Finite Group Databasebeta

← C5×#7646 #11930366

Subgroups — C5×#7646 #11930366

Order 1280.

490 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1817C212yesmaximal
3C5×#1271C214yesmaximal, complemented
4C2×C5×#117C411yescharacteristic
5C2×C5×#117C411yescharacteristic
6C22×C42×C5C2211yescharacteristic
7C2×C5×C22⋊C8—22no—
8C5×#389C412yes—
9C5×#389C2212yes—
10C5×#385—22no—
11C4×C5×C4⋊C4—22no—
12C5×#336—22no—
13C5×#336C2214yes—
14#7646C511yesmaximal, characteristic, direct product factor, Sylow
15C23×C4×C5C2×C411yescharacteristic
16C23×C4×C5D412yes—
17C22×C5×C8—24no—
18C5×#117—24no—
19C5×#117—42no—
20C2×C5×C4⋊C4—22no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4C2×C412yes—
23C2×C5×C4⋊C4C2×C412yes—
24C2×C5×C22⋊C4—21no—
25C2×C5×C22⋊C4—21no—
26C2×C42×C5—21no—
27C2×C42×C5—21no—
28C2×C42×C5—42no—
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D412yes—
31C2×C42×C5C2311yescharacteristic
32C5×C22⋊C8—44no—
33C5×#95—22no—
34C5×#95—22no—
35#2296C2×C511yescharacteristic
36#1817C2×C512yes—
37#1271C2×C514yescomplemented
38C24×C5C22⋊C411yescharacteristic
39C22×C4×C5—22no—
40C22×C4×C5—22no—
41C22×C4×C5—22no—
42C22×C4×C5—24no—
43C22×C4×C5—22no—
44C22×C4×C5—24no—
45C22×C4×C5—22no—
46C22×C4×C5—42no—
47C22×C4×C5C22⋊C412yes—
48C22×C4×C5C22⋊C411yescharacteristic
49C22×C4×C5C22×C411yescharacteristic
50C22×C4×C5C2×D412yes—
51C2×C5×C8—44no—
52C2×C5×C8—44no—
53C2×C5×C8—44no—
54C5×C4⋊C4—22no—
55C5×C4⋊C4—42no—
56C5×C4⋊C4—44no—
57C5×C4⋊C4—44no—
58C5×C4⋊C4M1614yes—
59C5×C22⋊C4—24no—
60C5×C22⋊C4—42no—
61C42×C5—24no—
62C42×C5—41no—
63C42×C5—42no—
64C42×C5—41no—
65C42×C5—42no—
66C2×#117C4×C511yescharacteristic
67C2×#117C4×C511yescharacteristic
68C22×C42C22×C511yescharacteristic
69C2×C22⋊C8—22no—
70#389C4×C512yes—
71#389C22×C512yes—
72#385—22no—
73C4×C4⋊C4—22no—
74#336—22no—
75#336C22×C514yes—
76C23×C5—21no—
77C23×C5—21no—
78C23×C5—22no—
79C23×C5—22no—
80C23×C5#9912yes—
81C23×C5C2×C22⋊C411yescharacteristic
82C2×C4×C5—28no—
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5—21no—
88C2×C4×C5—22no—
89C2×C4×C5—24no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—22no—
93C2×C4×C5—48no—
94C2×C4×C5—42no—
95C2×C4×C5—42no—
96C2×C4×C5—42no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5#10112yes—
100C2×C4×C5C2×M1612yes—
101C2×C4×C5#13514yes—
102C5×C8—84no—
103C23×C4C2×C4×C511yescharacteristic
104C23×C4C5×D412yes—
105C22×C8—24no—
106#117—24no—
107#117—42no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×C4×C512yes—
111C2×C4⋊C4C2×C4×C512yes—
112C2×C22⋊C4—21no—
113C2×C22⋊C4—21no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—42no—
117C2×C42C2×C4×C511yescharacteristic
118C2×C42C5×D412yes—
119C2×C42C23×C511yescharacteristic
120C22⋊C8—44no—
121#95—22no—
122#95—22no—
123C22×C5—22no—
124C22×C5—24no—
125C22×C5—41no—
126C22×C5—41no—
127C22×C5—42no—
128C22×C5#40711yescharacteristic
129C22×C5C2×#9911yescharacteristic
130C22×C5C2×#10111yescharacteristic
131C22×C5#41612yes—
132C22×C5#42112yes—
133C4×C5—22no—
134C4×C5—22no—
135C4×C5—24no—
136C4×C5—44no—
137C4×C5—42no—
138C4×C5—82no—
139C24C5×C22⋊C411yescharacteristic
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—24no—
145C22×C4—24no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4C5×C22⋊C412yes—
149C22×C4C5×C22⋊C411yescharacteristic
150C22×C4C22×C4×C511yescharacteristic
151C22×C4C2×C5×D412yes—
152C2×C8—44no—
153C2×C8—44no—
154C2×C8—44no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—44no—
158C4⋊C4—44no—
159C4⋊C4C5×M1614yes—
160C22⋊C4—24no—
161C22⋊C4—42no—
162C42—24no—
163C42—41no—
164C42—42no—
165C42—41no—
166C42—42no—
167C2×C5—42no—
168C2×C5#146311yescharacteristic
169C2×C5#148812yes—
170C2×C5#151612yes—
171C2×C5#153711yescharacteristic
172C2×C5#154411yescharacteristic
173C23—21no—
174C23—21no—
175C23—22no—
176C23—22no—
177C23C5×#9912yes—
178C23C2×C5×C22⋊C411yescharacteristic
179C2×C4—28no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—48no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4C5×#10112yes—
197C2×C4C2×C5×M1612yes—
198C2×C4C5×#13514yes—
199C8—84no—
200C5#764611yescharacteristic, direct product factor, Sylow
201C22—24no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22C5×#40711yescharacteristic
207C22C2×C5×#9911yescharacteristic
208C22C2×C5×#10111yescharacteristic
209C22C5×#41612yes—
210C22C5×#42112yes—
211C4—24no—
212C4—22no—
213C4—22no—
214C4—42no—
215C4—44no—
216C4—82no—
217C2—42no—
218C2C5×#146311yescharacteristic
219C2C5×#148812yes—
220C2C5×#151612yes—
221C2C5×#153711yescharacteristic
222C2C5×#154411yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1271C2semidirect
14. #7646C5direct (N × H)
37. #1271C2×C5semidirect
200. C5#7646direct (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×#18172
C5×#12712
#76465