Finite Group Databasebeta

← C5×#25990 #11948710

Subgroups — C5×#25990 #11948710

Order 1280.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2440C211yesmaximal, characteristic
2C5×#2344C211yesmaximal, characteristic
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2088C211yesmaximal, characteristic, complemented
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#1987C211yesmaximal, characteristic, complemented
8C5×#1948C211yesmaximal, characteristic, complemented
9C5×#1920C211yesmaximal, characteristic, complemented
10C5×#1920C211yesmaximal, characteristic, complemented
11C5×#1853C211yesmaximal, characteristic
12C5×#1850C211yesmaximal, characteristic
13C5×#1823C211yesmaximal, characteristic
14C5×#1807C211yesmaximal, characteristic
15C2×C5×#340C211yesmaximal, characteristic
16C23×C5×C8C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8—21no—
19C2×C5×#117—21no—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×C4⋊C8C2211yescharacteristic
28C2×C5×C22⋊C8C2211yescharacteristic
29C5×#398—21no—
30C5×#395—21no—
31C5×#389C2211yescharacteristic
32C5×#389C2211yescharacteristic
33C5×#389C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#387—21no—
36C5×#387—21no—
37C5×#385—21no—
38C5×#384C2211yescharacteristic
39C5×#381—21no—
40C5×#380C2211yescharacteristic
41C5×#380C2211yescharacteristic
42C4×C5×C4⋊C4C2211yescharacteristic
43C4×C5×C4⋊C4C2211yescharacteristic
44C4×C5×C22⋊C4C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
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#25990C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C23×C4×C5—21no—
62C23×C4×C5—21no—
63C23×C4×C5C2311yescharacteristic
64C22×C5×C8—22no—
65C22×C5×C8—22no—
66C22×C5×C8—41no—
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C5×C4⋊Q8—22no—
72C5×C4⋊Q8—41no—
73C5×C22⋊Q8—44no—
74C5×#117—44no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
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—41no—
87C2×C5×C4⋊C4Q814yescomplemented
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4D411yescharacteristic
99C2×C5×C22⋊C4D411yescharacteristic
100C2×C42×C5—21no—
101C2×C42×C5—21no—
102C2×C42×C5C2311yescharacteristic
103C2×C42×C5C2311yescharacteristic
104C5×#106—22no—
105C5×#106—22no—
106C5×#106—41no—
107C5×#106—41no—
108C5×C4⋊C8—22no—
109C5×C4⋊C8—41no—
110C5×C22⋊C8—22no—
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#2440C2×C511yescharacteristic
122#2344C2×C511yescharacteristic
123#2100C2×C511yescharacteristic, complemented
124#2088C2×C511yescharacteristic, complemented
125#2088C2×C511yescharacteristic, complemented
126#2058C2×C511yescharacteristic, complemented
127#1987C2×C511yescharacteristic, complemented
128#1948C2×C511yescharacteristic, complemented
129#1920C2×C511yescharacteristic, complemented
130#1920C2×C511yescharacteristic, complemented
131#1853C2×C511yescharacteristic
132#1850C2×C511yescharacteristic
133#1823C2×C511yescharacteristic
134#1807C2×C511yescharacteristic
135C2×#340C2×C511yescharacteristic
136C24×C5C2×D411yescharacteristic
137C2×C5×Q8—42no—
138C2×C5×Q8—42no—
139C2×C5×Q8—81no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—24no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
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—42no—
154C22×C4×C5—42no—
155C22×C4×C5—42no—
156C22×C4×C5—42no—
157C22×C4×C5—81no—
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×Q812yes—
164C22×C4×C5#4112yes—
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—44no—
178C2×C5×C8#4112yes—
179C5×C4⋊C4—24no—
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—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—42no—
