Finite Group Databasebeta

← C5×#11568 #11934288

Subgroups — C5×#11568 #11934288

Order 1280.

394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2546C211yesmaximal, characteristic
2C5×#1467C211yesmaximal, characteristic
3C5×#1461C211yesmaximal, characteristic
4C5×#1319C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C5×C4⋊Q8C412yes—
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#432—21no—
9C5×#431—21no—
10C5×#398—21no—
11C5×#398—21no—
12C5×#391C2212yes—
13C5×#389—21no—
14C5×#389—21no—
15C4×C5×C4⋊C4C411yescharacteristic
16C5×#324—21no—
17C5×#324—21no—
18C5×#324C2212yes—
19C5×#324C2212yes—
20#11568C511yesmaximal, characteristic, direct product factor, Sylow
21C22×C5×Q8C2×C412yes—
22C22×C5×Q8C2×C411yescharacteristic
23C5×C4⋊Q8—41no—
24C5×C4⋊Q8—41no—
25C5×C4⋊Q8—44no—
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C4⋊C4C2311yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C412yes—
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C5×C4⋊C8—41no—
41C5×C4⋊C8—41no—
42C5×C22⋊C8—22no—
43C5×C22⋊C8—22no—
44C5×#97—41no—
45C4×C5×C8—41no—
46C5×#95—21no—
47C5×#95—22no—
48C5×#95—22no—
49#2546C2×C511yescharacteristic
50#1467C2×C511yescharacteristic
51#1461C2×C511yescharacteristic
52#1319C2×C514yes—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—24no—
56C2×C5×Q8—41no—
57C2×C5×Q8—42no—
58C2×C5×Q8—42no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C2×C5×C8—42no—
69C2×C5×C8—42no—
70C5×C4⋊C4—24no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—44no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—44no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—21no—
85C42×C5—42no—
86C2×C4⋊Q8C4×C511yescharacteristic
87C2×C4⋊Q8C4×C512yes—
88C2×C4×Q8C22×C511yescharacteristic
89#432—21no—
90#431—21no—
91#398—21no—
92#398—21no—
93#391C22×C512yes—
94#389—21no—
95#389—21no—
96C4×C4⋊C4C4×C511yescharacteristic
97#324—21no—
98#324—21no—
99#324C22×C512yes—
100#324C22×C512yes—
101C23×C5C2×C22⋊C411yescharacteristic
102C5×Q8—44no—
103C5×Q8—84no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—22no—
109C2×C4×C5—24no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5#9911yescharacteristic
125C2×C4×C5#9911yescharacteristic
126C2×C4×C5#10012yes—
127C2×C4×C5#13112yes—
128C5×C8—82no—
129C5×C8—82no—
130C22×Q8C2×C4×C512yes—
131C22×Q8C2×C4×C511yescharacteristic
132C4⋊Q8—41no—
133C4⋊Q8—41no—
134C4⋊Q8—44no—
135C4×Q8—41no—
136C4×Q8—41no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4C5×D411yescharacteristic
143C2×C4⋊C4C5×D411yescharacteristic
144C2×C4⋊C4C23×C511yescharacteristic
145C2×C42C2×C4×C511yescharacteristic
146C2×C42C2×C4×C512yes—
147C2×C42C5×D411yescharacteristic
148C2×C42C5×D411yescharacteristic
149C4⋊C8—41no—
150C4⋊C8—41no—
151C22⋊C8—22no—
152C22⋊C8—22no—
153#97—41no—
154C4×C8—41no—
155#95—21no—
156#95—22no—
157#95—22no—
158C22×C5—21no—
159C22×C5—21no—
160C22×C5#40811yescharacteristic
161C22×C5C2×#9911yescharacteristic
162C22×C5C2×#10011yescharacteristic
163C4×C5—21no—
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—44no—
167C4×C5—41no—
168C4×C5—41no—
169C4×C5—41no—
170C4×C5—41no—
171C4×C5—82no—
172C4×C5#35612yes—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—24no—
176C2×Q8—41no—
177C2×Q8—42no—
178C2×Q8—42no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C5×C22⋊C411yescharacteristic
182C22×C4C5×C22⋊C411yescharacteristic
183C22×C4C5×C22⋊C411yescharacteristic
184C22×C4C5×C22⋊C411yescharacteristic
185C22×C4C22×C4×C511yescharacteristic
186C22×C4C2×C5×D411yescharacteristic
187C22×C4C2×C5×D411yescharacteristic
188C2×C8—42no—
189C2×C8—42no—
190C4⋊C4—24no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—44no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—44no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—42no—
206C2×C5—21no—
207C2×C5—21no—
208C2×C5#147111yescharacteristic
209C2×C5#212911yescharacteristic
210C2×C5C2×#35611yescharacteristic
211C23C2×C5×C22⋊C411yescharacteristic
212Q8—44no—
213Q8—84no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4C5×#9911yescharacteristic
235C2×C4C5×#9911yescharacteristic
236C2×C4C5×#10012yes—
237C2×C4C5×#13112yes—
238C8—82no—
239C8—82no—
240C5#1156811yescharacteristic, direct product factor, Sylow
241C22—21no—
242C22—21no—
243C22C5×#40811yescharacteristic
244C22C2×C5×#9911yescharacteristic
245C22C2×C5×#10011yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4C5×#35612yes—
256C2—21no—
257C2—21no—
258C2C5×#147111yescharacteristic
259C2C5×#212911yescharacteristic
260C2C2×C5×#35611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC23×C5C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
20. #11568C5direct (N × H)
240. C5#11568direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25462
C5×#14672
C5×#14612
C5×#13192
#115685