Finite Group Databasebeta

← C5×#26413 #11949133

Subgroups — C5×#26413 #11949133

Order 1280.

746 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2439C211yesmaximal, characteristic
2C5×#2362C211yesmaximal, characteristic
3C5×#2101C211yesmaximal, characteristic, complemented
4C5×#2087C211yesmaximal, characteristic, complemented
5C5×#2068C211yesmaximal, characteristic, complemented
6C5×#2024C211yesmaximal, characteristic, complemented
7C5×#1988C211yesmaximal, characteristic, complemented
8C5×#1920C211yesmaximal, characteristic, complemented
9C5×#1892C211yesmaximal, characteristic
10C5×#1873C211yesmaximal, characteristic
11C5×#1865C211yesmaximal, characteristic, complemented
12C5×#1854C211yesmaximal, characteristic
13C5×#1850C211yesmaximal, characteristic
14C5×#1805C211yesmaximal, characteristic, complemented
15C5×#1735C211yesmaximal, characteristic
16C23×C5×C8C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×C5×#107C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
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×#396—21no—
32C5×#393—21no—
33C5×#391—21no—
34C5×#391C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#388—21no—
39C5×#388—21no—
40C5×#387—21no—
41C5×#387—21no—
42C5×#382C2211yescharacteristic
43C5×#380C2211yescharacteristic
44C4×C5×C4⋊C4—21no—
45C4×C5×C4⋊C4C2211yescharacteristic
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#26413C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C22×C5×Q8C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C22×C5×C8—22no—
64C22×C5×C8—41no—
65C22×C5×C8—41no—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C5×C4⋊Q8—22no—
71C5×C4⋊Q8—41no—
72C5×C22⋊Q8—22no—
73C5×C22⋊Q8Q814yescomplemented
74C4×C5×Q8—22no—
75C4×C5×Q8—41no—
76C5×#117—22no—
77C5×#117—22no—
78C5×#117—41no—
79C5×#117—41no—
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⋊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⋊C4D411yescharacteristic
98C2×C5×C22⋊C4D411yescharacteristic
99C2×C42×C5—21no—
100C2×C42×C5—21no—
101C2×C42×C5—21no—
102C2×C42×C5—21no—
103C2×C42×C5C2311yescharacteristic
104C2×C42×C5C2311yescharacteristic
105C5×#107—41no—
106C5×#106—22no—
107C5×C4⋊C8—41no—
108C5×C4⋊C8—41no—
109C5×#103—22no—
110C5×#103—41no—
111C5×#103—41no—
112C5×#103—41no—
113C5×C22⋊C8—22no—
114C5×#95—21no—
115C5×#95—21no—
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#2439C2×C511yescharacteristic
126#2362C2×C511yescharacteristic
127#2101C2×C511yescharacteristic, complemented
128#2087C2×C511yescharacteristic, complemented
129#2068C2×C511yescharacteristic, complemented
130#2024C2×C511yescharacteristic, complemented
131#1988C2×C511yescharacteristic, complemented
132#1920C2×C511yescharacteristic, complemented
133#1892C2×C511yescharacteristic
134#1873C2×C511yescharacteristic
135#1865C2×C511yescharacteristic, complemented
136#1854C2×C511yescharacteristic
137#1850C2×C511yescharacteristic
138#1805C2×C511yescharacteristic, complemented
139#1735C2×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×Q8—42no—
147C2×C5×Q8—42no—
148C2×C5×Q8—81no—
149C2×C5×Q8C2×Q812yes—
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×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
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—21no—
182C2×C5×C8—44no—
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—81no—
200C5×C4⋊C4C2×Q812yes—
201C5×C4⋊C4#4112yes—
202C5×C4⋊C4#4112yes—
203C5×C22⋊C4—24no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—41no—
206C5×C22⋊C4—42no—
