Finite Group Databasebeta

← C5×#12761 #11935481

Subgroups — C5×#12761 #11935481

Order 1280.

936 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#551C211yesmaximal, characteristic
2C2×C5×#354C211yesmaximal, characteristic, complemented
3C2×C5×#352C211yesmaximal, characteristic, complemented
4C2×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic
5C5×#1890C211yesmaximal, characteristic, complemented
6C5×#1889C211yesmaximal, characteristic
7C5×#1885C211yesmaximal, characteristic, complemented
8C5×#551—22no—
9C5×#551—22no—
10C5×#551—22no—
11C5×#551C414yescomplemented
12C2×C5×#126—21no—
13C2×C5×#124C2211yescharacteristic
14C2×C5×#123—21no—
15C2×C5×#123C2211yescharacteristic
16C2×C5×C22⋊Q8—21no—
17C2×C5×#120C2211yescharacteristic
18C5×#518C2211yescharacteristic
19C2×C4×C5×D4—21no—
20C2×C5×#117—21no—
21C22×C5×C22⋊C4—21no—
22C5×#419—21no—
23C2×C5×#100C2211yescharacteristic
24C2×C5×#99C2211yescharacteristic
25C2×C5×#99C2211yescharacteristic
26C5×#381—21no—
27C5×#379—21no—
28C5×#354—22no—
29C5×#352—22no—
30C5×AΣL(1,𝔽16)—22no—
31C5×#342—21no—
32C5×#342—21no—
33C5×#339—21no—
34#12761C511yesmaximal, characteristic, direct product factor, Sylow
35C25×C5D411yescharacteristic
36C22×C5×Q8D411yescharacteristic
37C22×C5×D4—21no—
38C22×C5×D4C2311yescharacteristic
39C23×C4×C5—21no—
40C23×C4×C5—21no—
41C23×C4×C5D411yescharacteristic
42C2×C5×M16—21no—
43C5×#126—24no—
44C5×#126—24no—
45C5×#124—21no—
46C5×#124—21no—
47C5×#124C2×C412yes—
48C5×#124D412yes—
49C5×#123—24no—
50C5×#123—21no—
51C5×#123—21no—
52C5×#123—24no—
53C5×#123C2×C412yes—
54C5×#123D412yes—
55C5×C22⋊Q8—24no—
56C5×C22⋊Q8—24no—
57C5×#120—21no—
58C5×#120—21no—
59C5×#120C2×C412yes—
60C5×#120D412yes—
61C4×C5×D4—24no—
62C4×C5×D4—24no—
63C4×C5×D4—42no—
64C5×#117—24no—
65C5×#117—24no—
66C5×#117—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C22⋊C4—21no—
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—24no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4—42no—
84C2×C5×C22⋊C4D411yescharacteristic
85C2×C5×C22⋊C4D411yescharacteristic
86C2×C42×C5—21no—
87C2×C42×C5D411yescharacteristic
88C5×#103—42no—
89C5×#100—21no—
90C5×#100—21no—
91C5×#99—21no—
92C5×#99—21no—
93C5×#99—21no—
94C5×#99—21no—
95C5×#95—42no—
96C2×#551C2×C511yescharacteristic
97C2×#354C2×C511yescharacteristic, complemented
98C2×#352C2×C511yescharacteristic, complemented
99C2×AΣL(1,𝔽16)C2×C511yescharacteristic
100#1890C2×C511yescharacteristic, complemented
101#1889C2×C511yescharacteristic
102#1885C2×C511yescharacteristic, complemented
103C24×C5—21no—
104C24×C5—21no—
105C24×C5—41no—
106C24×C5—44no—
107C24×C5—41no—
108C24×C5C22⋊C412yes—
109C24×C5C2×D411yescharacteristic
110C24×C5C2×D411yescharacteristic
111C2×C5×Q8—21no—
112C2×C5×Q8—41no—
113C2×C5×Q8—41no—
114C2×C5×Q8C22⋊C412yescomplemented
115C2×C5×D4—22no—
116C2×C5×D4—22no—
117C2×C5×D4—41no—
118C2×C5×D4—41no—
119C2×C5×D4—44no—
120C2×C5×D4C22×C411yescharacteristic
121C2×C5×D4C2×D411yescharacteristic
122C2×C5×D4C2×D411yescharacteristic
123C2×C5×D4C2×D411yescharacteristic
124C22×C4×C5—24no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—24no—
131C22×C4×C5—21no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—44no—
135C22×C4×C5—41no—
136C22×C4×C5—41no—
137C22×C4×C5—41no—
138C22×C4×C5—41no—
139C22×C4×C5—81no—
140C22×C4×C5—81no—
141C22×C4×C5C22⋊C412yescomplemented
142C22×C4×C5C2×D411yescharacteristic
143C5×M16—41no—
