Finite Group Databasebeta

← C5×#32861 #11955581

Subgroups — C5×#32861 #11955581

Order 1280.

654 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2863C211yesmaximal, characteristic, complemented
2C5×#2860C211yesmaximal, characteristic
3C5×#2088C211yesmaximal, characteristic, complemented
4C5×#2087C211yesmaximal, characteristic, complemented
5C5×#2086C211yesmaximal, characteristic, complemented
6C5×#2068C211yesmaximal, characteristic, complemented
7C5×#2068C211yesmaximal, characteristic, complemented
8C5×#2067C211yesmaximal, characteristic
9C5×#2067C211yesmaximal, characteristic
10C5×#2066C211yesmaximal, characteristic, complemented
11C5×#2065C211yesmaximal, characteristic
12C5×#2055C211yesmaximal, characteristic
13C5×#2055C211yesmaximal, characteristic
14C5×#2055C211yesmaximal, characteristic
15C5×#1842C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C2×C5×#126—21no—
18C2×C5×#107C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C5×#391C2211yescharacteristic
34C5×#391C2211yescharacteristic
35C5×#391C2211yescharacteristic
36C5×#390C2211yescharacteristic
37C5×#390C2211yescharacteristic
38C5×#390C2211yescharacteristic
39C5×#389C2211yescharacteristic
40C5×#389C2211yescharacteristic
41C5×#389C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#388—21no—
46C5×#388—21no—
47C5×#388—21no—
48C5×#387—21no—
49C5×#387—21no—
50C5×#387—21no—
51C5×#383—21no—
52C43×C5C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59#32861C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4C2311yescharacteristic
62C2×C5×SD16—41no—
63C2×C5×SD16—41no—
64C2×C5×SD16—41no—
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C5×#126—44no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—21no—
88C2×C42×C5D411yescharacteristic
89C2×C42×C5D411yescharacteristic
90C2×C42×C5D411yescharacteristic
91C2×C42×C5D411yescharacteristic
92C2×C42×C5C2311yescharacteristic
93C2×C42×C5C2311yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C5×#107—41no—
96C5×#107—41no—
97C5×#106—41no—
98C5×C4⋊C8—41no—
99C5×C4⋊C8—41no—
100C5×C4⋊C8—41no—
101C5×C4⋊C8—41no—
102C5×C4⋊C8—41no—
103C5×C4⋊C8—41no—
104C5×#103—41no—
105C5×#103—41no—
106C5×#103—41no—
107C5×#102—41no—
108C5×#102—41no—
109C5×#102—41no—
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—
121C5×#95—21no—
122#2863C2×C511yescharacteristic, complemented
123#2860C2×C511yescharacteristic
124#2088C2×C511yescharacteristic, complemented
125#2087C2×C511yescharacteristic, complemented
126#2086C2×C511yescharacteristic, complemented
127#2068C2×C511yescharacteristic, complemented
128#2068C2×C511yescharacteristic, complemented
129#2067C2×C511yescharacteristic
130#2067C2×C511yescharacteristic
131#2066C2×C511yescharacteristic, complemented
132#2065C2×C511yescharacteristic
133#2055C2×C511yescharacteristic
134#2055C2×C511yescharacteristic
135#2055C2×C511yescharacteristic
136#1842C2×C511yescharacteristic, complemented
137C24×C5—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4—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×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2411yescharacteristic
164C5×SD16—44no—
165C2×C5×C8—21no—
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—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
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—42no—
190C5×C4⋊C4—42no—
191C5×C4⋊C4—42no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4—42no—
194C5×C4⋊C4—42no—
195C5×C22⋊C4—42no—
196C5×C22⋊C4—42no—
197C5×C22⋊C4—42no—
198C5×C22⋊C4—42no—
199C5×C22⋊C4—42no—
200C5×C22⋊C4—42no—
201C42×C5—22no—
202C42×C5—22no—
203C42×C5—22no—
204C42×C5—21no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5—41no—
211C22×SD16C22×C511yescharacteristic
212C2×#126—21no—
213C2×#107C22×C511yescharacteristic
214C2×#107C22×C511yescharacteristic
215C2×#106C22×C511yescharacteristic
216C2×C4⋊C8C22×C511yescharacteristic
217C2×C4⋊C8C22×C511yescharacteristic
218C2×C4⋊C8C22×C511yescharacteristic
219C2×C4⋊C8C22×C511yescharacteristic
220C2×C4⋊C8C22×C511yescharacteristic
221C2×C4⋊C8C22×C511yescharacteristic
222C2×#103C22×C511yescharacteristic
223C2×#103C22×C511yescharacteristic
224C2×#103C22×C511yescharacteristic
225C2×#102C22×C511yescharacteristic
226C2×#102C22×C511yescharacteristic
227C2×#102C22×C511yescharacteristic
228#391C22×C511yescharacteristic
229#391C22×C511yescharacteristic
230#391C22×C511yescharacteristic
231#390C22×C511yescharacteristic
232#390C22×C511yescharacteristic
233#390C22×C511yescharacteristic
234#389C22×C511yescharacteristic
235#389C22×C511yescharacteristic
236#389C22×C511yescharacteristic
237#389C22×C511yescharacteristic
238#389C22×C511yescharacteristic
239#389C22×C511yescharacteristic
240#388—21no—
241#388—21no—
242#388—21no—
243#387—21no—
244#387—21no—
245#387—21no—
246#383—21no—
247C43C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249#340C22×C511yescharacteristic
250#340C22×C511yescharacteristic
251#340C22×C511yescharacteristic
252#340C22×C511yescharacteristic
253#340C22×C511yescharacteristic
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5C22×D411yescharacteristic
262C5×Q8—41no—
263C5×Q8—41no—
264C5×Q8—41no—
265C5×Q8—41no—
266C5×D4—41no—