207C5×C22⋊C4—42no—
208C5×C22⋊C4—81no—
209C42×C5—21no—
210C42×C5—21no—
211C42×C5—21no—
212C42×C5—21no—
213C42×C5—42no—
214C42×C5—42no—
215C42×C5—42no—
216C42×C5—42no—
217C23×C8C22×C511yescharacteristic
218C2×C4⋊Q8C22×C511yescharacteristic
219C2×C22⋊Q8C22×C511yescharacteristic
220C2×C4×Q8C22×C511yescharacteristic
221C2×#117C22×C511yescharacteristic
222C2×#117C22×C511yescharacteristic
223C2×#107C22×C511yescharacteristic
224C2×#106C22×C511yescharacteristic
225C2×C4⋊C8C22×C511yescharacteristic
226C2×C4⋊C8C22×C511yescharacteristic
227C2×#103C22×C511yescharacteristic
228C2×#103C22×C511yescharacteristic
229C2×#103C22×C511yescharacteristic
230C2×#103C22×C511yescharacteristic
231C2×C22⋊C8C22×C511yescharacteristic
232#396—21no—
233#393—21no—
234#391—21no—
235#391C22×C511yescharacteristic
236#389C22×C511yescharacteristic
237#389C22×C511yescharacteristic
238#389C22×C511yescharacteristic
239#388—21no—
240#388—21no—
241#387—21no—
242#387—21no—
243#382C22×C511yescharacteristic
244#380C22×C511yescharacteristic
245C4×C4⋊C4—21no—
246C4×C4⋊C4C22×C511yescharacteristic
247C4×C22⋊C4C22×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#336C22×C511yescharacteristic
259#336C22×C511yescharacteristic
260C23×C5—21no—
261C23×C5—21no—
262C23×C5—21no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5C22⋊Q812yes—
267C23×C5C22×D411yescharacteristic
268C5×Q8—22no—
269C5×Q8—22no—
270C5×Q8—41no—
271C5×Q8—41no—
272C5×Q8—84no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
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—21no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
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—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×C5C22⋊Q812yes—
315C2×C4×C5#13512yes—
316C2×C4×C5C22×Q811yescharacteristic
317C2×C4×C5C2×#4111yescharacteristic
318C2×C4×C5C2×#4111yescharacteristic
319C2×C4×C5C2×#4111yescharacteristic
320C2×C4×C5H(5,𝔽2)11yescharacteristic
321C2×C4×C5H(5,𝔽2)11yescharacteristic
322C5×C8—41no—
323C5×C8—41no—
324C5×C8—41no—
325C5×C8—41no—
326C22×Q8—21no—
327C22×Q8C23×C511yescharacteristic
328C23×C4C23×C511yescharacteristic
329C22×C8—22no—
330C22×C8—41no—
331C22×C8—41no—
332C22×C8C23×C511yescharacteristic
333C22×C8C23×C511yescharacteristic
334C22×C8C23×C511yescharacteristic
335C22×C8C23×C511yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—41no—
338C22⋊Q8—22no—
339C22⋊Q8C5×Q814yescomplemented
340C4×Q8—22no—
341C4×Q8—41no—
342#117—22no—
343#117—22no—
344#117—41no—
345#117—41no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
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×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4C5×D411yescharacteristic
364C2×C22⋊C4C5×D411yescharacteristic
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42C23×C511yescharacteristic
370C2×C42C23×C511yescharacteristic
371#107—41no—
372#106—22no—
373C4⋊C8—41no—
374C4⋊C8—41no—
375#103—22no—
376#103—41no—
377#103—41no—
378#103—41no—
379C22⋊C8—22no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95C5×D411yescharacteristic
390#95C5×D411yescharacteristic
391C22×C5—22no—
392C22×C5—22no—
393C22×C5—22no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5C2×C22⋊Q811yescharacteristic
399C22×C5#54611yescharacteristic
400C22×C5#54611yescharacteristic
401C22×C5C2×#13511yescharacteristic
402C22×C5#57511yescharacteristic
403C22×C5#57711yescharacteristic
404C22×C5#57811yescharacteristic
405C4×C5—22no—
406C4×C5—22no—
407C4×C5—42no—
408C4×C5—42no—
409C4×C5—42no—
410C4×C5—41no—
