Finite Group Databasebeta

← C5×#11448 #11934168

Subgroups — C5×#11448 #11934168

Order 1280.

454 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2317C211yesmaximal, characteristic
2C2×C5×#324C212yesmaximal
3C5×#1325C212yesmaximal, complemented
4C5×#1324C212yesmaximal, complemented
5C2×C5×#117C411yescharacteristic
6C2×C5×#117C411yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C2×C5×C22⋊C8—22no—
9C5×#389—22no—
10C5×#385—22no—
11C5×#384C411yescharacteristic
12C5×#384C2211yescharacteristic
13C5×#382C411yescharacteristic
14C5×#382C2211yescharacteristic
15C5×#324—22no—
16C5×#324C2214yes—
17#11448C511yesmaximal, characteristic, direct product factor, Sylow
18C23×C4×C5C2×C411yescharacteristic
19C23×C4×C5D412yes—
20C22×C5×C8—42no—
21C5×#117—22no—
22C5×#117—42no—
23C5×#117C814yescomplemented
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4—22no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—42no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4D412yes—
32C2×C5×C4⋊C4C2311yescharacteristic
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—21no—
35C2×C42×C5—21no—
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C5×C22⋊C8—24no—
39C5×C22⋊C8—42no—
40C5×#95—22no—
41C5×#95—22no—
42#2317C2×C511yescharacteristic
43C2×#324C2×C512yes—
44#1325C2×C512yescomplemented
45#1324C2×C512yescomplemented
46C24×C5C22⋊C411yescharacteristic
47C22×C4×C5—22no—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5—22no—
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—82no—
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22⋊C412yes—
58C22×C4×C5C2×C812yes—
59C22×C4×C5M1612yes—
60C22×C4×C5C22×C411yescharacteristic
61C22×C4×C5C2×D412yes—
62C2×C5×C8—44no—
63C2×C5×C8—84no—
64C5×C4⋊C4—24no—
65C5×C4⋊C4—41no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—41no—
68C5×C4⋊C4—41no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—82no—
71C5×C4⋊C4—82no—
72C5×C22⋊C4—24no—
73C5×C22⋊C4—42no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—42no—
77C42×C5C2×C812yescomplemented
78C42×C5C2×C812yescomplemented
79C2×#117C4×C511yescharacteristic
80C2×#117C4×C511yescharacteristic
81C22×C4⋊C4C22×C511yescharacteristic
82C2×C22⋊C8—22no—
83#389—22no—
84#385—22no—
85#384C4×C511yescharacteristic
86#384C22×C511yescharacteristic
87#382C4×C511yescharacteristic
88#382C22×C511yescharacteristic
89#324—22no—
90#324C22×C514yes—
91C23×C5—41no—
92C23×C5—41no—
93C23×C5C22⋊C812yes—
94C23×C5#9912yes—
95C23×C5#10112yes—
96C23×C5C2×C22⋊C411yescharacteristic
97C2×C4×C5—24no—
98C2×C4×C5—24no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—44no—
110C2×C4×C5—41no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—82no—
119C2×C4×C5C22⋊C812yes—
120C2×C4×C5C22×C811yescharacteristic
121C2×C4×C5C2×M1611yescharacteristic
122C5×C8—84no—
123C23×C4C2×C4×C511yescharacteristic
124C23×C4C5×D412yes—
125C22×C8—42no—
126#117—22no—
127#117—42no—
128#117C5×C814yescomplemented
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4C2×C4×C511yescharacteristic
134C2×C4⋊C4C2×C4×C511yescharacteristic
135C2×C4⋊C4C2×C4×C511yescharacteristic
136C2×C4⋊C4C5×D412yes—
137C2×C4⋊C4C23×C511yescharacteristic
138C2×C22⋊C4—21no—
139C2×C22⋊C4—21no—
140C2×C42—21no—
141C2×C42C2×C4×C511yescharacteristic
142C2×C42C2×C4×C511yescharacteristic
143C22⋊C8—24no—
144C22⋊C8—42no—
145#95—22no—
146#95—22no—
147C22×C5—21no—
148C22×C5—22no—
149C22×C5—21no—
150C22×C5—22no—
151C22×C5—42no—
152C22×C5—42no—
153C22×C5#32414yes—
154C22×C5C2×C22⋊C811yescharacteristic
155C22×C5C2×#9911yescharacteristic
156C22×C5C2×#10111yescharacteristic
157C4×C5—22no—
158C4×C5—21no—
159C4×C5—21no—
160C4×C5—42no—
161C4×C5—42no—
162C4×C5—42no—
163C4×C5—42no—
164C4×C5—81no—
165C4×C5—81no—
166C24C5×C22⋊C411yescharacteristic
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—82no—
176C22×C4C5×C22⋊C411yescharacteristic
177C22×C4C5×C22⋊C412yes—
178C22×C4C2×C5×C812yes—
179C22×C4C5×M1612yes—
180C22×C4C22×C4×C511yescharacteristic
181C22×C4C2×C5×D412yes—
182C2×C8—44no—
183C2×C8—84no—
184C4⋊C4—24no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C22⋊C4—24no—
193C22⋊C4—42no—
194C42—21no—
195C42—21no—
196C42—42no—
197C42C2×C5×C812yescomplemented
198C42C2×C5×C812yescomplemented
199C2×C5—21no—
200C2×C5—24no—
201C2×C5—21no—
202C2×C5C2×#32411yescharacteristic
203C2×C5#212711yescharacteristic
204C2×C5#213311yescharacteristic
205C23—41no—
206C23—41no—
207C23C5×C22⋊C812yes—
208C23C5×#9912yes—
209C23C5×#10112yes—
210C23C2×C5×C22⋊C411yescharacteristic
211C2×C4—24no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—44no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—82no—
233C2×C4C5×C22⋊C812yes—
234C2×C4C22×C5×C811yescharacteristic
235C2×C4C2×C5×M1611yescharacteristic
236C8—84no—
237C5#1144811yescharacteristic, direct product factor, Sylow
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22C5×#32414yes—
245C22C2×C5×C22⋊C811yescharacteristic
246C22C2×C5×#9911yescharacteristic
247C22C2×C5×#10111yescharacteristic
248C4—21no—
249C4—21no—
250C4—22no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—24no—
259C2—21no—
260C2C2×C5×#32411yescharacteristic
261C2C5×#212711yescharacteristic
262C2C5×#213311yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC2×C4C22×C5×C8
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1325C2semidirect
4. C5×#1324C2semidirect
17. #11448C5direct (N × H)
23. C5×#117C8semidirect
44. #1325C2×C5semidirect
45. #1324C2×C5semidirect
77. C42×C5C2×C8semidirect
78. C42×C5C2×C8semidirect
128. #117C5×C8semidirect
197. C42C2×C5×C8semidirect
198. C42C2×C5×C8semidirect
237. C5#11448direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23172
C2×C5×#3242
C5×#13252
C5×#13242
#114485