Finite Group Databasebeta

← C5×#7643 #11930363

Subgroups — C5×#7643 #11930363

Order 1280.

646 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 174 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×#1797C212yesmaximal
3C5×#1272C214yesmaximal, complemented
4C23×C5×Q8C411yescharacteristic
5C22×C5×C4⋊C4C411yescharacteristic
6C22×C42×C5C2211yescharacteristic
7C2×C5×C4⋊C8—22no—
8C2×C5×C22⋊C8—22no—
9C5×#391—22no—
10C5×#391C412yes—
11C5×#391C2212yes—
12C2×C5×#95—22no—
13C5×#336C2214yes—
14#7643C511yesmaximal, 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×C4⋊C8—44no—
33C5×C22⋊C8—44no—
34C5×#95—24no—
35C5×#95—24no—
36C2×#391C2×C511yescharacteristic
37#1797C2×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—22no—
53C22×C4×C5—22no—
54C22×C4×C5—42no—
55C22×C4×C5—42no—
56C22×C4×C5—42no—
57C22×C4×C5—42no—
58C22×C4×C5—44no—
59C22×C4×C5—42no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5SD1614yes—
63C22×C4×C5Q1614yes—
64C22×C4×C5C22×C411yescharacteristic
65C22×C4×C5C2×D412yes—
66C2×C5×C8—44no—
67C2×C5×C8—44no—
68C2×C5×C8—44no—
69C5×C4⋊C4—42no—
70C5×C4⋊C4—42no—
71C42×C5—24no—
72C42×C5—41no—
73C42×C5—41no—
74C23×Q8C4×C511yescharacteristic
75C22×C4⋊C4C4×C511yescharacteristic
76C22×C42C22×C511yescharacteristic
77C2×C4⋊C8—22no—
78C2×C22⋊C8—22no—
79#391—22no—
80#391C4×C512yes—
81#391C22×C512yes—
82C2×#95—22no—
83#336C22×C514yes—
84C23×C5—21no—
85C23×C5—21no—
86C23×C5—22no—
87C23×C5#10012yes—
88C23×C5#10314yes—
89C23×C5C2×C22⋊C411yescharacteristic
90C5×Q8—44no—
91C5×Q8—48no—
92C5×Q8—44no—
93C2×C4×C5—28no—
94C2×C4×C5—21no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—24no—
103C2×C4×C5—44no—
104C2×C4×C5—44no—
105C2×C4×C5—48no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—44no—
110C2×C4×C5—84no—
111C2×C4×C5#9912yes—
112C2×C4×C5#10314yes—
113C2×C4×C5C2×M1612yes—
114C2×C4×C5C2×SD1612yes—
115C2×C4×C5C2×Q1612yes—
116C5×C8—84no—
117C22×Q8—24no—
118C22×Q8—21no—
119C22×Q8—42no—
120C22×Q8—42no—
121C22×Q8C2×C4×C512yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4C2×C4×C511yescharacteristic
125C23×C4C5×D412yes—
126C22×C8—24no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4C2×C4×C512yes—
130C2×C42—42no—
131C2×C42C2×C4×C511yescharacteristic
132C2×C42C5×D412yes—
133C2×C42C23×C511yescharacteristic
134C4⋊C8—44no—
135C22⋊C8—44no—
136#95—24no—
137#95—24no—
138C22×C5—22no—
139C22×C5—24no—
140C22×C5—24no—
141C22×C5—22no—
142C22×C5#33314yes—
143C22×C5#40711yescharacteristic
144C22×C5C2×#9911yescharacteristic
145C22×C5C2×#10011yescharacteristic
146C22×C5C2×#10312yes—
147C22×C5#42112yes—
148C4×C5—22no—
149C4×C5—22no—
150C4×C5—22no—
151C4×C5—24no—
152C4×C5—22no—
153C4×C5—44no—
154C4×C5—82no—
155C24C5×C22⋊C411yescharacteristic
156C2×Q8—24no—
157C2×Q8—22no—
158C2×Q8—416no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8C5×M1614yes—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—24no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—44no—
175C22×C4—42no—
176C22×C4C5×C22⋊C411yescharacteristic
177C22×C4C5×C22⋊C412yes—
178C22×C4C5×SD1614yes—
179C22×C4C5×Q1614yes—
180C22×C4C22×C4×C511yescharacteristic
181C22×C4C2×C5×D412yes—
182C2×C8—44no—
183C2×C8—44no—
184C2×C8—44no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C42—24no—
188C42—41no—
189C42—41no—
190C2×C5—24no—
191C2×C5#146211yescharacteristic
192C2×C5#148712yes—
193C2×C5#152012yes—
194C2×C5#153311yescharacteristic
195C2×C5C2×#33311yescharacteristic
196C23—21no—
197C23—21no—
198C23—22no—
199C23C5×#10012yes—
200C23C5×#10314yes—
201C23C2×C5×C22⋊C411yescharacteristic
202Q8—44no—
203Q8—44no—
204Q8—48no—
205C2×C4—28no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—44no—
216C2×C4—44no—
217C2×C4—48no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4—84no—
223C2×C4C5×#9912yes—
224C2×C4C5×#10314yes—
225C2×C4C2×C5×M1612yes—
226C2×C4C2×C5×SD1612yes—
227C2×C4C2×C5×Q1612yes—
228C8—84no—
229C5#764311yescharacteristic, direct product factor, Sylow
230C22—24no—
231C22—22no—
232C22—22no—
233C22—24no—
234C22C5×#33314yes—
235C22C5×#40711yescharacteristic
236C22C2×C5×#9911yescharacteristic
237C22C2×C5×#10011yescharacteristic
238C22C2×C5×#10312yes—
239C22C5×#42112yes—
240C4—22no—
241C4—22no—
242C4—24no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—82no—
247C2—24no—
248C2C5×#146211yescharacteristic
249C2C5×#148712yes—
250C2C5×#152012yes—
251C2C5×#153311yescharacteristic
252C2C2×C5×#33311yescharacteristic
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. #7643C5direct (N × H)
38. #1272C2×C5semidirect
229. C5#7643direct (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×#17972
C5×#12722
#76435