Finite Group Databasebeta

← C5×#11453 #11934173

Subgroups — C5×#11453 #11934173

Order 1280.

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

normal subgroups only

This group has 562 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×#2315C211yesmaximal, characteristic
2C2×C5×#323C212yesmaximal
3C5×#1326C214yesmaximal, complemented
4C22×C5×C22⋊C4C411yescharacteristic
5C22×C5×C22⋊C4C411yescharacteristic
6C22×C5×C22⋊C4C2211yescharacteristic
7C2×C5×C22⋊C8—22no—
8C5×#385—22no—
9C5×#385C412yes—
10C5×#385C2212yes—
11C5×#380—22no—
12C5×#323—22no—
13C5×#323C2214yes—
14#11453C511yesmaximal, characteristic, direct product factor, Sylow
15C25×C5C2×C411yescharacteristic
16C23×C4×C5—21no—
17C23×C4×C5C2×C412yes—
18C23×C4×C5D412yes—
19C22×C5×C8—42no—
20C2×C5×C4⋊C4—22no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C22⋊C4—21no—
23C2×C5×C22⋊C4—22no—
24C2×C5×C22⋊C4—21no—
25C2×C5×C22⋊C4—21no—
26C2×C5×C22⋊C4—42no—
27C2×C5×C22⋊C4—42no—
28C2×C5×C22⋊C4C814yescomplemented
29C2×C5×C22⋊C4C2×C412yes—
30C2×C5×C22⋊C4C2×C411yescharacteristic
31C2×C5×C22⋊C4D412yes—
32C2×C5×C22⋊C4C2311yescharacteristic
33C5×C22⋊C8—24no—
34C5×C22⋊C8—42no—
35C5×#95—22no—
36C5×#95—22no—
37#2315C2×C511yescharacteristic
38C2×#323C2×C512yes—
39#1326C2×C514yescomplemented
40C24×C5—22no—
41C24×C5—22no—
42C24×C5—82no—
43C24×C5C22⋊C411yescharacteristic
44C24×C5C22⋊C411yescharacteristic
45C24×C5C2×C812yes—
46C24×C5M1612yes—
47C24×C5C22×C411yescharacteristic
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—24no—
51C22×C4×C5—22no—
52C22×C4×C5—22no—
53C22×C4×C5—42no—
54C22×C4×C5—82no—
55C22×C4×C5—82no—
56C22×C4×C5—82no—
57C22×C4×C5C22⋊C412yes—
58C22×C4×C5C2×D412yes—
59C2×C5×C8—44no—
60C2×C5×C8—84no—
61C5×C4⋊C4—82no—
62C5×C4⋊C4—82no—
63C5×C22⋊C4—24no—
64C5×C22⋊C4—22no—
65C5×C22⋊C4—41no—
66C5×C22⋊C4—42no—
67C5×C22⋊C4—41no—
68C5×C22⋊C4—42no—
69C5×C22⋊C4—42no—
70C5×C22⋊C4C2×C814yescomplemented
71C22×C22⋊C4C4×C511yescharacteristic
72C22×C22⋊C4C4×C511yescharacteristic
73C22×C22⋊C4C22×C511yescharacteristic
74C2×C22⋊C8—22no—
75#385—22no—
76#385C4×C512yes—
77#385C22×C512yes—
78#380—22no—
79#323—22no—
80#323C22×C514yes—
81C23×C5—21no—
82C23×C5—21no—
83C23×C5—21no—
84C23×C5—21no—
85C23×C5—24no—
86C23×C5—24no—
87C23×C5—42no—
88C23×C5—42no—
89C23×C5—42no—
90C23×C5—82no—
91C23×C5—82no—
92C23×C5—82no—
93C23×C5—82no—
94C23×C5—84no—
95C23×C5C22⋊C812yes—
96C23×C5C22⋊C812yes—
97C23×C5#9912yes—
98C23×C5#10112yes—
99C23×C5C2×C22⋊C411yescharacteristic
100C23×C5C22×C811yescharacteristic
101C23×C5C2×M1611yescharacteristic
102C2×C4×C5—24no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5—44no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—42no—
112C2×C4×C5—42no—
113C2×C4×C5—82no—
114C2×C4×C5—84no—
115C2×C4×C5—84no—
116C5×C8—84no—
117C25C2×C4×C511yescharacteristic
118C23×C4—21no—
119C23×C4C2×C4×C512yes—
120C23×C4C5×D412yes—
