Finite Group Databasebeta

← C5×#9321 #11932041

Subgroups — C5×#9321 #11932041

Order 1280.

474 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3079C211yesmaximal, characteristic
2C5×#2989C211yesmaximal, characteristic
3C5×#1981C211yesmaximal, characteristic, complemented
4C5×#1806C211yesmaximal, characteristic
5C5×#1549C211yesmaximal, characteristic, complemented
6C5×#1303C211yesmaximal, characteristic, complemented
7C5×#1292C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C4×C5×#41C2211yescharacteristic
10C5×#477C412yescomplemented
11C5×#476C412yescomplemented
12C5×#475—21no—
13C5×#474—21no—
14C5×#446—21no—
15C5×#436—21no—
16C5×#435—22no—
17C5×#432—21no—
18C5×#431C2211yescharacteristic
19C5×#428—21no—
20C5×#423—21no—
21C5×#423C2211yescharacteristic
22C5×#423C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×#104—21no—
25C5×#417—21no—
26C2×C5×#103—22no—
27C4×C5×C4⋊C4C2211yescharacteristic
28C5×#339—21no—
29C5×#332—21no—
30C5×#332—21no—
31#9321C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41D411yescharacteristic
33C22×C5×Q8—21no—
34C2×C5×M16—21no—
35C2×C5×M16—22no—
36C2×C5×M16—21no—
37C22×C5×C8D412yes—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8C2×C412yes—
42C4×C5×Q8C2×C411yescharacteristic
43C4×C5×Q8D411yescharacteristic
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4C2×C411yescharacteristic
47C4×C5×D4D411yescharacteristic
48C5×#117—21no—
49C5×#117D411yescharacteristic
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C42×C5—21no—
54C2×C42×C5—21no—
55C2×C42×C5C2311yescharacteristic
56C5×#107—22no—
57C5×#106—22no—
58C5×C4⋊C8—22no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8C2×C412yes—
65C5×C4⋊C8D411yescharacteristic
66C5×C4⋊C8D411yescharacteristic
67C5×#104—42no—
68C5×#103—22no—
69C5×#103—44no—
70C5×#102—22no—
71C5×C22⋊C8—22no—
72C5×C22⋊C8—21no—
73C5×#97—22no—
74C4×C5×C8—21no—
75C5×#95—21no—
76#3079C2×C511yescharacteristic
77#2989C2×C511yescharacteristic
78#1981C2×C511yescharacteristic, complemented
79#1806C2×C511yescharacteristic
80#1549C2×C511yescharacteristic, complemented
81#1303C2×C511yescharacteristic, complemented
82#1292C2×C511yescharacteristic, complemented
83C5×#41—21no—
84C5×#41—21no—
85C5×#41—21no—
86C5×#41—21no—
87C2×C5×Q8—22no—
88C2×C5×Q8—42no—
89C2×C5×Q8—42no—
90C2×C5×Q8—41no—
91C2×C5×Q8C22⋊C411yescharacteristic
92C2×C5×D4—21no—
93C2×C5×D4C22⋊C411yescharacteristic
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5#4111yescharacteristic
102C5×M16—41no—
103C5×M16—41no—
104C5×M16—41no—
105C5×M16—41no—
106C5×M16—82no—
107C2×C5×C8—22no—
108C2×C5×C8—22no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C2×C5×C8—42no—
112C2×C5×C8—41no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—22no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4C22⋊C411yescharacteristic
122C5×C4⋊C4C22⋊C411yescharacteristic
123C5×C22⋊C4—21no—
124C5×C22⋊C4—21no—
125C5×C22⋊C4—21no—
126C42×C5—21no—
127C42×C5—21no—
128C42×C5—21no—
129C42×C5—41no—
130C42×C5—41no—
131C42×C5C22×C411yescharacteristic
132C42×C5C2×D411yescharacteristic
133C42×C5C2×D411yescharacteristic
134C42×C5#4111yescharacteristic
135C2×C4⋊Q8C22×C511yescharacteristic
136C4×#41C22×C511yescharacteristic
137#477C4×C512yescomplemented
138#476C4×C512yescomplemented
139#475—21no—
140#474—21no—
141#446—21no—
142#436—21no—
143#435—22no—
144#432—21no—
145#431C22×C511yescharacteristic
146#428—21no—
147#423—21no—
148#423C22×C511yescharacteristic
149#423C22×C511yescharacteristic
150C2×C4⋊C8C22×C511yescharacteristic
151C2×#104—21no—
152#417—21no—
153C2×#103—22no—
154C4×C4⋊C4C22×C511yescharacteristic
155#339—21no—
156#332—21no—
157#332—21no—
158C23×C5—21no—
159C23×C5#12111yescharacteristic
160C5×Q8—21no—
161C5×Q8—21no—
162C5×Q8—44no—
163C5×Q8—81no—
164C5×Q8—81no—
165C5×D4—21no—
166C5×D4—21no—
167C5×D4—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—42no—
181C2×C4×C5—81no—
182C2×C4×C5—81no—
183C2×C4×C5—82no—
184C2×C4×C5—81no—
185C2×C4×C5C2×C22⋊C411yescharacteristic
186C2×C4×C5C4×D411yescharacteristic
187C2×C4×C5C4×D411yescharacteristic
188C2×C4×C5#12011yescharacteristic
189C2×C4×C5#12111yescharacteristic
190C2×C4×C5#12311yescharacteristic
191C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C5#13711yescharacteristic
