Finite Group Databasebeta

← C5×#18531 #11941251

Subgroups — C5×#18531 #11941251

Order 1280.

982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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×#559C211yesmaximal, characteristic
2C5×#3138C211yesmaximal, characteristic
3C5×#3113C212yesmaximal, complemented
4C5×#1640C218yesmaximal, complemented
5C5×#1555C211yesmaximal, characteristic
6C5×#1491C212yesmaximal, complemented
7C5×#559—22no—
8C5×#559—24no—
9C5×#559C2214yes—
10C5×#533C2211yescharacteristic
11C2×C5×#127C2211yescharacteristic
12C2×C5×#124—22no—
13C2×C5×#123—22no—
14C2×C4×C5×Q8C2212yes—
15C2×C4×C5×D4—22no—
16C5×#490—22no—
17C5×#486C2214yes—
18C5×#483—22no—
19C5×#475C2214yescomplemented
20C5×#462C2214yescomplemented
21C5×#451—22no—
22C5×#441—24no—
23C5×#432C2212yes—
24C5×#418—22no—
25C4×C5×M16C2211yescharacteristic
26C5×#331C2214yes—
27C5×Q8⋊C8C2218yescomplemented
28#18531C511yesmaximal, characteristic, direct product factor, Sylow
29C22×C5×Q8D412yes—
30C22×C5×D4—22no—
31C22×C5×D4D412yes—
32C23×C4×C5—22no—
33C2×C5×Q16—24no—
34C2×C5×M16—21no—
35C5×C4⋊Q8C2312yes—
36C5×#127—22no—
37C5×#127D412yes—
38C5×#127C2312yes—
39C5×#125—21no—
40C5×#124—28no—
41C5×#124—28no—
42C5×#123—28no—
43C5×#123—28no—
44C5×C22⋊Q8—22no—
45C4×C5×Q8—22no—
46C4×C5×Q8—22no—
47C4×C5×Q8—22no—
48C4×C5×Q8D414yes—
49C4×C5×Q8C2314yes—
50C4×C5×D4—28no—
51C4×C5×D4—28no—
52C5×#117—21no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4D412yes—
55C2×C5×C22⋊C4—24no—
56C2×C5×C22⋊C4—22no—
57C2×C42×C5—22no—
58C2×C42×C5C2311yescharacteristic
59C5×#106—24no—
60C5×C4⋊C8C2314yes—
61C5×#103—24no—
62C5×#103—24no—
63C5×#102—28no—
64C5×C22⋊C8—22no—
65C5×#97—21no—
66C5×#97—22no—
67C4×C5×C8C2312yes—
68C2×#559C2×C511yescharacteristic
69#3138C2×C511yescharacteristic
70#3113C2×C512yescomplemented
71#1640C2×C518yescomplemented
72#1555C2×C511yescharacteristic
73#1491C2×C512yescomplemented
74C24×C5—22no—
75C2×C5×Q8—22no—
76C2×C5×Q8—22no—
77C2×C5×Q8—44no—
78C2×C5×Q8C2×D414yes—
79C2×C5×D4—24no—
80C2×C5×D4—22no—
81C2×C5×D4—24no—
82C2×C5×D4—48no—
83C2×C5×D4—44no—
84C2×C5×D4C2×D414yes—
85C22×C4×C5—22no—
86C22×C4×C5—22no—
87C22×C4×C5—28no—
88C22×C4×C5—84no—
89C22×C4×C5C2×D412yes—
90C22×C4×C5C2×D411yescharacteristic
91C5×Q16—48no—
92C5×M16—42no—
93C2×C5×C8—22no—
94C2×C5×C8—24no—
95C5×C4⋊C4—24no—
96C5×C4⋊C4—22no—
97C5×C4⋊C4—24no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4—42no—
101C5×C4⋊C4C2×D414yes—
102C5×C22⋊C4—216no—
103C5×C22⋊C4—28no—
104C5×C22⋊C4—41no—
105C42×C5—24no—
106C42×C5—24no—
107C42×C5—41no—
108C42×C5C2×D412yes—
109C42×C5C2×D411yescharacteristic
110C42×C5C2411yescharacteristic
111#559—22no—
112#559—24no—
113#559C22×C514yes—
114#533C22×C511yescharacteristic
115C2×#127C22×C511yescharacteristic
116C2×#124—22no—
117C2×#123—22no—
118C2×C4×Q8C22×C512yes—
119C2×C4×D4—22no—
120#490—22no—
121#486C22×C514yes—
122#483—22no—
123#475C22×C514yescomplemented
124#462C22×C514yescomplemented
125#451—22no—
126#441—24no—
127#432C22×C512yes—
128#418—22no—
129C4×M16C22×C511yescharacteristic
130#331C22×C514yes—
131Q8⋊C8C22×C518yescomplemented
132C23×C5—24no—
133C23×C5—48no—
134C23×C5—44no—
135C23×C5#12011yescharacteristic
136C5×Q8—24no—
137C5×Q8—24no—
138C5×Q8—44no—
139C5×Q8—44no—
140C5×D4—44no—
141C5×D4—48no—
142C5×D4—48no—
143C5×D4—82no—