144C5×M16—41no—
145C2×C5×C8—41no—
146C5×C4⋊C4—24no—
147C5×C4⋊C4—24no—
148C5×C4⋊C4—24no—
149C5×C4⋊C4—22no—
150C5×C4⋊C4—22no—
151C5×C4⋊C4—22no—
152C5×C22⋊C4—24no—
153C5×C22⋊C4—24no—
154C5×C22⋊C4—22no—
155C5×C22⋊C4—22no—
156C5×C22⋊C4—22no—
157C5×C22⋊C4—22no—
158C5×C22⋊C4—22no—
159C5×C22⋊C4—22no—
160C5×C22⋊C4—21no—
161C5×C22⋊C4—21no—
162C5×C22⋊C4—22no—
163C5×C22⋊C4—22no—
164C5×C22⋊C4—41no—
165C5×C22⋊C4—41no—
166C5×C22⋊C4—41no—
167C5×C22⋊C4—41no—
168C5×C22⋊C4—41no—
169C5×C22⋊C4—41no—
170C5×C22⋊C4—41no—
171C5×C22⋊C4—84no—
172C5×C22⋊C4C22⋊C412yes—
173C5×C22⋊C4C22⋊C412yescomplemented
174C42×C5—24no—
175C42×C5—21no—
176C42×C5—41no—
177C42×C5C22⋊C412yescomplemented
178#551—22no—
179#551—22no—
180#551—22no—
181#551C4×C514yescomplemented
182C2×#126—21no—
183C2×#124C22×C511yescharacteristic
184C2×#123—21no—
185C2×#123C22×C511yescharacteristic
186C2×C22⋊Q8—21no—
187C2×#120C22×C511yescharacteristic
188#518C22×C511yescharacteristic
189C2×C4×D4—21no—
190C2×#117—21no—
191C22×C22⋊C4—21no—
192#419—21no—
193C2×#100C22×C511yescharacteristic
194C2×#99C22×C511yescharacteristic
195C2×#99C22×C511yescharacteristic
196#381—21no—
197#379—21no—
198#354—22no—
199#352—22no—
200AΣL(1,𝔽16)—22no—
201#342—21no—
202#342—21no—
203#339—21no—
204C23×C5—24no—
205C23×C5—22no—
206C23×C5—21no—
207C23×C5—21no—
208C23×C5—21no—
209C23×C5—21no—
210C23×C5—42no—
211C23×C5—42no—
212C23×C5—44no—
213C23×C5—42no—
214C23×C5—42no—
215C23×C5—44no—
216C23×C5—41no—
217C23×C5—41no—
218C23×C5—44no—
219C23×C5—81no—
220C23×C5—84no—
221C23×C5—82no—
222C23×C5C2×C22⋊C411yescharacteristic
223C23×C5C2×C22⋊C411yescharacteristic
224C23×C5#12011yescharacteristic
225C23×C5#12011yescharacteristic
226C23×C5#12011yescharacteristic
227C5×Q8—42no—
228C5×Q8—81no—
229C5×D4—41no—
230C5×D4—41no—
231C5×D4—41no—
232C5×D4—41no—
233C5×D4—44no—
234C5×D4—44no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—48no—
245C2×C4×C5—42no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—42no—
251C2×C4×C5—42no—
252C2×C4×C5—81no—
253C2×C4×C5—84no—
254C2×C4×C5—82no—
255C2×C4×C5—82no—
256C2×C4×C5—81no—
257C2×C4×C5—81no—
258C2×C4×C5—82no—
259C2×C4×C5—82no—
260C2×C4×C5C2×C22⋊C411yescharacteristic
261C2×C4×C5#12011yescharacteristic
262C5×C8—81no—
263C25C5×D411yescharacteristic
264C22×Q8C5×D411yescharacteristic
265C22×D4—21no—
266C22×D4C23×C511yescharacteristic
267C23×C4—21no—
268C23×C4—21no—
269C23×C4C5×D411yescharacteristic
270C2×M16—21no—
271#126—24no—
272#126—24no—
273#124—21no—
274#124—21no—
275#124C2×C4×C512yes—
276#124C5×D412yes—
277#123—24no—
278#123—21no—
279#123—21no—
280#123—24no—
281#123C2×C4×C512yes—
282#123C5×D412yes—
283C22⋊Q8—24no—
284C22⋊Q8—24no—
285#120—21no—
286#120—21no—
287#120C2×C4×C512yes—
288#120C5×D412yes—
289C4×D4—24no—
290C4×D4—24no—
291C4×D4—42no—
292#117—24no—
293#117—24no—
294#117—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4C5×D411yescharacteristic
313C2×C22⋊C4C5×D411yescharacteristic
314C2×C42—21no—
315C2×C42C5×D411yescharacteristic
316#103—42no—
317#100—21no—
318#100—21no—
319#99—21no—
320#99—21no—
321#99—21no—
322#99—21no—
323#95—42no—
324C22×C5—22no—
325C22×C5—24no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—41no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5—41no—
334C22×C5—42no—
335C22×C5—44no—
336C22×C5—44no—
337C22×C5—42no—
338C22×C5—42no—
339C22×C5—44no—
340C22×C5—42no—
341C22×C5—81no—
342C22×C5—81no—
