Finite Group Databasebeta

← C5×#9277 #11931997

Subgroups — C5×#9277 #11931997

Order 1280.

648 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
1C5×#3186C211yesmaximal, characteristic
2C5×#2364C211yesmaximal, characteristic, complemented
3C5×#1964C211yesmaximal, characteristic, complemented
4C5×#1519C211yesmaximal, characteristic, complemented
5C2×C5×#327C211yesmaximal, characteristic, complemented
6C5×#1294C211yesmaximal, characteristic, complemented
7C5×#1282C211yesmaximal, characteristic, complemented
8C2×C5×#121C2211yescharacteristic
9C2×C5×#121C2211yescharacteristic
10C2×C4×C5×D4—21no—
11C5×#480—21no—
12C5×#480C412yescomplemented
13C5×#466—22no—
14C5×#447—21no—
15C5×#447C412yescomplemented
16C2×C5×#99—21no—
17C2×C5×#99—21no—
18C2×C5×C22⋊C8C2211yescharacteristic
19C2×C5×C22⋊C8C2211yescharacteristic
20C5×#388—21no—
21C5×#387—21no—
22C5×#386—21no—
23C5×#386—21no—
24C5×#380C2211yescharacteristic
25C4×C5×C22⋊C4—21no—
26C4×C5×C22⋊C4C2211yescharacteristic
27C2×C5×#95C2211yescharacteristic
28C5×#327—21no—
29C5×#327—21no—
30C5×#327—22no—
31#9277C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×D4—21no—
33C22×C5×D4—21no—
34C22×C5×D4C2×C411yescharacteristic, complemented
35C22×C5×D4D411yescharacteristic
36C23×C4×C5—21no—
37C23×C4×C5—21no—
38C23×C4×C5C2311yescharacteristic
39C2×C5×D8—22no—
40C22×C5×C8—21no—
41C22×C5×C8—21no—
42C5×#121—21no—
43C5×#121—21no—
44C5×#121—21no—
45C5×#121—21no—
46C5×#121—21no—
47C5×#121—21no—
48C5×#121C2×C412yes—
49C5×#121D412yes—
50C4×C5×D4—42no—
51C4×C5×D4—42no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
55C2×C5×C4⋊C4D411yescharacteristic
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4D411yescharacteristic
63C2×C5×C22⋊C4D411yescharacteristic
64C2×C42×C5—21no—
65C2×C42×C5—21no—
66C5×#107—22no—
67C5×#102—22no—
68C5×#102—22no—
69C5×#99—42no—
70C5×#99—42no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8C2×C412yescomplemented
75C5×#95—21no—
76C5×#95—21no—
77C5×#95—21no—
78C5×#95—21no—
79C5×#95—21no—
80C5×#95D411yescharacteristic
81C5×#95D411yescharacteristic
82#3186C2×C511yescharacteristic
83#2364C2×C511yescharacteristic, complemented
84#1964C2×C511yescharacteristic, complemented
85#1519C2×C511yescharacteristic, complemented
86C2×#327C2×C511yescharacteristic, complemented
87#1294C2×C511yescharacteristic, complemented
88#1282C2×C511yescharacteristic, complemented
89C24×C5—21no—
90C24×C5—21no—
91C24×C5C2×D411yescharacteristic
92C2×C5×D4—22no—
93C2×C5×D4—22no—
94C2×C5×D4—21no—
95C2×C5×D4—21no—
96C2×C5×D4—21no—
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—81no—
108C2×C5×D4—81no—
109C2×C5×D4C22⋊C412yes—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—42no—
117C22×C4×C5—42no—
118C22×C4×C5—42no—
119C22×C4×C5—41no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—81no—
123C22×C4×C5—81no—
124C22×C4×C5—81no—
125C22×C4×C5C22×C411yescharacteristic
126C22×C4×C5C2×D411yescharacteristic
127C22×C4×C5C2×D411yescharacteristic
128C22×C4×C5C2×D411yescharacteristic
129C22×C4×C5#4111yescharacteristic
130C22×C4×C5#4111yescharacteristic
131C5×D8—82no—
132C2×C5×C8—22no—
133C2×C5×C8—41no—
134C2×C5×C8—81no—
135C2×C5×C8—81no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—42no—
140C5×C4⋊C4—81no—
141C5×C4⋊C4C22⋊C412yes—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—22no—
144C5×C22⋊C4—22no—
145C5×C22⋊C4—21no—
146C5×C22⋊C4—21no—
