Finite Group Databasebeta

← C5×#9165 #11931885

Subgroups — C5×#9165 #11931885

Order 1280.

486 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3110C211yesmaximal, characteristic
2C5×#2974C211yesmaximal, characteristic
3C5×#1762C211yesmaximal, characteristic
4C5×#1531C211yesmaximal, characteristic, complemented
5C5×#1503C211yesmaximal, characteristic, complemented
6C5×#1302C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C5×#484—21no—
11C5×#474C411yescharacteristic, complemented
12C5×#474C411yescharacteristic, complemented
13C5×#461C411yescharacteristic, complemented
14C5×#461C411yescharacteristic, complemented
15C5×#450—21no—
16C5×#440—21no—
17C5×#440—21no—
18C5×#436—21no—
19C5×#435—22no—
20C5×C8×D4—21no—
21C5×#432C2211yescharacteristic
22C5×#432C2211yescharacteristic
23C5×#431C2211yescharacteristic
24C2×C5×#102—21no—
25C5×#407—21no—
26C2×C5×C22⋊C8—21no—
27C2×C5×#97C2211yescharacteristic
28C4×C5×C4⋊C4C2211yescharacteristic
29C5×#340—21no—
30C5×#330—22no—
31C5×#328—21no—
32C5×#328—21no—
33#9165C511yesmaximal, characteristic, direct product factor, Sylow
34C22×C5×D4D411yescharacteristic
35C23×C4×C5—21no—
36C2×C5×SD16—21no—
37C2×C5×SD16—21no—
38C2×C5×M16—22no—
39C22×C5×C8—21no—
40C22×C5×C8—22no—
41C5×C4⋊Q8C2×C411yescharacteristic
42C5×C4⋊Q8C2×C411yescharacteristic
43C5×#125—21no—
44C5×C22⋊Q8—21no—
45C5×C22⋊Q8—21no—
46C4×C5×Q8—21no—
47C4×C5×Q8—21no—
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C4×C5×D4C2×C411yescharacteristic
51C4×C5×D4C2×C411yescharacteristic
52C4×C5×D4D411yescharacteristic
53C4×C5×D4D411yescharacteristic
54C5×#117—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4D411yescharacteristic
57C2×C5×C22⋊C4—21no—
58C2×C42×C5—21no—
59C2×C42×C5C2311yescharacteristic
60C5×#107—21no—
61C5×#107—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8C2×C411yescharacteristic
65C5×C4⋊C8C2×C411yescharacteristic
66C5×#103—21no—
67C5×#103—21no—
68C5×#102—24no—
69C5×#102—21no—
70C5×#102—21no—
71C5×C22⋊C8—22no—
72C5×C22⋊C8—22no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8D411yescharacteristic
76C5×C22⋊C8D411yescharacteristic
77C5×#97—21no—
78C5×#97—21no—
79C5×#97—21no—
80C5×#97D412yes—
81C4×C5×C8—21no—
82C5×#95—21no—
83#3110C2×C511yescharacteristic
84#2974C2×C511yescharacteristic
85#1762C2×C511yescharacteristic
86#1531C2×C511yescharacteristic, complemented
87#1503C2×C511yescharacteristic, complemented
88#1302C2×C511yescharacteristic, complemented
89#1285C2×C511yescharacteristic, complemented
90C24×C5—21no—
91C2×C5×Q8—21no—
92C2×C5×Q8—21no—
93C2×C5×D4—22no—
94C2×C5×D4—21no—
95C2×C5×D4—41no—
96C2×C5×D4C22⋊C411yescharacteristic
97C2×C5×D4C22⋊C411yescharacteristic
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—41no—
104C22×C4×C5—82no—
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C22×C4×C5#4111yescharacteristic
108C5×SD16—42no—
109C5×SD16—42no—
110C5×M16—82no—
111C2×C5×C8—22no—
112C2×C5×C8—21no—
113C2×C5×C8—21no—
114C2×C5×C8—21no—
115C2×C5×C8—22no—
116C2×C5×C8—21no—
117C2×C5×C8—41no—
118C2×C5×C8—41no—
119C2×C5×C8—82no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—41no—
127C5×C4⋊C4—41no—
128C5×C4⋊C4—41no—
129C5×C4⋊C4C22⋊C411yescharacteristic
130C5×C4⋊C4C22⋊C411yescharacteristic
131C5×C22⋊C4—21no—
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C5×C22⋊C4—41no—
136C42×C5—41no—
137C42×C5—81no—
138C42×C5C22×C411yescharacteristic
139C42×C5C2×D411yescharacteristic
140C42×C5C2×D411yescharacteristic
141C42×C5#4111yescharacteristic
142#533C22×C511yescharacteristic
143C2×C4×D4C22×C511yescharacteristic
144#484—21no—
145#474C4×C511yescharacteristic, complemented
146#474C4×C511yescharacteristic, complemented
147#461C4×C511yescharacteristic, complemented
148#461C4×C511yescharacteristic, complemented
149#450—21no—
150#440—21no—
151#440—21no—
152#436—21no—
153#435—22no—
154C8×D4—21no—
155#432C22×C511yescharacteristic
156#432C22×C511yescharacteristic
157#431C22×C511yescharacteristic
158C2×#102—21no—
159#407—21no—
160C2×C22⋊C8—21no—
161C2×#97C22×C511yescharacteristic
162C4×C4⋊C4C22×C511yescharacteristic
163#340—21no—
164#330—22no—
165#328—21no—
166#328—21no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—42no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—81no—
173C23×C5#12111yescharacteristic
174C5×Q8—41no—
175C5×Q8—41no—
176C5×Q8—81no—
177C5×D4—21no—
178C5×D4—21no—
179C5×D4—21no—
180C5×D4—42no—
181C5×D4#10412yes—