267C5×D4—41no—
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—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—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
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#13512yes—
307C2×C4×C5AGL(1,ℤ/8)12yes—
308C2×C4×C5#13712yes—
309C2×C4×C5H(5,𝔽2)11yescharacteristic
310C2×C4×C5H(5,𝔽2)11yescharacteristic
311C2×C4×C5H(5,𝔽2)11yescharacteristic
312C2×C4×C52−1+411yescharacteristic
313C2×C4×C52−1+411yescharacteristic
314C2×C4×C52−1+411yescharacteristic
315C5×C8—41no—
316C5×C8—41no—
317C5×C8—41no—
318C5×C8—41no—
319C22×Q8C23×C511yescharacteristic
320C22×D4C23×C511yescharacteristic
321C2×SD16—41no—
322C2×SD16—41no—
323C2×SD16—41no—
324C22×C8C23×C511yescharacteristic
325C22×C8C23×C511yescharacteristic
326C22×C8C23×C511yescharacteristic
327C22×C8C23×C511yescharacteristic
328#126—44no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4C23×C511yescharacteristic
336C2×C4⋊C4C23×C511yescharacteristic
337C2×C4⋊C4C23×C511yescharacteristic
338C2×C4⋊C4C23×C511yescharacteristic
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42C5×D411yescharacteristic
348C2×C42C5×D411yescharacteristic
349C2×C42C5×D411yescharacteristic
350C2×C42C5×D411yescharacteristic
351C2×C42C23×C511yescharacteristic
352C2×C42C23×C511yescharacteristic
353C2×C42C23×C511yescharacteristic
354#107—41no—
355#107—41no—
356#106—41no—
357C4⋊C8—41no—
358C4⋊C8—41no—
359C4⋊C8—41no—
360C4⋊C8—41no—
361C4⋊C8—41no—
362C4⋊C8—41no—
363#103—41no—
364#103—41no—
365#103—41no—
366#102—41no—
367#102—41no—
368#102—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#95—21no—
380#95—21no—
381C22×C5—81no—
382C22×C5—81no—
383C22×C5—81no—
384C22×C5—81no—
385C22×C5—81no—
386C22×C5—81no—
387C22×C5—81no—
388C22×C5#53711yescharacteristic
389C22×C5#53711yescharacteristic
390C22×C5#53711yescharacteristic
391C22×C5C2×#13511yescharacteristic
392C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C5C2×#13711yescharacteristic
394C22×C5#57511yescharacteristic
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—22no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5—81no—
402C4×C5—81no—
403C4×C5—81no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5—81no—
407C4×C5—81no—
408C4×C5#56011yescharacteristic
409C4×C5#56311yescharacteristic
410C4×C5#56311yescharacteristic
411C4×C5#56311yescharacteristic
412C24—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4C2×C5×D411yescharacteristic
433C22×C4C2×C5×D411yescharacteristic
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C24×C511yescharacteristic
439SD16—44no—
440C2×C8—21no—
441C2×C8—21no—
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—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
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—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—41no—
486C2×C5—161no—
487C2×C5#282311yescharacteristic
488C2×C5#324711yescharacteristic
489C2×C5#324811yescharacteristic
490C2×C5#325011yescharacteristic
491C2×C5#325111yescharacteristic
492C2×C5#325211yescharacteristic
493C2×C5#325411yescharacteristic
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23C22×C5×D411yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—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—21no—
525C2×C4—41no—
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×C4C5×#13512yes—
547C2×C4C5×AGL(1,ℤ/8)12yes—
548C2×C4C5×#13712yes—
549C2×C4C5×H(5,𝔽2)11yescharacteristic
550C2×C4C5×H(5,𝔽2)11yescharacteristic
551C2×C4C5×H(5,𝔽2)11yescharacteristic
552C2×C4C5×2−1+411yescharacteristic
553C2×C4C5×2−1+411yescharacteristic
554C2×C4C5×2−1+411yescharacteristic
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C5#3286111yescharacteristic, direct product factor, Sylow
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C5×#53711yescharacteristic
568C22C5×#53711yescharacteristic
569C22C5×#53711yescharacteristic
570C22C2×C5×#13511yescharacteristic
571C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
572C22C2×C5×#13711yescharacteristic
573C22C5×#57511yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C5×#56011yescharacteristic
588C4C5×#56311yescharacteristic
589C4C5×#56311yescharacteristic
590C4C5×#56311yescharacteristic
591C2—161no—
592C2C5×#282311yescharacteristic
593C2C5×#324711yescharacteristic
594C2C5×#324811yescharacteristic
595C2C5×#325011yescharacteristic
596C2C5×#325111yescharacteristic
597C2C5×#325211yescharacteristic
598C2C5×#325411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C43×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2863C2semidirect
3. C5×#2088C2semidirect
4. C5×#2087C2semidirect
5. C5×#2086C2semidirect
6. C5×#2068C2semidirect
7. C5×#2068C2semidirect
10. C5×#2066C2semidirect
15. C5×#1842C2semidirect
59. #32861C5direct (N × H)
122. #2863C2×C5semidirect
124. #2088C2×C5semidirect
125. #2087C2×C5semidirect
126. #2086C2×C5semidirect
127. #2068C2×C5semidirect
128. #2068C2×C5semidirect
131. #2066C2×C5semidirect
136. #1842C2×C5semidirect
559. C5#32861direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28632
C5×#28602
C5×#20882
C5×#20872
C5×#20862
C5×#20682
C5×#20672
C5×#20662
C5×#20652
C5×#20552
C5×#18422
#328615