Finite Group Databasebeta

← C5×#26762 #11949482

Subgroups — C5×#26762 #11949482

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2509C211yesmaximal, characteristic, complemented
2C5×#2367C211yesmaximal, characteristic
3C5×#2073C211yesmaximal, characteristic
4C5×#2067C211yesmaximal, characteristic
5C5×#2042C211yesmaximal, characteristic
6C5×#2042C211yesmaximal, characteristic
7C5×#1933C211yesmaximal, characteristic, complemented
8C5×#1928C211yesmaximal, characteristic, complemented
9C5×#1921C211yesmaximal, characteristic, complemented
10C5×#1918C211yesmaximal, characteristic, complemented
11C5×#1916C211yesmaximal, characteristic, complemented
12C5×#1863C211yesmaximal, characteristic, complemented
13C5×#1862C211yesmaximal, characteristic
14C5×#1805C211yesmaximal, characteristic, complemented
15C4×C5×#102C211yesmaximal, characteristic
16C2×C5×#124C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×#103C2211yescharacteristic
23C2×C5×#103C2211yescharacteristic
24C2×C5×#103C2211yescharacteristic
25C2×C5×#103C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C4×C5×C8C2211yescharacteristic
31C5×#400—21no—
32C5×#400—21no—
33C5×#391C2211yescharacteristic
34C5×#390C2211yescharacteristic
35C5×#389—21no—
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#389C2211yescharacteristic
39C5×#389C2211yescharacteristic
40C5×#388—21no—
41C5×#388—21no—
42C5×#387—21no—
43C5×#385—21no—
44C5×#382C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C4×C5×C4⋊C4C2211yescharacteristic
47C4×C5×C4⋊C4C2211yescharacteristic
48C4×C5×C22⋊C4—21no—
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#336C2211yescharacteristic
56C5×#336C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#26762C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C5×#124—22no—
68C5×#124—22no—
69C4×C5×Q8—22no—
70C4×C5×Q8—41no—
71C4×C5×D4—22no—
72C4×C5×D4—41no—
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⋊C4D411yescharacteristic
79C2×C5×C4⋊C4D411yescharacteristic
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×C5×C22⋊C4—21no—
91C2×C42×C5—21no—
92C2×C42×C5—21no—
93C2×C42×C5—21no—
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C2×C42×C5C2311yescharacteristic
97C5×#107—22no—
98C5×#107—22no—
99C5×C4⋊C8—41no—
100C5×#103—22no—
101C5×#103—22no—
102C5×#103—22no—
103C5×#103—41no—
104C5×#102—22no—
105C5×#102—22no—
106C5×#102—22no—
107C5×#102—41no—
108C4×C5×C8—41no—
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×#95D411yescharacteristic
120C5×#95D411yescharacteristic
121#2509C2×C511yescharacteristic, complemented
122#2367C2×C511yescharacteristic
123#2073C2×C511yescharacteristic
124#2067C2×C511yescharacteristic
125#2042C2×C511yescharacteristic
126#2042C2×C511yescharacteristic
127#1933C2×C511yescharacteristic, complemented
128#1928C2×C511yescharacteristic, complemented
129#1921C2×C511yescharacteristic, complemented
130#1918C2×C511yescharacteristic, complemented
131#1916C2×C511yescharacteristic, complemented
132#1863C2×C511yescharacteristic, complemented
133#1862C2×C511yescharacteristic
134#1805C2×C511yescharacteristic, complemented
135C4×#102C2×C511yescharacteristic
136C24×C5—21no—
137C2×C5×Q8—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8#4112yes—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4#4112yes—
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—42no—
157C22×C4×C5—42no—
158C22×C4×C5—81no—
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
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—21no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—21no—
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—41no—
190C5×C4⋊C4—42no—
191C5×C4⋊C4—42no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4—81no—
194C5×C4⋊C4—81no—
195C5×C4⋊C4#4112yes—
196C5×C4⋊C4#4112yes—
197C5×C22⋊C4—24no—
198C5×C22⋊C4—24no—
199C5×C22⋊C4—42no—
200C5×C22⋊C4—42no—
201C5×C22⋊C4—81no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—42no—
209C42×C5—81no—
210C42×C5—81no—
211C2×#124C22×C511yescharacteristic
212C2×C4×Q8C22×C511yescharacteristic
213C2×C4×D4C22×C511yescharacteristic
214C2×#107C22×C511yescharacteristic
215C2×#107C22×C511yescharacteristic
216C2×C4⋊C8C22×C511yescharacteristic
217C2×#103C22×C511yescharacteristic
218C2×#103C22×C511yescharacteristic
219C2×#103C22×C511yescharacteristic
220C2×#103C22×C511yescharacteristic
221C2×#102C22×C511yescharacteristic
222C2×#102C22×C511yescharacteristic
223C2×#102C22×C511yescharacteristic
224C2×#102C22×C511yescharacteristic
225C2×C4×C8C22×C511yescharacteristic
226#400—21no—
227#400—21no—
228#391C22×C511yescharacteristic
229#390C22×C511yescharacteristic
230#389—21no—
231#389C22×C511yescharacteristic
232#389C22×C511yescharacteristic
233#389C22×C511yescharacteristic
234#389C22×C511yescharacteristic
235#388—21no—
236#388—21no—
237#387—21no—
238#385—21no—
239#382C22×C511yescharacteristic
240C4×C4⋊C4C22×C511yescharacteristic
241C4×C4⋊C4C22×C511yescharacteristic
242C4×C4⋊C4C22×C511yescharacteristic
243C4×C22⋊C4—21no—
244#340C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249#340C22×C511yescharacteristic
250#336C22×C511yescharacteristic
251#336C22×C511yescharacteristic
