Finite Group Databasebeta

← C5×#26124 #11948844

Subgroups — C5×#26124 #11948844

Order 1280.

764 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×#2552C211yesmaximal, characteristic, complemented
2C5×#2349C211yesmaximal, characteristic
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2099C211yesmaximal, characteristic, complemented
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2087C211yesmaximal, characteristic, complemented
7C5×#1949C211yesmaximal, characteristic, complemented
8C5×#1940C211yesmaximal, characteristic, complemented
9C5×#1864C211yesmaximal, characteristic
10C5×#1862C211yesmaximal, characteristic
11C5×#1836C211yesmaximal, characteristic, complemented
12C5×#1802C211yesmaximal, characteristic
13C5×#1802C211yesmaximal, characteristic
14C5×#1802C211yesmaximal, characteristic
15C5×#1762C211yesmaximal, characteristic
16C2×C5×#125—21no—
17C2×C4×C5×D4C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#97C2211yescharacteristic
30C5×#398—21no—
31C5×#398—21no—
32C5×#389—21no—
33C5×#389C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#385—21no—
38C5×#385—21no—
39C5×#384C2211yescharacteristic
40C5×#384C2211yescharacteristic
41C5×#384C2211yescharacteristic
42C5×#382C2211yescharacteristic
43C5×#380—21no—
44C4×C5×C4⋊C4C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C2×C5×#95—21no—
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#26124C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4C2311yescharacteristic
61C23×C4×C5—21no—
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C5×#125—44no—
69C4×C5×D4—22no—
70C4×C5×D4—22no—
71C4×C5×D4—22no—
72C4×C5×D4—41no—
73C4×C5×D4—41no—
74C4×C5×D4Q814yes—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
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⋊C4D411yescharacteristic
86C2×C5×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C42×C5—21no—
98C2×C42×C5C2311yescharacteristic
99C2×C42×C5C2311yescharacteristic
100C2×C42×C5C2311yescharacteristic
101C5×#107—41no—
102C5×#106—41no—
103C5×C4⋊C8—22no—
104C5×C4⋊C8—41no—
105C5×C4⋊C8—41no—
106C5×#102—22no—
107C5×#102—22no—
108C5×#102—22no—
109C5×#102—22no—
110C5×#97—22no—
111C5×#95—21no—
112C5×#95—21no—
113C5×#95—21no—
114C5×#95—21no—
115C5×#95—21no—
116C5×#95—21no—
117C5×#95—21no—
118C5×#95D411yescharacteristic
119C5×#95D411yescharacteristic
120#2552C2×C511yescharacteristic, complemented
121#2349C2×C511yescharacteristic
122#2100C2×C511yescharacteristic, complemented
123#2099C2×C511yescharacteristic, complemented
124#2088C2×C511yescharacteristic, complemented
125#2087C2×C511yescharacteristic, complemented
126#1949C2×C511yescharacteristic, complemented
127#1940C2×C511yescharacteristic, complemented
128#1864C2×C511yescharacteristic
129#1862C2×C511yescharacteristic
130#1836C2×C511yescharacteristic, complemented
131#1802C2×C511yescharacteristic
132#1802C2×C511yescharacteristic
133#1802C2×C511yescharacteristic
134#1762C2×C511yescharacteristic
135C24×C5—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4C2×Q812yes—
140C2×C5×D4#4112yes—
141C2×C5×D4#4112yes—
142C22×C4×C5—21no—
143C22×C4×C5—24no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5—81no—
155C22×C4×C5—81no—
156C22×C4×C5—81no—
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×D411yescharacteristic
164C22×C4×C5C2411yescharacteristic
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—22no—
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—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4—42no—
194C5×C4⋊C4—42no—
195C5×C4⋊C4—42no—
196C5×C4⋊C4—42no—
197C5×C4⋊C4—81no—
198C5×C4⋊C4—81no—
199C5×C4⋊C4—81no—
200C5×C4⋊C4—81no—
201C5×C4⋊C4—81no—
202C5×C4⋊C4C2×Q812yes—
203C5×C22⋊C4—24no—
204C5×C22⋊C4—42no—
205C5×C22⋊C4—42no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5—42no—
211C42×C5C2×Q812yes—
212C42×C5#4112yes—
213C2×#125—21no—
214C2×C4×D4C22×C511yescharacteristic
215C2×C4×D4C22×C511yescharacteristic
216C2×C4×D4C22×C511yescharacteristic
217C2×#107C22×C511yescharacteristic
218C2×#106C22×C511yescharacteristic
219C2×C4⋊C8C22×C511yescharacteristic
220C2×C4⋊C8C22×C511yescharacteristic
221C2×C4⋊C8C22×C511yescharacteristic
222C2×#102C22×C511yescharacteristic
223C2×#102C22×C511yescharacteristic
224C2×#102C22×C511yescharacteristic
225C2×#102C22×C511yescharacteristic
226C2×#97C22×C511yescharacteristic
227#398—21no—
228#398—21no—
229#389—21no—
230#389C22×C511yescharacteristic
231#389C22×C511yescharacteristic
232#389C22×C511yescharacteristic
233#389C22×C511yescharacteristic
234#385—21no—
235#385—21no—
236#384C22×C511yescharacteristic
237#384C22×C511yescharacteristic
238#384C22×C511yescharacteristic
239#382C22×C511yescharacteristic
240#380—21no—
241C4×C4⋊C4C22×C511yescharacteristic
242C4×C4⋊C4C22×C511yescharacteristic
243C2×#95—21no—
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#336C22×C511yescharacteristic
255#336C22×C511yescharacteristic
256C23×C5—22no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5C22×D411yescharacteristic
264C5×D4—22no—
265C5×D4—22no—
266C5×D4—22no—
267C5×D4#12514yescomplemented
