Finite Group Databasebeta

← C2×C5×#1325 #11934166

Subgroups — C2×C5×#1325 #11934166

Order 1280.

598 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 158 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×#384C211yesmaximal, characteristic
2C2×C5×#324C212yesmaximal
3C5×#1325C214yesmaximal, direct product factor
4C22×C5×C4⋊C4—22no—
5C22×C5×C4⋊C4C411yescharacteristic
6C22×C5×C4⋊C4C2211yescharacteristic
7C22×C42×C5C411yescharacteristic
8C2×C5×C22⋊C8—22no—
9C5×#384—22no—
10C5×#384C412yes—
11C5×#384C2212yes—
12C5×#324—22no—
13C5×#324C2214yes—
14C2×#1325C511yesmaximal, characteristic, direct product factor, Sylow
15C23×C4×C5—21no—
16C23×C4×C5—21no—
17C23×C4×C5C2×C411yescharacteristic
18C23×C4×C5D412yes—
19C22×C5×C8—42no—
20C2×C5×C4⋊C4—21no—
21C2×C5×C4⋊C4—24no—
22C2×C5×C4⋊C4—24no—
23C2×C5×C4⋊C4—41no—
24C2×C5×C4⋊C4—41no—
25C2×C5×C4⋊C4—41no—
26C2×C5×C4⋊C4—41no—
27C2×C5×C4⋊C4—48no—
28C2×C5×C4⋊C4C2×C412yes—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4C2311yescharacteristic
32C2×C42×C5—21no—
33C2×C42×C5—22no—
34C2×C42×C5C814yescomplemented
35C2×C42×C5C2×C412yes—
36C5×C22⋊C8—24no—
37C5×C22⋊C8—42no—
38C2×#384C2×C511yescharacteristic
39C2×#324C2×C512yes—
40#1325C2×C514yesdirect product factor
41C24×C5C22⋊C411yescharacteristic
42C22×C4×C5—24no—
43C22×C4×C5—24no—
44C22×C4×C5—24no—
45C22×C4×C5—21no—
46C22×C4×C5—21no—
47C22×C4×C5—22no—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5—44no—
53C22×C4×C5—44no—
54C22×C4×C5—41no—
55C22×C4×C5—41no—
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—41no—
65C5×C4⋊C4—42no—
66C5×C4⋊C4—41no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—48no—
69C5×C4⋊C4—48no—
70C5×C4⋊C4—42no—
71C42×C5—24no—
72C42×C5—22no—
73C42×C5C2×C814yescomplemented
74C22×C4⋊C4—22no—
75C22×C4⋊C4C4×C511yescharacteristic
76C22×C4⋊C4C22×C511yescharacteristic
77C22×C42C4×C511yescharacteristic
78C2×C22⋊C8—22no—
79#384—22no—
80#384C4×C512yes—
81#384C22×C512yes—
82#324—22no—
83#324C22×C514yes—
84C23×C5—22no—
85C23×C5—22no—
86C23×C5C22⋊C812yes—
87C23×C5#9911yescharacteristic
88C23×C5#9911yescharacteristic
89C23×C5#10112yes—
90C23×C5C2×C22⋊C411yescharacteristic
91C2×C4×C5—24no—
92C2×C4×C5—216no—
93C2×C4×C5—24no—
94C2×C4×C5—22no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
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—44no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—44no—
109C2×C4×C5—42no—
110C2×C4×C5—82no—
111C2×C4×C5—82no—
112C2×C4×C5—82no—
113C2×C4×C5C22⋊C812yes—
114C2×C4×C5C22×C811yescharacteristic
115C2×C4×C5C2×M1611yescharacteristic
116C5×C8—84no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4C2×C4×C511yescharacteristic
120C23×C4C5×D412yes—
121C22×C8—42no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—48no—
130C2×C4⋊C4C2×C4×C512yes—
131C2×C4⋊C4C2×C4×C511yescharacteristic
132C2×C4⋊C4C5×D412yes—
