Finite Group Databasebeta

← C5×#7629 #11930349

Subgroups — C5×#7629 #11930349

Order 1280.

658 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C5×#391C211yesmaximal, characteristic
2C5×#1749C212yesmaximal
3C5×#1272C214yesmaximal, complemented
4C23×C5×Q8C411yescharacteristic
5C22×C5×C4⋊C4C411yescharacteristic
6C22×C42×C5C2211yescharacteristic
7C2×C5×C22⋊C8—22no—
8C2×C5×#97—22no—
9C5×#391—22no—
10C5×#391C412yes—
11C5×#391C2212yes—
12C2×C5×#95—22no—
13C5×#336C2214yes—
14#7629C511yesmaximal, characteristic, direct product factor, Sylow
15C22×C5×Q8—24no—
16C22×C5×Q8—21no—
17C22×C5×Q8—42no—
18C22×C5×Q8—42no—
19C22×C5×Q8C2×C412yes—
20C23×C4×C5—21no—
21C23×C4×C5—21no—
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D412yes—
24C22×C5×C8—24no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—42no—
27C2×C5×C4⋊C4C2×C412yes—
28C2×C42×C5—42no—
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D412yes—
31C2×C42×C5C2311yescharacteristic
32C5×C22⋊C8—28no—
33C5×#97—44no—
34C5×#95—24no—
35C5×#95—24no—
36C2×#391C2×C511yescharacteristic
37#1749C2×C512yes—
38#1272C2×C514yescomplemented
39C24×C5C22⋊C411yescharacteristic
40C2×C5×Q8—24no—
41C2×C5×Q8—22no—
42C2×C5×Q8—416no—
43C2×C5×Q8—42no—
44C2×C5×Q8—42no—
45C2×C5×Q8—42no—
46C2×C5×Q8—42no—
47C2×C5×Q8M1614yes—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—24no—
52C22×C4×C5—24no—
53C22×C4×C5—22no—
54C22×C4×C5—24no—
55C22×C4×C5—22no—
56C22×C4×C5—42no—
57C22×C4×C5—42no—
58C22×C4×C5—42no—
59C22×C4×C5—42no—
60C22×C4×C5—44no—
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D412yes—
65C2×C5×C8—28no—
66C2×C5×C8—44no—
67C2×C5×C8—44no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C42×C5—24no—
71C42×C5—41no—
72C42×C5—41no—
73C23×Q8C4×C511yescharacteristic
74C22×C4⋊C4C4×C511yescharacteristic
75C22×C42C22×C511yescharacteristic
76C2×C22⋊C8—22no—
77C2×#97—22no—
78#391—22no—
79#391C4×C512yes—
80#391C22×C512yes—
81C2×#95—22no—
82#336C22×C514yes—
83C23×C5—21no—
84C23×C5—21no—
85C23×C5—22no—
86C23×C5#10012yes—
87C23×C5#10414yes—
88C23×C5C2×C22⋊C411yescharacteristic
89C5×Q8—44no—
90C5×Q8—48no—
91C5×Q8—44no—
92C2×C4×C5—28no—
93C2×C4×C5—21no—
94C2×C4×C5—22no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5—24no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—48no—
104C2×C4×C5—48no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—44no—
109C2×C4×C5—84no—
110C2×C4×C5#9912yes—
111C2×C4×C5C2×M1612yes—
112C2×C4×C5#13714yes—
113C5×C8—48no—
114C22×Q8—24no—
115C22×Q8—21no—
116C22×Q8—42no—
117C22×Q8—42no—
118C22×Q8C2×C4×C512yes—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4C2×C4×C511yescharacteristic
122C23×C4C5×D412yes—
123C22×C8—24no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4C2×C4×C512yes—
127C2×C42—42no—
128C2×C42C2×C4×C511yescharacteristic
129C2×C42C5×D412yes—
130C2×C42C23×C511yescharacteristic
131C22⋊C8—28no—
132#97—44no—
133#95—24no—
134#95—24no—
135C22×C5—22no—
136C22×C5—22no—
137C22×C5—24no—
138C22×C5—24no—
139C22×C5#32914yes—
140C22×C5#40711yescharacteristic
141C22×C5C2×#9911yescharacteristic
142C22×C5C2×#10011yescharacteristic
143C22×C5#41912yes—
144C22×C5C2×#10412yes—
145C4×C5—22no—
146C4×C5—22no—
147C4×C5—24no—
148C4×C5—44no—
149C4×C5—42no—
150C4×C5—82no—
151C24C5×C22⋊C411yescharacteristic
152C2×Q8—24no—
153C2×Q8—22no—
154C2×Q8—416no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8C5×M1614yes—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—24no—
166C22×C4—24no—
167C22×C4—22no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—44no—
173C22×C4C5×C22⋊C412yes—
174C22×C4C5×C22⋊C411yescharacteristic
175C22×C4C22×C4×C511yescharacteristic
176C22×C4C2×C5×D412yes—
177C2×C8—28no—
178C2×C8—44no—
179C2×C8—44no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C42—24no—
183C42—41no—
184C42—41no—
185C2×C5—24no—
186C2×C5#146211yescharacteristic
187C2×C5#149112yes—
188C2×C5#150812yes—
189C2×C5C2×#32911yescharacteristic
190C2×C5#155811yescharacteristic
191C23—21no—
192C23—21no—
193C23—22no—
194C23C5×#10012yes—
195C23C5×#10414yes—
196C23C2×C5×C22⋊C411yescharacteristic
197Q8—44no—
198Q8—44no—
199Q8—48no—
200C2×C4—28no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—48no—
212C2×C4—48no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—44no—
217C2×C4—84no—
218C2×C4C5×#9912yes—
219C2×C4C2×C5×M1612yes—
220C2×C4C5×#13714yes—
221C8—48no—
222C5#762911yescharacteristic, direct product factor, Sylow
223C22—24no—
224C22—22no—
225C22—22no—
226C22—24no—
227C22C5×#32914yes—
228C22C5×#40711yescharacteristic
229C22C2×C5×#9911yescharacteristic
230C22C2×C5×#10011yescharacteristic
231C22C5×#41912yes—
232C22C2×C5×#10412yes—
233C4—24no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—44no—
238C4—82no—
239C2—24no—
240C2C5×#146211yescharacteristic
241C2C5×#149112yes—
242C2C5×#150812yes—
243C2C2×C5×#32911yescharacteristic
244C2C5×#155811yescharacteristic
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×#1272C2semidirect
14. #7629C5direct (N × H)
38. #1272C2×C5semidirect
222. C5#7629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3912
C5×#17492
C5×#12722
#76295