Finite Group Databasebeta

← C5×#13083 #11935803

Subgroups — C5×#13083 #11935803

Order 1280.

818 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#413C211yesmaximal, characteristic, complemented
2C5×#2404C211yesmaximal, characteristic
3C2×C5×AΣL(1,𝔽16)C212yesmaximal, complemented
4C5×#1782C211yesmaximal, characteristic, complemented
5C5×#1390C212yesmaximal, complemented
6C22×C5×#41C2211yescharacteristic
7C22×C5×M16—21no—
8C2×C5×#120C411yescharacteristic, complemented
9C2×C5×#120C2211yescharacteristic
10C22×C5×C22⋊C4C411yescharacteristic, complemented
11C5×#413—24no—
12C2×C5×#101—21no—
13C2×C5×#100C2212yes—
14C2×C5×#99—21no—
15C2×C5×#99C2212yes—
16C5×#393—21no—
17C5×#392—21no—
18C5×#386—21no—
19C5×#386—21no—
20C5×#386C411yescharacteristic, complemented
21C5×#386C2211yescharacteristic
22C5×#381—21no—
23C5×#381C411yescharacteristic, complemented
24C5×AΣL(1,𝔽16)—24no—
25#13083C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5C2×C411yescharacteristic
27C2×C5×#41—22no—
28C2×C5×#41—22no—
29C2×C5×#41—41no—
30C2×C5×#41—41no—
31C2×C5×#41—42no—
32C22×C5×Q8D411yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4C2×C411yescharacteristic
36C22×C5×D4D411yescharacteristic
37C22×C5×D4C2311yescharacteristic
38C23×C4×C5C2×C411yescharacteristic
39C23×C4×C5C2×C411yescharacteristic
40C23×C4×C5D411yescharacteristic
41C23×C4×C5D411yescharacteristic
42C2×C5×M16—24no—
43C2×C5×M16—22no—
44C2×C5×M16—42no—
45C2×C5×M16—41no—
46C22×C5×C8—41no—
47C5×#120—22no—
48C5×#120—22no—
49C5×#120—42no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—22no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—41no—
58C2×C5×C22⋊C4—41no—
59C2×C5×C22⋊C4C2×C411yescharacteristic
60C2×C5×C22⋊C4C2×C411yescharacteristic
61C5×#101—24no—
62C5×#100—22no—
63C5×#100D414yescomplemented
64C5×#99—22no—
65C5×#99—22no—
66C5×#99—42no—
67C5×#95—21no—
68C5×#95—21no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—41no—
72C5×#95—41no—
73C2×#413C2×C511yescharacteristic, complemented
74#2404C2×C511yescharacteristic
75C2×AΣL(1,𝔽16)C2×C512yescomplemented
76#1782C2×C511yescharacteristic, complemented
77#1390C2×C512yescomplemented
78C24×C5—21no—
79C24×C5—22no—
80C24×C5—41no—
81C24×C5—42no—
82C24×C5—41no—
83C24×C5—81no—
84C24×C5C22⋊C411yescharacteristic
85C24×C5C22×C411yescharacteristic
86C24×C5C2×D411yescharacteristic
87C5×#41—44no—
88C5×#41—44no—
89C5×#41—44no—
90C5×#41—44no—
91C2×C5×Q8—21no—
92C2×C5×Q8—21no—
93C2×C5×Q8—41no—
94C2×C5×Q8—41no—
95C2×C5×D4—22no—
96C2×C5×D4—22no—
97C2×C5×D4—22no—
98C2×C5×D4—22no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—42no—
104C2×C5×D4—42no—
105C2×C5×D4—42no—
106C2×C5×D4—42no—
107C2×C5×D4—81no—
108C2×C5×D4—81no—
109C2×C5×D4C2×D412yes—
110C2×C5×D4#4112yes—
111C22×C4×C5—22no—
112C22×C4×C5—21no—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—41no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5—42no—
129C22×C4×C5—81no—
130C22×C4×C5C22⋊C411yescharacteristic
131C22×C4×C5C22⋊C411yescharacteristic
132C22×C4×C5C22⋊C411yescharacteristic
133C22×C4×C5C2×D411yescharacteristic
134C5×M16—24no—
