Finite Group Databasebeta

← C5×#8577 #11931297

Subgroups — C5×#8577 #11931297

Order 1280.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#121C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic, complemented
3C2×C5×#327C212yesmaximal
4C5×C4⋊#95C211yesmaximal, characteristic, complemented
5C5×#1294C212yesmaximal, complemented
6C2×C5×#121C2211yescharacteristic
7C2×C4×C5×D4—21no—
8C2×C4×C5×D4C411yescharacteristic, complemented
9C22×C5×C4⋊C4—21no—
10C22×C42×C5C2211yescharacteristic
11C2×C5×C4⋊C8—21no—
12C2×C5×C22⋊C8C2212yes—
13C5×#390C411yescharacteristic, complemented
14C5×#389C411yescharacteristic, complemented
15C5×#388—21no—
16C5×#386—21no—
17C5×#380C2211yescharacteristic
18C4×C5×C4⋊C4C411yescharacteristic, complemented
19C4×C5×C22⋊C4—21no—
20C2×C5×#95—21no—
21C2×C5×#95C2212yes—
22C5×#336—21no—
23C5×#327—24no—
24#8577C511yesmaximal, characteristic, direct product factor, Sylow
25C22×C5×D4—21no—
26C22×C5×D4C2×C411yescharacteristic
27C23×C4×C5—22no—
28C23×C4×C5—21no—
29C23×C4×C5D411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C23×C4×C5C2311yescharacteristic
32C22×C5×C8—22no—
33C5×#121—21no—
34C5×#121—21no—
35C5×#121D412yes—
36C5×#121Q812yes—
37C4×C5×D4—42no—
38C4×C5×D4—42no—
39C4×C5×D4—42no—
40C2×C5×C4⋊C4—24no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—42no—
43C2×C5×C4⋊C4—42no—
44C2×C5×C4⋊C4C2×C411yescharacteristic
45C2×C5×C4⋊C4C2×C411yescharacteristic
46C2×C5×C4⋊C4C2×C411yescharacteristic
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C42×C5—21no—
53C2×C42×C5—42no—
54C2×C42×C5C2×C411yescharacteristic
55C2×C42×C5C2×C411yescharacteristic
56C2×C42×C5D411yescharacteristic
57C2×C42×C5D411yescharacteristic
58C5×C4⋊C8—42no—
59C5×C22⋊C8—22no—
60C5×C22⋊C8—22no—
61C5×#95—21no—
62C5×#95—21no—
63C5×#95—21no—
64C5×#95—22no—
65C5×#95—22no—
66C5×#95—42no—
67C4×#121C2×C511yescharacteristic
68#1797C2×C511yescharacteristic, complemented
69C2×#327C2×C512yes—
70C4⋊#95C2×C511yescharacteristic, complemented
71#1294C2×C512yescomplemented
72C24×C5—21no—
73C24×C5C2×D411yescharacteristic
74C2×C5×D4—22no—
75C2×C5×D4—22no—
76C2×C5×D4—21no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4C4⋊C412yescomplemented
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—22no—
87C22×C4×C5—22no—
88C22×C4×C5—21no—
89C22×C4×C5—24no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—42no—
97C22×C4×C5—42no—
98C22×C4×C5—42no—
99C22×C4×C5—42no—
100C22×C4×C5—42no—
101C22×C4×C5—42no—
102C22×C4×C5—42no—
103C22×C4×C5—42no—
104C22×C4×C5—42no—
105C22×C4×C5C22⋊C411yescharacteristic
106C22×C4×C5C22⋊C411yescharacteristic
107C22×C4×C5C22⋊C411yescharacteristic
108C22×C4×C5C22⋊C411yescharacteristic
109C22×C4×C5D812yes—
110C22×C4×C5SD1612yes—
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5C2×Q811yescharacteristic
115C22×C4×C5#4111yescharacteristic
116C22×C4×C5#4111yescharacteristic
117C2×C5×C8—42no—
118C2×C5×C8—42no—
119C2×C5×C8—42no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—48no—
124C5×C4⋊C4—42no—
125C5×C4⋊C4C4⋊C412yescomplemented
126C5×C22⋊C4—22no—
127C5×C22⋊C4—22no—
128C5×C22⋊C4—41no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—42no—
131C5×C22⋊C4—42no—
132C5×C22⋊C4—42no—
133C42×C5—22no—
134C42×C5—22no—
135C42×C5—41no—
136C42×C5—41no—
137C42×C5—42no—
138C2×#121C22×C511yescharacteristic
139C2×C4×D4—21no—
