Finite Group Databasebeta

← C5×#29635 #11952355

Subgroups — C5×#29635 #11952355

Order 1280.

1596 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#534C211yesmaximal, characteristic
2C5×#2483C211yesmaximal, characteristic, complemented
3C5×#2405C212yesmaximal, complemented
4C5×#2044C214yesmaximal, complemented
5C5×#2022C214yesmaximal, complemented
6C5×#1819C211yesmaximal, characteristic, complemented
7C5×#1781C212yesmaximal, complemented
8C23×C5×D4C2212yes—
9C5×#534—24no—
10C5×#534—22no—
11C5×#534C2214yes—
12C2×C5×#123—22no—
13C2×C5×#123C2214yescomplemented
14C2×C5×#121—21no—
15C2×C5×#121—21no—
16C2×C5×#120—22no—
17C22×C5×C22⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C2×C5×#99C2218yescomplemented
20C5×#397—22no—
21C5×#394—24no—
22C5×#386C2214yescomplemented
23C5×#385—21no—
24C5×#385—22no—
25C5×#385C2212yescomplemented
26C5×#381—21no—
27C5×#381C2212yescomplemented
28C5×#379—22no—
29C5×#379C2211yescharacteristic
30C5×#379C2212yes—
31C5×#342C2214yescomplemented
32#29635C511yesmaximal, characteristic, direct product factor, Sylow
33C25×C5D412yes—
34C25×C5C2311yescharacteristic
35C22×C5×D4—22no—
36C22×C5×D4—22no—
37C22×C5×D4—22no—
38C22×C5×D4—22no—
39C22×C5×D4—21no—
40C22×C5×D4—21no—
41C22×C5×D4—48no—
42C22×C5×D4D414yes—
43C22×C5×D4C2314yes—
44C23×C4×C5D411yescharacteristic
45C23×C4×C5D412yes—
46C23×C4×C5D411yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C5×#123—28no—
50C5×#123—28no—
51C5×#123—48no—
52C5×#121—24no—
53C5×#121—24no—
54C5×#121—24no—
55C5×#121—24no—
56C5×#120—28no—
57C5×#120—28no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—24no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C22⋊C4—22no—
63C2×C5×C22⋊C4—22no—
64C2×C5×C22⋊C4—22no—
65C2×C5×C22⋊C4—22no—
66C2×C5×C22⋊C4—22no—
67C2×C5×C22⋊C4—22no—
68C2×C5×C22⋊C4—24no—
69C2×C5×C22⋊C4—21no—
70C2×C5×C22⋊C4—21no—
71C2×C5×C22⋊C4—22no—
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—22no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4D412yes—
77C2×C5×C22⋊C4C2312yes—
78C2×C5×C22⋊C4C2314yes—
79C2×C5×C22⋊C4C2312yes—
80C5×#99—48no—
81C5×#95—22no—
82C5×#95—22no—
83C5×#95—22no—
84C5×#95—24no—
85C2×#534C2×C511yescharacteristic
86#2483C2×C511yescharacteristic, complemented
87#2405C2×C512yescomplemented
88#2044C2×C514yescomplemented
89#2022C2×C514yescomplemented
90#1819C2×C511yescharacteristic, complemented
91#1781C2×C512yescomplemented
92C24×C5—24no—
93C24×C5—22no—
94C24×C5—22no—
95C24×C5—44no—
96C24×C5—42no—
97C24×C5—44no—
98C24×C5—81no—
99C24×C5—82no—
100C24×C5C2×D412yes—
101C24×C5C2×D411yescharacteristic
102C24×C5C2×D414yes—
103C24×C5C2×D412yes—
104C24×C5C2×D411yescharacteristic
105C24×C5C2411yescharacteristic
106C2×C5×D4—24no—
107C2×C5×D4—24no—
108C2×C5×D4—24no—
109C2×C5×D4—24no—
110C2×C5×D4—28no—
111C2×C5×D4—28no—
112C2×C5×D4—24no—
113C2×C5×D4—24no—
114C2×C5×D4—44no—
115C2×C5×D4—44no—
116C2×C5×D4—48no—
117C2×C5×D4—48no—
118C2×C5×D4—48no—
119C2×C5×D4—48no—
120C2×C5×D4—82no—
121C2×C5×D4—82no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—24no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—24no—
135C22×C4×C5—44no—
136C22×C4×C5—42no—
137C22×C4×C5—81no—
138C22×C4×C5—81no—
139C22×C4×C5C2×D414yes—
140C22×C4×C5C2×D412yes—
141C22×C4×C5C2×D412yes—
142C5×C4⋊C4—24no—
143C5×C4⋊C4—24no—
144C5×C4⋊C4—48no—
145C5×C4⋊C4—82no—