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—41no—
189C2×C4×C5—42no—
190C2×C4×C5—42no—
191C2×C4×C5—42no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—81no—
195C2×C4×C5—81no—
196C2×C4×C5—81no—
197C2×C4×C5—81no—
198C2×C4×C5—81no—
199C2×C4×C5C2×C22⋊C411yescharacteristic
200C2×C4×C5C4×D411yescharacteristic
201C2×C4×C5C4×D411yescharacteristic
202C2×C4×C5#12011yescharacteristic
203C2×C4×C5#12111yescharacteristic
204C2×C4×C5#12311yescharacteristic
205C5×C8—42no—
206C5×C8—41no—
207C5×C8—42no—
208C5×C8—41no—
209C5×C8—41no—
210C5×C8—41no—
211C22×D4C5×D411yescharacteristic
212C23×C4—21no—
213C2×SD16—21no—
214C2×SD16—21no—
215C2×M16—22no—
216C22×C8—21no—
217C22×C8—22no—
218C4⋊Q8C2×C4×C511yescharacteristic
219C4⋊Q8C2×C4×C511yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4C2×C4×C511yescharacteristic
228C4×D4C2×C4×C511yescharacteristic
229C4×D4C5×D411yescharacteristic
230C4×D4C5×D411yescharacteristic
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C5×D411yescharacteristic
234C2×C22⋊C4—21no—
235C2×C42—21no—
236C2×C42C23×C511yescharacteristic
237#107—21no—
238#107—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C511yescharacteristic
242C4⋊C8C2×C4×C511yescharacteristic
243#103—21no—
244#103—21no—
245#102—24no—
246#102—21no—
247#102—21no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8C5×D411yescharacteristic
253C22⋊C8C5×D411yescharacteristic
254#97—21no—
255#97—21no—
256#97—21no—
257#97C5×D412yes—
258C4×C8—21no—
259#95—21no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5—22no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5—82no—
269C22×C5—82no—
270C22×C5#38611yescharacteristic
271C22×C5#47111yescharacteristic
272C22×C5#47311yescharacteristic
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—41no—
279C4×C5—41no—
280C4×C5—82no—
281C4×C5—81no—
282C4×C5—81no—
283C4×C5C2×#10411yescharacteristic
284C4×C5#42111yescharacteristic
285C24—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4C5×C22⋊C411yescharacteristic
292C2×D4C5×C22⋊C411yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—82no—
300C22×C4C2×C5×D411yescharacteristic
301C22×C4C2×C5×D411yescharacteristic
302C22×C4C5×#4111yescharacteristic
303SD16—42no—
304SD16—42no—
305M16—82no—
306C2×C8—22no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—82no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C5×C22⋊C411yescharacteristic
325C4⋊C4C5×C22⋊C411yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—41no—
331C42—41no—
332C42—81no—
333C42C22×C4×C511yescharacteristic
334C42C2×C5×D411yescharacteristic
335C42C2×C5×D411yescharacteristic
336C42C5×#4111yescharacteristic
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—42no—
340C2×C5—81no—
341C2×C5#187111yescharacteristic
342C2×C5#190411yescharacteristic
343C2×C5#190811yescharacteristic
344C23—21no—
345C23—21no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—81no—
350C23C5×#12111yescharacteristic
351Q8—41no—
352Q8—41no—
353Q8—81no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4C5×#10412yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4C2×C5×C22⋊C411yescharacteristic
377C2×C4C4×C5×D411yescharacteristic
378C2×C4C4×C5×D411yescharacteristic
379C2×C4C5×#12011yescharacteristic
380C2×C4C5×#12111yescharacteristic
381C2×C4C5×#12311yescharacteristic
382C8—42no—
383C8—41no—
384C8—42no—
385C8—41no—
386C8—41no—
387C8—41no—
388C5#916511yescharacteristic, direct product factor, Sylow
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—82no—
398C22—82no—
399C22C5×#38611yescharacteristic
400C22C5×#47111yescharacteristic
401C22C5×#47311yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4C2×C5×#10411yescharacteristic
413C4C5×#42111yescharacteristic
414C2—21no—
415C2—21no—
416C2—42no—
417C2—81no—
418C2C5×#187111yescharacteristic
419C2C5×#190411yescharacteristic
420C2C5×#190811yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1531C2semidirect
5. C5×#1503C2semidirect
6. C5×#1302C2semidirect
7. C5×#1285C2semidirect
11. C5×#474C4semidirect
12. C5×#474C4semidirect
13. C5×#461C4semidirect
14. C5×#461C4semidirect
33. #9165C5direct (N × H)
86. #1531C2×C5semidirect
87. #1503C2×C5semidirect
88. #1302C2×C5semidirect
89. #1285C2×C5semidirect
145. #474C4×C5semidirect
146. #474C4×C5semidirect
147. #461C4×C5semidirect
148. #461C4×C5semidirect
388. C5#9165direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31102
C5×#29742
C5×#17622
C5×#15312
C5×#15032
C5×#13022
C5×#12852
#91655