Finite Group Databasebeta

← C5×#10409 #11933129

Subgroups — C5×#10409 #11933129

Order 1280.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2541C211yesmaximal, characteristic
2C5×#1957C211yesmaximal, characteristic, complemented
3C5×#1948C211yesmaximal, characteristic, complemented
4C5×#1802C211yesmaximal, characteristic, complemented
5C2×C5×#331C211yesmaximal, characteristic, complemented
6C2×C5×D4⋊C8C211yesmaximal, characteristic, complemented
7C5×#1279C211yesmaximal, characteristic, complemented
8C2×C5×#127—21no—
9C2×C5×#127C2211yescharacteristic
10C2×C5×#121—21no—
11C2×C5×#121—21no—
12C2×C4×C5×D4C2211yescharacteristic
13C2×C5×#106—21no—
14C2×C5×C4⋊C8C2211yescharacteristic
15C2×C5×C4⋊C8C2211yescharacteristic
16C2×C5×#102—21no—
17C2×C5×#102—22no—
18C2×C4×C5×C8C2211yescharacteristic
19C5×#392—22no—
20C5×#390—21no—
21C5×#384C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C5×#340—21no—
24C5×#340—21no—
25C5×#331—22no—
26C5×D4⋊C8—22no—
27#10409C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×D4—22no—
29C22×C5×D4—22no—
30C22×C5×D4—21no—
31C22×C5×D4—21no—
32C22×C5×D4D411yescharacteristic
33C22×C5×D4D412yes—
34C23×C4×C5—21no—
35C22×C5×C8—21no—
36C22×C5×C8—21no—
37C22×C5×C8—21no—
38C5×#127—21no—
39C5×#127—21no—
40C5×#127—21no—
41C5×#127—21no—
42C5×#127—42no—
43C5×#127—42no—
44C5×#121—42no—
45C5×#121—42no—
46C5×#121—42no—
47C5×#121—42no—
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C4×C5×D4—21no—
51C4×C5×D4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4D411yescharacteristic
56C2×C5×C4⋊C4D411yescharacteristic
57C2×C5×C4⋊C4D411yescharacteristic
58C2×C5×C22⋊C4—22no—
59C2×C5×C22⋊C4—22no—
60C2×C5×C22⋊C4—21no—
61C2×C42×C5—21no—
62C2×C42×C5C2311yescharacteristic
63C5×#106—42no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8—21no—
67C5×C4⋊C8D412yescomplemented
68C5×#102—44no—
69C5×#102—42no—
70C4×C5×C8—21no—
71C4×C5×C8—21no—
72C5×#95—21no—
73#2541C2×C511yescharacteristic
74#1957C2×C511yescharacteristic, complemented
75#1948C2×C511yescharacteristic, complemented
76#1802C2×C511yescharacteristic, complemented
77C2×#331C2×C511yescharacteristic, complemented
78C2×D4⋊C8C2×C511yescharacteristic, complemented
79#1279C2×C511yescharacteristic, complemented
80C24×C5—21no—
81C24×C5—22no—
82C2×C5×D4—21no—
83C2×C5×D4—22no—
84C2×C5×D4—21no—
85C2×C5×D4—22no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—42no—
90C2×C5×D4—42no—
91C2×C5×D4—44no—
92C2×C5×D4—44no—
93C2×C5×D4—44no—
94C2×C5×D4—44no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4—41no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—82no—
108C2×C5×D4—82no—
109C2×C5×D4SD1612yes—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—41no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—41no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2×D411yescharacteristic
123C2×C5×C8—22no—
124C2×C5×C8—22no—
125C2×C5×C8—41no—
126C2×C5×C8—41no—
127C2×C5×C8—41no—
128C2×C5×C8—41no—
129C2×C5×C8—41no—
130C2×C5×C8—41no—
131C2×C5×C8—41no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—42no—
137C5×C4⋊C4—41no—
138C5×C4⋊C4—41no—
139C5×C4⋊C4—41no—
140C5×C4⋊C4—41no—
141C5×C4⋊C4D812yes—
142C5×C4⋊C4SD1612yes—
143C5×C22⋊C4—44no—
144C5×C22⋊C4—44no—
145C5×C22⋊C4—41no—
146C5×C22⋊C4—41no—
147C42×C5—41no—
148C42×C5—41no—
149C42×C5C2×D411yescharacteristic
150C42×C5#4111yescharacteristic
