Finite Group Databasebeta

← C5×#12793 #11935513

Subgroups — C5×#12793 #11935513

Order 1280.

808 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#120C211yesmaximal, characteristic
2C2×C5×AΣL(1,𝔽16)C212yesmaximal
3C5×#1800C211yesmaximal, characteristic, complemented
4C5×#1799C211yesmaximal, characteristic, complemented
5C5×#1390C212yesmaximal, complemented
6C24×C4×C5C411yescharacteristic, complemented
7C2×C5×#120C2211yescharacteristic
8C2×C4×C5×D4—21no—
9C2×C4×C5×D4C2211yescharacteristic
10C5×#423—21no—
11C2×C5×#100C2212yes—
12C2×C5×#99C2212yes—
13C5×#386—21no—
14C5×#386C2211yescharacteristic
15C5×#385—21no—
16C5×#385C411yescharacteristic, complemented
17C5×#380—21no—
18C5×#379C411yescharacteristic, complemented
19C4×C5×C22⋊C4—21no—
20C4×C5×C22⋊C4C411yescharacteristic, complemented
21C5×AΣL(1,𝔽16)—24no—
22C5×#343—21no—
23C5×#342—21no—
24#12793C511yesmaximal, characteristic, direct product factor, Sylow
25C25×C5C2×C411yescharacteristic
26C22×C5×D4—21no—
27C22×C5×D4C2311yescharacteristic
28C23×C4×C5—21no—
29C23×C4×C5—21no—
30C23×C4×C5—44no—
31C23×C4×C5—41no—
32C23×C4×C5—41no—
33C23×C4×C5C2×C411yescharacteristic
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C2×C5×M16—22no—
37C5×#120—21no—
38C5×#120—21no—
39C5×#120D412yes—
40C5×#120Q812yes—
41C4×C5×D4—41no—
42C4×C5×D4—41no—
43C4×C5×D4—44no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—41no—
46C2×C5×C4⋊C4D411yescharacteristic
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—22no—
52C2×C5×C22⋊C4C2×C411yescharacteristic
53C2×C5×C22⋊C4C2×C411yescharacteristic
54C2×C5×C22⋊C4C2×C411yescharacteristic
55C2×C5×C22⋊C4D411yescharacteristic
56C2×C42×C5—21no—
57C2×C42×C5D411yescharacteristic
58C5×C4⋊C8—41no—
59C5×C4⋊C8—41no—
60C5×#100—22no—
61C5×#100—22no—
62C5×#99—22no—
63C5×#99—22no—
64C5×#95—21no—
65C5×#95—21no—
66C5×#95—21no—
67C5×#95—41no—
68C4×#120C2×C511yescharacteristic
69C2×AΣL(1,𝔽16)C2×C512yes—
70#1800C2×C511yescharacteristic, complemented
71#1799C2×C511yescharacteristic, complemented
72#1390C2×C512yescomplemented
73C24×C5—21no—
74C24×C5—21no—
75C24×C5—42no—
76C24×C5—41no—
77C24×C5—42no—
78C24×C5—41no—
79C24×C5C4⋊C412yescomplemented
80C24×C5C22×C411yescharacteristic
81C24×C5C2×D411yescharacteristic
82C2×C5×D4—22no—
83C2×C5×D4—22no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—42no—
87C2×C5×D4—42no—
88C2×C5×D4C2×D411yescharacteristic
89C2×C5×D4C2×Q811yescharacteristic
90C2×C5×D4#4111yescharacteristic
91C2×C5×D4#4111yescharacteristic
92C22×C4×C5—24no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—42no—
101C22×C4×C5—42no—
102C22×C4×C5—42no—
103C22×C4×C5—42no—
104C22×C4×C5—42no—
105C22×C4×C5—42no—
106C22×C4×C5—42no—
107C22×C4×C5—44no—
108C22×C4×C5—44no—
109C22×C4×C5—44no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5—41no—
113C22×C4×C5—44no—
114C22×C4×C5—42no—
115C22×C4×C5C22⋊C411yescharacteristic
116C22×C4×C5C22⋊C411yescharacteristic
117C22×C4×C5C22⋊C411yescharacteristic
118C22×C4×C5C22⋊C411yescharacteristic
119C22×C4×C5C2×D411yescharacteristic
120C5×M16—42no—
121C5×M16—42no—
122C2×C5×C8—42no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—42no—
125C5×C4⋊C4—82no—
126C5×C22⋊C4—21no—
127C5×C22⋊C4—22no—
128C5×C22⋊C4—22no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—42no—
132C5×C22⋊C4—42no—
133C5×C22⋊C4—42no—
134C5×C22⋊C4—41no—
135C5×C22⋊C4—42no—
136C5×C22⋊C4—42no—