140C2×C4×D4C4×C511yescharacteristic, complemented
141C22×C4⋊C4—21no—
142C22×C42C22×C511yescharacteristic
143C2×C4⋊C8—21no—
144C2×C22⋊C8C22×C512yes—
145#390C4×C511yescharacteristic, complemented
146#389C4×C511yescharacteristic, complemented
147#388—21no—
148#386—21no—
149#380C22×C511yescharacteristic
150C4×C4⋊C4C4×C511yescharacteristic, complemented
151C4×C22⋊C4—21no—
152C2×#95—21no—
153C2×#95C22×C512yes—
154#336—21no—
155#327—24no—
156C23×C5—21no—
157C23×C5—21no—
158C23×C5—21no—
159C23×C5—21no—
160C23×C5—22no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5—41no—
167C23×C5C2×C22⋊C411yescharacteristic
168C23×C5#12111yescharacteristic
169C23×C5C22⋊Q811yescharacteristic
170C23×C5C2×D811yescharacteristic
171C23×C5C2×SD1611yescharacteristic
172C23×C5AGL(1,ℤ/8)11yescharacteristic
173C23×C5#13711yescharacteristic
174C5×D4—42no—
175C5×D4—42no—
176C5×D4—42no—
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—42no—
180C2×C4×C5—24no—
181C2×C4×C5—24no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—42no—
196C2×C4×C5—42no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—44no—
204C2×C4×C5—44no—
205C2×C4×C5—44no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—84no—
213C2×C4×C5—82no—
214C2×C4×C5—82no—
215C2×C4×C5—82no—
216C2×C4×C5—82no—
217C2×C4×C5#9912yes—
218C2×C4×C5#10212yes—
219C2×C4×C5#10212yes—
220C2×C4×C5#10412yes—
221C2×C4×C5C2×C4⋊C411yescharacteristic
222C2×C4×C5#11711yescharacteristic
223C2×C4×C5#12111yescharacteristic
224C2×C4×C5C22⋊Q811yescharacteristic
225C5×C8—82no—
226C22×D4—21no—
227C22×D4C2×C4×C511yescharacteristic
228C23×C4—22no—
229C23×C4—21no—
230C23×C4C5×D411yescharacteristic
231C23×C4C5×D411yescharacteristic
232C23×C4C23×C511yescharacteristic
233C22×C8—22no—
234#121—21no—
235#121—21no—
236#121C5×D412yes—
237#121C5×Q812yes—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4—42no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4C2×C4×C511yescharacteristic
246C2×C4⋊C4C2×C4×C511yescharacteristic
247C2×C4⋊C4C2×C4×C511yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42—21no—
254C2×C42—42no—
255C2×C42C2×C4×C511yescharacteristic
256C2×C42C2×C4×C511yescharacteristic
257C2×C42C5×D411yescharacteristic
258C2×C42C5×D411yescharacteristic
259C4⋊C8—42no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—22no—
266#95—22no—
267#95—42no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—42no—
281C22×C5—42no—
282C22×C5—42no—
283C22×C5—81no—
284C22×C5—81no—
285C22×C5—81no—
286C22×C5—81no—
287C22×C5#38011yescharacteristic
288C22×C5C2×#9911yescharacteristic
289C22×C5#41011yescharacteristic
290C22×C5C2×#10211yescharacteristic
291C22×C5#41711yescharacteristic
292C22×C5C2×#10411yescharacteristic
293C22×C5#42111yescharacteristic
294C22×C5#45911yescharacteristic
295C22×C5#46111yescharacteristic
296C22×C5#47411yescharacteristic
297C22×C5#47611yescharacteristic
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—22no—
303C4×C5—22no—
304C4×C5—22no—
305C4×C5—22no—
306C4×C5—42no—
307C4×C5—84no—
308C4×C5—81no—
309C4×C5—81no—
310C24—21no—
311C24C2×C5×D411yescharacteristic
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4C5×C4⋊C412yescomplemented
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—24no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4C5×C22⋊C411yescharacteristic
