Finite Group Databasebeta

← C5×#12960 #11935680

Subgroups — C5×#12960 #11935680

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2375C211yesmaximal, characteristic
2C2×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic
3C5×#1889C211yesmaximal, characteristic
4C5×#1867C211yesmaximal, characteristic, complemented
5C5×#1856C211yesmaximal, characteristic, complemented
6C5×#1393C211yesmaximal, characteristic, complemented
7C5×#1390C211yesmaximal, characteristic, complemented
8C2×C5×#120C2211yescharacteristic
9C5×#518C2211yescharacteristic
10C5×#428—21no—
11C2×C5×#100C2211yescharacteristic
12C2×C5×#99C2211yescharacteristic
13C2×C5×#99C2211yescharacteristic
14C5×#390—21no—
15C5×#390C2211yescharacteristic
16C5×#388—21no—
17C5×#388—21no—
18C5×#388—21no—
19C5×#386—21no—
20C5×#386C2211yescharacteristic
21C5×#385—21no—
22C5×#379—21no—
23C5×#379—21no—
24C5×AΣL(1,𝔽16)C414yescomplemented
25C5×#342—21no—
26C5×#342—21no—
27C5×#339—21no—
28#12960C511yesmaximal, characteristic, direct product factor, Sylow
29C25×C5D411yescharacteristic
30C22×C5×D4—21no—
31C22×C5×D4C2311yescharacteristic
32C23×C4×C5D411yescharacteristic
33C2×C5×M16—21no—
34C5×#120—21no—
35C5×#120—21no—
36C5×#120C2×C412yes—
37C5×#120Q812yes—
38C4×C5×D4—41no—
39C4×C5×D4—41no—
40C5×#117—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—41no—
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—41no—
57C2×C5×C22⋊C4—41no—
58C2×C5×C22⋊C4D411yescharacteristic
59C2×C5×C22⋊C4D411yescharacteristic
60C2×C42×C5—21no—
61C2×C42×C5D411yescharacteristic
62C5×#107—41no—
63C5×#106—41no—
64C5×#100—21no—
65C5×#100C2×C412yes—
66C5×#99—21no—
67C5×#99—21no—
68C5×#99—21no—
69C5×#99C2×C412yes—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—41no—
74#2375C2×C511yescharacteristic
75C2×AΣL(1,𝔽16)C2×C511yescharacteristic
76#1889C2×C511yescharacteristic
77#1867C2×C511yescharacteristic, complemented
78#1856C2×C511yescharacteristic, complemented
79#1393C2×C511yescharacteristic, complemented
80#1390C2×C511yescharacteristic, complemented
81C24×C5—21no—
82C24×C5—21no—
83C24×C5—41no—
84C24×C5—41no—
85C24×C5—81no—
86C24×C5—81no—
87C24×C5C4⋊C412yescomplemented
88C24×C5C2×D411yescharacteristic
89C24×C5C2×D411yescharacteristic
90C2×C5×D4—22no—
91C2×C5×D4—22no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—81no—
95C2×C5×D4—81no—
96C2×C5×D4C22×C411yescharacteristic
97C2×C5×D4C2×Q811yescharacteristic
98C2×C5×D4#4111yescharacteristic
99C2×C5×D4#4111yescharacteristic
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—41no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5—81no—
113C22×C4×C5C2×D411yescharacteristic
114C5×M16—22no—
115C5×M16—41no—
116C2×C5×C8—41no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—81no—
121C5×C4⋊C4—82no—
122C5×C22⋊C4—21no—
123C5×C22⋊C4—22no—
124C5×C22⋊C4—22no—
125C5×C22⋊C4—22no—
126C5×C22⋊C4—41no—
127C5×C22⋊C4—41no—
128C5×C22⋊C4—41no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—41no—
132C5×C22⋊C4—41no—
133C5×C22⋊C4—81no—
134C5×C22⋊C4—81no—
135C5×C22⋊C4—81no—
136C5×C22⋊C4—81no—
137C5×C22⋊C4—81no—
138C5×C22⋊C4—81no—
139C5×C22⋊C4—81no—
140C5×C22⋊C4—82no—
141C5×C22⋊C4—82no—
142C5×C22⋊C4C4⋊C412yescomplemented
143C42×C5—41no—
144C42×C5—41no—
145C42×C5—81no—
146C2×#120C22×C511yescharacteristic
147#518C22×C511yescharacteristic
148#428—21no—
149C2×#100C22×C511yescharacteristic
150C2×#99C22×C511yescharacteristic
151C2×#99C22×C511yescharacteristic
152#390—21no—
153#390C22×C511yescharacteristic
154#388—21no—
155#388—21no—
156#388—21no—
157#386—21no—
158#386C22×C511yescharacteristic
159#385—21no—
160#379—21no—
161#379—21no—
162AΣL(1,𝔽16)C4×C514yescomplemented
163#342—21no—
164#342—21no—
165#339—21no—
166C23×C5—21no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—21no—
170C23×C5—22no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—42no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5—41no—
180C23×C5—42no—
181C23×C5—42no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—81no—
185C23×C5—82no—
186C23×C5—82no—
187C23×C5—81no—
188C23×C5—81no—
189C23×C5—84no—
190C23×C5C2×C4⋊C411yescharacteristic
191C23×C5C4×D411yescharacteristic
192C23×C5#12011yescharacteristic
193C23×C5C22⋊Q811yescharacteristic
194C23×C5#12311yescharacteristic
195C5×D4—41no—
196C5×D4—41no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—82no—
200C5×D4—82no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—22no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—42no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—42no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—81no—
223C2×C4×C5—81no—