146C5×C22⋊C4—28no—
147C5×C22⋊C4—28no—
148C5×C22⋊C4—24no—
149C5×C22⋊C4—24no—
150C5×C22⋊C4—28no—
151C5×C22⋊C4—24no—
152C5×C22⋊C4—42no—
153C5×C22⋊C4—44no—
154C5×C22⋊C4—48no—
155C5×C22⋊C4—42no—
156C5×C22⋊C4—41no—
157C5×C22⋊C4—41no—
158C5×C22⋊C4—82no—
159C5×C22⋊C4—84no—
160C5×C22⋊C4—81no—
161C23×D4C22×C512yes—
162#534—24no—
163#534—22no—
164#534C22×C514yes—
165C2×#123—22no—
166C2×#123C22×C514yescomplemented
167C2×#121—21no—
168C2×#121—21no—
169C2×#120—22no—
170C22×C22⋊C4C22×C511yescharacteristic
171C22×C22⋊C4C22×C511yescharacteristic
172C2×#99C22×C518yescomplemented
173#397—22no—
174#394—24no—
175#386C22×C514yescomplemented
176#385—22no—
177#385—21no—
178#385C22×C512yescomplemented
179#381—21no—
180#381C22×C512yescomplemented
181#379—22no—
182#379C22×C512yes—
183#379C22×C511yescharacteristic
184#342C22×C514yescomplemented
185C23×C5—24no—
186C23×C5—22no—
187C23×C5—22no—
188C23×C5—24no—
189C23×C5—24no—
190C23×C5—22no—
191C23×C5—24no—
192C23×C5—24no—
193C23×C5—24no—
194C23×C5—41no—
195C23×C5—41no—
196C23×C5—41no—
197C23×C5—42no—
198C23×C5—41no—
199C23×C5—42no—
200C23×C5—41no—
201C23×C5—42no—
202C23×C5—44no—
203C23×C5—44no—
204C23×C5—44no—
205C23×C5—44no—
206C23×C5—44no—
207C23×C5—44no—
208C23×C5—82no—
209C23×C5—82no—
210C23×C5—88no—
211C23×C5—816no—
212C23×C5#12012yes—
213C23×C5#12011yescharacteristic
214C23×C5#12011yescharacteristic
215C23×C5C22×D412yes—
216C23×C5C22×D411yescharacteristic
217C23×C5H(5,𝔽2)14yes—
218C5×D4—48no—
219C5×D4—48no—
220C5×D4—48no—
221C5×D4—48no—
222C5×D4—84no—
223C5×D4—84no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—24no—
227C2×C4×C5—24no—
228C2×C4×C5—24no—
229C2×C4×C5—44no—
230C2×C4×C5—44no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—44no—
237C2×C4×C5—44no—
238C2×C4×C5—42no—
239C2×C4×C5—44no—
240C2×C4×C5—42no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—44no—
244C2×C4×C5—44no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—81no—
248C2×C4×C5—81no—
249C25C5×D412yes—
250C25C23×C511yescharacteristic
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—48no—
258C22×D4C5×D414yes—
259C22×D4C23×C514yes—
260C23×C4C5×D411yescharacteristic
261C23×C4C5×D412yes—
262C23×C4C5×D411yescharacteristic
263C23×C4C23×C511yescharacteristic
264C23×C4C23×C511yescharacteristic
265#123—28no—
266#123—28no—
267#123—48no—
268#121—24no—
269#121—24no—
270#121—24no—
271#121—24no—
272#120—28no—
273#120—28no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4C5×D412yes—
293C2×C22⋊C4C23×C514yes—
294C2×C22⋊C4C23×C512yes—
295C2×C22⋊C4C23×C512yes—
296#99—48no—
297#95—22no—
298#95—22no—
299#95—22no—
300#95—24no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—22no—
304C22×C5—21no—
305C22×C5—22no—
306C22×C5—21no—
307C22×C5—22no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—22no—
311C22×C5—21no—
312C22×C5—22no—
313C22×C5—44no—
314C22×C5—44no—
315C22×C5—48no—
316C22×C5—48no—
317C22×C5—44no—
318C22×C5—44no—
319C22×C5—44no—
320C22×C5—84no—
321C22×C5—82no—
322C22×C5—84no—
323C22×C5—88no—
324C22×C5—88no—
325C22×C5#45812yes—
326C22×C5C2×#12011yescharacteristic
327C22×C5#53414yes—
328C22×C5#53512yes—
329C4×C5—44no—
330C4×C5—42no—
331C4×C5—42no—
332C4×C5—84no—
333C4×C5—82no—
334C4×C5—81no—
335C4×C5—81no—
336C24—24no—
337C24—22no—
338C24—22no—
339C24—44no—
340C24—42no—
341C24—44no—
342C24—81no—
343C24—82no—