344C22×C4C5×C22⋊C411yescharacteristic
345C22×C4C5×C22⋊C411yescharacteristic
346C22×C4C5×C22⋊C411yescharacteristic
347C22×C4C5×D812yes—
348C22×C4C5×SD1612yes—
349C22×C4C22×C4×C511yescharacteristic
350C22×C4C2×C5×D411yescharacteristic
351C22×C4C2×C5×D411yescharacteristic
352C22×C4C2×C5×Q811yescharacteristic
353C22×C4C5×#4111yescharacteristic
354C22×C4C5×#4111yescharacteristic
355C2×C8—42no—
356C2×C8—42no—
357C2×C8—42no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—48no—
362C4⋊C4—42no—
363C4⋊C4C5×C4⋊C412yescomplemented
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C42—22no—
372C42—22no—
373C42—41no—
374C42—41no—
375C42—42no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—82no—
381C2×C5#150211yescharacteristic
382C2×C5#150411yescharacteristic
383C2×C5#151211yescharacteristic
384C2×C5#151911yescharacteristic
385C2×C5#179911yescharacteristic
386C2×C5#180211yescharacteristic
387C2×C5#180611yescharacteristic
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—22no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23C2×C5×C22⋊C411yescharacteristic
400C23C5×#12111yescharacteristic
401C23C5×C22⋊Q811yescharacteristic
402C23C2×C5×D811yescharacteristic
403C23C2×C5×SD1611yescharacteristic
404C23C5×AGL(1,ℤ/8)11yescharacteristic
405C23C5×#13711yescharacteristic
406D4—42no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—42no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—84no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4C5×#9912yes—
450C2×C4C5×#10212yes—
451C2×C4C5×#10212yes—
452C2×C4C5×#10412yes—
453C2×C4C2×C5×C4⋊C411yescharacteristic
454C2×C4C5×#11711yescharacteristic
455C2×C4C5×#12111yescharacteristic
456C2×C4C5×C22⋊Q811yescharacteristic
457C8—82no—
458C5#857711yescharacteristic, direct product factor, Sylow
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22C5×#38011yescharacteristic
479C22C2×C5×#9911yescharacteristic
480C22C5×#41011yescharacteristic
481C22C2×C5×#10211yescharacteristic
482C22C5×#41711yescharacteristic
483C22C2×C5×#10411yescharacteristic
484C22C5×#42111yescharacteristic
485C22C5×#45911yescharacteristic
486C22C5×#46111yescharacteristic
487C22C5×#47411yescharacteristic
488C22C5×#47611yescharacteristic
489C4—22no—
490C4—22no—
491C4—22no—
492C4—22no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—42no—
498C4—84no—
499C4—81no—
500C4—81no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—82no—
506C2C5×#150211yescharacteristic
507C2C5×#150411yescharacteristic
508C2C5×#151211yescharacteristic
509C2C5×#151911yescharacteristic
510C2C5×#179911yescharacteristic
511C2C5×#180211yescharacteristic
512C2C5×#180611yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1797C2semidirect
4. C5×C4⋊#95C2semidirect
5. C5×#1294C2semidirect
8. C2×C4×C5×D4C4semidirect
13. C5×#390C4semidirect
14. C5×#389C4semidirect
18. C4×C5×C4⋊C4C4semidirect
24. #8577C5direct (N × H)
68. #1797C2×C5semidirect
70. C4⋊#95C2×C5semidirect
71. #1294C2×C5semidirect
83. C2×C5×D4C4⋊C4semidirect
125. C5×C4⋊C4C4⋊C4semidirect
140. C2×C4×D4C4×C5semidirect
145. #390C4×C5semidirect
146. #389C4×C5semidirect
150. C4×C4⋊C4C4×C5semidirect
321. C2×D4C5×C4⋊C4semidirect
363. C4⋊C4C5×C4⋊C4semidirect
458. C5#8577direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1212
C5×#17972
C2×C5×#3272
C5×C4⋊#952
C5×#12942
#85775