Finite Group Databasebeta

← C5×#26009 #11948729

Subgroups — C5×#26009 #11948729

Order 1280.

740 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2440C211yesmaximal, characteristic
2C5×#2346C211yesmaximal, characteristic
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2088C211yesmaximal, characteristic, complemented
5C5×#2087C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#1988C211yesmaximal, characteristic, complemented
8C5×#1948C211yesmaximal, characteristic, complemented
9C5×#1920C211yesmaximal, characteristic, complemented
10C5×#1918C211yesmaximal, characteristic, complemented
11C5×#1853C211yesmaximal, characteristic
12C5×#1851C211yesmaximal, characteristic
13C5×#1825C211yesmaximal, characteristic
14C5×#1809C211yesmaximal, characteristic
15C5×#1736C211yesmaximal, characteristic
16C22×C5×M16C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8—21no—
19C2×C5×#117C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×C22⋊C8C2211yescharacteristic
28C5×#398—21no—
29C5×#395—21no—
30C5×#389C2211yescharacteristic
31C5×#389C2211yescharacteristic
32C5×#389C2211yescharacteristic
33C5×#389C2211yescharacteristic
34C5×#388—21no—
35C5×#388—21no—
36C5×#385—21no—
37C5×#384C2211yescharacteristic
38C5×#382—21no—
39C5×#380C2211yescharacteristic
40C5×#380C2211yescharacteristic
41C4×C5×C4⋊C4C2211yescharacteristic
42C4×C5×C4⋊C4C2211yescharacteristic
43C4×C5×C22⋊C4C2211yescharacteristic
44C5×#376—21no—
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#26009C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C23×C4×C5—21no—
62C23×C4×C5C2311yescharacteristic
63C2×C5×M16—22no—
64C2×C5×M16—22no—
65C2×C5×M16—41no—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C5×C4⋊Q8—22no—
71C5×C4⋊Q8—41no—
72C5×C22⋊Q8—44no—
73C5×#117—22no—
74C5×#117Q814yescomplemented
75C2×C5×C4⋊C4—22no—
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—41no—
85C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
97C2×C5×C22⋊C4D411yescharacteristic
98C2×C42×C5—21no—
99C2×C42×C5—21no—
100C2×C42×C5—21no—
101C2×C42×C5C2311yescharacteristic
102C2×C42×C5C2311yescharacteristic
103C5×#107—22no—
104C5×#106—22no—
105C5×#106—41no—
106C5×#106—41no—
107C5×C4⋊C8—22no—
108C5×C4⋊C8—41no—
109C5×C22⋊C8—22no—
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×#95D411yescharacteristic
119C5×#95D411yescharacteristic
120#2440C2×C511yescharacteristic
121#2346C2×C511yescharacteristic
122#2100C2×C511yescharacteristic, complemented
123#2088C2×C511yescharacteristic, complemented
124#2087C2×C511yescharacteristic, complemented
125#2058C2×C511yescharacteristic, complemented
126#1988C2×C511yescharacteristic, complemented
127#1948C2×C511yescharacteristic, complemented
128#1920C2×C511yescharacteristic, complemented
129#1918C2×C511yescharacteristic, complemented
130#1853C2×C511yescharacteristic
131#1851C2×C511yescharacteristic
132#1825C2×C511yescharacteristic
133#1809C2×C511yescharacteristic
134#1736C2×C511yescharacteristic
135C24×C5C2×D411yescharacteristic
136C2×C5×Q8—42no—
137C2×C5×Q8—42no—
138C2×C5×Q8—81no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
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—21no—
151C22×C4×C5—42no—
152C22×C4×C5—42no—
153C22×C4×C5—81no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×Q812yes—
160C22×C4×C5#4112yes—
161C22×C4×C5C2411yescharacteristic
162C5×M16—44no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
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#4112yes—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—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—42no—