137C5×C22⋊C4C4⋊C412yescomplemented
138C42×C5—21no—
139C42×C5—21no—
140C42×C5—42no—
141C24×C4C4×C511yescharacteristic, complemented
142C2×#120C22×C511yescharacteristic
143C2×C4×D4—21no—
144C2×C4×D4C22×C511yescharacteristic
145#423—21no—
146C2×#100C22×C512yes—
147C2×#99C22×C512yes—
148#386—21no—
149#386C22×C511yescharacteristic
150#385—21no—
151#385C4×C511yescharacteristic, complemented
152#380—21no—
153#379C4×C511yescharacteristic, complemented
154C4×C22⋊C4—21no—
155C4×C22⋊C4C4×C511yescharacteristic, complemented
156AΣL(1,𝔽16)—24no—
157#343—21no—
158#342—21no—
159C23×C5—22no—
160C23×C5—22no—
161C23×C5—22no—
162C23×C5—21no—
163C23×C5—21no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—41no—
167C23×C5—44no—
168C23×C5—42no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—44no—
173C23×C5—42no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—42no—
177C23×C5—42no—
178C23×C5—42no—
179C23×C5—48no—
180C23×C5—42no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5C2×C22⋊C411yescharacteristic
184C23×C5C2×C4⋊C411yescharacteristic
185C23×C5#11711yescharacteristic
186C23×C5#12111yescharacteristic
187C23×C5C22⋊Q811yescharacteristic
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—44no—
193C5×D4—44no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—44no—
203C2×C4×C5—42no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—48no—
208C2×C4×C5—42no—
209C2×C4×C5—41no—
210C2×C4×C5—42no—
211C2×C4×C5—44no—
212C2×C4×C5—42no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—42no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—81no—
221C2×C4×C5—82no—
222C2×C4×C5—82no—
223C2×C4×C5—82no—
224C2×C4×C5#9911yescharacteristic
225C2×C4×C5#9911yescharacteristic
226C2×C4×C5#12111yescharacteristic
227C2×C4×C5C22⋊Q811yescharacteristic
228C5×C8—82no—
229C25C2×C4×C511yescharacteristic
230C22×D4—21no—
231C22×D4C23×C511yescharacteristic
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—44no—
235C23×C4—41no—
236C23×C4—41no—
237C23×C4C2×C4×C511yescharacteristic
238C23×C4C2×C4×C511yescharacteristic
239C23×C4C5×D411yescharacteristic
240C2×M16—22no—
241#120—21no—
242#120—21no—
243#120C5×D412yes—
244#120C5×Q812yes—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—44no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4C5×D411yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4C2×C4×C511yescharacteristic
257C2×C22⋊C4C2×C4×C511yescharacteristic
258C2×C22⋊C4C2×C4×C511yescharacteristic
259C2×C22⋊C4C5×D411yescharacteristic
260C2×C42—21no—
261C2×C42C5×D411yescharacteristic
262C4⋊C8—41no—
263C4⋊C8—41no—
264#100—22no—
265#100—22no—
266#99—22no—
267#99—22no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—41no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—24no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—42no—
284C22×C5—42no—
285C22×C5—42no—
286C22×C5—42no—
287C22×C5—44no—
288C22×C5—44no—
289C22×C5—44no—
290C22×C5—44no—
291C22×C5—42no—
292C22×C5—42no—
293C22×C5—41no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5—42no—
297C22×C5—41no—
298C22×C5—81no—
299C22×C5#38011yescharacteristic
300C22×C5C2×#9911yescharacteristic
301C22×C5#41011yescharacteristic
302C4×C5—21no—
303C4×C5—21no—
304C4×C5—21no—
305C4×C5—42no—
306C4×C5—42no—
307C4×C5—41no—
308C4×C5—41no—
309C4×C5—41no—
310C4×C5—81no—
311C4×C5—162no—
312C4×C5AΣL(1,𝔽16)12yescomplemented
313C24—21no—
