Finite Group Databasebeta

← C5×#11510 #11934230

Subgroups — C5×#11510 #11934230

Order 1280.

510 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2310C211yesmaximal, characteristic
2C5×#1464C212yesmaximal
3C5×#1319C214yesmaximal, complemented
4C23×C5×Q8C411yescharacteristic
5C2×C5×#117C411yescharacteristic
6C2×C5×#117C2211yescharacteristic
7C5×#432—22no—
8C5×#391—22no—
9C5×#391C412yes—
10C5×#391C2212yes—
11C5×#381—22no—
12C5×#324C2214yes—
13C5×#323—22no—
14#11510C511yesmaximal, characteristic, direct product factor, Sylow
15C22×C5×Q8—24no—
16C22×C5×Q8—21no—
17C22×C5×Q8—42no—
18C22×C5×Q8—42no—
19C22×C5×Q8C2×C412yes—
20C23×C4×C5—21no—
21C23×C4×C5C2×C411yescharacteristic
22C5×#117—42no—
23C5×#117—42no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4C2311yescharacteristic
27C2×C5×C22⋊C4—21no—
28C2×C5×C22⋊C4D412yes—
29C2×C42×C5C2×C412yes—
30C2×C42×C5D412yes—
31C5×C4⋊C8—42no—
32C5×C22⋊C8—24no—
33C5×#97—42no—
34C5×#95—24no—
35C5×#95—24no—
36#2310C2×C511yescharacteristic
37#1464C2×C512yes—
38#1319C2×C514yescomplemented
39C24×C5C22⋊C411yescharacteristic
40C2×C5×Q8—24no—
41C2×C5×Q8—22no—
42C2×C5×Q8—416no—
43C2×C5×Q8—42no—
44C2×C5×Q8—42no—
45C2×C5×Q8—42no—
46C2×C5×Q8—42no—
47C2×C5×Q8M1614yes—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—24no—
52C22×C4×C5—22no—
53C22×C4×C5—22no—
54C22×C4×C5—42no—
55C22×C4×C5—42no—
56C22×C4×C5C22⋊C412yes—
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22×C411yescharacteristic
59C22×C4×C5C2×D412yes—
60C2×C5×C8—44no—
61C5×C4⋊C4—41no—
62C5×C4⋊C4—41no—
63C5×C4⋊C4—42no—
64C5×C22⋊C4—42no—
65C5×C22⋊C4—42no—
66C42×C5—22no—
67C42×C5—22no—
68C42×C5—42no—
69C23×Q8C4×C511yescharacteristic
70C2×#117C4×C511yescharacteristic
71C2×#117C22×C511yescharacteristic
72#432—22no—
73#391—22no—
74#391C4×C512yes—
75#391C22×C512yes—
76#381—22no—
77#324C22×C514yes—
78#323—22no—
79C23×C5—21no—
80C23×C5—21no—
81C23×C5—41no—
82C23×C5—41no—
83C23×C5#10012yes—
84C23×C5C2×C22⋊C411yescharacteristic
85C5×Q8—44no—
86C5×Q8—48no—
87C5×Q8—44no—
88C2×C4×C5—28no—
89C2×C4×C5—21no—
90C2×C4×C5—21no—
91C2×C4×C5—21no—
92C2×C4×C5—21no—
93C2×C4×C5—24no—
94C2×C4×C5—22no—
95C2×C4×C5—22no—
96C2×C4×C5—48no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5—42no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5#9912yes—
105C2×C4×C5C2×M1612yes—
106C5×C8—84no—
107C22×Q8—24no—
108C22×Q8—21no—
109C22×Q8—42no—
110C22×Q8—42no—
111C22×Q8C2×C4×C512yes—
112C23×C4—21no—
113C23×C4C2×C4×C511yescharacteristic
114#117—42no—
115#117—42no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4C2×C4×C511yescharacteristic
118C2×C4⋊C4C23×C511yescharacteristic
119C2×C22⋊C4—21no—
120C2×C22⋊C4C5×D412yes—
121C2×C42C2×C4×C512yes—
122C2×C42C5×D412yes—
123C4⋊C8—42no—
124C22⋊C8—24no—
125#97—42no—
126#95—24no—
127#95—24no—
128C22×C5—21no—
129C22×C5—21no—
130C22×C5—22no—
131C22×C5—42no—
132C22×C5—42no—
133C22×C5—41no—
134C22×C5—41no—
135C22×C5#40711yescharacteristic
136C22×C5C2×#9911yescharacteristic
137C22×C5C2×#10011yescharacteristic
138C4×C5—22no—
139C4×C5—22no—
140C4×C5—42no—
141C4×C5—42no—
142C4×C5—44no—
143C4×C5—82no—
144C24C5×C22⋊C411yescharacteristic
145C2×Q8—24no—
146C2×Q8—22no—
147C2×Q8—416no—
148C2×Q8—42no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8C5×M1614yes—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4C5×C22⋊C411yescharacteristic
162C22×C4C5×C22⋊C412yes—
163C22×C4C22×C4×C511yescharacteristic
164C22×C4C2×C5×D412yes—
165C2×C8—44no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—22no—
172C42—22no—
173C42—42no—
174C2×C5—21no—
175C2×C5—21no—
176C2×C5—42no—
177C2×C5#146211yescharacteristic
178C2×C5#212911yescharacteristic
179C2×C5#213511yescharacteristic
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23C5×#10012yes—
185C23C2×C5×C22⋊C411yescharacteristic
186Q8—44no—
187Q8—44no—
188Q8—48no—
189C2×C4—28no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—48no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4C5×#9912yes—
206C2×C4C2×C5×M1612yes—
207C8—84no—
208C5#1151011yescharacteristic, direct product factor, Sylow
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22C5×#40711yescharacteristic
217C22C2×C5×#9911yescharacteristic
218C22C2×C5×#10011yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—44no—
224C4—82no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2C5×#146211yescharacteristic
229C2C5×#212911yescharacteristic
230C2C5×#213511yescharacteristic
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 ◁ C22×C4×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1319C2semidirect
14. #11510C5direct (N × H)
38. #1319C2×C5semidirect
208. C5#11510direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23102
C5×#14642
C5×#13192
#115105