133C2×C4⋊C4C23×C511yescharacteristic
134C2×C42—21no—
135C2×C42—22no—
136C2×C42C5×C814yescomplemented
137C2×C42C2×C4×C512yes—
138C22⋊C8—24no—
139C22⋊C8—42no—
140C22×C5—24no—
141C22×C5—24no—
142C22×C5—21no—
143C22×C5—21no—
144C22×C5—21no—
145C22×C5—21no—
146C22×C5#32412yes—
147C22×C5#32412yes—
148C22×C5#35312yes—
149C22×C5#35612yes—
150C22×C5C2×C22⋊C811yescharacteristic
151C22×C5C2×#9911yescharacteristic
152C22×C5C2×#10111yescharacteristic
153C4×C5—28no—
154C4×C5—22no—
155C4×C5—21no—
156C4×C5—21no—
157C4×C5—42no—
158C4×C5—42no—
159C4×C5—82no—
160C24C5×C22⋊C411yescharacteristic
161C22×C4—24no—
162C22×C4—24no—
163C22×C4—22no—
164C22×C4—24no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—44no—
172C22×C4—44no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4C5×C22⋊C411yescharacteristic
176C22×C4C5×C22⋊C412yes—
177C22×C4C2×C5×C812yes—
178C22×C4C5×M1612yes—
179C22×C4C22×C4×C511yescharacteristic
180C22×C4C2×C5×D412yes—
181C2×C8—44no—
182C2×C8—84no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—48no—
188C4⋊C4—48no—
189C4⋊C4—42no—
190C42—22no—
191C42—24no—
192C42C2×C5×C814yescomplemented
193C2×C5—21no—
194C2×C5—22no—
195C2×C5—21no—
196C2×C5#132514yesdirect product factor
197C2×C5C2×#32411yescharacteristic
198C2×C5C2×#35311yescharacteristic
199C2×C5C2×#35611yescharacteristic
200C23—22no—
201C23—22no—
202C23C5×C22⋊C812yes—
203C23C5×#9911yescharacteristic
204C23C5×#9911yescharacteristic
205C23C5×#10112yes—
206C23C2×C5×C22⋊C411yescharacteristic
207C2×C4—24no—
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—44no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4C5×C22⋊C812yes—
230C2×C4C22×C5×C811yescharacteristic
231C2×C4C2×C5×M1611yescharacteristic
232C8—84no—
233C5C2×#132511yescharacteristic, direct product factor, Sylow
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—24no—
239C22—24no—
240C22C5×#32412yes—
241C22C5×#32412yes—
242C22C5×#35312yes—
243C22C5×#35612yes—
244C22C2×C5×C22⋊C811yescharacteristic
245C22C2×C5×#9911yescharacteristic
246C22C2×C5×#10111yescharacteristic
247C4—28no—
248C4—21no—
249C4—21no—
250C4—22no—
251C4—42no—
252C4—42no—
253C4—82no—
254C2—21no—
255C2—22no—
256C2—21no—
257C2C5×#132514yesdirect product factor
258C2C2×C5×#32411yescharacteristic
259C2C2×C5×#35311yescharacteristic
260C2C2×C5×#35611yescharacteristic
subgroupG/H
center, socleC23×C5#99
commutatorC2×C4C22×C5×C8
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C24×C5 ◁ C22×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1325C2direct (N × H)
14. C2×#1325C5direct (N × H)
34. C2×C42×C5C8semidirect
40. #1325C2×C5direct (N × H)
73. C42×C5C2×C8semidirect
136. C2×C42C5×C8semidirect
192. C42C2×C5×C8semidirect
196. C2×C5#1325direct (N × H)
233. C5C2×#1325direct (N × H)
257. C2C5×#1325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3842
C2×C5×#3242
C5×#13252
C2×#13255