5×#26432 #11949152

Subgroups — C5×#26432 #11949152

Order 1280.

748 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2441C211yesmaximal, characteristic
2C5×#2360C211yesmaximal, characteristic
3C5×#2099C211yesmaximal, characteristic, complemented
4C5×#2087C211yesmaximal, characteristic, complemented
5C5×#2068C211yesmaximal, characteristic, complemented
6C5×#2026C211yesmaximal, characteristic, complemented
7C5×#1989C211yesmaximal, characteristic, complemented
8C5×#1918C211yesmaximal, characteristic, complemented
9C5×#1894C211yesmaximal, characteristic
10C5×#1873C211yesmaximal, characteristic
11C5×#1863C211yesmaximal, characteristic, complemented
12C5×#1852C211yesmaximal, characteristic
13C5×#1851C211yesmaximal, characteristic
14C5×#1803C211yesmaximal, characteristic, complemented
15C5×#1736C211yesmaximal, characteristic
16C22×C5×M16C2211yescharacteristic
17C2×C5×#125C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C2×C5×#107C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C5×#399—21no—
32C5×#396—21no—
33C5×#391C2211yescharacteristic
34C5×#389—21no—
35C5×#389—21no—
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#389C2211yescharacteristic
39C5×#387—21no—
40C5×#387—21no—
41C5×#385—21no—
42C5×#384C2211yescharacteristic
43C5×#380C2211yescharacteristic
44C4×C5×C4⋊C4C2211yescharacteristic
45C4×C5×C22⋊C4—21no—
46C4×C5×C22⋊C4C2211yescharacteristic
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#26432C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C23×C4×C5—21no—
62C23×C4×C5C2311yescharacteristic
63C2×C5×M16—22no—
64C2×C5×M16—41no—
65C2×C5×M16—41no—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C5×#125—22no—
71C5×#125—41no—
72C5×C22⋊Q8—22no—
73C5×C22⋊Q8Q814yes—
74C4×C5×Q8—22no—
75C4×C5×Q8—41no—
76C5×#117—22no—
77C5×#117—41no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
101C2×C5×C22⋊C4D411yescharacteristic
102C2×C42×C5—21no—
103C2×C42×C5—21no—
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C2×C42×C5C2311yescharacteristic
107C5×#107—22no—
108C5×#107—41no—
109C5×C4⋊C8—41no—
110C5×C4⋊C8—41no—
111C5×#103—22no—
112C5×#103—41no—
113C5×#103—41no—
114C5×#103—41no—
115C5×C22⋊C8—22no—
116C5×#95—21no—
117C5×#95—21no—
118C5×#95—21no—
119C5×#95—21no—
120C5×#95—21no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95D411yescharacteristic
124C5×#95D411yescharacteristic
125#2441C2×C511yescharacteristic
126#2360C2×C511yescharacteristic
127#2099C2×C511yescharacteristic, complemented
128#2087C2×C511yescharacteristic, complemented
129#2068C2×C511yescharacteristic, complemented
130#2026C2×C511yescharacteristic, complemented
131#1989C2×C511yescharacteristic, complemented
132#1918C2×C511yescharacteristic, complemented
133#1894C2×C511yescharacteristic
134#1873C2×C511yescharacteristic
135#1863C2×C511yescharacteristic, complemented
136#1852C2×C511yescharacteristic
137#1851C2×C511yescharacteristic
138#1803C2×C511yescharacteristic, complemented
139#1736C2×C511yescharacteristic
140C24×C5C2×D411yescharacteristic
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8C2×Q812yes—
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—42no—
161C22×C4×C5—81no—
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×Q812yes—
168C22×C4×C5#4112yes—
169C22×C4×C5C2411yescharacteristic
170C5×M16—44no—
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—21no—
182C2×C5×C8—21no—
183C5×C4⋊C4—24no—
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—81no—
