Finite Group Databasebeta

← C5×#9963 #11932683

Subgroups — C5×#9963 #11932683

Order 1280.

1046 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#450C211yesmaximal, characteristic, complemented
2C2×C5×#447C211yesmaximal, characteristic
3C5×#2639C211yesmaximal, characteristic, complemented
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×C5×#327C211yesmaximal, characteristic, complemented
6C5×#1438C211yesmaximal, characteristic, complemented
7C5×#1280C211yesmaximal, characteristic, complemented
8C23×C5×D4C2211yescharacteristic
9C22×C5×SD16—21no—
10C22×C5×D8—21no—
11C2×C5×C22⋊Q8C2211yescharacteristic
12C2×C5×#121C2211yescharacteristic
13C22×C5×C22⋊C4—22no—
14C5×#450—22no—
15C5×#450—22no—
16C5×#447—22no—
17C5×#447—22no—
18C2×C5×#102—21no—
19C2×C5×#102—21no—
20C2×C5×C22⋊C8C2211yescharacteristic
21C2×C5×C22⋊C8C2211yescharacteristic
22C5×#400—21no—
23C5×#397—21no—
24C5×#394—21no—
25C5×#393—21no—
26C5×#386—22no—
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C5×#328—22no—
30C5×#327—22no—
31#9963C511yesmaximal, characteristic, direct product factor, Sylow
32C25×C5—21no—
33C22×C5×Q8D411yescharacteristic
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C22×C5×D4—21no—
37C22×C5×D4—21no—
38C22×C5×D4—21no—
39C22×C5×D4—21no—
40C22×C5×D4—44no—
41C22×C5×D4D411yescharacteristic
42C22×C5×D4D412yes—
43C23×C4×C5—21no—
44C23×C4×C5D412yes—
45C23×C4×C5C2311yescharacteristic
46C2×C5×SD16—24no—
47C2×C5×SD16—44no—
48C2×C5×D8—24no—
49C2×C5×D8—44no—
50C22×C5×C8—21no—
51C22×C5×C8—21no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8—21no—
54C5×C22⋊Q8—21no—
55C5×C22⋊Q8—21no—
56C5×#121—21no—
57C5×#121—21no—
58C5×#121—21no—
59C5×#121—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4D411yescharacteristic
62C2×C5×C4⋊C4D411yescharacteristic
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4—22no—
66C2×C5×C22⋊C4—22no—
67C2×C5×C22⋊C4—44no—
68C2×C5×C22⋊C4—44no—
69C2×C5×C22⋊C4—44no—
70C5×#102—24no—
71C5×#102—24no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8D412yes—
75C5×C22⋊C8D412yes—
76C5×#95—22no—
77C5×#95—22no—
78C5×#95—21no—
79C5×#95—21no—
80C5×#95—21no—
81C5×#95—21no—
82C2×#450C2×C511yescharacteristic, complemented
83C2×#447C2×C511yescharacteristic
84#2639C2×C511yescharacteristic, complemented
85C2×#328C2×C511yescharacteristic, complemented
86C2×#327C2×C511yescharacteristic, complemented
87#1438C2×C511yescharacteristic, complemented
88#1280C2×C511yescharacteristic, complemented
89C24×C5—24no—
90C24×C5—22no—
91C24×C5—21no—
92C24×C5—42no—
93C24×C5—42no—
94C24×C5—42no—
95C24×C5—41no—
96C24×C5—41no—
97C24×C5—42no—
98C24×C5—42no—
99C24×C5C2×D411yescharacteristic
100C2×C5×Q8—21no—
101C2×C5×Q8—21no—
102C2×C5×Q8—42no—
103C2×C5×D4—24no—
104C2×C5×D4—24no—
105C2×C5×D4—22no—
106C2×C5×D4—22no—
107C2×C5×D4—21no—
108C2×C5×D4—21no—
109C2×C5×D4—42no—
110C2×C5×D4—42no—
111C2×C5×D4—42no—
112C2×C5×D4—44no—
113C2×C5×D4—44no—
114C2×C5×D4—44no—
115C2×C5×D4—44no—
116C2×C5×D4—41no—
117C2×C5×D4—41no—
118C2×C5×D4—42no—
119C2×C5×D4—42no—
120C2×C5×D4—41no—
121C2×C5×D4—41no—
122C22×C4×C5—22no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—42no—
130C22×C4×C5—42no—
131C22×C4×C5—42no—
132C22×C4×C5—42no—
133C22×C4×C5—41no—
134C22×C4×C5—41no—
135C22×C4×C5—42no—
136C22×C4×C5C2×D411yescharacteristic
137C22×C4×C5C2×D411yescharacteristic
138C22×C4×C5C2×D411yescharacteristic
139C22×C4×C5C2×D411yescharacteristic
140C22×C4×C5C2×D411yescharacteristic
141C22×C4×C5#4111yescharacteristic
142C5×SD16—48no—