194C5×C4⋊C4—42no—
195C5×C4⋊C4—42no—
196C5×C4⋊C4—42no—
197C5×C4⋊C4—42no—
198C5×C4⋊C4—42no—
199C5×C4⋊C4—42no—
200C5×C4⋊C4—81no—
201C5×C4⋊C4C2×Q812yes—
202C5×C4⋊C4C2×Q812yes—
203C5×C4⋊C4#4112yes—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—42no—
206C5×C22⋊C4—42no—
207C5×C22⋊C4SD1614yes—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5—21no—
211C42×C5—21no—
212C42×C5—42no—
213C42×C5—42no—
214C23×C8C22×C511yescharacteristic
215C2×C4⋊Q8C22×C511yescharacteristic
216C2×C22⋊Q8—21no—
217C2×#117—21no—
218C22×C4⋊C4C22×C511yescharacteristic
219C22×C4⋊C4C22×C511yescharacteristic
220C2×#106C22×C511yescharacteristic
221C2×#106C22×C511yescharacteristic
222C2×#106C22×C511yescharacteristic
223C2×#106C22×C511yescharacteristic
224C2×C4⋊C8C22×C511yescharacteristic
225C2×C4⋊C8C22×C511yescharacteristic
226C2×C22⋊C8C22×C511yescharacteristic
227#398—21no—
228#395—21no—
229#389C22×C511yescharacteristic
230#389C22×C511yescharacteristic
231#389C22×C511yescharacteristic
232#389C22×C511yescharacteristic
233#387—21no—
234#387—21no—
235#385—21no—
236#384C22×C511yescharacteristic
237#381—21no—
238#380C22×C511yescharacteristic
239#380C22×C511yescharacteristic
240C4×C4⋊C4C22×C511yescharacteristic
241C4×C4⋊C4C22×C511yescharacteristic
242C4×C22⋊C4C22×C511yescharacteristic
243#340C22×C511yescharacteristic
244#340C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249#340C22×C511yescharacteristic
250#340C22×C511yescharacteristic
251#340C22×C511yescharacteristic
252#340C22×C511yescharacteristic
253#340C22×C511yescharacteristic
254#340C22×C511yescharacteristic
255#336C22×C511yescharacteristic
256#336C22×C511yescharacteristic
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5C22⋊Q812yes—
262C23×C5C2×SD1612yes—
263C23×C5AGL(1,ℤ/8)12yes—
264C23×C5C22×D411yescharacteristic
265C5×Q8—84no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—21no—
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—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—48no—
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—84no—
308C2×C4×C5C22⋊Q812yes—
309C2×C4×C5C2×SD1612yes—
310C2×C4×C5C2×SD1612yes—
311C2×C4×C5C22×Q811yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5H(5,𝔽2)11yescharacteristic
316C2×C4×C52−1+411yescharacteristic
317C5×C8—22no—
318C5×C8—41no—
319C5×C8—41no—
320C5×C8—41no—
321C22×Q8—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4C23×C511yescharacteristic
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—41no—
328C22×C8C23×C511yescharacteristic
329C22×C8C23×C511yescharacteristic
330C22×C8C23×C511yescharacteristic
331C22×C8C23×C511yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—41no—
334C22⋊Q8—44no—
335#117—44no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4C5×Q814yescomplemented
349C2×C4⋊C4C23×C511yescharacteristic
350C2×C4⋊C4C23×C511yescharacteristic
351C2×C4⋊C4C23×C511yescharacteristic
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C4⋊C4C23×C511yescharacteristic
355C2×C4⋊C4C23×C511yescharacteristic
356C2×C4⋊C4C23×C511yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4C5×D411yescharacteristic
360C2×C22⋊C4C5×D411yescharacteristic
361C2×C42—21no—
362C2×C42—21no—
363C2×C42C23×C511yescharacteristic
364C2×C42C23×C511yescharacteristic
365#106—22no—
366#106—22no—
367#106—41no—
368#106—41no—
369C4⋊C8—22no—
370C4⋊C8—41no—
371C22⋊C8—22no—
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#95C5×D411yescharacteristic
381#95C5×D411yescharacteristic
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—22no—
387C22×C5—22no—
388C22×C5#47614yes—
389C22×C5C2×C22⋊Q811yescharacteristic
390C22×C5#54611yescharacteristic