202C5×C4⋊C4—81no—
203C5×C4⋊C4—81no—
204C5×C4⋊C4C2×Q812yes—
205C5×C4⋊C4#4112yes—
206C5×C4⋊C4#4112yes—
207C5×C22⋊C4—24no—
208C5×C22⋊C4—22no—
209C5×C22⋊C4—41no—
210C5×C22⋊C4—42no—
211C5×C22⋊C4—81no—
212C42×C5—21no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5—21no—
216C42×C5—42no—
217C42×C5—42no—
218C42×C5—81no—
219C22×M16C22×C511yescharacteristic
220C2×#125C22×C511yescharacteristic
221C2×C22⋊Q8C22×C511yescharacteristic
222C2×C4×Q8C22×C511yescharacteristic
223C2×#117C22×C511yescharacteristic
224C22×C4⋊C4C22×C511yescharacteristic
225C2×#107C22×C511yescharacteristic
226C2×#107C22×C511yescharacteristic
227C2×C4⋊C8C22×C511yescharacteristic
228C2×C4⋊C8C22×C511yescharacteristic
229C2×#103C22×C511yescharacteristic
230C2×#103C22×C511yescharacteristic
231C2×#103C22×C511yescharacteristic
232C2×#103C22×C511yescharacteristic
233C2×C22⋊C8C22×C511yescharacteristic
234#399—21no—
235#396—21no—
236#391C22×C511yescharacteristic
237#389—21no—
238#389—21no—
239#389C22×C511yescharacteristic
240#389C22×C511yescharacteristic
241#389C22×C511yescharacteristic
242#387—21no—
243#387—21no—
244#385—21no—
245#384C22×C511yescharacteristic
246#380C22×C511yescharacteristic
247C4×C4⋊C4C22×C511yescharacteristic
248C4×C22⋊C4—21no—
249C4×C22⋊C4C22×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#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×C5C22⋊Q812yes—
269C23×C5C22×D411yescharacteristic
270C5×Q8—22no—
271C5×Q8—22no—
272C5×Q8—41no—
273C5×Q8—41no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
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—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—84no—
316C2×C4×C5C22⋊Q812yes—
317C2×C4×C5#13712yes—
318C2×C4×C5C22×Q811yescharacteristic
319C2×C4×C5C2×#4111yescharacteristic
320C2×C4×C5C2×#4111yescharacteristic
321C2×C4×C5C2×#4111yescharacteristic
322C2×C4×C5H(5,𝔽2)11yescharacteristic
323C2×C4×C5H(5,𝔽2)11yescharacteristic
324C5×C8—41no—
325C5×C8—41no—
326C5×C8—41no—
327C5×C8—41no—
328C22×Q8C23×C511yescharacteristic
329C23×C4—21no—
330C23×C4C23×C511yescharacteristic
331C2×M16—22no—
332C2×M16—41no—
333C2×M16—41no—
334C22×C8C23×C511yescharacteristic
335C22×C8C23×C511yescharacteristic
336C22×C8C23×C511yescharacteristic
337C22×C8C23×C511yescharacteristic
338#125—22no—
339#125—41no—
340C22⋊Q8—22no—
341C22⋊Q8C5×Q814yes—
342C4×Q8—22no—
343C4×Q8—41no—
344#117—22no—
345#117—41no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
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⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—41no—
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⋊C4C5×D411yescharacteristic
369C2×C22⋊C4C5×D411yescharacteristic
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42C23×C511yescharacteristic
374C2×C42C23×C511yescharacteristic
375#107—22no—
376#107—41no—
377C4⋊C8—41no—
378C4⋊C8—41no—
379#103—22no—
380#103—41no—
381#103—41no—
382#103—41no—
383C22⋊C8—22no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95C5×D411yescharacteristic
392#95C5×D411yescharacteristic
393C22×C5—22no—
394C22×C5—22no—
395C22×C5—22no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×C22⋊Q811yescharacteristic
401C22×C5#54611yescharacteristic
402C22×C5#54611yescharacteristic
403C22×C5C2×#13711yescharacteristic
404C22×C5#57511yescharacteristic
405C22×C5#57611yescharacteristic
406C22×C5#57811yescharacteristic
407C4×C5—22no—
408C4×C5—22no—
409C4×C5—41no—
410C4×C5—42no—
411C4×C5—42no—
