Finite Group Databasebeta

← C5×#11521 #11934241

Subgroups — C5×#11521 #11934241

Order 1280.

330 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2920C211yesmaximal, characteristic
2C5×#2165C212yesmaximal, complemented
3C5×#1327C212yesmaximal, complemented
4C5×#1320C212yesmaximal
5C22×C42×C5C411yescharacteristic
6C5×#432—22no—
7C5×#431—22no—
8C5×#423C411yescharacteristic
9C5×#423C2211yescharacteristic
10C5×#407C411yescharacteristic
11C5×#407C2211yescharacteristic
12C4×C5×M16C411yescharacteristic
13C4×C5×M16C2211yescharacteristic
14C5×#364—22no—
15C5×#349C2214yes—
16C5×#347—22no—
17#11521C511yesmaximal, characteristic, direct product factor, Sylow
18C23×C4×C5—21no—
19C23×C4×C5C2×C411yescharacteristic
20C2×C5×M16C2×C411yescharacteristic
21C2×C5×M16C2×C411yescharacteristic
22C2×C5×M16C2×C411yescharacteristic
23C2×C5×M16C2311yescharacteristic
24C2×C42×C5—21no—
25C2×C42×C5—21no—
26C2×C42×C5—21no—
27C2×C42×C5—21no—
28C2×C42×C5—21no—
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C5×M32—24no—
32C5×C4⋊C8—22no—
33C5×C4⋊C8—22no—
34C5×C22⋊C8—22no—
35C5×C22⋊C8—22no—
36C5×#97—21no—
37C5×#97D412yes—
38C4×C5×C8—21no—
39C4×C5×C8D412yes—
40#2920C2×C511yescharacteristic
41#2165C2×C512yescomplemented
42#1327C2×C512yescomplemented
43#1320C2×C512yes—
44C24×C5M1611yescharacteristic
45C22×C4×C5—21no—
46C22×C4×C5—21no—
47C22×C4×C5—21no—
48C22×C4×C5—21no—
49C22×C4×C5—21no—
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5—44no—
54C22×C4×C5—41no—
55C22×C4×C5—41no—
56C22×C4×C5M1611yescharacteristic
57C22×C4×C5C22×C411yescharacteristic
58C5×M16—41no—
59C5×M16—41no—
60C5×M16—41no—
61C5×M16—41no—
62C2×C5×C8—21no—
63C2×C5×C8—21no—
64C2×C5×C8C22⋊C412yes—
65C2×C5×C8C2×D412yes—
66C42×C5—21no—
67C42×C5—21no—
68C42×C5—21no—
69C42×C5—21no—
70C42×C5—21no—
71C42×C5—21no—
72C42×C5C22⋊C411yescharacteristic
73C42×C5C22⋊C411yescharacteristic
74C42×C5M1611yescharacteristic
75C42×C5M1611yescharacteristic
76C5×C16—44no—
77C22×C42C4×C511yescharacteristic
78#432—22no—
79#431—22no—
80#423C4×C511yescharacteristic
81#423C22×C511yescharacteristic
82#407C4×C511yescharacteristic
83#407C22×C511yescharacteristic
84C4×M16C4×C511yescharacteristic
85C4×M16C22×C511yescharacteristic
86#364—22no—
87#349C22×C514yes—
88#347—22no—
89C23×C5—21no—
90C23×C5—42no—
91C23×C5—41no—
92C23×C5C2×M1611yescharacteristic
93C2×C4×C5—24no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—42no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—41no—
110C2×C4×C5C2×C22⋊C411yescharacteristic
111C2×C4×C5C2×M1611yescharacteristic
112C5×C8—22no—
113C5×C8—22no—
114C5×C8—41no—
115C5×C8—41no—
116C23×C4—21no—
117C23×C4C2×C4×C511yescharacteristic
118C2×M16C2×C4×C511yescharacteristic
119C2×M16C2×C4×C511yescharacteristic
120C2×M16C2×C4×C511yescharacteristic
121C2×M16C23×C511yescharacteristic
122C2×C42—21no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42C2×C4×C511yescharacteristic
128C2×C42C2×C4×C511yescharacteristic
129M32—24no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—22no—
134#97—21no—
135#97C5×D412yes—
136C4×C8—21no—
137C4×C8C5×D412yes—
138C22×C5—22no—
139C22×C5—21no—
140C22×C5—41no—
141C22×C5—41no—
142C22×C5—42no—
143C22×C5—42no—
144C22×C5—41no—
145C22×C5#40711yescharacteristic
146C4×C5—22no—
147C4×C5—22no—
148C4×C5—21no—
149C4×C5—41no—
150C4×C5—41no—
151C4×C5—41no—
152C4×C5#41011yescharacteristic
153C4×C5#41311yescharacteristic
154C24C5×M1611yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—44no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4C5×M1611yescharacteristic
167C22×C4C22×C4×C511yescharacteristic
168M16—41no—
169M16—41no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8C5×C22⋊C412yes—
175C2×C8C2×C5×D412yes—
176C42—21no—
177C42—21no—
178C42—21no—
179C42—21no—
180C42—21no—
181C42—21no—
182C42C5×C22⋊C411yescharacteristic
183C42C5×C22⋊C411yescharacteristic
184C42C5×M1611yescharacteristic
185C42C5×M1611yescharacteristic
186C16—44no—
187C2×C5—21no—
188C2×C5—42no—
189C2×C5—41no—
190C2×C5#146411yescharacteristic
191C23—21no—
192C23—42no—
193C23—41no—
194C23C2×C5×M1611yescharacteristic
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4C2×C5×C22⋊C411yescharacteristic
213C2×C4C2×C5×M1611yescharacteristic
214C8—22no—
215C8—22no—
216C8—41no—
217C8—41no—
218C5#1152111yescharacteristic, direct product factor, Sylow
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22C5×#40711yescharacteristic
227C4—22no—
228C4—22no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4C5×#41011yescharacteristic
234C4C5×#41311yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2C5×#146411yescharacteristic
subgroupG/H
centerC4×C5#410
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×M16C23×C5
socleC2×C5#1464
prime radicalC24×C5M16
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C42×C5 ◁ C4×C5×M16 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2165C2semidirect
3. C5×#1327C2semidirect
17. #11521C5direct (N × H)
41. #2165C2×C5semidirect
42. #1327C2×C5semidirect
218. C5#11521direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29202
C5×#21652
C5×#13272
C5×#13202
#115215