Finite Group Databasebeta

← C5×#11506 #11934226

Subgroups — C5×#11506 #11934226

Order 1280.

598 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 118 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×#391C211yesmaximal, characteristic
2C5×#1463C212yesmaximal
3C5×#1319C214yesmaximal, complemented
4C23×C5×Q8C411yescharacteristic
5C22×C5×C4⋊C4C2211yescharacteristic
6C22×C42×C5C411yescharacteristic
7C5×#407—22no—
8C5×#391—22no—
9C5×#391C412yes—
10C5×#391C2212yes—
11C2×C5×#95—22no—
12C5×#324—22no—
13C5×#324C2214yes—
14#11506C511yesmaximal, characteristic, direct product factor, Sylow
15C22×C5×Q8—24no—
16C22×C5×Q8—21no—
17C22×C5×Q8—42no—
18C22×C5×Q8—41no—
19C22×C5×Q8—41no—
20C22×C5×Q8C2×C412yes—
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5C2×C411yescharacteristic
24C23×C4×C5D412yes—
25C2×C5×M16—42no—
26C2×C5×C4⋊C4—41no—
27C2×C5×C4⋊C4—41no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4D412yes—
30C2×C5×C4⋊C4C2311yescharacteristic
31C2×C42×C5—21no—
32C2×C42×C5—42no—
33C2×C42×C5C2×C412yes—
34C5×C22⋊C8—24no—
35C5×C22⋊C8—42no—
36C5×#95—24no—
37C5×#95—24no—
38C2×#391C2×C511yescharacteristic
39#1463C2×C512yes—
40#1319C2×C514yescomplemented
41C24×C5C22⋊C411yescharacteristic
42C2×C5×Q8—24no—
43C2×C5×Q8—22no—
44C2×C5×Q8—48no—
45C2×C5×Q8—48no—
46C2×C5×Q8—42no—
47C2×C5×Q8—42no—
48C2×C5×Q8—42no—
49C2×C5×Q8—42no—
50C2×C5×Q8M1614yescomplemented
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5—22no—
54C22×C4×C5—22no—
55C22×C4×C5—24no—
56C22×C4×C5—24no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—42no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5—41no—
65C22×C4×C5—41no—
66C22×C4×C5—44no—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C412yes—
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D412yes—
71C5×M16—84no—
72C2×C5×C8—44no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—41no—
76C42×C5—42no—
77C42×C5—42no—
78C23×Q8C4×C511yescharacteristic
79C22×C4⋊C4C22×C511yescharacteristic
80C22×C42C4×C511yescharacteristic
81#407—22no—
82#391—22no—
83#391C4×C512yes—
84#391C22×C512yes—
85C2×#95—22no—
86#324—22no—
87#324C22×C514yes—
88C23×C5—22no—
89C23×C5—22no—
90C23×C5—21no—
91C23×C5—21no—
92C23×C5#9911yescharacteristic
93C23×C5#9911yescharacteristic
94C23×C5C2×C22⋊C411yescharacteristic
95C5×Q8—44no—
96C5×Q8—48no—
97C5×Q8—44no—
98C2×C4×C5—24no—
99C2×C4×C5—24no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—24no—
105C2×C4×C5—24no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—48no—
109C2×C4×C5—42no—
110C2×C4×C5—44no—
111C2×C4×C5—44no—
112C2×C4×C5—44no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—82no—
119C2×C4×C5#10012yes—
120C2×C4×C5C2×M1612yes—
121C5×C8—84no—
122C22×Q8—24no—
123C22×Q8—21no—
124C22×Q8—42no—
125C22×Q8—41no—
126C22×Q8—41no—
127C22×Q8C2×C4×C512yes—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4C2×C4×C511yescharacteristic
131C23×C4C5×D412yes—
132C2×M16—42no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4C2×C4×C511yescharacteristic
136C2×C4⋊C4C5×D412yes—
137C2×C4⋊C4C23×C511yescharacteristic
138C2×C42—21no—
139C2×C42—42no—
140C2×C42C2×C4×C512yes—
141C22⋊C8—24no—
142C22⋊C8—42no—
143#95—24no—
144#95—24no—
145C22×C5—24no—
146C22×C5—24no—
147C22×C5—21no—
148C22×C5—21no—
149C22×C5—21no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5—21no—
153C22×C5#35412yes—
154C22×C5#35612yes—
155C22×C5#40711yescharacteristic
156C22×C5C2×#9911yescharacteristic
157C22×C5C2×#10011yescharacteristic
158C4×C5—22no—
159C4×C5—22no—
160C4×C5—44no—
161C4×C5—42no—
162C4×C5—42no—
163C4×C5—44no—
164C24C5×C22⋊C411yescharacteristic
165C2×Q8—24no—
166C2×Q8—22no—
167C2×Q8—48no—
168C2×Q8—48no—
169C2×Q8—42no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—42no—
173C2×Q8C5×M1614yescomplemented
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—24no—
179C22×C4—24no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—44no—
190C22×C4C5×C22⋊C411yescharacteristic
191C22×C4C5×C22⋊C412yes—
192C22×C4C22×C4×C511yescharacteristic
193C22×C4C2×C5×D412yes—
194M16—84no—
195C2×C8—44no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C42—42no—
200C42—42no—
201C2×C5—21no—
202C2×C5—22no—
203C2×C5—22no—
204C2×C5—21no—
205C2×C5#146211yescharacteristic
206C2×C5C2×#35411yescharacteristic
207C2×C5C2×#35611yescharacteristic
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23C5×#9911yescharacteristic
213C23C5×#9911yescharacteristic
214C23C2×C5×C22⋊C411yescharacteristic
215Q8—44no—
216Q8—44no—
217Q8—48no—
218C2×C4—24no—
219C2×C4—24no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—24no—
225C2×C4—24no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4—48no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4C5×#10012yes—
240C2×C4C2×C5×M1612yes—
241C8—84no—
242C5#1150611yescharacteristic, direct product factor, Sylow
243C22—24no—
244C22—24no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22C5×#35412yes—
252C22C5×#35612yes—
253C22C5×#40711yescharacteristic
254C22C2×C5×#9911yescharacteristic
255C22C2×C5×#10011yescharacteristic
256C4—22no—
257C4—22no—
258C4—44no—
259C4—42no—
260C4—42no—
261C4—44no—
262C2—21no—
263C2—21no—
264C2—22no—
265C2—22no—
266C2C5×#146211yescharacteristic
267C2C2×C5×#35411yescharacteristic
268C2C2×C5×#35611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×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×#1319C2semidirect
14. #11506C5direct (N × H)
40. #1319C2×C5semidirect
50. C2×C5×Q8M16semidirect
173. C2×Q8C5×M16semidirect
242. C5#11506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3912
C5×#14632
C5×#13192
#115065