189C5×C4⋊C4—42no—
190C5×C4⋊C4—42no—
191C5×C4⋊C4—42no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4—81no—
194C5×C4⋊C4—81no—
195C5×C4⋊C4—81no—
196C5×C4⋊C4C2×Q812yes—
197C5×C4⋊C4C2×Q812yes—
198C5×C4⋊C4#4112yes—
199C5×C22⋊C4—24no—
200C5×C22⋊C4—22no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4—42no—
203C5×C22⋊C4—81no—
204C42×C5—24no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C42×C5—42no—
210C42×C5—42no—
211C22×M16C22×C511yescharacteristic
212C2×C4⋊Q8C22×C511yescharacteristic
213C2×C22⋊Q8—21no—
214C2×#117C22×C511yescharacteristic
215C22×C4⋊C4C22×C511yescharacteristic
216C2×#107C22×C511yescharacteristic
217C2×#106C22×C511yescharacteristic
218C2×#106C22×C511yescharacteristic
219C2×#106C22×C511yescharacteristic
220C2×C4⋊C8C22×C511yescharacteristic
221C2×C4⋊C8C22×C511yescharacteristic
222C2×C22⋊C8C22×C511yescharacteristic
223#398—21no—
224#395—21no—
225#389C22×C511yescharacteristic
226#389C22×C511yescharacteristic
227#389C22×C511yescharacteristic
228#389C22×C511yescharacteristic
229#388—21no—
230#388—21no—
231#385—21no—
232#384C22×C511yescharacteristic
233#382—21no—
234#380C22×C511yescharacteristic
235#380C22×C511yescharacteristic
236C4×C4⋊C4C22×C511yescharacteristic
237C4×C4⋊C4C22×C511yescharacteristic
238C4×C22⋊C4C22×C511yescharacteristic
239#376—21no—
240#340C22×C511yescharacteristic
241#340C22×C511yescharacteristic
242#340C22×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#336C22×C511yescharacteristic
253#336C22×C511yescharacteristic
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5C22⋊Q812yes—
261C23×C5C22×D411yescharacteristic
262C5×Q8—84no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
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—41no—
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×C5C22⋊Q812yes—
305C2×C4×C5AGL(1,ℤ/8)12yes—
306C2×C4×C5#13712yes—
307C2×C4×C5C22×Q811yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C2×C4×C5C2×#4111yescharacteristic
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5H(5,𝔽2)11yescharacteristic
312C2×C4×C52−1+411yescharacteristic
313C5×C8—22no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8—41no—
317C22×Q8—21no—
318C23×C4—21no—
319C23×C4C23×C511yescharacteristic
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—41no—
323C22×C8C23×C511yescharacteristic
324C22×C8C23×C511yescharacteristic
325C22×C8C23×C511yescharacteristic
326C22×C8C23×C511yescharacteristic
327C4⋊Q8—22no—
328C4⋊Q8—41no—
329C22⋊Q8—44no—
330#117—22no—
331#117C5×Q814yescomplemented
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
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—41no—
342C2×C4⋊C4C23×C511yescharacteristic
343C2×C4⋊C4C23×C511yescharacteristic
344C2×C4⋊C4C23×C511yescharacteristic
345C2×C4⋊C4C23×C511yescharacteristic
346C2×C4⋊C4C23×C511yescharacteristic
347C2×C4⋊C4C23×C511yescharacteristic
348C2×C4⋊C4C23×C511yescharacteristic
349C2×C4⋊C4C23×C511yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4C5×D411yescharacteristic
354C2×C22⋊C4C5×D411yescharacteristic
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42C23×C511yescharacteristic
359C2×C42C23×C511yescharacteristic
360#107—22no—
361#106—22no—
362#106—41no—
363#106—41no—
364C4⋊C8—22no—
365C4⋊C8—41no—
366C22⋊C8—22no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95C5×D411yescharacteristic
376#95C5×D411yescharacteristic
377C22×C5—22no—
378C22×C5—22no—
379C22×C5—22no—
380C22×C5—41no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5C2×C22⋊Q811yescharacteristic
385C22×C5#54611yescharacteristic
386C22×C5#54711yescharacteristic