193C2×C4×C5#13711yescharacteristic
194C2×C4×C5#13711yescharacteristic
195C5×C8—42no—
196C5×C8—42no—
197C5×C8—41no—
198C5×C8—41no—
199C5×C8—81no—
200C2×#41C5×D411yescharacteristic
201C22×Q8—21no—
202C2×M16—21no—
203C2×M16—22no—
204C2×M16—21no—
205C22×C8C5×D412yes—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8C2×C4×C512yes—
210C4×Q8C2×C4×C511yescharacteristic
211C4×Q8C5×D411yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4C2×C4×C511yescharacteristic
215C4×D4C5×D411yescharacteristic
216#117—21no—
217#117C5×D411yescharacteristic
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42C23×C511yescharacteristic
224#107—22no—
225#106—22no—
226C4⋊C8—22no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8C2×C4×C512yes—
233C4⋊C8C5×D411yescharacteristic
234C4⋊C8C5×D411yescharacteristic
235#104—42no—
236#103—22no—
237#103—44no—
238#102—22no—
239C22⋊C8—22no—
240C22⋊C8—21no—
241#97—22no—
242C4×C8—21no—
243#95—21no—
244C22×C5—21no—
245C22×C5—21no—
246C22×C5—41no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5#38611yescharacteristic
250C22×C5#46811yescharacteristic
251C22×C5#47011yescharacteristic
252C4×C5—21no—
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—82no—
259C4×C5—82no—
260C4×C5#41711yescharacteristic
261C4×C5#41911yescharacteristic
262C4×C5#45311yescharacteristic
263C4×C5#45411yescharacteristic
264C4×C5#46811yescharacteristic
265C4×C5#47011yescharacteristic
266#41—21no—
267#41—21no—
268#41—21no—
269#41—21no—
270C2×Q8—22no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8C5×C22⋊C411yescharacteristic
275C2×D4—21no—
276C2×D4C5×C22⋊C411yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×C5×D411yescharacteristic
283C22×C4C2×C5×D411yescharacteristic
284C22×C4C5×#4111yescharacteristic
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289M16—82no—
290C2×C8—22no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—42no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C5×C22⋊C411yescharacteristic
305C4⋊C4C5×C22⋊C411yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C42—21no—
310C42—21no—
311C42—21no—
312C42—41no—
313C42—41no—
314C42C22×C4×C511yescharacteristic
315C42C2×C5×D411yescharacteristic
316C42C2×C5×D411yescharacteristic
317C42C5×#4111yescharacteristic
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—81no—
321C2×C5#188311yescharacteristic
322C2×C5#189411yescharacteristic
323C2×C5#190211yescharacteristic
324C23—21no—
325C23C5×#12111yescharacteristic
326Q8—21no—
327Q8—21no—
328Q8—44no—
329Q8—81no—
330Q8—81no—
331D4—21no—
332D4—21no—
333D4—41no—
334D4—41no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4C2×C5×C22⋊C411yescharacteristic
352C2×C4C4×C5×D411yescharacteristic
353C2×C4C4×C5×D411yescharacteristic
354C2×C4C5×#12011yescharacteristic
355C2×C4C5×#12111yescharacteristic
356C2×C4C5×#12311yescharacteristic
357C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
358C2×C4C5×#13711yescharacteristic
359C2×C4C5×#13711yescharacteristic
360C2×C4C5×#13711yescharacteristic
361C8—42no—
362C8—42no—
363C8—41no—
364C8—41no—
365C8—81no—
366C5#932111yescharacteristic, direct product factor, Sylow
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22C5×#38611yescharacteristic
373C22C5×#46811yescharacteristic
374C22C5×#47011yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—82no—
382C4—82no—
383C4C5×#41711yescharacteristic
384C4C5×#41911yescharacteristic
385C4C5×#45311yescharacteristic
386C4C5×#45411yescharacteristic
387C4C5×#46811yescharacteristic
388C4C5×#47011yescharacteristic
389C2—21no—
390C2—21no—
391C2—81no—
392C2C5×#188311yescharacteristic
393C2C5×#189411yescharacteristic
394C2C5×#190211yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#41D4
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
3. C5×#1981C2semidirect
5. C5×#1549C2semidirect
6. C5×#1303C2semidirect
7. C5×#1292C2semidirect
10. C5×#477C4semidirect
11. C5×#476C4semidirect
31. #9321C5direct (N × H)
78. #1981C2×C5semidirect
80. #1549C2×C5semidirect
81. #1303C2×C5semidirect
82. #1292C2×C5semidirect
137. #477C4×C5semidirect
138. #476C4×C5semidirect
366. C5#9321direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30792
C5×#29892
C5×#19812
C5×#18062
C5×#15492
C5×#13032
C5×#12922
#93215