151C42×C5#4111yescharacteristic
152C42×C5#4111yescharacteristic
153C2×#127—21no—
154C2×#127C22×C511yescharacteristic
155C2×#121—21no—
156C2×#121—21no—
157C2×C4×D4C22×C511yescharacteristic
158C2×#106—21no—
159C2×C4⋊C8C22×C511yescharacteristic
160C2×C4⋊C8C22×C511yescharacteristic
161C2×#102—21no—
162C2×#102—22no—
163C2×C4×C8C22×C511yescharacteristic
164#392—22no—
165#390—21no—
166#384C22×C511yescharacteristic
167C4×C4⋊C4C22×C511yescharacteristic
168#340—21no—
169#340—21no—
170#331—22no—
171D4⋊C8—22no—
172C23×C5—22no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5—42no—
180C23×C5—42no—
181C23×C5—42no—
182C23×C5—42no—
183C23×C5—42no—
184C23×C5—42no—
185C23×C5—42no—
186C23×C5#12011yescharacteristic
187C5×D4—22no—
188C5×D4—22no—
189C5×D4—44no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—82no—
193C5×D4—88no—
194C5×D4—88no—
195C5×D4—81no—
196C5×D4—81no—
197C5×D4—81no—
198C5×D4—81no—
199C5×D4—81no—
200C5×D4—81no—
201C5×D4—81no—
202C5×D4—81no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—81no—
215C2×C4×C5—81no—
216C2×C4×C5—81no—
217C2×C4×C5—81no—
218C2×C4×C5—81no—
219C2×C4×C5—81no—
220C2×C4×C5—81no—
221C2×C4×C5#12111yescharacteristic
222C2×C4×C5#12111yescharacteristic
223C2×C4×C5#12111yescharacteristic
224C2×C4×C5#12311yescharacteristic
225C2×C4×C5#12311yescharacteristic
226C2×C4×C5#12411yescharacteristic
227C2×C4×C5C2×D811yescharacteristic
228C2×C4×C5C2×SD1611yescharacteristic
229C2×C4×C5C2×SD1611yescharacteristic
230C2×C4×C5#13511yescharacteristic
231C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
232C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
233C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
234C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
235C5×C8—42no—
236C5×C8—42no—
237C5×C8—81no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4C5×D411yescharacteristic
243C22×D4C5×D412yes—
244C23×C4—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248#127—21no—
249#127—21no—
250#127—21no—
251#127—21no—
252#127—42no—
253#127—42no—
254#121—42no—
255#121—42no—
256#121—42no—
257#121—42no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C5×D411yescharacteristic
266C2×C4⋊C4C5×D411yescharacteristic
267C2×C4⋊C4C5×D411yescharacteristic
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C42—21no—
272C2×C42C23×C511yescharacteristic
273#106—42no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8C5×D412yescomplemented
278#102—44no—
279#102—42no—
280C4×C8—21no—
281C4×C8—21no—
282#95—21no—
283C22×C5—42no—
284C22×C5—42no—
285C22×C5—42no—
286C22×C5—81no—
287C22×C5—81no—
288C22×C5—81no—
289C22×C5—81no—
290C22×C5—82no—
291C22×C5—82no—
292C22×C5—82no—
293C22×C5—82no—
294C22×C5—82no—
295C22×C5—82no—
296C22×C5—82no—
297C22×C5#39411yescharacteristic
298C22×C5#44711yescharacteristic
299C22×C5#44911yescharacteristic
300C22×C5#45011yescharacteristic
301C22×C5#45011yescharacteristic
302C22×C5#45311yescharacteristic
303C22×C5#45511yescharacteristic
304C4×C5—21no—
305C4×C5—21no—
306C4×C5—42no—
307C4×C5—42no—
308C4×C5—81no—
309C4×C5—161no—
310C4×C5#45911yescharacteristic
311C4×C5#46011yescharacteristic
312C4×C5#46511yescharacteristic
313C4×C5#46911yescharacteristic
314C4×C5#48111yescharacteristic
315C4×C5#48211yescharacteristic
316C4×C5#48611yescharacteristic
317C4×C5#49011yescharacteristic
318C24—21no—
319C24—22no—
