Finite Group Databasebeta

← C5×#18529 #11941249

Subgroups — C5×#18529 #11941249

Order 1280.

1630 conjugacy classes of subgroups; only the 246 normal subgroups are shown.

normal subgroups only

This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D42C211yesmaximal, characteristic
2C5×#3138C211yesmaximal, characteristic, complemented
3C5×#3110C212yesmaximal, complemented
4C5×#1639C218yesmaximal, complemented
5C5×#1555C211yesmaximal, characteristic, complemented
6C5×#1490C212yesmaximal, complemented
7C23×C5×D4—22no—
8C5×D42—22no—
9C5×D42—24no—
10C5×D42C2214yes—
11C5×#533C2211yescharacteristic, complemented
12C2×C5×#127C2211yescharacteristic
13C2×C5×#121—22no—
14C2×C5×#120—22no—
15C2×C4×C5×D4C2212yes—
16C5×#490—22no—
17C5×#486C2214yescomplemented
18C5×#484—22no—
19C5×#474C2214yescomplemented
20C5×#461C2214yescomplemented
21C5×#450—22no—
22C5×#440—24no—
23C5×#432C2212yescomplemented
24C5×#418—22no—
25C4×C5×M16C2211yescharacteristic, complemented
26C5×#331C2214yescomplemented
27C5×D4⋊C8C2218yescomplemented
28#18529C511yesmaximal, characteristic, direct product factor, Sylow
29C25×C5—22no—
30C22×C5×D4—24no—
31C22×C5×D4—28no—
32C22×C5×D4—28no—
33C22×C5×D4—22no—
34C22×C5×D4—416no—
35C22×C5×D4D412yes—
36C22×C5×D4D412yes—
37C23×C4×C5—22no—
38C2×C5×SD16—24no—
39C2×C5×M16—21no—
40C5×C4⋊Q8C2312yescomplemented
41C5×#127—22no—
42C5×#127D412yes—
43C5×#127C2312yes—
44C5×#125—21no—
45C5×C22⋊Q8—22no—
46C5×#121—28no—
47C5×#121—28no—
48C5×#120—28no—
49C5×#120—28no—
50C4×C5×Q8—22no—
51C4×C5×D4—22no—
52C4×C5×D4—22no—
53C4×C5×D4D414yes—
54C4×C5×D4C2314yes—
55C5×#117—21no—
56C2×C5×C4⋊C4D412yes—
57C2×C5×C22⋊C4—22no—
58C2×C5×C22⋊C4—22no—
59C2×C42×C5C2311yescharacteristic
60C5×#107—24no—
61C5×C4⋊C8C2314yescomplemented
62C5×#103—24no—
63C5×#102—28no—
64C5×#102—24no—
65C5×C22⋊C8—22no—
66C5×#97—21no—
67C5×#97—22no—
68C4×C5×C8C2312yescomplemented
69C2×D42C2×C511yescharacteristic
70#3138C2×C511yescharacteristic, complemented
71#3110C2×C512yescomplemented
72#1639C2×C518yescomplemented
73#1555C2×C511yescharacteristic, complemented
74#1490C2×C512yescomplemented
75C24×C5—22no—
76C24×C5—28no—
77C24×C5—22no—
78C24×C5—416no—
79C24×C5—84no—
80C2×C5×Q8—22no—
81C2×C5×D4—28no—
82C2×C5×D4—216no—
83C2×C5×D4—22no—
84C2×C5×D4—24no—
85C2×C5×D4—22no—
86C2×C5×D4—24no—
87C2×C5×D4—48no—
88C2×C5×D4—44no—
89C2×C5×D4—432no—
90C2×C5×D4—416no—
91C2×C5×D4—416no—
92C2×C5×D4—416no—
93C2×C5×D4C2×D414yes—
94C2×C5×D4C2×D414yes—
95C22×C4×C5—22no—
96C22×C4×C5—24no—
97C22×C4×C5—24no—
98C22×C4×C5—48no—
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5C2×D412yes—
101C5×SD16—48no—
102C5×M16—42no—
103C2×C5×C8—22no—
104C2×C5×C8—24no—