391C22×C5#54711yescharacteristic
392C22×C5C22×SD1611yescharacteristic
393C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C5#57711yescharacteristic
395C22×C5#57811yescharacteristic
396C4×C5—22no—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—42no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5—81no—
407C4×C5—81no—
408C4×C5—81no—
409C4×C5#53311yescharacteristic
410C4×C5#54411yescharacteristic
411C4×C5#55111yescharacteristic
412C4×C5#55211yescharacteristic
413C24C2×C5×D411yescharacteristic
414C2×Q8—42no—
415C2×Q8—42no—
416C2×Q8—81no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
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×Q812yes—
441C22×C4C5×#4112yes—
442C22×C4C24×C511yescharacteristic
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—
454C2×C8—44no—
455C2×C8C5×#4112yes—
456C4⋊C4—24no—
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—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4C2×C5×Q812yes—
479C4⋊C4C2×C5×Q812yes—
480C4⋊C4C5×#4112yes—
481C22⋊C4—22no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4C5×SD1614yes—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—42no—
491C2×C5—24no—
492C2×C5#243811yescharacteristic
493C2×C5C2×#47611yescharacteristic
494C2×C5#308211yescharacteristic
495C2×C5#329811yescharacteristic
496C2×C5#331011yescharacteristic
497C2×C5#333511yescharacteristic
498C2×C5#334311yescharacteristic
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23C5×C22⋊Q812yes—
504C23C2×C5×SD1612yes—
505C23C5×AGL(1,ℤ/8)12yes—
506C23C22×C5×D411yescharacteristic
507Q8—84no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—48no—
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×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—84no—
550C2×C4C5×C22⋊Q812yes—
551C2×C4C2×C5×SD1612yes—
552C2×C4C2×C5×SD1612yes—
553C2×C4C22×C5×Q811yescharacteristic
554C2×C4C2×C5×#4111yescharacteristic
555C2×C4C2×C5×#4111yescharacteristic
556C2×C4C2×C5×#4111yescharacteristic
557C2×C4C5×H(5,𝔽2)11yescharacteristic
558C2×C4C5×2−1+411yescharacteristic
559C8—22no—
560C8—41no—
561C8—41no—
562C8—41no—
563C5#2599011yescharacteristic, direct product factor, Sylow
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22C5×#47614yes—
571C22C2×C5×C22⋊Q811yescharacteristic
572C22C5×#54611yescharacteristic
573C22C5×#54711yescharacteristic
574C22C22×C5×SD1611yescharacteristic
575C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
576C22C5×#57711yescharacteristic
577C22C5×#57811yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C5×#53311yescharacteristic
592C4C5×#54411yescharacteristic
593C4C5×#55111yescharacteristic
594C4C5×#55211yescharacteristic
595C2—24no—
596C2C5×#243811yescharacteristic
597C2C2×C5×#47611yescharacteristic
598C2C5×#308211yescharacteristic
599C2C5×#329811yescharacteristic
600C2C5×#331011yescharacteristic
601C2C5×#333511yescharacteristic
602C2C5×#334311yescharacteristic
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×#2100C2semidirect
4. C5×#2088C2semidirect
5. C5×#2088C2semidirect
6. C5×#2058C2semidirect
7. C5×#1987C2semidirect
8. C5×#1948C2semidirect
9. C5×#1920C2semidirect
10. C5×#1920C2semidirect
59. #25990C5direct (N × H)
87. C2×C5×C4⋊C4Q8semidirect
123. #2100C2×C5semidirect
124. #2088C2×C5semidirect
125. #2088C2×C5semidirect
126. #2058C2×C5semidirect
127. #1987C2×C5semidirect
128. #1948C2×C5semidirect
129. #1920C2×C5semidirect
130. #1920C2×C5semidirect
348. C2×C4⋊C4C5×Q8semidirect
563. C5#25990direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24402
C5×#23442
C5×#21002
C5×#20882
C5×#20582
C5×#19872
C5×#19482
C5×#19202
C5×#18532
C5×#18502
C5×#18232
C5×#18072
C2×C5×#3402
#259905