Finite Group Databasebeta

← C5×#7635 #11930355

Subgroups — C5×#7635 #11930355

Order 1280.

520 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C4×C5×#124C211yesmaximal, characteristic
2C5×#1767C212yesmaximal, complemented
3C5×#1272C212yesmaximal, complemented
4C5×#1270C212yesmaximal
5C2×C5×#124C411yescharacteristic
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×D4C411yescharacteristic
8C2×C5×C4⋊C8—22no—
9C2×C5×#97—22no—
10C5×#391C2211yescharacteristic
11C5×#390C2211yescharacteristic
12C5×#388—22no—
13C5×#382C411yescharacteristic
14C4×C5×C22⋊C4—22no—
15C43×C5C2211yescharacteristic
16C5×#336C2214yes—
17#7635C511yesmaximal, characteristic, direct product factor, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×C5×D4C2×C411yescharacteristic
20C23×C4×C5—21no—
21C22×C5×C8—24no—
22C5×#124—22no—
23C5×#124—22no—
24C4×C5×Q8—42no—
25C4×C5×D4—42no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C22⋊C4—22no—
30C2×C5×C22⋊C4—21no—
31C2×C5×C22⋊C4—22no—
32C2×C42×C5—21no—
33C2×C42×C5C2×C411yescharacteristic
34C2×C42×C5C2×C411yescharacteristic
35C2×C42×C5D412yes—
36C2×C42×C5D412yes—
37C2×C42×C5C2311yescharacteristic
38C5×C4⋊C8—28no—
39C5×#97—44no—
40C5×#95—22no—
41C5×#95—22no—
42C4×#124C2×C511yescharacteristic
43#1767C2×C512yescomplemented
44#1272C2×C512yescomplemented
45#1270C2×C512yes—
46C24×C5—21no—
47C2×C5×Q8—21no—
48C2×C5×Q8—41no—
49C2×C5×Q8—41no—
50C2×C5×Q8M1612yes—
51C2×C5×D4—21no—
52C2×C5×D4—41no—
53C2×C5×D4—41no—
54C2×C5×D4M1612yes—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—42no—
59C22×C4×C5—44no—
60C22×C4×C5C22⋊C411yescharacteristic
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—41no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—42no—
71C5×C22⋊C4—28no—
72C5×C22⋊C4—42no—
73C5×C22⋊C4—42no—
74C5×C22⋊C4—42no—
75C42×C5—22no—
76C42×C5—24no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—22no—
80C42×C5—22no—
81C42×C5—41no—
82C42×C5—42no—
83C2×#124C4×C511yescharacteristic
84C2×C4×Q8C4×C511yescharacteristic
85C2×C4×D4C4×C511yescharacteristic
86C2×C4⋊C8—22no—
87C2×#97—22no—
88#391C22×C511yescharacteristic
89#390C22×C511yescharacteristic
90#388—22no—
91#382C4×C511yescharacteristic
92C4×C22⋊C4—22no—
93C43C22×C511yescharacteristic
94#336C22×C514yes—
95C23×C5—22no—
96C23×C5—41no—
97C23×C5—41no—
98C23×C5—42no—
99C23×C5—42no—
100C23×C5C2×C22⋊C411yescharacteristic
101C5×Q8—42no—
102C5×Q8—42no—
103C5×D4—42no—
104C5×D4—42no—
105C2×C4×C5—22no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—22no—
109C2×C4×C5—22no—
110C2×C4×C5—22no—
111C2×C4×C5—21no—
112C2×C4×C5—22no—
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—84no—
122C2×C4×C5#10012yes—
123C2×C4×C5#10414yes—
124C2×C4×C5C2×M1611yescharacteristic
125C2×C4×C5C2×M1611yescharacteristic
126C2×C4×C5AGL(1,ℤ/8)12yes—
127C2×C4×C5#13712yes—
128C5×C8—48no—
129C22×Q8C2×C4×C511yescharacteristic
130C22×D4C2×C4×C511yescharacteristic
131C23×C4—21no—
132C22×C8—24no—
133#124—22no—
134#124—22no—
135C4×Q8—42no—
136C4×D4—42no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4C2×C4×C511yescharacteristic
139C2×C4⋊C4C2×C4×C511yescharacteristic
140C2×C22⋊C4—22no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—22no—
143C2×C42—21no—
144C2×C42C2×C4×C511yescharacteristic
145C2×C42C2×C4×C511yescharacteristic
146C2×C42C5×D412yes—
147C2×C42C5×D412yes—
148C2×C42C23×C511yescharacteristic
149C4⋊C8—28no—
150#97—44no—
151#95—22no—
152#95—22no—
153C22×C5—42no—
154C22×C5—44no—
155C22×C5—81no—
156C22×C5—82no—
157C22×C5—81no—
158C22×C5#40711yescharacteristic
159C22×C5#41011yescharacteristic
160C22×C5C2×#10011yescharacteristic
161C22×C5#41712yes—
162C22×C5C2×#10412yes—
163C4×C5—21no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—22no—
167C4×C5—41no—
168C4×C5—42no—
169C4×C5—42no—
170C4×C5—81no—
171C4×C5—81no—
172C4×C5#32914yes—
173C24—21no—
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8C5×M1612yes—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4C5×M1612yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—42no—
186C22×C4—44no—
187C22×C4C5×C22⋊C412yes—
188C22×C4C5×C22⋊C411yescharacteristic
189C22×C4C5×C22⋊C411yescharacteristic
190C22×C4C22×C4×C511yescharacteristic
191C22×C4C2×C5×D412yes—
192C2×C8—28no—
193C2×C8—44no—
194C2×C8—44no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C22⋊C4—28no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C42—21no—
203C42—21no—
204C42—22no—
205C42—22no—
206C42—22no—
207C42—24no—
208C42—41no—
209C42—42no—
210C2×C5—82no—
211C2×C5#146611yescharacteristic
212C2×C5#148912yes—
213C2×C5#150912yes—
214C2×C5C2×#32911yescharacteristic
215C2×C5#156011yescharacteristic
216C23—22no—
217C23—41no—
218C23—41no—
219C23—42no—
220C23—42no—
221C23C2×C5×C22⋊C411yescharacteristic
222Q8—42no—
223Q8—42no—
224D4—42no—
225D4—42no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—84no—
243C2×C4C5×#10012yes—
244C2×C4C5×#10414yes—
245C2×C4C2×C5×M1611yescharacteristic
246C2×C4C2×C5×M1611yescharacteristic
247C2×C4C5×AGL(1,ℤ/8)12yes—
248C2×C4C5×#13712yes—
249C8—48no—
250C5#763511yescharacteristic, direct product factor, Sylow
251C22—42no—
252C22—44no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22C5×#40711yescharacteristic
257C22C5×#41011yescharacteristic
258C22C2×C5×#10011yescharacteristic
259C22C5×#41712yes—
260C22C2×C5×#10412yes—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—21no—
265C4—41no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—81no—
270C4C5×#32914yes—
271C2—82no—
272C2C5×#146611yescharacteristic
273C2C5×#148912yes—
274C2C5×#150912yes—
275C2C2×C5×#32911yescharacteristic
276C2C5×#156011yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C43×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1767C2semidirect
3. C5×#1272C2semidirect
17. #7635C5direct (N × H)
43. #1767C2×C5semidirect
44. #1272C2×C5semidirect
250. C5#7635direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1242
C5×#17672
C5×#12722
C5×#12702
#76355