121C22×C8—42no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C22⋊C4—21no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—21no—
127C2×C22⋊C4—21no—
128C2×C22⋊C4—42no—
129C2×C22⋊C4—42no—
130C2×C22⋊C4C5×C814yescomplemented
131C2×C22⋊C4C2×C4×C512yes—
132C2×C22⋊C4C2×C4×C511yescharacteristic
133C2×C22⋊C4C5×D412yes—
134C2×C22⋊C4C23×C511yescharacteristic
135C22⋊C8—24no—
136C22⋊C8—42no—
137#95—22no—
138#95—22no—
139C22×C5—22no—
140C22×C5—22no—
141C22×C5—22no—
142C22×C5—22no—
143C22×C5—21no—
144C22×C5—21no—
145C22×C5—42no—
146C22×C5—42no—
147C22×C5—42no—
148C22×C5—41no—
149C22×C5—41no—
150C22×C5—42no—
151C22×C5—42no—
152C22×C5—42no—
153C22×C5—42no—
154C22×C5—84no—
155C22×C5—84no—
156C22×C5#32414yes—
157C22×C5C2×C22⋊C811yescharacteristic
158C22×C5C2×#9911yescharacteristic
159C22×C5C2×#10111yescharacteristic
160C4×C5—44no—
161C4×C5—42no—
162C4×C5—42no—
163C4×C5—82no—
164C24—22no—
165C24—22no—
166C24—82no—
167C24C5×C22⋊C411yescharacteristic
168C24C5×C22⋊C411yescharacteristic
169C24C2×C5×C812yes—
170C24C5×M1612yes—
171C24C22×C4×C511yescharacteristic
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—82no—
179C22×C4—82no—
180C22×C4—82no—
181C22×C4C5×C22⋊C412yes—
182C22×C4C2×C5×D412yes—
183C2×C8—44no—
184C2×C8—84no—
185C4⋊C4—82no—
186C4⋊C4—82no—
187C22⋊C4—22no—
188C22⋊C4—24no—
189C22⋊C4—41no—
190C22⋊C4—42no—
191C22⋊C4—41no—
192C22⋊C4—42no—
193C22⋊C4—42no—
194C22⋊C4C2×C5×C814yescomplemented
195C2×C5—21no—
196C2×C5—21no—
197C2×C5—24no—
198C2×C5—42no—
199C2×C5—41no—
200C2×C5—41no—
201C2×C5C2×#32411yescharacteristic
202C2×C5#212112yes—
203C23—21no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23—24no—
208C23—24no—
209C23—42no—
210C23—42no—
211C23—42no—
212C23—82no—
213C23—82no—
214C23—82no—
215C23—82no—
216C23—84no—
217C23C5×C22⋊C812yes—
218C23C5×C22⋊C812yes—
219C23C5×#9912yes—
220C23C5×#10112yes—
221C23C2×C5×C22⋊C411yescharacteristic
222C23C22×C5×C811yescharacteristic
223C23C2×C5×M1611yescharacteristic
224C2×C4—24no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—84no—
237C2×C4—84no—
238C8—84no—
239C5#1145311yescharacteristic, direct product factor, Sylow
240C22—22no—
241C22—22no—
242C22—22no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—84no—
257C22C5×#32414yes—
258C22C2×C5×C22⋊C811yescharacteristic
259C22C2×C5×#9911yescharacteristic
260C22C2×C5×#10111yescharacteristic
261C4—44no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—24no—
268C2—41no—
269C2—41no—
270C2—42no—
271C2C2×C5×#32411yescharacteristic
272C2C5×#212112yes—
subgroupG/H
center, socleC22×C5C2×#99
commutatorC23C22×C5×C8
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC25×C5C2×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1326C2semidirect
14. #11453C5direct (N × H)
28. C2×C5×C22⋊C4C8semidirect
39. #1326C2×C5semidirect
70. C5×C22⋊C4C2×C8semidirect
130. C2×C22⋊C4C5×C8semidirect
194. C22⋊C4C2×C5×C8semidirect
239. C5#11453direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23152
C2×C5×#3232
C5×#13262
#114535