144C2×C4×C5—22no—
145C2×C4×C5—24no—
146C2×C4×C5—24no—
147C2×C4×C5—24no—
148C2×C4×C5—44no—
149C2×C4×C5—44no—
150C2×C4×C5—42no—
151C2×C4×C5—88no—
152C2×C4×C5#12012yes—
153C2×C4×C5#12011yescharacteristic
154C2×C4×C5C22×D411yescharacteristic
155C2×C4×C5C22×D412yes—
156C5×C8—42no—
157C5×C8—44no—
158C22×Q8C5×D412yes—
159C22×D4—22no—
160C22×D4C5×D412yes—
161C23×C4—22no—
162C2×Q16—24no—
163C2×M16—21no—
164C4⋊Q8C23×C512yes—
165#127—22no—
166#127C5×D412yes—
167#127C23×C512yes—
168#125—21no—
169#124—28no—
170#124—28no—
171#123—28no—
172#123—28no—
173C22⋊Q8—22no—
174C4×Q8—22no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×Q8C5×D414yes—
178C4×Q8C23×C514yes—
179C4×D4—28no—
180C4×D4—28no—
181#117—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4C5×D412yes—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—22no—
186C2×C42—22no—
187C2×C42C23×C511yescharacteristic
188#106—24no—
189C4⋊C8C23×C514yes—
190#103—24no—
191#103—24no—
192#102—28no—
193C22⋊C8—22no—
194#97—21no—
195#97—22no—
196C4×C8C23×C512yes—
197C22×C5—22no—
198C22×C5—48no—
199C22×C5—44no—
200C22×C5—88no—
201C22×C5#45512yes—
202C22×C5C2×#12011yescharacteristic
203C4×C5—22no—
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—44no—
207C4×C5—44no—
208C4×C5—82no—
209C4×C5#57514yes—
210C24—22no—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—44no—
214C2×Q8C2×C5×D414yes—
215C2×D4—24no—
216C2×D4—22no—
217C2×D4—24no—
218C2×D4—48no—
219C2×D4—44no—
220C2×D4C2×C5×D414yes—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—28no—
224C22×C4—84no—
225C22×C4C2×C5×D412yes—
226C22×C4C2×C5×D411yescharacteristic
227Q16—48no—
228M16—42no—
229C2×C8—22no—
230C2×C8—24no—
231C4⋊C4—24no—
232C4⋊C4—22no—
233C4⋊C4—24no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4C2×C5×D414yes—
238C22⋊C4—216no—
239C22⋊C4—28no—
240C22⋊C4—41no—
241C42—24no—
242C42—24no—
243C42—41no—
244C42C2×C5×D412yes—
245C42C2×C5×D411yescharacteristic
246C42C24×C511yescharacteristic
247C2×C5—22no—
248C2×C5—84no—
249C2×C5#300512yes—
250C2×C5C2×#45511yescharacteristic
251C23—24no—
252C23—48no—
253C23—44no—
254C23C5×#12011yescharacteristic
255Q8—24no—
256Q8—24no—
257Q8—44no—
258Q8—44no—
259D4—44no—
260D4—48no—
261D4—48no—
262D4—82no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—88no—
271C2×C4C5×#12012yes—
272C2×C4C5×#12011yescharacteristic
273C2×C4C22×C5×D411yescharacteristic
274C2×C4C22×C5×D412yes—
275C8—42no—
276C8—44no—
277C5#1853111yescharacteristic, direct product factor, Sylow
278C22—22no—
279C22—48no—
280C22—44no—
281C22—88no—
282C22C5×#45512yes—
283C22C2×C5×#12011yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—44no—
288C4—44no—
289C4—82no—
290C4C5×#57514yes—
291C2—22no—
292C2—84no—
293C2C5×#300512yes—
294C2C2×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC2×C5×#127C22
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×#3113C2semidirect
4. C5×#1640C2semidirect
6. C5×#1491C2semidirect
19. C5×#475C22semidirect
20. C5×#462C22semidirect
27. C5×Q8⋊C8C22semidirect
28. #18531C5direct (N × H)
70. #3113C2×C5semidirect
71. #1640C2×C5semidirect
73. #1491C2×C5semidirect
123. #475C22×C5semidirect
124. #462C22×C5semidirect
131. Q8⋊C8C22×C5semidirect
277. C5#18531direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5592
C5×#31382
C5×#31132
C5×#16402
C5×#15552
C5×#14912
#185315