135C5×M16—44no—
136C5×M16—42no—
137C2×C5×C8—44no—
138C2×C5×C8—42no—
139C5×C22⋊C4—22no—
140C5×C22⋊C4—42no—
141C5×C22⋊C4—42no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—41no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—41no—
146C5×C22⋊C4—41no—
147C5×C22⋊C4—42no—
148C5×C22⋊C4—42no—
149C5×C22⋊C4—81no—
150C5×C22⋊C4—81no—
151C22×#41C22×C511yescharacteristic
152C22×M16—21no—
153C2×#120C4×C511yescharacteristic, complemented
154C2×#120C22×C511yescharacteristic
155C22×C22⋊C4C4×C511yescharacteristic, complemented
156#413—24no—
157C2×#101—21no—
158C2×#100C22×C512yes—
159C2×#99—21no—
160C2×#99C22×C512yes—
161#393—21no—
162#392—21no—
163#386—21no—
164#386—21no—
165#386C4×C511yescharacteristic, complemented
166#386C22×C511yescharacteristic
167#381—21no—
168#381C4×C511yescharacteristic, complemented
169AΣL(1,𝔽16)—24no—
170C23×C5—21no—
171C23×C5—21no—
172C23×C5—21no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—21no—
176C23×C5—22no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5—41no—
180C23×C5—41no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5—41no—
186C23×C5—42no—
187C23×C5—42no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5—82no—
192C23×C5—84no—
193C23×C5—84no—
194C23×C5—82no—
195C23×C5#9912yes—
196C23×C5C2×C22⋊C411yescharacteristic
197C23×C5C4×D412yes—
198C23×C5#12112yes—
199C5×Q8—42no—
200C5×Q8—42no—
201C5×D4—42no—
202C5×D4—42no—
203C5×D4—44no—
204C5×D4—44no—
205C5×D4—84no—
206C5×D4—84no—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—22no—
210C2×C4×C5—22no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—42no—
222C2×C4×C5—42no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—82no—
235C2×C4×C5—82no—
236C2×C4×C5—82no—
237C2×C4×C5—82no—
238C2×C4×C5#9911yescharacteristic
239C2×C4×C5#9911yescharacteristic
240C2×C4×C5#12011yescharacteristic
241C2×C4×C5#12311yescharacteristic
242C5×C8—44no—
243C25C2×C4×C511yescharacteristic
244C2×#41—22no—
245C2×#41—22no—
246C2×#41—41no—
247C2×#41—41no—
248C2×#41—42no—
249C22×Q8C5×D411yescharacteristic
250C22×D4—21no—
251C22×D4—21no—
252C22×D4C2×C4×C511yescharacteristic
253C22×D4C5×D411yescharacteristic
254C22×D4C23×C511yescharacteristic
255C23×C4C2×C4×C511yescharacteristic
256C23×C4C2×C4×C511yescharacteristic
257C23×C4C5×D411yescharacteristic
258C23×C4C5×D411yescharacteristic
259C2×M16—24no—
260C2×M16—22no—
261C2×M16—42no—
262C2×M16—41no—
263C22×C8—41no—
264#120—22no—
265#120—22no—
266#120—42no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4—41no—
276C2×C22⋊C4C2×C4×C511yescharacteristic
277C2×C22⋊C4C2×C4×C511yescharacteristic
278#101—24no—
279#100—22no—
280#100C5×D414yescomplemented
281#99—22no—
282#99—22no—
283#99—42no—
284#95—21no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—41no—
289#95—41no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—22no—
293C22×C5—22no—
294C22×C5—22no—
295C22×C5—42no—
296C22×C5—42no—
297C22×C5—42no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—41no—
306C22×C5—41no—
307C22×C5—42no—
308C22×C5—81no—
309C22×C5—81no—
310C22×C5—81no—
311C22×C5—81no—
312C22×C5—84no—