344C24C2×C5×D412yes—
345C24C2×C5×D411yescharacteristic
346C24C2×C5×D414yes—
347C24C2×C5×D412yes—
348C24C2×C5×D411yescharacteristic
349C24C24×C511yescharacteristic
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—28no—
355C2×D4—28no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—44no—
359C2×D4—44no—
360C2×D4—48no—
361C2×D4—48no—
362C2×D4—48no—
363C2×D4—48no—
364C2×D4—82no—
365C2×D4—82no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—81no—
382C22×C4—81no—
383C22×C4C2×C5×D414yes—
384C22×C4C2×C5×D412yes—
385C22×C4C2×C5×D412yes—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—48no—
389C4⋊C4—82no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—24no—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—28no—
396C22⋊C4—48no—
397C22⋊C4—42no—
398C22⋊C4—44no—
399C22⋊C4—42no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—82no—
403C22⋊C4—84no—
404C22⋊C4—81no—
405C2×C5—24no—
406C2×C5—22no—
407C2×C5—22no—
408C2×C5—41no—
409C2×C5—42no—
410C2×C5—84no—
411C2×C5#261311yescharacteristic
412C2×C5C2×#45811yescharacteristic
413C2×C5#302611yescharacteristic
414C23—22no—
415C23—24no—
416C23—24no—
417C23—22no—
418C23—24no—
419C23—22no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—42no—
427C23—41no—
428C23—42no—
429C23—41no—
430C23—42no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—82no—
438C23—82no—
439C23—88no—
440C23—816no—
441C23C5×#12012yes—
442C23C5×#12011yescharacteristic
443C23C5×#12011yescharacteristic
444C23C22×C5×D412yes—
445C23C22×C5×D411yescharacteristic
446C23C5×H(5,𝔽2)14yes—
447D4—48no—
448D4—48no—
449D4—48no—
450D4—48no—
451D4—84no—
452D4—84no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—81no—
477C2×C4—81no—
478C5#2963511yescharacteristic, direct product factor, Sylow
479C22—21no—
480C22—22no—
481C22—21no—
482C22—22no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—21no—
488C22—22no—
489C22—22no—
490C22—21no—
491C22—44no—
492C22—48no—
493C22—44no—
494C22—48no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22—84no—
499C22—82no—
500C22—84no—
501C22—88no—
502C22—88no—
503C22C5×#45812yes—
504C22C2×C5×#12011yescharacteristic
505C22C5×#53414yes—
506C22C5×#53512yes—
507C4—42no—
508C4—42no—
509C4—44no—
510C4—84no—
511C4—82no—
512C4—81no—
513C4—81no—
514C2—24no—
515C2—22no—
516C2—22no—
517C2—42no—
518C2—41no—
519C2—84no—
520C2C5×#261311yescharacteristic
521C2C2×C5×#45811yescharacteristic
522C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
prime radicalC2×C5×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2483C2semidirect
3. C5×#2405C2semidirect
4. C5×#2044C2semidirect
5. C5×#2022C2semidirect
6. C5×#1819C2semidirect
7. C5×#1781C2semidirect
13. C2×C5×#123C22semidirect
19. C2×C5×#99C22semidirect
22. C5×#386C22semidirect
25. C5×#385C22semidirect
27. C5×#381C22semidirect
31. C5×#342C22semidirect
32. #29635C5direct (N × H)
86. #2483C2×C5semidirect
87. #2405C2×C5semidirect
88. #2044C2×C5semidirect
89. #2022C2×C5semidirect
90. #1819C2×C5semidirect
91. #1781C2×C5semidirect
166. C2×#123C22×C5semidirect
172. C2×#99C22×C5semidirect
175. #386C22×C5semidirect
178. #385C22×C5semidirect
180. #381C22×C5semidirect
184. #342C22×C5semidirect
478. C5#29635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5342
C5×#24832
C5×#24052
C5×#20442
C5×#20222
C5×#18192
C5×#17812
#296355