143C5×D8—48no—
144C2×C5×C8—22no—
145C2×C5×C8—22no—
146C2×C5×C8—42no—
147C2×C5×C8—42no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—41no—
153C5×C4⋊C4—41no—
154C5×C22⋊C4—416no—
155C5×C22⋊C4—41no—
156C5×C22⋊C4—41no—
157C5×C22⋊C4—41no—
158C5×C22⋊C4—41no—
159C5×C22⋊C4—82no—
160C5×C22⋊C4—82no—
161C23×D4C22×C511yescharacteristic
162C22×SD16—21no—
163C22×D8—21no—
164C2×C22⋊Q8C22×C511yescharacteristic
165C2×#121C22×C511yescharacteristic
166C22×C22⋊C4—22no—
167#450—22no—
168#450—22no—
169#447—22no—
170#447—22no—
171C2×#102—21no—
172C2×#102—21no—
173C2×C22⋊C8C22×C511yescharacteristic
174C2×C22⋊C8C22×C511yescharacteristic
175#400—21no—
176#397—21no—
177#394—21no—
178#393—21no—
179#386—22no—
180C2×#95C22×C511yescharacteristic
181C2×#95C22×C511yescharacteristic
182#328—22no—
183#327—22no—
184C23×C5—21no—
185C23×C5—21no—
186C23×C5—22no—
187C23×C5—24no—
188C23×C5—44no—
189C23×C5—44no—
190C23×C5—42no—
191C23×C5—44no—
192C23×C5—44no—
193C23×C5—44no—
194C23×C5—44no—
195C23×C5—42no—
196C23×C5—44no—
197C23×C5—44no—
198C23×C5—41no—
199C23×C5—42no—
200C23×C5—41no—
201C23×C5—41no—
202C23×C5—42no—
203C23×C5—82no—
204C23×C5—82no—
205C23×C5—82no—
206C23×C5—82no—
207C23×C5—82no—
208C23×C5—82no—
209C23×C5—81no—
210C23×C5—81no—
211C23×C5—81no—
212C23×C5—81no—
213C23×C5#12011yescharacteristic
214C23×C5#12111yescharacteristic
215C23×C5#12711yescharacteristic
216C23×C5#13512yes—
217C23×C5AGL(1,ℤ/8)12yes—
218C5×Q8—42no—
219C5×Q8—81no—
220C5×D4—24no—
221C5×D4—24no—
222C5×D4—42no—
223C5×D4—42no—
224C5×D4—44no—
225C5×D4—44no—
226C5×D4—42no—
227C5×D4—81no—
228C5×D4—82no—
229C5×D4—81no—
230C5×D4—81no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—44no—
238C2×C4×C5—44no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—41no—
246C2×C4×C5—42no—
247C2×C4×C5—41no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—82no—
251C2×C4×C5—81no—
252C2×C4×C5—81no—
253C2×C4×C5—82no—
254C2×C4×C5#12011yescharacteristic
255C2×C4×C5#12011yescharacteristic
256C2×C4×C5#12111yescharacteristic
257C2×C4×C5#12111yescharacteristic
258C5×C8—42no—
259C5×C8—42no—
260C25—21no—
261C22×Q8C5×D411yescharacteristic
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—44no—
269C22×D4C5×D411yescharacteristic
270C22×D4C5×D412yes—
271C23×C4—21no—
272C23×C4C5×D412yes—
273C23×C4C23×C511yescharacteristic
274C2×SD16—24no—
275C2×SD16—44no—
276C2×D8—24no—
277C2×D8—44no—
278C22×C8—21no—
279C22×C8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284#121—21no—
285#121—21no—
286#121—21no—
287#121—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4C5×D411yescharacteristic
290C2×C4⋊C4C5×D411yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—44no—
296C2×C22⋊C4—44no—
297C2×C22⋊C4—44no—
298#102—24no—
299#102—24no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8C5×D412yes—
303C22⋊C8C5×D412yes—
304#95—22no—
305#95—22no—
306#95—21no—
307#95—21no—
308#95—21no—
309#95—21no—
310C22×C5—22no—
311C22×C5—22no—
312C22×C5—22no—
313C22×C5—22no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5—48no—
319C22×C5—44no—
320C22×C5—84no—
321C22×C5—84no—
322C22×C5—84no—
323C22×C5—84no—
324C22×C5—84no—
325C22×C5—82no—
326C22×C5—82no—
327C22×C5—82no—
328C22×C5—82no—
329C22×C5—81no—
330C22×C5—81no—
331C22×C5—81no—
332C22×C5#39211yescharacteristic
333C22×C5#44912yes—
334C22×C5#45311yescharacteristic
335C22×C5#45411yescharacteristic
336C22×C5B(4,𝔽2)12yes—
337C22×C5#46312yes—
338C22×C5#49511yescharacteristic
339C22×C5#49611yescharacteristic
340C4×C5—21no—
341C4×C5—21no—