268C2×C4×C5—21no—
269C2×C4×C5—21no—
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—22no—
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—41no—
284C2×C4×C5—41no—
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—84no—
304C2×C4×C5—84no—
305C2×C4×C5—84no—
306C2×C4×C5C22⋊Q812yes—
307C2×C4×C5C22⋊Q812yes—
308C2×C4×C5AGL(1,ℤ/8)12yes—
309C2×C4×C5#13712yes—
310C2×C4×C5C22×Q811yescharacteristic
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×D4C23×C511yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C22×C8C23×C511yescharacteristic
325C22×C8C23×C511yescharacteristic
326C22×C8C23×C511yescharacteristic
327C22×C8C23×C511yescharacteristic
328#125—44no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—41no—
333C4×D4—41no—
334C4×D4C5×Q814yes—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
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⋊C4C5×D411yescharacteristic
346C2×C4⋊C4C5×D411yescharacteristic
347C2×C4⋊C4C23×C511yescharacteristic
348C2×C4⋊C4C23×C511yescharacteristic
349C2×C4⋊C4C23×C511yescharacteristic
350C2×C4⋊C4C23×C511yescharacteristic
351C2×C4⋊C4C23×C511yescharacteristic
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42—21no—
358C2×C42C23×C511yescharacteristic
359C2×C42C23×C511yescharacteristic
360C2×C42C23×C511yescharacteristic
361#107—41no—
362#106—41no—
363C4⋊C8—22no—
364C4⋊C8—41no—
365C4⋊C8—41no—
366#102—22no—
367#102—22no—
368#102—22no—
369#102—22no—
370#97—22no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95C5×D411yescharacteristic
379#95C5×D411yescharacteristic
380C22×C5—24no—
381C22×C5—42no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5—42no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5C2×C22⋊Q811yescharacteristic
388C22×C5#54611yescharacteristic
389C22×C5#54811yescharacteristic
390C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
391C22×C5C2×#13711yescharacteristic
392C22×C5#57611yescharacteristic
393C22×C5#57711yescharacteristic
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—22no—
398C4×C5—42no—
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×C5C2×#12511yescharacteristic
408C4×C5#54411yescharacteristic
409C4×C5#55211yescharacteristic
410C4×C5#55311yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4C2×C5×Q812yes—
416C2×D4C5×#4112yes—
417C2×D4C5×#4112yes—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C2×C5×D411yescharacteristic
440C22×C4C24×C511yescharacteristic
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—
452C2×C8—21no—
453C4⋊C4—22no—
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—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4C2×C5×Q812yes—
479C22⋊C4—24no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42C2×C5×Q812yes—
488C42C5×#4112yes—
489C2×C5—44no—
490C2×C5#244211yescharacteristic
491C2×C5#307911yescharacteristic
492C2×C5#308111yescharacteristic
493C2×C5#330611yescharacteristic
494C2×C5#331411yescharacteristic
495C2×C5#336611yescharacteristic
496C2×C5#337211yescharacteristic
497C23—22no—
498C23—22no—
499C23—22no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23C22×C5×D411yescharacteristic
505D4—22no—
506D4—22no—
507D4—22no—
508D4C5×#12514yescomplemented
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
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—84no—
545C2×C4—84no—
546C2×C4—84no—
547C2×C4C5×C22⋊Q812yes—
548C2×C4C5×C22⋊Q812yes—
549C2×C4C5×AGL(1,ℤ/8)12yes—
550C2×C4C5×#13712yes—
551C2×C4C22×C5×Q811yescharacteristic
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#2612411yescharacteristic, direct product factor, Sylow
562C22—24no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22C2×C5×C22⋊Q811yescharacteristic
570C22C5×#54611yescharacteristic
571C22C5×#54811yescharacteristic
572C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
573C22C2×C5×#13711yescharacteristic
574C22C5×#57611yescharacteristic
575C22C5×#57711yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C2×C5×#12511yescharacteristic
590C4C5×#54411yescharacteristic
591C4C5×#55211yescharacteristic
592C4C5×#55311yescharacteristic
593C2—44no—
594C2C5×#244211yescharacteristic
595C2C5×#307911yescharacteristic
596C2C5×#308111yescharacteristic
597C2C5×#330611yescharacteristic
598C2C5×#331411yescharacteristic
599C2C5×#336611yescharacteristic
600C2C5×#337211yescharacteristic
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×#2552C2semidirect
3. C5×#2100C2semidirect
4. C5×#2099C2semidirect
5. C5×#2088C2semidirect
6. C5×#2087C2semidirect
7. C5×#1949C2semidirect
8. C5×#1940C2semidirect
11. C5×#1836C2semidirect
59. #26124C5direct (N × H)
120. #2552C2×C5semidirect
122. #2100C2×C5semidirect
123. #2099C2×C5semidirect
124. #2088C2×C5semidirect
125. #2087C2×C5semidirect
126. #1949C2×C5semidirect
127. #1940C2×C5semidirect
130. #1836C2×C5semidirect
267. C5×D4#125semidirect
508. D4C5×#125semidirect
561. C5#26124direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25522
C5×#23492
C5×#21002
C5×#20992
C5×#20882
C5×#20872
C5×#19492
C5×#19402
C5×#18642
C5×#18622
C5×#18362
C5×#18022
C5×#17622
#261245