147C5×C22⋊C4—42no—
148C5×C22⋊C4—42no—
149C5×C22⋊C4—41no—
150C5×C22⋊C4—41no—
151C5×C22⋊C4—41no—
152C5×C22⋊C4—41no—
153C5×C22⋊C4—81no—
154C5×C22⋊C4D812yescomplemented
155C42×C5—42no—
156C42×C5—81no—
157C2×#121C22×C511yescharacteristic
158C2×#121C22×C511yescharacteristic
159C2×C4×D4—21no—
160#480—21no—
161#480C4×C512yescomplemented
162#466—22no—
163#447—21no—
164#447C4×C512yescomplemented
165C2×#99—21no—
166C2×#99—21no—
167C2×C22⋊C8C22×C511yescharacteristic
168C2×C22⋊C8C22×C511yescharacteristic
169#388—21no—
170#387—21no—
171#386—21no—
172#386—21no—
173#380C22×C511yescharacteristic
174C4×C22⋊C4—21no—
175C4×C22⋊C4C22×C511yescharacteristic
176C2×#95C22×C511yescharacteristic
177#327—22no—
178#327—21no—
179#327—21no—
180C23×C5—22no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5—41no—
186C23×C5—41no—
187C23×C5—41no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5—41no—
192C23×C5—81no—
193C23×C5—81no—
194C23×C5C4×D411yescharacteristic
195C23×C5#12011yescharacteristic
196C23×C5#12111yescharacteristic
197C23×C5C2×D811yescharacteristic
198C23×C5#13511yescharacteristic
199C23×C5AGL(1,ℤ/8)11yescharacteristic
200C23×C5AGL(1,ℤ/8)11yescharacteristic
201C5×D4—42no—
202C5×D4—42no—
203C5×D4—42no—
204C5×D4—42no—
205C5×D4—42no—
206C5×D4—42no—
207C5×D4—81no—
208C5×D4—81no—
209C5×D4—81no—
210C5×D4—81no—
211C5×D4—81no—
212C5×D4—81no—
213C2×C4×C5—22no—
214C2×C4×C5—22no—
215C2×C4×C5—22no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
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—41no—
237C2×C4×C5—84no—
238C2×C4×C5—82no—
239C2×C4×C5—82no—
240C2×C4×C5—81no—
241C2×C4×C5—81no—
242C2×C4×C5—81no—
243C2×C4×C5C2×C22⋊C411yescharacteristic
244C2×C4×C5C4×D411yescharacteristic
245C2×C4×C5#12111yescharacteristic
246C2×C4×C5#12311yescharacteristic
247C5×C8—42no—
248C5×C8—81no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4C2×C4×C511yescharacteristic, complemented
252C22×D4C5×D411yescharacteristic
253C23×C4—21no—
254C23×C4—21no—
255C23×C4C23×C511yescharacteristic
256C2×D8—22no—
257C22×C8—21no—
258C22×C8—21no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121C2×C4×C512yes—
266#121C5×D412yes—
267C4×D4—42no—
268C4×D4—42no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C4×C511yescharacteristic, complemented
272C2×C4⋊C4C5×D411yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4C5×D411yescharacteristic
280C2×C22⋊C4C5×D411yescharacteristic
281C2×C42—21no—
282C2×C42—21no—
283#107—22no—
284#102—22no—
285#102—22no—
286#99—42no—
287#99—42no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8C2×C4×C512yescomplemented
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95C5×D411yescharacteristic
298#95C5×D411yescharacteristic
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—41no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—42no—
310C22×C5—42no—
311C22×C5—42no—
312C22×C5—81no—
313C22×C5—81no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5—161no—
320C22×C5—161no—
321C22×C5#38611yescharacteristic
322C22×C5C4×D811yescharacteristic
323C22×C5#44211yescharacteristic
324C22×C5#44711yescharacteristic
325C22×C5#44911yescharacteristic
326C22×C5#45911yescharacteristic
327C22×C5#46311yescharacteristic
328C4×C5—21no—
329C4×C5—21no—
330C4×C5—21no—
331C4×C5—21no—
332C4×C5—42no—
333C4×C5—42no—
334C4×C5—42no—
335C4×C5—81no—
336C4×C5—81no—
337C4×C5—81no—
338C4×C5—161no—
