Finite Group Databasebeta

← C5×#9482 #11932202

Subgroups — C5×#9482 #11932202

Order 1280.

518 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C5×#2484C211yesmaximal, characteristic
2C5×#2313C211yesmaximal, characteristic
3C5×#1826C212yesmaximal
4C5×#1463C211yesmaximal, characteristic
5C5×#1284C212yesmaximal
6C2×C5×#117C2211yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C5×#407C2212yes—
9C5×#400C412yescomplemented
10C5×#398C412yescomplemented
11C5×#387—22no—
12C5×#387—24no—
13C5×#385—21no—
14C5×#381—21no—
15C5×#381—21no—
16C5×#381C2211yescharacteristic
17C5×#380—21no—
18C4×C5×C22⋊C4C2212yes—
19C5×#339—24no—
20C5×#324—22no—
21#9482C511yesmaximal, characteristic, direct product factor, Sylow
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C2×C5×M16—22no—
26C5×#117—22no—
27C5×#117—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4C2×C412yes—
35C2×C5×C4⋊C4D412yes—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C42×C5—21no—
40C2×C42×C5D414yes—
41C5×C22⋊C8—22no—
42C5×C22⋊C8—22no—
43C5×#95—22no—
44C5×#95—24no—
45C5×#95—22no—
46C5×#95—22no—
47C5×#95—22no—
48C5×#95—22no—
49C5×#95—21no—
50C5×#95C2×C412yes—
51#2484C2×C511yescharacteristic
52#2313C2×C511yescharacteristic
53#1826C2×C512yes—
54#1463C2×C511yescharacteristic
55#1284C2×C512yes—
56C24×C5C2×D411yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—22no—
64C22×C4×C5—24no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5—42no—
68C22×C4×C5C22⋊C412yes—
69C22×C4×C5C22⋊C412yes—
70C22×C4×C5C22×C411yescharacteristic
71C22×C4×C5C2×D412yes—
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5#4112yes—
74C5×M16—44no—
75C2×C5×C8—42no—
76C5×C4⋊C4—24no—
77C5×C4⋊C4—24no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4—44no—
81C5×C4⋊C4—82no—
82C5×C22⋊C4—44no—
83C5×C22⋊C4—42no—
84C5×C22⋊C4—41no—
85C5×C22⋊C4—41no—
86C42×C5—44no—
87C42×C5—42no—
88C2×#117C22×C511yescharacteristic
89C22×C4⋊C4C22×C511yescharacteristic
90#407C22×C512yes—
91#400C4×C512yescomplemented
92#398C4×C512yescomplemented
93#387—22no—
94#387—24no—
95#385—21no—
96#381—21no—
97#381—21no—
98#381C22×C511yescharacteristic
99#380—21no—
100C4×C22⋊C4C22×C512yes—
101#339—24no—
102#324—22no—
103C23×C5—22no—
104C23×C5—22no—
105C23×C5—41no—
106C23×C5C2×C22⋊C411yescharacteristic
107C23×C5#12011yescharacteristic
108C23×C5#12311yescharacteristic
109C2×C4×C5—24no—
110C2×C4×C5—22no—
111C2×C4×C5—22no—
112C2×C4×C5—22no—
113C2×C4×C5—22no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—44no—
123C2×C4×C5—42no—
124C2×C4×C5—44no—
125C2×C4×C5—42no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—44no—
131C2×C4×C5—81no—
132C2×C4×C5C4×D412yes—
133C2×C4×C5#12112yes—
134C5×C8—82no—
135C23×C4C5×D411yescharacteristic
136C23×C4C5×D411yescharacteristic
137C23×C4C23×C511yescharacteristic
138C2×M16—22no—
139#117—22no—
140#117—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4C2×C4×C511yescharacteristic
146C2×C4⋊C4C2×C4×C511yescharacteristic
147C2×C4⋊C4C2×C4×C512yes—
148C2×C4⋊C4C5×D412yes—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—21no—
152C2×C42—21no—
153C2×C42C5×D414yes—
154C22⋊C8—22no—
155C22⋊C8—22no—
156#95—22no—
157#95—24no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162#95—21no—
163#95C2×C4×C512yes—
164C22×C5—21no—
165C22×C5—21no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—44no—
172C22×C5#38611yescharacteristic
173C22×C5#42112yes—
174C22×C5#45812yes—
175C4×C5—22no—
176C4×C5—22no—
177C4×C5—42no—
178C4×C5—42no—
179C4×C5—84no—
180C4×C5—82no—
181C4×C5—81no—
182C4×C5—81no—
183C24C2×C5×D411yescharacteristic
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—24no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4C5×C22⋊C412yes—
196C22×C4C5×C22⋊C412yes—
197C22×C4C22×C4×C511yescharacteristic
198C22×C4C2×C5×D412yes—
199C22×C4C2×C5×D411yescharacteristic
200C22×C4C5×#4112yes—
201M16—44no—
202C2×C8—42no—
203C4⋊C4—24no—
204C4⋊C4—24no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—44no—
208C4⋊C4—82no—
209C22⋊C4—44no—
210C22⋊C4—42no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C42—44no—
214C42—42no—
215C2×C5—22no—
216C2×C5—22no—
217C2×C5—41no—
218C2×C5#189011yescharacteristic
219C2×C5#189711yescharacteristic
220C2×C5#191211yescharacteristic
221C23—22no—
222C23—22no—
223C23—41no—
224C23C2×C5×C22⋊C411yescharacteristic
225C23C5×#12011yescharacteristic
226C23C5×#12311yescharacteristic
227C2×C4—24no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—44no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—81no—
250C2×C4C4×C5×D412yes—
251C2×C4C5×#12112yes—
252C8—82no—
253C5#948211yescharacteristic, direct product factor, Sylow
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22C5×#38611yescharacteristic
263C22C5×#42112yes—
264C22C5×#45812yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—84no—
270C4—82no—
271C4—81no—
272C4—81no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2C5×#189011yescharacteristic
277C2C5×#189711yescharacteristic
278C2C5×#191211yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
9. C5×#400C4semidirect
10. C5×#398C4semidirect
21. #9482C5direct (N × H)
91. #400C4×C5semidirect
92. #398C4×C5semidirect
253. C5#9482direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24842
C5×#23132
C5×#18262
C5×#14632
C5×#12842
#94825