320C2×D4—21no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—44no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—44no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—82no—
346C2×D4—82no—
347C2×D4C5×SD1612yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4C2×C5×D411yescharacteristic
359C22×C4C2×C5×D411yescharacteristic
360C22×C4C2×C5×D411yescharacteristic
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—42no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C5×D812yes—
380C4⋊C4C5×SD1612yes—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C42—41no—
386C42—41no—
387C42C2×C5×D411yescharacteristic
388C42C5×#4111yescharacteristic
389C42C5×#4111yescharacteristic
390C42C5×#4111yescharacteristic
391C2×C5—82no—
392C2×C5—162no—
393C2×C5#162111yescharacteristic
394C2×C5#162911yescharacteristic
395C2×C5#163911yescharacteristic
396C2×C5#164211yescharacteristic
397C2×C5#203411yescharacteristic
398C2×C5#203711yescharacteristic
399C2×C5#204111yescharacteristic
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23C5×#12011yescharacteristic
415D4—22no—
416D4—22no—
417D4—44no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—88no—
422D4—88no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4C5×#12111yescharacteristic
450C2×C4C5×#12111yescharacteristic
451C2×C4C5×#12111yescharacteristic
452C2×C4C5×#12311yescharacteristic
453C2×C4C5×#12311yescharacteristic
454C2×C4C5×#12411yescharacteristic
455C2×C4C2×C5×D811yescharacteristic
456C2×C4C2×C5×SD1611yescharacteristic
457C2×C4C2×C5×SD1611yescharacteristic
458C2×C4C5×#13511yescharacteristic
459C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
460C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
461C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
462C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
463C8—42no—
464C8—42no—
465C8—81no—
466C5#1040911yescharacteristic, direct product factor, Sylow
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22C5×#39411yescharacteristic
482C22C5×#44711yescharacteristic
483C22C5×#44911yescharacteristic
484C22C5×#45011yescharacteristic
485C22C5×#45011yescharacteristic
486C22C5×#45311yescharacteristic
487C22C5×#45511yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—161no—
494C4C5×#45911yescharacteristic
495C4C5×#46011yescharacteristic
496C4C5×#46511yescharacteristic
497C4C5×#46911yescharacteristic
498C4C5×#48111yescharacteristic
499C4C5×#48211yescharacteristic
500C4C5×#48611yescharacteristic
501C4C5×#49011yescharacteristic
502C2—82no—
503C2—162no—
504C2C5×#162111yescharacteristic
505C2C5×#162911yescharacteristic
506C2C5×#163911yescharacteristic
507C2C5×#164211yescharacteristic
508C2C5×#203411yescharacteristic
509C2C5×#203711yescharacteristic
510C2C5×#204111yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#2541C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1957C2semidirect
3. C5×#1948C2semidirect
4. C5×#1802C2semidirect
5. C2×C5×#331C2semidirect
6. C2×C5×D4⋊C8C2semidirect
7. C5×#1279C2semidirect
27. #10409C5direct (N × H)
67. C5×C4⋊C8D4semidirect
74. #1957C2×C5semidirect
75. #1948C2×C5semidirect
76. #1802C2×C5semidirect
77. C2×#331C2×C5semidirect
78. C2×D4⋊C8C2×C5semidirect
79. #1279C2×C5semidirect
277. C4⋊C8C5×D4semidirect
466. C5#10409direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25412
C5×#19572
C5×#19482
C5×#18022
C2×C5×#3312
C2×C5×D4⋊C82
C5×#12792
#104095