252#336C22×C511yescharacteristic
253#336C22×C511yescharacteristic
254C23×C5—22no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5C22×D411yescharacteristic
262C5×Q8—22no—
263C5×Q8—22no—
264C5×Q8—41no—
265C5×Q8—41no—
266C5×D4—22no—
267C5×D4—22no—
268C5×D4—41no—
269C5×D4—41no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
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—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—84no—
309C2×C4×C5#13512yes—
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5H(5,𝔽2)11yescharacteristic
315C2×C4×C52−1+411yescharacteristic
316C5×C8—41no—
317C5×C8—41no—
318C5×C8—41no—
319C5×C8—41no—
320C22×Q8C23×C511yescharacteristic
321C22×D4C23×C511yescharacteristic
322C23×C4—21no—
323C22×C8C23×C511yescharacteristic
324C22×C8C23×C511yescharacteristic
325C22×C8C23×C511yescharacteristic
326C22×C8C23×C511yescharacteristic
327#124—22no—
328#124—22no—
329C4×Q8—22no—
330C4×Q8—41no—
331C4×D4—22no—
332C4×D4—41no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C5×D411yescharacteristic
339C2×C4⋊C4C5×D411yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C4⋊C4C23×C511yescharacteristic
342C2×C4⋊C4C23×C511yescharacteristic
343C2×C4⋊C4C23×C511yescharacteristic
344C2×C4⋊C4C23×C511yescharacteristic
345C2×C4⋊C4C23×C511yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42C23×C511yescharacteristic
355C2×C42C23×C511yescharacteristic
356C2×C42C23×C511yescharacteristic
357#107—22no—
358#107—22no—
359C4⋊C8—41no—
360#103—22no—
361#103—22no—
362#103—22no—
363#103—41no—
364#102—22no—
365#102—22no—
366#102—22no—
367#102—41no—
368C4×C8—41no—
369#95—21no—
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#95C5×D411yescharacteristic
380#95C5×D411yescharacteristic
381C22×C5—42no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5—81no—
385C22×C5—81no—
386C22×C5—81no—
387C22×C5—81no—
388C22×C5#52511yescharacteristic
389C22×C5#54611yescharacteristic
390C22×C5#54811yescharacteristic
391C22×C5C2×#13511yescharacteristic
392C22×C5#57511yescharacteristic
393C22×C5#57611yescharacteristic
394C22×C5#57811yescharacteristic
395C4×C5—22no—
396C4×C5—41no—
397C4×C5—42no—
398C4×C5—41no—
399C4×C5—42no—
400C4×C5—41no—
401C4×C5—42no—
402C4×C5—41no—
403C4×C5—41no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5—81no—
407C4×C5—81no—
408C4×C5#52911yescharacteristic
409C4×C5#53911yescharacteristic
410C4×C5#55211yescharacteristic
411C4×C5#55311yescharacteristic
412C24—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8C5×#4112yes—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C5×#4112yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C2×C5×D411yescharacteristic
440C22×C4C2×C5×D411yescharacteristic
441C22×C4C24×C511yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4C5×#4112yes—
472C4⋊C4C5×#4112yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—81no—
486C42—81no—
487C2×C5—82no—
488C2×C5#246011yescharacteristic
489C2×C5#310211yescharacteristic
490C2×C5#312411yescharacteristic
491C2×C5#329711yescharacteristic
492C2×C5#331311yescharacteristic
493C2×C5#336411yescharacteristic
494C2×C5#337011yescharacteristic
495C23—22no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C22×C5×D411yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507D4—22no—
508D4—22no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
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—84no—
550C2×C4C5×#13512yes—
551C2×C4C2×C5×#4111yescharacteristic
552C2×C4C2×C5×#4111yescharacteristic
553C2×C4C2×C5×#4111yescharacteristic
554C2×C4C2×C5×#4111yescharacteristic
555C2×C4C5×H(5,𝔽2)11yescharacteristic
556C2×C4C5×2−1+411yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C5#2676211yescharacteristic, direct product factor, Sylow
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C5×#52511yescharacteristic
570C22C5×#54611yescharacteristic
571C22C5×#54811yescharacteristic
572C22C2×C5×#13511yescharacteristic
573C22C5×#57511yescharacteristic
574C22C5×#57611yescharacteristic
575C22C5×#57811yescharacteristic
576C4—22no—
577C4—41no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C5×#52911yescharacteristic
590C4C5×#53911yescharacteristic
591C4C5×#55211yescharacteristic
592C4C5×#55311yescharacteristic
593C2—82no—
594C2C5×#246011yescharacteristic
595C2C5×#310211yescharacteristic
596C2C5×#312411yescharacteristic
597C2C5×#329711yescharacteristic
598C2C5×#331311yescharacteristic
599C2C5×#336411yescharacteristic
600C2C5×#337011yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2509C2semidirect
7. C5×#1933C2semidirect
8. C5×#1928C2semidirect
9. C5×#1921C2semidirect
10. C5×#1918C2semidirect
11. C5×#1916C2semidirect
12. C5×#1863C2semidirect
14. C5×#1805C2semidirect
59. #26762C5direct (N × H)
121. #2509C2×C5semidirect
127. #1933C2×C5semidirect
128. #1928C2×C5semidirect
129. #1921C2×C5semidirect
130. #1918C2×C5semidirect
131. #1916C2×C5semidirect
132. #1863C2×C5semidirect
134. #1805C2×C5semidirect
561. C5#26762direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25092
C5×#23672
C5×#20732
C5×#20672
C5×#20422
C5×#19332
C5×#19282
C5×#19212
C5×#19182
C5×#19162
C5×#18632
C5×#18622
C5×#18052
C4×C5×#1022
#267625