Finite Group Databasebeta

← C5×#11518 #11934238

Subgroups — C5×#11518 #11934238

Order 1280.

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

normal subgroups only

This group has 446 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×#2296C211yesmaximal, characteristic
2C5×#1464C212yesmaximal
3C5×#1326C214yesmaximal
4C2×C5×#117C411yescharacteristic
5C2×C5×#117C2211yescharacteristic
6C22×C42×C5C411yescharacteristic
7C5×#432—22no—
8C5×#389—22no—
9C5×#385C412yes—
10C5×#385C2212yes—
11C4×C5×C4⋊C4—22no—
12C5×#324—22no—
13C5×#323C2214yes—
14#11518C511yesmaximal, characteristic, direct product factor, Sylow
15C23×C4×C5C2×C411yescharacteristic
16C23×C4×C5C2×C412yes—
17C5×#117—24no—
18C5×#117—42no—
19C2×C5×C4⋊C4—21no—
20C2×C5×C4⋊C4—22no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4D412yes—
23C2×C5×C22⋊C4C2×C412yes—
24C2×C5×C22⋊C4C2×C411yescharacteristic
25C2×C5×C22⋊C4C2311yescharacteristic
26C2×C42×C5—21no—
27C2×C42×C5—21no—
28C2×C42×C5—21no—
29C2×C42×C5—42no—
30C2×C42×C5D412yes—
31C5×C4⋊C8—42no—
32C5×C22⋊C8—24no—
33C5×#97—42no—
34C5×#95—22no—
35C5×#95—22no—
36#2296C2×C511yescharacteristic
37#1464C2×C512yes—
38#1326C2×C514yes—
39C24×C5C22×C411yescharacteristic
40C22×C4×C5—22no—
41C22×C4×C5—22no—
42C22×C4×C5—22no—
43C22×C4×C5—22no—
44C22×C4×C5—22no—
45C22×C4×C5—44no—
46C22×C4×C5—42no—
47C22×C4×C5C22⋊C411yescharacteristic
48C22×C4×C5C22⋊C412yes—
49C22×C4×C5C22⋊C411yescharacteristic
50C22×C4×C5C2×D412yes—
51C2×C5×C8—44no—
52C5×C4⋊C4—24no—
53C5×C4⋊C4—42no—
54C5×C4⋊C4—44no—
55C5×C4⋊C4—44no—
56C5×C22⋊C4—22no—
57C5×C22⋊C4—41no—
58C5×C22⋊C4—41no—
59C5×C22⋊C4M1614yes—
60C42×C5—24no—
61C42×C5—22no—
62C42×C5—22no—
63C42×C5—42no—
64C42×C5—42no—
65C2×#117C4×C511yescharacteristic
66C2×#117C22×C511yescharacteristic
67C22×C42C4×C511yescharacteristic
68#432—22no—
69#389—22no—
70#385C4×C512yes—
71#385C22×C512yes—
72C4×C4⋊C4—22no—
73#324—22no—
74#323C22×C514yes—
75C23×C5—21no—
76C23×C5—21no—
77C23×C5—42no—
78C23×C5C2×C22⋊C411yescharacteristic
79C23×C5C2×M1612yes—
80C2×C4×C5—28no—
81C2×C4×C5—21no—
82C2×C4×C5—21no—
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5—24no—
86C2×C4×C5—24no—
87C2×C4×C5—22no—
88C2×C4×C5—22no—
89C2×C4×C5—42no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5—44no—
93C2×C4×C5—42no—
94C2×C4×C5—42no—
95C2×C4×C5—42no—
96C2×C4×C5—44no—
97C2×C4×C5#9912yes—
98C2×C4×C5#10112yes—
99C5×C8—84no—
100C23×C4C2×C4×C511yescharacteristic
101C23×C4C2×C4×C512yes—
102#117—24no—
103#117—42no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4C5×D412yes—
108C2×C22⋊C4C2×C4×C512yes—
109C2×C22⋊C4C2×C4×C511yescharacteristic
110C2×C22⋊C4C23×C511yescharacteristic
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—42no—
115C2×C42C5×D412yes—
116C4⋊C8—42no—
117C22⋊C8—24no—
118#97—42no—
119#95—22no—
120#95—22no—
121C22×C5—22no—
122C22×C5—22no—
123C22×C5—42no—
124C22×C5—42no—
125C22×C5—42no—
126C22×C5#40711yescharacteristic
127C22×C5C2×#9911yescharacteristic
128C22×C5C2×#10111yescharacteristic
129C4×C5—22no—
130C4×C5—22no—
131C4×C5—44no—
132C4×C5—42no—
133C4×C5—42no—
134C4×C5—44no—
135C24C22×C4×C511yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—44no—
142C22×C4—42no—
143C22×C4C5×C22⋊C411yescharacteristic
144C22×C4C5×C22⋊C411yescharacteristic
145C22×C4C5×C22⋊C412yes—
146C22×C4C2×C5×D412yes—
147C2×C8—44no—
148C4⋊C4—24no—
149C4⋊C4—42no—
150C4⋊C4—44no—
151C4⋊C4—44no—
152C22⋊C4—22no—
153C22⋊C4—41no—
154C22⋊C4—41no—
155C22⋊C4C5×M1614yes—
156C42—24no—
157C42—22no—
158C42—22no—
159C42—42no—
160C42—42no—
161C2×C5—21no—
162C2×C5—21no—
163C2×C5—42no—
164C2×C5#146311yescharacteristic
165C2×C5#212012yes—
166C23—21no—
167C23—21no—
168C23—42no—
169C23C2×C5×C22⋊C411yescharacteristic
170C23C2×C5×M1612yes—
171C2×C4—28no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4C5×#9912yes—
189C2×C4C5×#10112yes—
190C8—84no—
191C5#1151811yescharacteristic, direct product factor, Sylow
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C5×#40711yescharacteristic
198C22C2×C5×#9911yescharacteristic
199C22C2×C5×#10111yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—42no—
204C4—44no—
205C4—42no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2C5×#146311yescharacteristic
210C2C5×#212012yes—
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. #11518C5direct (N × H)
191. C5#11518direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#22962
C5×#14642
C5×#13262
#115185