Finite Group Databasebeta

← C5×#11452 #11934172

Subgroups — C5×#11452 #11934172

Order 1280.

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

normal subgroups only

This group has 462 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×#2296C211yesmaximal, characteristic
2C5×#1458C212yesmaximal
3C5×#1326C214yesmaximal
4C2×C5×#117C411yescharacteristic
5C2×C5×#117C2211yescharacteristic
6C22×C42×C5C411yescharacteristic
7C5×#431—22no—
8C5×#389—22no—
9C5×#385C412yes—
10C5×#385C2212yes—
11C4×C5×C4⋊C4—22no—
12C5×#324—22no—
13C5×#323C2214yes—
14#11452C511yesmaximal, characteristic, direct product factor, Sylow
15C23×C4×C5C2×C411yescharacteristic
16C23×C4×C5C2×C412yes—
17C5×#117—22no—
18C5×#117—41no—
19C5×#117—41no—
20C5×#117C814yescomplemented
21C2×C5×C4⋊C4—21no—
22C2×C5×C4⋊C4—22no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4D412yes—
25C2×C5×C22⋊C4C2×C412yes—
26C2×C5×C22⋊C4C2×C411yescharacteristic
27C2×C5×C22⋊C4C2311yescharacteristic
28C2×C42×C5—21no—
29C2×C42×C5—21no—
30C2×C42×C5—21no—
31C2×C42×C5—41no—
32C2×C42×C5—41no—
33C2×C42×C5D412yes—
34C5×C4⋊C8—42no—
35C5×C22⋊C8—24no—
36C4×C5×C8—42no—
37C5×#95—22no—
38C5×#95—22no—
39#2296C2×C511yescharacteristic
40#1458C2×C512yes—
41#1326C2×C514yes—
42C24×C5C22×C411yescharacteristic
43C22×C4×C5—21no—
44C22×C4×C5—21no—
45C22×C4×C5—22no—
46C22×C4×C5—22no—
47C22×C4×C5—22no—
48C22×C4×C5—44no—
49C22×C4×C5—42no—
50C22×C4×C5C22⋊C411yescharacteristic
51C22×C4×C5C22⋊C412yes—
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C2×C812yes—
54C22×C4×C5M1612yes—
55C22×C4×C5C2×D412yes—
56C2×C5×C8—44no—
57C5×C4⋊C4—24no—
58C5×C4⋊C4—42no—
59C5×C4⋊C4—44no—
60C5×C4⋊C4—44no—
61C5×C22⋊C4—22no—
62C5×C22⋊C4—41no—
63C5×C22⋊C4—41no—
64C5×C22⋊C4C2×C814yes—
65C42×C5—24no—
66C42×C5—22no—
67C42×C5—22no—
68C42×C5—42no—
69C42×C5—41no—
70C42×C5—41no—
71C2×#117C4×C511yescharacteristic
72C2×#117C22×C511yescharacteristic
73C22×C42C4×C511yescharacteristic
74#431—22no—
75#389—22no—
76#385C4×C512yes—
77#385C22×C512yes—
78C4×C4⋊C4—22no—
79#324—22no—
80#323C22×C514yes—
81C23×C5—21no—
82C23×C5—21no—
83C23×C5—42no—
84C23×C5C2×C22⋊C411yescharacteristic
85C23×C5C22×C811yescharacteristic
86C23×C5C2×M1611yescharacteristic
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—22no—
93C2×C4×C5—24no—
94C2×C4×C5—24no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—44no—
101C2×C4×C5—42no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—44no—
105C2×C4×C5C22⋊C812yes—
106C2×C4×C5C22⋊C812yes—
107C2×C4×C5#9911yescharacteristic
108C2×C4×C5#9911yescharacteristic
109C2×C4×C5#10112yes—
110C5×C8—84no—
111C23×C4C2×C4×C511yescharacteristic
112C23×C4C2×C4×C512yes—
113#117—22no—
114#117—41no—
115#117—41no—
116#117C5×C814yescomplemented
117C2×C4⋊C4—21no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4C5×D412yes—
121C2×C22⋊C4C2×C4×C512yes—
122C2×C22⋊C4C2×C4×C511yescharacteristic
123C2×C22⋊C4C23×C511yescharacteristic
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42C5×D412yes—
130C4⋊C8—42no—
131C22⋊C8—24no—
132C4×C8—42no—
133#95—22no—
134#95—22no—
135C22×C5—22no—
136C22×C5—21no—
137C22×C5—21no—
138C22×C5—41no—
139C22×C5—41no—
140C22×C5—42no—
141C22×C5—42no—
142C22×C5C2×C22⋊C811yescharacteristic
143C22×C5C2×#9911yescharacteristic
144C22×C5C2×#10111yescharacteristic
145C4×C5—22no—
146C4×C5—44no—
147C4×C5—42no—
148C4×C5—42no—
149C4×C5—44no—
150C4×C5#32412yes—
151C4×C5#32412yes—
152C24C22×C4×C511yescharacteristic
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—44no—
159C22×C4—42no—
160C22×C4C5×C22⋊C411yescharacteristic
161C22×C4C5×C22⋊C412yes—
162C22×C4C5×C22⋊C411yescharacteristic
163C22×C4C2×C5×C812yes—
164C22×C4C5×M1612yes—
165C22×C4C2×C5×D412yes—
166C2×C8—44no—
167C4⋊C4—24no—
168C4⋊C4—42no—
169C4⋊C4—44no—
170C4⋊C4—44no—
171C22⋊C4—22no—
172C22⋊C4—41no—
173C22⋊C4—41no—
174C22⋊C4C2×C5×C814yes—
175C42—24no—
176C42—22no—
177C42—22no—
178C42—42no—
179C42—41no—
180C42—41no—
181C2×C5—21no—
182C2×C5—21no—
183C2×C5—41no—
184C2×C5—41no—
185C2×C5C2×#32411yescharacteristic
186C2×C5#212012yes—
187C23—21no—
188C23—21no—
189C23—42no—
190C23C2×C5×C22⋊C411yescharacteristic
191C23C22×C5×C811yescharacteristic
192C23C2×C5×M1611yescharacteristic
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—24no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4C5×C22⋊C812yes—
212C2×C4C5×C22⋊C812yes—
213C2×C4C5×#9911yescharacteristic
214C2×C4C5×#9911yescharacteristic
215C2×C4C5×#10112yes—
216C8—84no—
217C5#1145211yescharacteristic, direct product factor, Sylow
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×C5×C22⋊C811yescharacteristic
226C22C2×C5×#9911yescharacteristic
227C22C2×C5×#10111yescharacteristic
228C4—22no—
229C4—44no—
230C4—42no—
231C4—44no—
232C4—42no—
233C4C5×#32412yes—
234C4C5×#32412yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×C5×#32411yescharacteristic
240C2C5×#212012yes—
subgroupG/H
centerC2×C4×C5#99
commutatorC23C22×C5×C8
Frattini, cosocleC2×C22⋊C4C23×C5
socleC22×C5C2×#99
prime radicalC24×C5C22×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
14. #11452C5direct (N × H)
20. C5×#117C8semidirect
116. #117C5×C8semidirect
217. C5#11452direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#22962
C5×#14582
C5×#13262
#114525