Finite Group Databasebeta

← C5×#8750 #11931470

Subgroups — C5×#8750 #11931470

Order 1280.

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

normal subgroups only

This group has 538 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×#2312C211yesmaximal, characteristic
2C5×#1819C212yesmaximal
3C5×#1304C214yesmaximal
4C22×C5×C22⋊C4C2211yescharacteristic
5C5×#388—24no—
6C5×#380C412yescomplemented
7C5×#379C2214yes—
8C5×#379C2212yes—
9C4×C5×C22⋊C4C412yescomplemented
10C5×#342—24no—
11#8750C511yesmaximal, characteristic, direct product factor, Sylow
12C25×C5C2311yescharacteristic
13C23×C4×C5C2×C411yescharacteristic
14C23×C4×C5C2×C411yescharacteristic
15C2×C5×C4⋊C4—22no—
16C2×C5×C22⋊C4—24no—
17C2×C5×C22⋊C4—24no—
18C2×C5×C22⋊C4—22no—
19C2×C5×C22⋊C4—22no—
20C2×C5×C22⋊C4—24no—
21C2×C5×C22⋊C4—24no—
22C2×C5×C22⋊C4C2×C414yes—
23C2×C5×C22⋊C4D414yes—
24C2×C42×C5—22no—
25C5×#95—22no—
26C5×#95—22no—
27#2312C2×C511yescharacteristic
28#1819C2×C512yes—
29#1304C2×C514yes—
30C24×C5—42no—
31C24×C5—81no—
32C24×C5—81no—
33C24×C5C22×C411yescharacteristic
34C24×C5C2×D412yes—
35C24×C5#4114yes—
36C22×C4×C5—22no—
37C22×C4×C5—22no—
38C22×C4×C5—24no—
39C22×C4×C5—44no—
40C22×C4×C5—81no—
41C22×C4×C5—81no—
42C22×C4×C5C22⋊C412yes—
43C22×C4×C5C22⋊C412yes—
44C5×C4⋊C4—82no—
45C5×C22⋊C4—28no—
46C5×C22⋊C4—44no—
47C5×C22⋊C4—48no—
48C5×C22⋊C4—82no—
49C5×C22⋊C4—82no—
50C5×C22⋊C4—84no—
51C5×C22⋊C4—84no—
52C42×C5—82no—
53C22×C22⋊C4C22×C511yescharacteristic
54#388—24no—
55#380C4×C512yescomplemented
56#379C22×C514yes—
57#379C22×C512yes—
58C4×C22⋊C4C4×C512yescomplemented
59#342—24no—
60C23×C5—22no—
61C23×C5—24no—
62C23×C5—41no—
63C23×C5—41no—
64C23×C5—42no—
65C23×C5—42no—
66C23×C5—44no—
67C23×C5—44no—
68C23×C5—44no—
69C23×C5—88no—
70C23×C5C2×C22⋊C411yescharacteristic
71C23×C5#11712yes—
72C23×C5#12314yes—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—42no—
76C2×C4×C5—42no—
77C2×C4×C5—44no—
78C2×C4×C5—44no—
79C2×C4×C5—44no—
80C2×C4×C5—82no—
81C2×C4×C5—82no—
82C2×C4×C5—84no—
83C2×C4×C5—84no—
84C2×C4×C5—84no—
85C25C23×C511yescharacteristic
86C23×C4C2×C4×C511yescharacteristic
87C23×C4C2×C4×C511yescharacteristic
88C2×C4⋊C4—22no—
89C2×C22⋊C4—24no—
90C2×C22⋊C4—24no—
91C2×C22⋊C4—22no—
92C2×C22⋊C4—22no—
93C2×C22⋊C4—24no—
94C2×C22⋊C4—24no—
95C2×C22⋊C4C2×C4×C514yes—
96C2×C22⋊C4C5×D414yes—
97C2×C42—22no—
98#95—22no—
99#95—22no—
100C22×C5—21no—
101C22×C5—21no—
102C22×C5—24no—
103C22×C5—22no—
104C22×C5—22no—
105C22×C5—22no—
106C22×C5—24no—
107C22×C5—24no—
108C22×C5—44no—
109C22×C5—84no—
110C22×C5—88no—
111C22×C5#38111yescharacteristic
112C22×C5#41012yes—
113C4×C5—42no—
114C4×C5—42no—
115C4×C5—84no—
116C4×C5—164no—
117C24—42no—
118C24—81no—
119C24—81no—
120C24C22×C4×C511yescharacteristic
121C24C2×C5×D412yes—
122C24C5×#4114yes—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—24no—
126C22×C4—44no—
127C22×C4—81no—
128C22×C4—81no—
129C22×C4C5×C22⋊C412yes—
130C22×C4C5×C22⋊C412yes—
131C4⋊C4—82no—
132C22⋊C4—28no—
133C22⋊C4—44no—
134C22⋊C4—48no—
135C22⋊C4—82no—
136C22⋊C4—82no—
137C22⋊C4—84no—
138C22⋊C4—84no—
139C42—82no—
140C2×C5—22no—
141C2×C5—44no—
142C2×C5—42no—
143C2×C5#182011yescharacteristic
144C2×C5#182811yescharacteristic
145C2×C5#182811yescharacteristic
146C23—22no—
147C23—24no—
148C23—41no—
149C23—41no—
150C23—42no—
151C23—42no—
152C23—44no—
153C23—44no—
154C23—44no—
155C23—88no—
156C23C2×C5×C22⋊C411yescharacteristic
157C23C5×#11712yes—
158C23C5×#12314yes—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—44no—
164C2×C4—44no—
165C2×C4—44no—
166C2×C4—82no—
167C2×C4—82no—
168C2×C4—84no—
169C2×C4—84no—
170C2×C4—84no—
171C5#875011yescharacteristic, direct product factor, Sylow
172C22—21no—
173C22—21no—
174C22—24no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—24no—
179C22—24no—
180C22—44no—
181C22—84no—
182C22—88no—
183C22C5×#38111yescharacteristic
184C22C5×#41012yes—
185C4—42no—
186C4—42no—
187C4—84no—
188C4—164no—
189C2—22no—
190C2—44no—
191C2—42no—
192C2C5×#182011yescharacteristic
193C2C5×#182811yescharacteristic
194C2C5×#182811yescharacteristic
subgroupG/H
center, socleC22×C5#381
commutatorC24C22×C4×C5
Frattini, cosocleC25C23×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C5×#380C4semidirect
9. C4×C5×C22⋊C4C4semidirect
11. #8750C5direct (N × H)
55. #380C4×C5semidirect
58. C4×C22⋊C4C4×C5semidirect
171. C5#8750direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23122
C5×#18192
C5×#13042
#87505