343C22×C5—84no—
344C22×C5—82no—
345C22×C5#37911yescharacteristic
346C22×C5B(4,𝔽2)11yescharacteristic
347C22×C5#45811yescharacteristic
348C4×C5—21no—
349C4×C5—21no—
350C4×C5—42no—
351C4×C5—42no—
352C4×C5—42no—
353C4×C5—42no—
354C4×C5—42no—
355C4×C5—82no—
356C4×C5—161no—
357C4×C5—161no—
358C24—21no—
359C24—21no—
360C24—41no—
361C24—44no—
362C24—41no—
363C24C5×C22⋊C412yes—
364C24C2×C5×D411yescharacteristic
365C24C2×C5×D411yescharacteristic
366C2×Q8—21no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8C5×C22⋊C412yescomplemented
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—44no—
375C2×D4C22×C4×C511yescharacteristic
376C2×D4C2×C5×D411yescharacteristic
377C2×D4C2×C5×D411yescharacteristic
378C2×D4C2×C5×D411yescharacteristic
379C22×C4—24no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—44no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4C5×C22⋊C412yescomplemented
397C22×C4C2×C5×D411yescharacteristic
398M16—41no—
399M16—41no—
400C2×C8—41no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—84no—
427C22⋊C4C5×C22⋊C412yes—
428C22⋊C4C5×C22⋊C412yescomplemented
429C42—24no—
430C42—21no—
431C42—41no—
432C42C5×C22⋊C412yescomplemented
433C2×C5—21no—
434C2×C5—21no—
435C2×C5—41no—
436C2×C5—41no—
437C2×C5—44no—
438C2×C5—41no—
439C2×C5—41no—
440C2×C5#179011yescharacteristic
441C2×C5#219712yes—
442C23—24no—
443C23—22no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—42no—
449C23—42no—
450C23—44no—
451C23—42no—
452C23—42no—
453C23—44no—
454C23—41no—
455C23—41no—
456C23—44no—
457C23—81no—
458C23—84no—
459C23—82no—
460C23C2×C5×C22⋊C411yescharacteristic
461C23C2×C5×C22⋊C411yescharacteristic
462C23C5×#12011yescharacteristic
463C23C5×#12011yescharacteristic
464C23C5×#12011yescharacteristic
465Q8—42no—
466Q8—81no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—44no—
472D4—44no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—48no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—81no—
491C2×C4—84no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4C2×C5×C22⋊C411yescharacteristic
499C2×C4C5×#12011yescharacteristic
500C8—81no—
501C5#1276111yescharacteristic, direct product factor, Sylow
502C22—22no—
503C22—24no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—44no—
519C22—81no—
520C22—81no—
521C22—84no—
522C22—82no—
523C22C5×#37911yescharacteristic
524C22C5×B(4,𝔽2)11yescharacteristic
525C22C5×#45811yescharacteristic
526C4—21no—
527C4—21no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—82no—
534C4—161no—
535C4—161no—
536C2—21no—
537C2—21no—
538C2—41no—
539C2—41no—
540C2—44no—
541C2—41no—
542C2—41no—
543C2C5×#179011yescharacteristic
544C2C5×#219712yes—
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
2. C2×C5×#354C2semidirect
3. C2×C5×#352C2semidirect
5. C5×#1890C2semidirect
7. C5×#1885C2semidirect
11. C5×#551C4semidirect
34. #12761C5direct (N × H)
97. C2×#354C2×C5semidirect
98. C2×#352C2×C5semidirect
100. #1890C2×C5semidirect
102. #1885C2×C5semidirect
114. C2×C5×Q8C22⋊C4semidirect
141. C22×C4×C5C22⋊C4semidirect
173. C5×C22⋊C4C22⋊C4semidirect
177. C42×C5C22⋊C4semidirect
181. #551C4×C5semidirect
369. C2×Q8C5×C22⋊C4semidirect
396. C22×C4C5×C22⋊C4semidirect
428. C22⋊C4C5×C22⋊C4semidirect
432. C42C5×C22⋊C4semidirect
501. C5#12761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5512
C2×C5×#3542
C2×C5×#3522
C2×C5×AΣL(1,𝔽16)2
C5×#18902
C5×#18892
C5×#18852
#127615