Finite Group Databasebeta

← C5×#11504 #11934224

Subgroups — C5×#11504 #11934224

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×#1317C214yesmaximal
4C23×C5×Q8C411yescharacteristic
5C2×C5×#117C411yescharacteristic
6C2×C5×#117C2211yescharacteristic
7C5×#432—22no—
8C5×#391—22no—
9C5×#391—22no—
10C5×#381C412yes—
11C5×#381C2212yes—
12C5×#324—22no—
13C5×#323C2214yes—
14#11504C511yesmaximal, characteristic, direct product factor, Sylow
15C22×C5×Q8—21no—
16C22×C5×Q8—21no—
17C22×C5×Q8—24no—
18C22×C5×Q8—41no—
19C22×C5×Q8—41no—
20C22×C5×Q8—42no—
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C412yes—
23C5×#117—41no—
24C5×#117—41no—
25C5×#117—42no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4D412yes—
28C2×C5×C22⋊C4C2×C412yes—
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5—21no—
32C2×C42×C5D412yes—
33C5×C4⋊C8—42no—
34C5×C22⋊C8—24no—
35C5×#97—42no—
36C5×#95—24no—
37C5×#95—24no—
38#2310C2×C511yescharacteristic
39#1464C2×C512yes—
40#1317C2×C514yes—
41C24×C5C22×C411yescharacteristic
42C2×C5×Q8—24no—
43C2×C5×Q8—24no—
44C2×C5×Q8—48no—
45C2×C5×Q8—48no—
46C2×C5×Q8—42no—
47C2×C5×Q8—42no—
48C2×C5×Q8—41no—
49C2×C5×Q8—41no—
50C2×C5×Q8—42no—
51C22×C4×C5—22no—
52C22×C4×C5—21no—
53C22×C4×C5—21no—
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—42no—
59C22×C4×C5—42no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5M1614yes—
64C22×C4×C5C2×D412yes—
65C2×C5×C8—44no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—42no—
68C5×C22⋊C4—41no—
69C5×C22⋊C4—41no—
70C5×C22⋊C4—42no—
71C42×C5—22no—
72C42×C5—22no—
73C42×C5—42no—
74C23×Q8C4×C511yescharacteristic
75C2×#117C4×C511yescharacteristic
76C2×#117C22×C511yescharacteristic
77#432—22no—
78#391—22no—
79#391—22no—
80#381C4×C512yes—
81#381C22×C512yes—
82#324—22no—
83#323C22×C514yes—
84C23×C5—21no—
85C23×C5—21no—
86C23×C5—42no—
87C23×C5C2×C22⋊C411yescharacteristic
88C23×C5C2×M1612yes—
89C5×Q8—44no—
90C5×Q8—44no—
91C5×Q8—48no—
92C2×C4×C5—24no—
93C2×C4×C5—24no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—24no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—44no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—44no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5—44no—
108C2×C4×C5—42no—
109C2×C4×C5#9911yescharacteristic
110C2×C4×C5#9911yescharacteristic
111C2×C4×C5#10012yes—
112C5×C8—84no—
113C22×Q8—21no—
114C22×Q8—21no—
115C22×Q8—24no—
116C22×Q8—41no—
117C22×Q8—41no—
118C22×Q8—42no—
119C23×C4C2×C4×C511yescharacteristic
120C23×C4C2×C4×C512yes—
121#117—41no—
122#117—41no—
123#117—42no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4C5×D412yes—
126C2×C22⋊C4C2×C4×C512yes—
127C2×C22⋊C4C2×C4×C511yescharacteristic
128C2×C22⋊C4C23×C511yescharacteristic
129C2×C42—21no—
130C2×C42C5×D412yes—
131C4⋊C8—42no—
132C22⋊C8—24no—
133#97—42no—
134#95—24no—
135#95—24no—
136C22×C5—22no—
137C22×C5—22no—
138C22×C5—42no—
139C22×C5—42no—
140C22×C5—42no—
141C22×C5#40711yescharacteristic
142C22×C5C2×#9911yescharacteristic
143C22×C5C2×#10011yescharacteristic
144C4×C5—21no—
145C4×C5—21no—
146C4×C5—22no—
147C4×C5—42no—
148C4×C5—42no—
149C4×C5—44no—
150C4×C5—82no—
151C24C22×C4×C511yescharacteristic
152C2×Q8—24no—
153C2×Q8—24no—
154C2×Q8—48no—
155C2×Q8—48no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—42no—
161C22×C4—22no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4C5×C22⋊C411yescharacteristic
171C22×C4C5×C22⋊C411yescharacteristic
172C22×C4C5×C22⋊C412yes—
173C22×C4C5×M1614yes—
174C22×C4C2×C5×D412yes—
175C2×C8—44no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—42no—
181C42—22no—
182C42—22no—
183C42—42no—
184C2×C5—21no—
185C2×C5—21no—
186C2×C5—42no—
187C2×C5#146211yescharacteristic
188C2×C5#212312yes—
189C23—21no—
190C23—21no—
191C23—42no—
192C23C2×C5×C22⋊C411yescharacteristic
193C23C2×C5×M1612yes—
194Q8—44no—
195Q8—44no—
196Q8—48no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4C5×#9911yescharacteristic
215C2×C4C5×#9911yescharacteristic
216C2×C4C5×#10012yes—
217C8—84no—
218C5#1150411yescharacteristic, direct product factor, Sylow
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C5×#40711yescharacteristic
225C22C2×C5×#9911yescharacteristic
226C22C2×C5×#10011yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—42no—
231C4—42no—
232C4—44no—
233C4—82no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2C5×#146211yescharacteristic
238C2C5×#212312yes—
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC24×C5C22×C4
LCSG ▷ C24 ▷ 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
14. #11504C5direct (N × H)
218. C5#11504direct (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×#13172
#115045