Finite Group Databasebeta

← C5×#11531 #11934251

Subgroups — C5×#11531 #11934251

Order 1280.

460 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 110 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×#1465C212yesmaximal
3C5×#1324C212yesmaximal, complemented
4C5×#1319C212yesmaximal, complemented
5C2×C5×#124C411yescharacteristic
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×D4C2211yescharacteristic
8C5×#407—22no—
9C5×#391C2211yescharacteristic
10C5×#390C411yescharacteristic
11C5×#388—22no—
12C5×#382C2211yescharacteristic
13C4×C5×C22⋊C4—22no—
14C43×C5C411yescharacteristic
15C5×#324C2214yes—
16C5×#323—22no—
17#11531C511yesmaximal, characteristic, direct product factor, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×C5×D4C2×C411yescharacteristic
20C23×C4×C5D412yes—
21C2×C5×M16—42no—
22C5×#124—22no—
23C5×#124—22no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4C2311yescharacteristic
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4—22no—
33C2×C5×C22⋊C4D412yes—
34C2×C42×C5—21no—
35C2×C42×C5—21no—
36C2×C42×C5—21no—
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5C2×C411yescharacteristic
39C2×C42×C5C2×C411yescharacteristic
40C5×C22⋊C8—24no—
41C5×C22⋊C8—42no—
42C5×#95—22no—
43C5×#95—22no—
44C4×#124C2×C511yescharacteristic
45#1465C2×C512yes—
46#1324C2×C512yescomplemented
47#1319C2×C512yescomplemented
48C24×C5C22⋊C412yes—
49C2×C5×Q8—21no—
50C2×C5×Q8—41no—
51C2×C5×Q8—41no—
52C2×C5×Q8M1612yescomplemented
53C2×C5×D4—21no—
54C2×C5×D4—21no—
55C2×C5×D4—41no—
56C2×C5×D4—41no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—21no—
63C22×C4×C5—44no—
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D412yes—
68C5×M16—84no—
69C2×C5×C8—44no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C5×C22⋊C4—28no—
74C5×C22⋊C4—42no—
75C5×C22⋊C4—44no—
76C42×C5—21no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—41no—
80C42×C5—42no—
81C42×C5—42no—
82C42×C5—41no—
83C42×C5—41no—
84C42×C5M1612yescomplemented
85C2×#124C4×C511yescharacteristic
86C2×C4×Q8C4×C511yescharacteristic
87C2×C4×D4C22×C511yescharacteristic
88#407—22no—
89#391C22×C511yescharacteristic
90#390C4×C511yescharacteristic
91#388—22no—
92#382C22×C511yescharacteristic
93C4×C22⋊C4—22no—
94C43C4×C511yescharacteristic
95#324C22×C514yes—
96#323—22no—
97C23×C5—22no—
98C23×C5—22no—
99C23×C5—22no—
100C23×C5—42no—
101C23×C5—42no—
102C23×C5C2×C22⋊C411yescharacteristic
103C5×Q8—42no—
104C5×Q8—42no—
105C5×D4—42no—
106C5×D4—42no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—22no—
110C2×C4×C5—22no—
111C2×C4×C5—22no—
112C2×C4×C5—22no—
113C2×C4×C5—21no—
114C2×C4×C5—22no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—44no—
122C2×C4×C5—41no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—41no—
126C2×C4×C5—82no—
127C2×C4×C5#9911yescharacteristic
128C2×C4×C5#9911yescharacteristic
129C2×C4×C5C2×M1611yescharacteristic
130C2×C4×C5C2×M1611yescharacteristic
131C5×C8—84no—
132C22×Q8C2×C4×C511yescharacteristic
133C22×D4C2×C4×C511yescharacteristic
134C23×C4C5×D412yes—
135C2×M16—42no—
136#124—22no—
137#124—22no—
138C4×Q8—41no—
139C4×Q8—41no—
140C4×D4—41no—
141C4×D4—41no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4C2×C4×C511yescharacteristic
144C2×C4⋊C4C23×C511yescharacteristic
145C2×C22⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4C5×D412yes—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42C2×C4×C511yescharacteristic
152C2×C42C2×C4×C511yescharacteristic
153C2×C42C2×C4×C511yescharacteristic
154C22⋊C8—24no—
155C22⋊C8—42no—
156#95—22no—
157#95—22no—
158C22×C5—21no—
159C22×C5—21no—
160C22×C5—44no—
161C22×C5—42no—
162C22×C5—42no—
163C22×C5—42no—
164C22×C5—82no—
165C22×C5#40711yescharacteristic
166C22×C5C2×#9911yescharacteristic
167C22×C5#41311yescharacteristic
168C4×C5—21no—
169C4×C5—21no—
170C4×C5—21no—
171C4×C5—42no—
172C4×C5—42no—
173C4×C5—42no—
174C4×C5—41no—
175C4×C5—42no—
176C4×C5—81no—
177C4×C5#35412yes—
178C24C5×C22⋊C412yes—
179C2×Q8—21no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8C5×M1612yescomplemented
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—44no—
194C22×C4C5×C22⋊C411yescharacteristic
195C22×C4C5×C22⋊C411yescharacteristic
196C22×C4C22×C4×C511yescharacteristic
197C22×C4C2×C5×D412yes—
198M16—84no—
199C2×C8—44no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C22⋊C4—28no—
204C22⋊C4—42no—
205C22⋊C4—44no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—41no—
210C42—42no—
211C42—42no—
212C42—41no—
213C42—41no—
214C42C5×M1612yescomplemented
215C2×C5—21no—
216C2×C5—21no—
217C2×C5—82no—
218C2×C5#146511yescharacteristic
219C2×C5C2×#35411yescharacteristic
220C2×C5#213211yescharacteristic
221C23—22no—
222C23—22no—
223C23—22no—
224C23—42no—
225C23—42no—
226C23C2×C5×C22⋊C411yescharacteristic
227Q8—42no—
228Q8—42no—
229D4—42no—
230D4—42no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—44no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—82no—
251C2×C4C5×#9911yescharacteristic
252C2×C4C5×#9911yescharacteristic
253C2×C4C2×C5×M1611yescharacteristic
254C2×C4C2×C5×M1611yescharacteristic
255C8—84no—
256C5#1153111yescharacteristic, direct product factor, Sylow
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—82no—
264C22C5×#40711yescharacteristic
265C22C2×C5×#9911yescharacteristic
266C22C5×#41311yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—42no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—81no—
276C4C5×#35412yes—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C5×#146511yescharacteristic
281C2C2×C5×#35411yescharacteristic
282C2C5×#213211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC22×C5×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1324C2semidirect
4. C5×#1319C2semidirect
17. #11531C5direct (N × H)
46. #1324C2×C5semidirect
47. #1319C2×C5semidirect
52. C2×C5×Q8M16semidirect
84. C42×C5M16semidirect
182. C2×Q8C5×M16semidirect
214. C42C5×M16semidirect
256. C5#11531direct (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×#14652
C5×#13242
C5×#13192
#115315