313C22×C5—84no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5#38611yescharacteristic
317C22×C5C2×#9911yescharacteristic
318C22×C5C2×#9911yescharacteristic
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—41no—
324C4×C5—41no—
325C4×C5—81no—
326C4×C5—81no—
327C4×C5—81no—
328C4×C5—162no—
329C24—21no—
330C24—22no—
331C24—41no—
332C24—42no—
333C24—41no—
334C24—81no—
335C24C5×C22⋊C411yescharacteristic
336C24C22×C4×C511yescharacteristic
337C24C2×C5×D411yescharacteristic
338#41—44no—
339#41—44no—
340#41—44no—
341#41—44no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—81no—
359C2×D4—81no—
360C2×D4C2×C5×D412yes—
361C2×D4C5×#4112yes—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—42no—
380C22×C4—81no—
381C22×C4C5×C22⋊C411yescharacteristic
382C22×C4C5×C22⋊C411yescharacteristic
383C22×C4C5×C22⋊C411yescharacteristic
384C22×C4C2×C5×D411yescharacteristic
385M16—24no—
386M16—44no—
387M16—42no—
388C2×C8—44no—
389C2×C8—42no—
390C22⋊C4—22no—
391C22⋊C4—42no—
392C22⋊C4—42no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—42no—
399C22⋊C4—42no—
400C22⋊C4—81no—
401C22⋊C4—81no—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5—42no—
405C2×C5—42no—
406C2×C5—42no—
407C2×C5—82no—
408C2×C5#189811yescharacteristic
409C2×C5#212011yescharacteristic
410C2×C5#212211yescharacteristic
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—42no—
428C23—42no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—82no—
433C23—84no—
434C23—84no—
435C23—82no—
436C23C5×#9912yes—
437C23C2×C5×C22⋊C411yescharacteristic
438C23C4×C5×D412yes—
439C23C5×#12112yes—
440Q8—42no—
441Q8—42no—
442D4—42no—
443D4—42no—
444D4—44no—
445D4—44no—
446D4—84no—
447D4—84no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4C5×#9911yescharacteristic
480C2×C4C5×#9911yescharacteristic
481C2×C4C5×#12011yescharacteristic
482C2×C4C5×#12311yescharacteristic
483C8—44no—
484C5#1308311yescharacteristic, direct product factor, Sylow
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—84no—
508C22—84no—
509C22—81no—
510C22—81no—
511C22C5×#38611yescharacteristic
512C22C2×C5×#9911yescharacteristic
513C22C2×C5×#9911yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—162no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—82no—
530C2C5×#189811yescharacteristic
531C2C5×#212011yescharacteristic
532C2C5×#212211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC5×#2404C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#413C2semidirect
3. C2×C5×AΣL(1,𝔽16)C2semidirect
4. C5×#1782C2semidirect
5. C5×#1390C2semidirect
8. C2×C5×#120C4semidirect
10. C22×C5×C22⋊C4C4semidirect
20. C5×#386C4semidirect
23. C5×#381C4semidirect
25. #13083C5direct (N × H)
63. C5×#100D4semidirect
73. C2×#413C2×C5semidirect
75. C2×AΣL(1,𝔽16)C2×C5semidirect
76. #1782C2×C5semidirect
77. #1390C2×C5semidirect
153. C2×#120C4×C5semidirect
155. C22×C22⋊C4C4×C5semidirect
165. #386C4×C5semidirect
168. #381C4×C5semidirect
280. #100C5×D4semidirect
484. C5#13083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4132
C5×#24042
C2×C5×AΣL(1,𝔽16)2
C5×#17822
C5×#13902
#130835