411C4×C5—42no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—81no—
415C4×C5—81no—
416C4×C5—81no—
417C4×C5—81no—
418C4×C5#52911yescharacteristic
419C4×C5#53811yescharacteristic
420C4×C5#55411yescharacteristic
421C4×C5#55411yescharacteristic
422C24C2×C5×D411yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—81no—
431C2×Q8C2×C5×Q812yes—
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×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C2×C5×D411yescharacteristic
447C22×C4C2×C5×D411yescharacteristic
448C22×C4C2×C5×D411yescharacteristic
449C22×C4C2×C5×Q812yes—
450C22×C4C5×#4112yes—
451C22×C4C24×C511yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
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—44no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
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—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4C2×C5×Q812yes—
483C4⋊C4C5×#4112yes—
484C4⋊C4C5×#4112yes—
485C22⋊C4—24no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—81no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—42no—
497C42—42no—
498C42—42no—
499C2×C5—42no—
500C2×C5#245011yescharacteristic
501C2×C5#307611yescharacteristic
502C2×C5#308211yescharacteristic
503C2×C5#329611yescharacteristic
504C2×C5#330211yescharacteristic
505C2×C5#331311yescharacteristic
506C2×C5#332111yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23C5×C22⋊Q812yes—
514C23C22×C5×D411yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—41no—
518Q8—41no—
519Q8—84no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
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×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4C5×C22⋊Q812yes—
562C2×C4C5×#13512yes—
563C2×C4C22×C5×Q811yescharacteristic
564C2×C4C2×C5×#4111yescharacteristic
565C2×C4C2×C5×#4111yescharacteristic
566C2×C4C2×C5×#4111yescharacteristic
567C2×C4C5×H(5,𝔽2)11yescharacteristic
568C2×C4C5×H(5,𝔽2)11yescharacteristic
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C5#2641311yescharacteristic, direct product factor, Sylow
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×C5×C22⋊Q811yescharacteristic
582C22C5×#54611yescharacteristic
583C22C5×#54611yescharacteristic
584C22C2×C5×#13511yescharacteristic
585C22C5×#57511yescharacteristic
586C22C5×#57711yescharacteristic
587C22C5×#57811yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4C5×#52911yescharacteristic
602C4C5×#53811yescharacteristic
603C4C5×#55411yescharacteristic
604C4C5×#55411yescharacteristic
605C2—42no—
606C2C5×#245011yescharacteristic
607C2C5×#307611yescharacteristic
608C2C5×#308211yescharacteristic
609C2C5×#329611yescharacteristic
610C2C5×#330211yescharacteristic
611C2C5×#331311yescharacteristic
612C2C5×#332111yescharacteristic
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×#2101C2semidirect
4. C5×#2087C2semidirect
5. C5×#2068C2semidirect
6. C5×#2024C2semidirect
7. C5×#1988C2semidirect
8. C5×#1920C2semidirect
11. C5×#1865C2semidirect
14. C5×#1805C2semidirect
59. #26413C5direct (N × H)
73. C5×C22⋊Q8Q8semidirect
127. #2101C2×C5semidirect
128. #2087C2×C5semidirect
129. #2068C2×C5semidirect
130. #2024C2×C5semidirect
131. #1988C2×C5semidirect
132. #1920C2×C5semidirect
135. #1865C2×C5semidirect
138. #1805C2×C5semidirect
339. C22⋊Q8C5×Q8semidirect
573. C5#26413direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24392
C5×#23622
C5×#21012
C5×#20872
C5×#20682
C5×#20242
C5×#19882
C5×#19202
C5×#18922
C5×#18732
C5×#18652
C5×#18542
C5×#18502
C5×#18052
C5×#17352
#264135