105C5×C4⋊C4—22no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—42no—
109C5×C4⋊C4C2×D414yes—
110C5×C22⋊C4—28no—
111C5×C22⋊C4—24no—
112C5×C22⋊C4—24no—
113C5×C22⋊C4—41no—
114C42×C5—41no—
115C42×C5C2×D411yescharacteristic
116C42×C5C2×D412yes—
117C42×C5C2411yescharacteristic
118C23×D4—22no—
119D42—22no—
120D42—24no—
121D42C22×C514yes—
122#533C22×C511yescharacteristic, complemented
123C2×#127C22×C511yescharacteristic
124C2×#121—22no—
125C2×#120—22no—
126C2×C4×D4C22×C512yes—
127#490—22no—
128#486C22×C514yescomplemented
129#484—22no—
130#474C22×C514yescomplemented
131#461C22×C514yescomplemented
132#450—22no—
133#440—24no—
134#432C22×C512yescomplemented
135#418—22no—
136C4×M16C22×C511yescharacteristic, complemented
137#331C22×C514yescomplemented
138D4⋊C8C22×C518yescomplemented
139C23×C5—28no—
140C23×C5—24no—
141C23×C5—24no—
142C23×C5—44no—
143C23×C5—48no—
144C23×C5—432no—
145C23×C5—44no—
146C23×C5—44no—
147C23×C5—88no—
148C23×C5—832no—
149C23×C5#12011yescharacteristic
150C5×Q8—44no—
151C5×D4—28no—
152C5×D4—24no—
153C5×D4—44no—
154C5×D4—48no—
155C5×D4—432no—
156C5×D4—48no—
157C5×D4—82no—
158C5×D4AGL(1,ℤ/8)18yes—
159C2×C4×C5—22no—
160C2×C4×C5—24no—
161C2×C4×C5—24no—
162C2×C4×C5—48no—
163C2×C4×C5—44no—
164C2×C4×C5—48no—
165C2×C4×C5—42no—
166C2×C4×C5#12011yescharacteristic
167C2×C4×C5#12012yes—
168C2×C4×C5C22×D411yescharacteristic
169C2×C4×C5C22×D412yes—
170C5×C8—42no—
171C5×C8—44no—
172C25—22no—
173C22×D4—24no—
174C22×D4—28no—
175C22×D4—28no—
176C22×D4—22no—
177C22×D4—416no—
178C22×D4C5×D412yes—
179C22×D4C5×D412yes—
180C23×C4—22no—
181C2×SD16—24no—
182C2×M16—21no—
183C4⋊Q8C23×C512yescomplemented
184#127—22no—
185#127C5×D412yes—
186#127C23×C512yes—
187#125—21no—
188C22⋊Q8—22no—
189#121—28no—
190#121—28no—
191#120—28no—
192#120—28no—
193C4×Q8—22no—
194C4×D4—22no—
195C4×D4—22no—
196C4×D4C5×D414yes—
197C4×D4C23×C514yes—
198#117—21no—
199C2×C4⋊C4C5×D412yes—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C42C23×C511yescharacteristic
203#107—24no—
204C4⋊C8C23×C514yescomplemented
205#103—24no—
206#102—28no—
207#102—24no—
208C22⋊C8—22no—
209#97—21no—
210#97—22no—
211C4×C8C23×C512yescomplemented
212C22×C5—22no—
213C22×C5—28no—
214C22×C5—416no—
215C22×C5—44no—
216C22×C5—44no—
217C22×C5—48no—
218C22×C5—44no—
219C22×C5—88no—
220C22×C5—832no—
221C22×C5#45512yes—
222C22×C5C2×#12011yescharacteristic
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—44no—
227C4×C5—82no—
228C4×C5C2×AGL(1,ℤ/8)14yes—
229C24—22no—
230C24—28no—
231C24—22no—
232C24—416no—
233C24—84no—
234C2×Q8—22no—
235C2×D4—28no—
236C2×D4—216no—
237C2×D4—22no—
238C2×D4—24no—
239C2×D4—22no—
240C2×D4—24no—
241C2×D4—48no—
242C2×D4—44no—
243C2×D4—432no—