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—82no—
345C4×C5—82no—
346C4×C5—81no—
347C4×C5—81no—
348C4×C5—81no—
349C24—24no—
350C24—22no—
351C24—21no—
352C24—42no—
353C24—42no—
354C24—42no—
355C24—41no—
356C24—41no—
357C24—42no—
358C24—42no—
359C24C2×C5×D411yescharacteristic
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—42no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—41no—
381C2×D4—41no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C2×C5×D411yescharacteristic
397C22×C4C2×C5×D411yescharacteristic
398C22×C4C2×C5×D411yescharacteristic
399C22×C4C2×C5×D411yescharacteristic
400C22×C4C2×C5×D411yescharacteristic
401C22×C4C5×#4111yescharacteristic
402SD16—48no—
403D8—48no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—42no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—416no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—82no—
420C22⋊C4—82no—
421C2×C5—21no—
422C2×C5—22no—
423C2×C5—21no—
424C2×C5—84no—
425C2×C5—161no—
426C2×C5#159712yes—
427C2×C5#160012yes—
428C2×C5#200611yescharacteristic
429C2×C5#201211yescharacteristic
430C2×C5#202111yescharacteristic
431C23—21no—
432C23—21no—
433C23—22no—
434C23—24no—
435C23—44no—
436C23—44no—
437C23—42no—
438C23—44no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—42no—
443C23—44no—
444C23—44no—
445C23—41no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—82no—
453C23—82no—
454C23—82no—
455C23—82no—
456C23—81no—
457C23—81no—
458C23—81no—
459C23—81no—
460C23C5×#12011yescharacteristic
461C23C5×#12111yescharacteristic
462C23C5×#12711yescharacteristic
463C23C5×#13512yes—
464C23C5×AGL(1,ℤ/8)12yes—
465Q8—42no—
466Q8—81no—
467D4—24no—
468D4—24no—
469D4—42no—
470D4—42no—
471D4—44no—
472D4—44no—
473D4—42no—
474D4—81no—
475D4—82no—
476D4—81no—
477D4—81no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—81no—
498C2×C4—82no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4C5×#12011yescharacteristic
502C2×C4C5×#12011yescharacteristic
503C2×C4C5×#12111yescharacteristic
504C2×C4C5×#12111yescharacteristic
505C8—42no—
506C8—42no—
507C5#996311yescharacteristic, direct product factor, Sylow
508C22—21no—
509C22—21no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—21no—
515C22—21no—
516C22—48no—
517C22—44no—
518C22—84no—
519C22—84no—
520C22—84no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—82no—
525C22—81no—
526C22—81no—
527C22—82no—
528C22—82no—
529C22—81no—
530C22C5×#39211yescharacteristic
531C22C5×#44912yes—
532C22C5×#45311yescharacteristic
533C22C5×#45411yescharacteristic
534C22C5×B(4,𝔽2)12yes—
535C22C5×#46312yes—
536C22C5×#49511yescharacteristic
537C22C5×#49611yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—82no—
546C4—81no—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—84no—
551C2—161no—
552C2C5×#159712yes—
553C2C5×#160012yes—
554C2C5×#200611yescharacteristic
555C2C5×#201211yescharacteristic
556C2C5×#202111yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#447C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#450C2semidirect
3. C5×#2639C2semidirect
4. C2×C5×#328C2semidirect
5. C2×C5×#327C2semidirect
6. C5×#1438C2semidirect
7. C5×#1280C2semidirect
31. #9963C5direct (N × H)
82. C2×#450C2×C5semidirect
84. #2639C2×C5semidirect
85. C2×#328C2×C5semidirect
86. C2×#327C2×C5semidirect
87. #1438C2×C5semidirect
88. #1280C2×C5semidirect
507. C5#9963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4502
C2×C5×#4472
C5×#26392
C2×C5×#3282
C2×C5×#3272
C5×#14382
C5×#12802
#99635