339C24—21no—
340C24—21no—
341C24C2×C5×D411yescharacteristic
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—81no—
358C2×D4—81no—
359C2×D4C5×C22⋊C412yes—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—81no—
373C22×C4—81no—
374C22×C4—81no—
375C22×C4C22×C4×C511yescharacteristic
376C22×C4C2×C5×D411yescharacteristic
377C22×C4C2×C5×D411yescharacteristic
378C22×C4C2×C5×D411yescharacteristic
379C22×C4C5×#4111yescharacteristic
380C22×C4C5×#4111yescharacteristic
381D8—82no—
382C2×C8—22no—
383C2×C8—41no—
384C2×C8—81no—
385C2×C8—81no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—42no—
390C4⋊C4—81no—
391C4⋊C4C5×C22⋊C412yes—
392C22⋊C4—21no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—42no—
398C22⋊C4—42no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—81no—
404C22⋊C4C5×D812yescomplemented
405C42—42no—
406C42—81no—
407C2×C5—21no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—21no—
412C2×C5—21no—
413C2×C5—82no—
414C2×C5—161no—
415C2×C5#187911yescharacteristic
416C2×C5#190611yescharacteristic
417C2×C5#191311yescharacteristic
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—81no—
431C23—81no—
432C23C4×C5×D411yescharacteristic
433C23C5×#12011yescharacteristic
434C23C5×#12111yescharacteristic
435C23C2×C5×D811yescharacteristic
436C23C5×#13511yescharacteristic
437C23C5×AGL(1,ℤ/8)11yescharacteristic
438C23C5×AGL(1,ℤ/8)11yescharacteristic
439D4—42no—
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—81no—
446D4—81no—
447D4—81no—
448D4—81no—
449D4—81no—
450D4—81no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—84no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4C2×C5×C22⋊C411yescharacteristic
482C2×C4C4×C5×D411yescharacteristic
483C2×C4C5×#12111yescharacteristic
484C2×C4C5×#12311yescharacteristic
485C8—42no—
486C8—81no—
487C5#927711yescharacteristic, direct product factor, Sylow
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—161no—
509C22—161no—
510C22C5×#38611yescharacteristic
511C22C4×C5×D811yescharacteristic
512C22C5×#44211yescharacteristic
513C22C5×#44711yescharacteristic
514C22C5×#44911yescharacteristic
515C22C5×#45911yescharacteristic
516C22C5×#46311yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—42no—
523C4—42no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—161no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—82no—
535C2—161no—
536C2C5×#187911yescharacteristic
537C2C5×#190611yescharacteristic
538C2C5×#191311yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC5×#3186C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2364C2semidirect
3. C5×#1964C2semidirect
4. C5×#1519C2semidirect
5. C2×C5×#327C2semidirect
6. C5×#1294C2semidirect
7. C5×#1282C2semidirect
12. C5×#480C4semidirect
15. C5×#447C4semidirect
31. #9277C5direct (N × H)
34. C22×C5×D4C2×C4semidirect
54. C2×C5×C4⋊C4C2×C4semidirect
74. C5×C22⋊C8C2×C4semidirect
83. #2364C2×C5semidirect
84. #1964C2×C5semidirect
85. #1519C2×C5semidirect
86. C2×#327C2×C5semidirect
87. #1294C2×C5semidirect
88. #1282C2×C5semidirect
154. C5×C22⋊C4D8semidirect
161. #480C4×C5semidirect
164. #447C4×C5semidirect
251. C22×D4C2×C4×C5semidirect
271. C2×C4⋊C4C2×C4×C5semidirect
291. C22⋊C8C2×C4×C5semidirect
404. C22⋊C4C5×D8semidirect
487. C5#9277direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31862
C5×#23642
C5×#19642
C5×#15192
C2×C5×#3272
C5×#12942
C5×#12822
#92775