244C2×D4—416no—
245C2×D4—416no—
246C2×D4—416no—
247C2×D4C2×C5×D414yes—
248C2×D4C2×C5×D414yes—
249C22×C4—22no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—48no—
253C22×C4C2×C5×D412yes—
254C22×C4C2×C5×D411yescharacteristic
255SD16—48no—
256M16—42no—
257C2×C8—22no—
258C2×C8—24no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—42no—
263C4⋊C4C2×C5×D414yes—
264C22⋊C4—28no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C22⋊C4—41no—
268C42—41no—
269C42C2×C5×D411yescharacteristic
270C42C2×C5×D412yes—
271C42C24×C511yescharacteristic
272C2×C5—22no—
273C2×C5—48no—
274C2×C5—84no—
275C2×C5#300312yes—
276C2×C5C2×#45511yescharacteristic
277C23—28no—
278C23—24no—
279C23—24no—
280C23—44no—
281C23—48no—
282C23—432no—
283C23—44no—
284C23—44no—
285C23—88no—
286C23—832no—
287C23C5×#12011yescharacteristic
288Q8—44no—
289D4—28no—
290D4—24no—
291D4—44no—
292D4—48no—
293D4—432no—
294D4—48no—
295D4—82no—
296D4C5×AGL(1,ℤ/8)18yes—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—48no—
303C2×C4—42no—
304C2×C4C5×#12011yescharacteristic
305C2×C4C5×#12012yes—
306C2×C4C22×C5×D411yescharacteristic
307C2×C4C22×C5×D412yes—
308C8—42no—
309C8—44no—
310C5#1852911yescharacteristic, direct product factor, Sylow
311C22—22no—
312C22—28no—
313C22—416no—
314C22—44no—
315C22—44no—
316C22—48no—
317C22—44no—
318C22—88no—
319C22—832no—
320C22C5×#45512yes—
321C22C2×C5×#12011yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—44no—
326C4—82no—
327C4C2×C5×AGL(1,ℤ/8)14yes—
328C2—22no—
329C2—48no—
330C2—84no—
331C2C5×#300312yes—
332C2C2×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC2×C5×D42C2
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
2. C5×#3138C2semidirect
3. C5×#3110C2semidirect
4. C5×#1639C2semidirect
5. C5×#1555C2semidirect
6. C5×#1490C2semidirect
11. C5×#533C22semidirect
17. C5×#486C22semidirect
19. C5×#474C22semidirect
20. C5×#461C22semidirect
23. C5×#432C22semidirect
25. C4×C5×M16C22semidirect
26. C5×#331C22semidirect
27. C5×D4⋊C8C22semidirect
28. #18529C5direct (N × H)
40. C5×C4⋊Q8C23semidirect
61. C5×C4⋊C8C23semidirect
68. C4×C5×C8C23semidirect
70. #3138C2×C5semidirect
71. #3110C2×C5semidirect
72. #1639C2×C5semidirect
73. #1555C2×C5semidirect
74. #1490C2×C5semidirect
122. #533C22×C5semidirect
128. #486C22×C5semidirect
130. #474C22×C5semidirect
131. #461C22×C5semidirect
134. #432C22×C5semidirect
136. C4×M16C22×C5semidirect
137. #331C22×C5semidirect
138. D4⋊C8C22×C5semidirect
183. C4⋊Q8C23×C5semidirect
204. C4⋊C8C23×C5semidirect
211. C4×C8C23×C5semidirect
310. C5#18529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×D422
C5×#31382
C5×#31102
C5×#16392
C5×#15552
C5×#14902
#185295