Finite Group Databasebeta

← C5×#8743 #11931463

Subgroups — C5×#8743 #11931463

Order 1280.

450 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 118 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×#1285C214yesmaximal, complemented
4C2×C5×#117C411yescharacteristic
5C2×C5×#117C2211yescharacteristic
6C22×C42×C5C411yescharacteristic
7C5×#432C2214yes—
8C5×#389—22no—
9C5×#385—22no—
10C4×C5×C4⋊C4C412yes—
11C4×C5×C4⋊C4C2212yes—
12C5×#324—22no—
13C5×#323—22no—
14#8743C511yesmaximal, characteristic, direct product factor, Sylow
15C23×C4×C5—21no—
16C23×C4×C5C2×C411yescharacteristic
17C5×#117—24no—
18C5×#117—42no—
19C2×C5×C4⋊C4—22no—
20C2×C5×C4⋊C4—21no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4D412yes—
23C2×C5×C22⋊C4—21no—
24C2×C5×C22⋊C4D412yes—
25C2×C42×C5—21no—
26C2×C42×C5—42no—
27C2×C42×C5C2×C411yescharacteristic
28C2×C42×C5C2×C412yes—
29C2×C42×C5C2×C412yes—
30C2×C42×C5C2311yescharacteristic
31C5×C4⋊C8—24no—
32C5×C22⋊C8—24no—
33C5×#97—24no—
34C5×#95—22no—
35C5×#95—22no—
36#2296C2×C511yescharacteristic
37#1464C2×C512yes—
38#1285C2×C514yescomplemented
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—44no—
54C5×C4⋊C4—44no—
55C5×C4⋊C4—42no—
56C5×C22⋊C4—24no—
57C5×C22⋊C4—42no—
58C42×C5—22no—
59C42×C5—42no—
60C42×C5—42no—
61C42×C5—42no—
62C42×C5#4114yes—
63C2×#117C4×C511yescharacteristic
64C2×#117C22×C511yescharacteristic
65C22×C42C4×C511yescharacteristic
66#432C22×C514yes—
67#389—22no—
68#385—22no—
69C4×C4⋊C4C4×C512yes—
70C4×C4⋊C4C22×C512yes—
71#324—22no—
72#323—22no—
73C23×C5—21no—
74C23×C5—21no—
75C23×C5—42no—
76C23×C5#10112yes—
77C23×C5C2×C22⋊C411yescharacteristic
78C2×C4×C5—28no—
79C2×C4×C5—21no—
80C2×C4×C5—21no—
81C2×C4×C5—21no—
82C2×C4×C5—21no—
83C2×C4×C5—24no—
84C2×C4×C5—22no—
85C2×C4×C5—42no—
86C2×C4×C5—42no—
87C2×C4×C5—48no—
88C2×C4×C5—42no—
89C2×C4×C5—42no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5#10012yes—
94C2×C4×C5#11712yes—
95C2×C4×C5#12314yes—
96C5×C8—84no—
97C23×C4—21no—
98C23×C4C2×C4×C511yescharacteristic
99#117—24no—
100#117—42no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4C5×D412yes—
105C2×C22⋊C4—21no—
106C2×C22⋊C4C5×D412yes—
107C2×C42—21no—
108C2×C42—42no—
109C2×C42C2×C4×C511yescharacteristic
110C2×C42C2×C4×C512yes—
111C2×C42C2×C4×C512yes—
112C2×C42C23×C511yescharacteristic
113C4⋊C8—24no—
114C22⋊C8—24no—
115#97—24no—
116#95—22no—
117#95—22no—
118C22×C5—22no—
119C22×C5—22no—
120C22×C5—42no—
121C22×C5—42no—
122C22×C5—42no—
123C22×C5#38111yescharacteristic
124C22×C5C2×#10011yescharacteristic
125C22×C5C2×#10111yescharacteristic
126C4×C5—22no—
127C4×C5—22no—
128C4×C5—24no—
129C4×C5—44no—
130C4×C5—42no—
131C4×C5—82no—
132C24C5×C22⋊C411yescharacteristic
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—44no—
139C22×C4—42no—
140C22×C4C5×C22⋊C411yescharacteristic
141C22×C4C5×C22⋊C412yes—
142C22×C4C22×C4×C511yescharacteristic
143C22×C4C2×C5×D412yes—
144C2×C8—44no—
145C4⋊C4—24no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—42no—
149C22⋊C4—24no—
150C22⋊C4—42no—
151C42—22no—
152C42—42no—
153C42—42no—
154C42—42no—
155C42C5×#4114yes—
156C2×C5—21no—
157C2×C5—21no—
158C2×C5—42no—
159C2×C5#182111yescharacteristic
160C2×C5#182712yes—
161C23—21no—
162C23—21no—
163C23—42no—
164C23C5×#10112yes—
165C23C2×C5×C22⋊C411yescharacteristic
166C2×C4—28no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—48no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4C5×#10012yes—
182C2×C4C5×#11712yes—
183C2×C4C5×#12314yes—
184C8—84no—
185C5#874311yescharacteristic, direct product factor, Sylow
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C5×#38111yescharacteristic
192C22C2×C5×#10011yescharacteristic
193C22C2×C5×#10111yescharacteristic
194C4—22no—
195C4—22no—
196C4—24no—
197C4—44no—
198C4—42no—
199C4—82no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2C5×#182111yescharacteristic
204C2C5×#182712yes—
subgroupG/H
center, socleC22×C5#381
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1285C2semidirect
14. #8743C5direct (N × H)
38. #1285C2×C5semidirect
185. C5#8743direct (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×#12852
#87435