314C24—21no—
315C24—42no—
316C24—41no—
317C24—42no—
318C24—41no—
319C24C5×C4⋊C412yescomplemented
320C24C22×C4×C511yescharacteristic
321C24C2×C5×D411yescharacteristic
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4C2×C5×D411yescharacteristic
329C2×D4C2×C5×Q811yescharacteristic
330C2×D4C5×#4111yescharacteristic
331C2×D4C5×#4111yescharacteristic
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—44no—
354C22×C4—42no—
355C22×C4C5×C22⋊C411yescharacteristic
356C22×C4C5×C22⋊C411yescharacteristic
357C22×C4C5×C22⋊C411yescharacteristic
358C22×C4C5×C22⋊C411yescharacteristic
359C22×C4C2×C5×D411yescharacteristic
360M16—42no—
361M16—42no—
362C2×C8—42no—
363C4⋊C4—41no—
364C4⋊C4—42no—
365C4⋊C4—82no—
366C22⋊C4—21no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—41no—
375C22⋊C4—42no—
376C22⋊C4—42no—
377C22⋊C4C5×C4⋊C412yescomplemented
378C42—21no—
379C42—21no—
380C42—42no—
381C2×C5—21no—
382C2×C5—21no—
383C2×C5—41no—
384C2×C5—44no—
385C2×C5—41no—
386C2×C5—41no—
387C2×C5—41no—
388C2×C5#179911yescharacteristic
389C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
390C2×C5#212011yescharacteristic
391C23—22no—
392C23—22no—
393C23—22no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—41no—
399C23—44no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—44no—
405C23—42no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—48no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23C2×C5×C22⋊C411yescharacteristic
416C23C2×C5×C4⋊C411yescharacteristic
417C23C5×#11711yescharacteristic
418C23C5×#12111yescharacteristic
419C23C5×C22⋊Q811yescharacteristic
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—44no—
425D4—44no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—48no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4C5×#9911yescharacteristic
457C2×C4C5×#9911yescharacteristic
458C2×C4C5×#12111yescharacteristic
459C2×C4C5×C22⋊Q811yescharacteristic
460C8—82no—
461C5#1279311yescharacteristic, direct product factor, Sylow
462C22—21no—
463C22—21no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—42no—
482C22—42no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—42no—
487C22—41no—
488C22—81no—
489C22C5×#38011yescharacteristic
490C22C2×C5×#9911yescharacteristic
491C22C5×#41011yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—81no—
501C4—162no—
502C4C5×AΣL(1,𝔽16)12yescomplemented
503C2—21no—
504C2—21no—
505C2—41no—
506C2—44no—
507C2—41no—
508C2—41no—
509C2—41no—
510C2C5×#179911yescharacteristic
511C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
512C2C5×#212011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC2×C5×#120C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1800C2semidirect
4. C5×#1799C2semidirect
5. C5×#1390C2semidirect
6. C24×C4×C5C4semidirect
16. C5×#385C4semidirect
18. C5×#379C4semidirect
20. C4×C5×C22⋊C4C4semidirect
24. #12793C5direct (N × H)
70. #1800C2×C5semidirect
71. #1799C2×C5semidirect
72. #1390C2×C5semidirect
79. C24×C5C4⋊C4semidirect
137. C5×C22⋊C4C4⋊C4semidirect
141. C24×C4C4×C5semidirect
151. #385C4×C5semidirect
153. #379C4×C5semidirect
155. C4×C22⋊C4C4×C5semidirect
312. C4×C5AΣL(1,𝔽16)semidirect
319. C24C5×C4⋊C4semidirect
377. C22⋊C4C5×C4⋊C4semidirect
461. C5#12793direct (N × H)
502. C4C5×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1202
C2×C5×AΣL(1,𝔽16)2
C5×#18002
C5×#17992
C5×#13902
#127935