412C4×C5—41no—
413C4×C5—42no—
414C4×C5—41no—
415C4×C5—42no—
416C4×C5—81no—
417C4×C5—81no—
418C4×C5—81no—
419C4×C5—81no—
420C4×C5#52911yescharacteristic
421C4×C5#53811yescharacteristic
422C4×C5#55411yescharacteristic
423C4×C5#55411yescharacteristic
424C24C2×C5×D411yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8C2×C5×Q812yes—
431C22×C4—21no—
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—42no—
444C22×C4—42no—
445C22×C4—81no—
446C22×C4C2×C5×D411yescharacteristic
447C22×C4C2×C5×D411yescharacteristic
448C22×C4C2×C5×D411yescharacteristic
449C22×C4C2×C5×D411yescharacteristic
450C22×C4C2×C5×D411yescharacteristic
451C22×C4C2×C5×Q812yes—
452C22×C4C5×#4112yes—
453C22×C4C24×C511yescharacteristic
454M16—44no—
455C2×C8—21no—
456C2×C8—21no—
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—
467C4⋊C4—24no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
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—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4C2×C5×Q812yes—
489C4⋊C4C5×#4112yes—
490C4⋊C4C5×#4112yes—
491C22⋊C4—24no—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—42no—
501C42—42no—
502C42—81no—
503C2×C5—42no—
504C2×C5#245011yescharacteristic
505C2×C5#307811yescharacteristic
506C2×C5#308311yescharacteristic
507C2×C5#331211yescharacteristic
508C2×C5#331511yescharacteristic
509C2×C5#332211yescharacteristic
510C2×C5#333311yescharacteristic
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C5×C22⋊Q812yes—
518C23C22×C5×D411yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
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×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—84no—
565C2×C4C5×C22⋊Q812yes—
566C2×C4C5×#13712yes—
567C2×C4C22×C5×Q811yescharacteristic
568C2×C4C2×C5×#4111yescharacteristic
569C2×C4C2×C5×#4111yescharacteristic
570C2×C4C2×C5×#4111yescharacteristic
571C2×C4C5×H(5,𝔽2)11yescharacteristic
572C2×C4C5×H(5,𝔽2)11yescharacteristic
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C5#2643211yescharacteristic, direct product factor, Sylow
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C5×C22⋊Q811yescharacteristic
586C22C5×#54611yescharacteristic
587C22C5×#54611yescharacteristic
588C22C2×C5×#13711yescharacteristic
589C22C5×#57511yescharacteristic
590C22C5×#57611yescharacteristic
591C22C5×#57811yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4C5×#52911yescharacteristic
606C4C5×#53811yescharacteristic
607C4C5×#55411yescharacteristic
608C4C5×#55411yescharacteristic
609C2—42no—
610C2C5×#245011yescharacteristic
611C2C5×#307811yescharacteristic
612C2C5×#308311yescharacteristic
613C2C5×#331211yescharacteristic
614C2C5×#331511yescharacteristic
615C2C5×#332211yescharacteristic
616C2C5×#333311yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C5×#2099C2semidirect
4. C5×#2087C2semidirect
5. C5×#2068C2semidirect
6. C5×#2026C2semidirect
7. C5×#1989C2semidirect
8. C5×#1918C2semidirect
11. C5×#1863C2semidirect
14. C5×#1803C2semidirect
59. #26432C5direct (N × H)
127. #2099C2×C5semidirect
128. #2087C2×C5semidirect
129. #2068C2×C5semidirect
130. #2026C2×C5semidirect
131. #1989C2×C5semidirect
132. #1918C2×C5semidirect
135. #1863C2×C5semidirect
138. #1803C2×C5semidirect
577. C5#26432direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24412
C5×#23602
C5×#20992
C5×#20872
C5×#20682
C5×#20262
C5×#19892
C5×#19182
C5×#18942
C5×#18732
C5×#18632
C5×#18522
C5×#18512
C5×#18032
C5×#17362
#264325