387C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C5C2×#13711yescharacteristic
389C22×C5#57711yescharacteristic
390C22×C5#57711yescharacteristic
391C4×C5—22no—
392C4×C5—22no—
393C4×C5—22no—
394C4×C5—41no—
395C4×C5—42no—
396C4×C5—42no—
397C4×C5—41no—
398C4×C5—42no—
399C4×C5—81no—
400C4×C5—81no—
401C4×C5—81no—
402C4×C5—81no—
403C4×C5—81no—
404C4×C5#53311yescharacteristic
405C4×C5#54411yescharacteristic
406C4×C5#55111yescharacteristic
407C4×C5#55211yescharacteristic
408C24C2×C5×D411yescharacteristic
409C2×Q8—42no—
410C2×Q8—42no—
411C2×Q8—81no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—81no—
427C22×C4C2×C5×D411yescharacteristic
428C22×C4C2×C5×D411yescharacteristic
429C22×C4C2×C5×D411yescharacteristic
430C22×C4C2×C5×D411yescharacteristic
431C22×C4C2×C5×D411yescharacteristic
432C22×C4C2×C5×Q812yes—
433C22×C4C5×#4112yes—
434C22×C4C24×C511yescharacteristic
435M16—44no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8C5×#4112yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—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—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4C2×C5×Q812yes—
470C4⋊C4C2×C5×Q812yes—
471C4⋊C4C5×#4112yes—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C42—24no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—42no—
484C2×C5—42no—
485C2×C5#243811yescharacteristic
486C2×C5#307911yescharacteristic
487C2×C5#308411yescharacteristic
488C2×C5#331011yescharacteristic
489C2×C5#332911yescharacteristic
490C2×C5#334411yescharacteristic
491C2×C5#335411yescharacteristic
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23C5×C22⋊Q812yes—
499C23C22×C5×D411yescharacteristic
500Q8—84no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
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—84no—
542C2×C4C5×C22⋊Q812yes—
543C2×C4C5×AGL(1,ℤ/8)12yes—
544C2×C4C5×#13712yes—
545C2×C4C22×C5×Q811yescharacteristic
546C2×C4C2×C5×#4111yescharacteristic
547C2×C4C2×C5×#4111yescharacteristic
548C2×C4C2×C5×#4111yescharacteristic
549C2×C4C5×H(5,𝔽2)11yescharacteristic
550C2×C4C5×2−1+411yescharacteristic
551C8—22no—
552C8—41no—
553C8—41no—
554C8—41no—
555C5#2600911yescharacteristic, direct product factor, Sylow
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C2×C5×C22⋊Q811yescharacteristic
564C22C5×#54611yescharacteristic
565C22C5×#54711yescharacteristic
566C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
567C22C2×C5×#13711yescharacteristic
568C22C5×#57711yescharacteristic
569C22C5×#57711yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4C5×#53311yescharacteristic
584C4C5×#54411yescharacteristic
585C4C5×#55111yescharacteristic
586C4C5×#55211yescharacteristic
587C2—42no—
588C2C5×#243811yescharacteristic
589C2C5×#307911yescharacteristic
590C2C5×#308411yescharacteristic
591C2C5×#331011yescharacteristic
592C2C5×#332911yescharacteristic
593C2C5×#334411yescharacteristic
594C2C5×#335411yescharacteristic
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×#2087C2semidirect
6. C5×#2058C2semidirect
7. C5×#1988C2semidirect
8. C5×#1948C2semidirect
9. C5×#1920C2semidirect
10. C5×#1918C2semidirect
59. #26009C5direct (N × H)
74. C5×#117Q8semidirect
122. #2100C2×C5semidirect
123. #2088C2×C5semidirect
124. #2087C2×C5semidirect
125. #2058C2×C5semidirect
126. #1988C2×C5semidirect
127. #1948C2×C5semidirect
128. #1920C2×C5semidirect
129. #1918C2×C5semidirect
331. #117C5×Q8semidirect
555. C5#26009direct (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×#23462
C5×#21002
C5×#20882
C5×#20872
C5×#20582
C5×#19882
C5×#19482
C5×#19202
C5×#19182
C5×#18532
C5×#18512
C5×#18252
C5×#18092
C5×#17362
#260095