224C2×C4×C5—81no—
225C2×C4×C5—81no—
226C2×C4×C5—81no—
227C2×C4×C5—81no—
228C2×C4×C5—81no—
229C2×C4×C5—81no—
230C2×C4×C5—81no—
231C2×C4×C5—81no—
232C2×C4×C5C4×D411yescharacteristic
233C2×C4×C5C22⋊Q811yescharacteristic
234C5×C8—42no—
235C25C5×D411yescharacteristic
236C22×D4—21no—
237C22×D4C23×C511yescharacteristic
238C23×C4C5×D411yescharacteristic
239C2×M16—21no—
240#120—21no—
241#120—21no—
242#120C2×C4×C512yes—
243#120C5×Q812yes—
244C4×D4—41no—
245C4×D4—41no—
246#117—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4C5×D411yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4C5×D411yescharacteristic
265C2×C22⋊C4C5×D411yescharacteristic
266C2×C42—21no—
267C2×C42C5×D411yescharacteristic
268#107—41no—
269#106—41no—
270#100—21no—
271#100C2×C4×C512yes—
272#99—21no—
273#99—21no—
274#99—21no—
275#99C2×C4×C512yes—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—41no—
280C22×C5—21no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5—41no—
287C22×C5—41no—
288C22×C5—41no—
289C22×C5—41no—
290C22×C5—42no—
291C22×C5—42no—
292C22×C5—41no—
293C22×C5—41no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5—44no—
297C22×C5—42no—
298C22×C5—81no—
299C22×C5—81no—
300C22×C5—81no—
301C22×C5—81no—
302C22×C5—82no—
303C22×C5—82no—
304C22×C5—82no—
305C22×C5—81no—
306C22×C5—81no—
307C22×C5#38511yescharacteristic
308C22×C5B(4,𝔽2)11yescharacteristic
309C22×C5#45811yescharacteristic
310C4×C5—21no—
311C4×C5—21no—
312C4×C5—42no—
313C4×C5—81no—
314C4×C5—81no—
315C4×C5—82no—
316C4×C5—81no—
317C4×C5—81no—
318C4×C5—81no—
319C4×C5—81no—
320C4×C5—161no—
321C24—21no—
322C24—21no—
323C24—41no—
324C24—41no—
325C24—81no—
326C24—81no—
327C24C5×C4⋊C412yescomplemented
328C24C2×C5×D411yescharacteristic
329C24C2×C5×D411yescharacteristic
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—81no—
335C2×D4—81no—
336C2×D4C22×C4×C511yescharacteristic
337C2×D4C2×C5×Q811yescharacteristic
338C2×D4C5×#4111yescharacteristic
339C2×D4C5×#4111yescharacteristic
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—81no—
353C22×C4C2×C5×D411yescharacteristic
354M16—22no—
355M16—41no—
356C2×C8—41no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—81no—
361C4⋊C4—82no—
362C22⋊C4—21no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—81no—
374C22⋊C4—81no—
375C22⋊C4—81no—
376C22⋊C4—81no—
377C22⋊C4—81no—
378C22⋊C4—81no—
379C22⋊C4—81no—
380C22⋊C4—82no—
381C22⋊C4—82no—
382C22⋊C4C5×C4⋊C412yescomplemented
383C42—41no—
384C42—41no—
385C42—81no—
386C2×C5—21no—
387C2×C5—21no—
388C2×C5—41no—
389C2×C5—41no—
390C2×C5—41no—
391C2×C5—41no—
392C2×C5—82no—
393C2×C5#186711yescharacteristic
394C2×C5#219911yescharacteristic
395C2×C5#220011yescharacteristic
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—42no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23—81no—
415C23—82no—
416C23—82no—
417C23—81no—
418C23—81no—
419C23—84no—
420C23C2×C5×C4⋊C411yescharacteristic
421C23C4×C5×D411yescharacteristic
422C23C5×#12011yescharacteristic
423C23C5×C22⋊Q811yescharacteristic
424C23C5×#12311yescharacteristic
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—82no—
430D4—82no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4C4×C5×D411yescharacteristic
463C2×C4C5×C22⋊Q811yescharacteristic
464C8—42no—
465C5#1296011yescharacteristic, direct product factor, Sylow
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—44no—
483C22—42no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22—81no—
492C22—81no—
493C22C5×#38511yescharacteristic
494C22C5×B(4,𝔽2)11yescharacteristic
495C22C5×#45811yescharacteristic
496C4—21no—
497C4—21no—
498C4—42no—
499C4—81no—
500C4—81no—
501C4—82no—
502C4—81no—
503C4—81no—
504C4—81no—
505C4—81no—
506C4—161no—
507C2—21no—
508C2—21no—
509C2—41no—
510C2—41no—
511C2—41no—
512C2—41no—
513C2—82no—
514C2C5×#186711yescharacteristic
515C2C5×#219911yescharacteristic
516C2C5×#220011yescharacteristic
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutatorC2×D4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC2×C5×#120C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1867C2semidirect
5. C5×#1856C2semidirect
6. C5×#1393C2semidirect
7. C5×#1390C2semidirect
24. C5×AΣL(1,𝔽16)C4semidirect
28. #12960C5direct (N × H)
77. #1867C2×C5semidirect
78. #1856C2×C5semidirect
79. #1393C2×C5semidirect
80. #1390C2×C5semidirect
87. C24×C5C4⋊C4semidirect
142. C5×C22⋊C4C4⋊C4semidirect
162. AΣL(1,𝔽16)C4×C5semidirect
327. C24C5×C4⋊C4semidirect
382. C22⋊C4C5×C4⋊C4semidirect
465. C5#12960direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23752
C2×C5×AΣL(1,𝔽16)2
C5×#18892
C5×#18672
C5×#18562
C5×#13932
C5×#13902
#129605