Finite Group Databasebeta

← C5×#13087 #11935807

Subgroups — C5×#13087 #11935807

Order 1280.

820 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#410C211yesmaximal, characteristic, complemented
2C5×#2404C211yesmaximal, characteristic
3C2×C5×AΣL(1,𝔽16)C212yesmaximal, complemented
4C5×#1785C211yesmaximal, characteristic, complemented
5C5×#1390C212yesmaximal, complemented
6C22×C5×#41C2211yescharacteristic
7C2×C5×#120C411yescharacteristic, complemented
8C2×C5×#120C2211yescharacteristic
9C2×C5×#117—21no—
10C22×C5×C22⋊C4C411yescharacteristic, complemented
11C2×C5×#101—21no—
12C2×C5×#100C2212yes—
13C5×#410—24no—
14C2×C5×#99—21no—
15C2×C5×#99C2212yes—
16C5×#407—21no—
17C5×#393—21no—
18C5×#392—21no—
19C5×#386—21no—
20C5×#386—21no—
21C5×#386C411yescharacteristic, complemented
22C5×#386C2211yescharacteristic
23C5×#381C411yescharacteristic, complemented
24C5×AΣL(1,𝔽16)—24no—
25#13087C511yesmaximal, 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—22no—
43C5×#120—22no—
44C5×#120—22no—
45C5×#120—42no—
46C5×#117—24no—
47C5×#117—42no—
48C2×C5×C4⋊C4—41no—
49C2×C5×C22⋊C4—22no—
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⋊C4C2×C411yescharacteristic
59C2×C5×C22⋊C4C2×C411yescharacteristic
60C2×C42×C5—41no—
61C5×#101—42no—
62C5×#100—22no—
63C5×#100—22no—
64C5×#99—24no—
65C5×#99—22no—
66C5×#99D414yescomplemented
67C5×C22⋊C8—41no—
68C5×C22⋊C8—41no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73C2×#410C2×C511yescharacteristic, complemented
74#2404C2×C511yescharacteristic
75C2×AΣL(1,𝔽16)C2×C512yescomplemented
76#1785C2×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—22no—
92C2×C5×Q8—22no—
93C2×C5×Q8—41no—
94C2×C5×D4—22no—
95C2×C5×D4—21no—
96C2×C5×D4—21no—
97C2×C5×D4—22no—
98C2×C5×D4—41no—
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—41no—
107C2×C5×D4—41no—
108C2×C5×D4—81no—
109C2×C5×D4—81no—
110C2×C5×D4C2×D412yes—
111C2×C5×D4#4112yes—
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—22no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5—42no—
129C22×C4×C5—41no—
130C22×C4×C5—81no—
131C22×C4×C5C22⋊C411yescharacteristic
132C22×C4×C5C22⋊C411yescharacteristic
133C22×C4×C5C22⋊C411yescharacteristic
134C22×C4×C5C2×D411yescharacteristic
135C5×M16—42no—
136C5×M16—42no—
137C2×C5×C8—42no—
138C5×C4⋊C4—44no—
139C5×C22⋊C4—22no—
140C5×C22⋊C4—24no—
141C5×C22⋊C4—42no—
142C5×C22⋊C4—42no—
143C5×C22⋊C4—41no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—42no—
146C5×C22⋊C4—42no—
147C5×C22⋊C4—41no—
148C5×C22⋊C4—81no—
149C5×C22⋊C4—81no—
150C42×C5—44no—
151C22×#41C22×C511yescharacteristic
152C2×#120C4×C511yescharacteristic, complemented
153C2×#120C22×C511yescharacteristic
154C2×#117—21no—
155C22×C22⋊C4C4×C511yescharacteristic, complemented
156C2×#101—21no—
157C2×#100C22×C512yes—
158#410—24no—
159C2×#99—21no—
160C2×#99C22×C512yes—
161#407—21no—
162#393—21no—
163#392—21no—
164#386—21no—
165#386—21no—
166#386C4×C511yescharacteristic, complemented
167#386C22×C511yescharacteristic
168#381C4×C511yescharacteristic, complemented
169AΣL(1,𝔽16)—24no—
170C23×C5—21no—
171C23×C5—21no—
172C23×C5—21no—
173C23×C5—21no—
174C23×C5—22no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—21no—
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—41no—
187C23×C5—42no—
188C23×C5—42no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5—41no—
192C23×C5—82no—
193C23×C5—84no—
194C23×C5—84no—
195C23×C5—82no—
196C23×C5C2×C22⋊C411yescharacteristic
197C23×C5C4×D412yes—
198C23×C5#12011yescharacteristic
199C23×C5#12311yescharacteristic
200C5×Q8—44no—
201C5×D4—42no—
202C5×D4—42no—
203C5×D4—44no—
204C5×D4—42no—
205C5×D4—42no—
206C5×D4—82no—
207C5×D4—82no—
208C5×D4—84no—
209C2×C4×C5—22no—
210C2×C4×C5—22no—
211C2×C4×C5—22no—
212C2×C4×C5—22no—
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—21no—
222C2×C4×C5—42no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—42no—
226C2×C4×C5—44no—
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—41no—
235C2×C4×C5—41no—
236C2×C4×C5—82no—
237C2×C4×C5—82no—
238C2×C4×C5—82no—
239C2×C4×C5#9912yes—
240C2×C4×C5#9911yescharacteristic
241C2×C4×C5#9911yescharacteristic
242C2×C4×C5#12112yes—
243C5×C8—82no—
244C25C2×C4×C511yescharacteristic
245C2×#41—22no—
246C2×#41—22no—
247C2×#41—41no—
248C2×#41—41no—
249C2×#41—42no—
250C22×Q8C5×D411yescharacteristic
251C22×D4—21no—
252C22×D4—21no—
253C22×D4C2×C4×C511yescharacteristic
254C22×D4C5×D411yescharacteristic
255C22×D4C23×C511yescharacteristic
256C23×C4C2×C4×C511yescharacteristic
257C23×C4C2×C4×C511yescharacteristic
258C23×C4C5×D411yescharacteristic
259C23×C4C5×D411yescharacteristic
260C2×M16—22no—
261#120—22no—
262#120—22no—
263#120—42no—
264#117—24no—
265#117—42no—
266C2×C4⋊C4—41no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
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
278C2×C42—41no—
279#101—42no—
280#100—22no—
281#100—22no—
282#99—24no—
283#99—22no—
284#99C5×D414yescomplemented
285C22⋊C8—41no—
286C22⋊C8—41no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—22no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5—42no—
302C22×C5—42no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—41no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5—42no—
309C22×C5—41no—
310C22×C5—41no—
311C22×C5—81no—
312C22×C5—81no—
313C22×C5—81no—
314C22×C5—81no—
315C22×C5—84no—
316C22×C5—84no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5#38611yescharacteristic
320C22×C5C2×#9911yescharacteristic
321C22×C5C2×#9911yescharacteristic
322C4×C5—22no—
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—22no—
326C4×C5—41no—
327C4×C5—81no—
328C4×C5—81no—
329C4×C5—84no—
330C4×C5—81no—
331C24—21no—
332C24—22no—
333C24—41no—
334C24—42no—
335C24—41no—
336C24—81no—
337C24C5×C22⋊C411yescharacteristic
338C24C22×C4×C511yescharacteristic
339C24C2×C5×D411yescharacteristic
340#41—44no—
341#41—44no—
342#41—44no—
343#41—44no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—41no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—81no—
362C2×D4—81no—
363C2×D4C2×C5×D412yes—
364C2×D4C5×#4112yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—42no—
382C22×C4—41no—
383C22×C4—81no—
384C22×C4C5×C22⋊C411yescharacteristic
385C22×C4C5×C22⋊C411yescharacteristic
386C22×C4C5×C22⋊C411yescharacteristic
387C22×C4C2×C5×D411yescharacteristic
388M16—42no—
389M16—42no—
390C2×C8—42no—
391C4⋊C4—44no—
392C22⋊C4—22no—
393C22⋊C4—24no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—42no—
400C22⋊C4—41no—
401C22⋊C4—81no—
402C22⋊C4—81no—
403C42—44no—
404C2×C5—21no—
405C2×C5—21no—
406C2×C5—41no—
407C2×C5—42no—
408C2×C5—41no—
409C2×C5—81no—
410C2×C5—82no—
411C2×C5#189811yescharacteristic
412C2×C5#212011yescharacteristic
413C2×C5#212211yescharacteristic
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—22no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—42no—
432C23—42no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—82no—
437C23—84no—
438C23—84no—
439C23—82no—
440C23C2×C5×C22⋊C411yescharacteristic
441C23C4×C5×D412yes—
442C23C5×#12011yescharacteristic
443C23C5×#12311yescharacteristic
444Q8—44no—
445D4—42no—
446D4—42no—
447D4—44no—
448D4—42no—
449D4—42no—
450D4—82no—
451D4—82no—
452D4—84no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—44no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4C5×#9911yescharacteristic
484C2×C4C5×#9911yescharacteristic
485C2×C4C5×#9912yes—
486C2×C4C5×#12112yes—
487C8—82no—
488C5#1308711yescharacteristic, direct product factor, Sylow
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—22no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—84no—
514C22—84no—
515C22—81no—
516C22—81no—
517C22C5×#38611yescharacteristic
518C22C2×C5×#9911yescharacteristic
519C22C2×C5×#9911yescharacteristic
520C4—22no—
521C4—21no—
522C4—21no—
523C4—22no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—84no—
528C4—81no—
529C2—21no—
530C2—21no—
531C2—41no—
532C2—42no—
533C2—41no—
534C2—81no—
535C2—82no—
536C2C5×#189811yescharacteristic
537C2C5×#212011yescharacteristic
538C2C5×#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×#410C2semidirect
3. C2×C5×AΣL(1,𝔽16)C2semidirect
4. C5×#1785C2semidirect
5. C5×#1390C2semidirect
7. C2×C5×#120C4semidirect
10. C22×C5×C22⋊C4C4semidirect
21. C5×#386C4semidirect
23. C5×#381C4semidirect
25. #13087C5direct (N × H)
66. C5×#99D4semidirect
73. C2×#410C2×C5semidirect
75. C2×AΣL(1,𝔽16)C2×C5semidirect
76. #1785C2×C5semidirect
77. #1390C2×C5semidirect
152. C2×#120C4×C5semidirect
155. C22×C22⋊C4C4×C5semidirect
166. #386C4×C5semidirect
168. #381C4×C5semidirect
284. #99C5×D4semidirect
488. C5#13087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4102
C5×#24042
C2×C5×AΣL(1,𝔽16)2
C5×#17852
C5×#13902
#130875