Finite Group Databasebeta

← C5×#11533 #11934253

Subgroups — C5×#11533 #11934253

Order 1280.

504 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2328C211yesmaximal, characteristic
2C5×#1465C212yesmaximal, complemented
3C5×#1324C212yesmaximal, complemented
4C5×#1318C212yesmaximal, complemented
5C2×C5×#127C411yescharacteristic
6C2×C4×C5×D4C411yescharacteristic
7C2×C4×C5×D4C2211yescharacteristic
8C5×#407—22no—
9C5×#390C411yescharacteristic
10C5×#390C2211yescharacteristic
11C5×#386—22no—
12C5×#386—22no—
13C5×#382C2211yescharacteristic
14C5×#376C411yescharacteristic
15C5×#324C2214yes—
16C5×#323—22no—
17#11533C511yesmaximal, characteristic, direct product factor, Sylow
18C22×C5×D4—22no—
19C22×C5×D4C2×C411yescharacteristic
20C22×C5×D4C2×C411yescharacteristic
21C23×C4×C5—21no—
22C23×C4×C5D412yes—
23C2×C5×M16—42no—
24C5×#127—22no—
25C5×#127—22no—
26C4×C5×D4—42no—
27C4×C5×D4—42no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4C2311yescharacteristic
30C2×C5×C22⋊C4—21no—
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4—22no—
33C2×C5×C22⋊C4D412yes—
34C2×C42×C5C2×C411yescharacteristic
35C2×C42×C5C2×C411yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C5×C22⋊C8—24no—
38C5×C22⋊C8—42no—
39C5×#95—21no—
40C5×#95—21no—
41C5×#95—22no—
42#2328C2×C511yescharacteristic
43#1465C2×C512yescomplemented
44#1324C2×C512yescomplemented
45#1318C2×C512yescomplemented
46C24×C5—21no—
47C24×C5C22⋊C412yes—
48C2×C5×D4—28no—
49C2×C5×D4—21no—
50C2×C5×D4—21no—
51C2×C5×D4—21no—
52C2×C5×D4—41no—
53C2×C5×D4—41no—
54C2×C5×D4—41no—
55C2×C5×D4—41no—
56C2×C5×D4—82no—
57C2×C5×D4—82no—
58C2×C5×D4M1612yescomplemented
59C22×C4×C5—21no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—42no—
65C22×C4×C5—82no—
66C22×C4×C5—82no—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D412yes—
71C5×M16—84no—
72C2×C5×C8—44no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—41no—
75C5×C22⋊C4—42no—
76C5×C22⋊C4—42no—
77C5×C22⋊C4—82no—
78C5×C22⋊C4—82no—
79C42×C5—22no—
80C42×C5—21no—
81C42×C5—41no—
82C42×C5M1612yescomplemented
83C2×#127C4×C511yescharacteristic
84C2×C4×D4C4×C511yescharacteristic
85C2×C4×D4C22×C511yescharacteristic
86#407—22no—
87#390C4×C511yescharacteristic
88#390C22×C511yescharacteristic
89#386—22no—
90#386—22no—
91#382C22×C511yescharacteristic
92#376C4×C511yescharacteristic
93#324C22×C514yes—
94#323—22no—
95C23×C5—22no—
96C23×C5—22no—
97C23×C5—22no—
98C23×C5—22no—
99C23×C5—42no—
100C23×C5—42no—
101C23×C5—42no—
102C23×C5—42no—
103C23×C5—41no—
104C23×C5—41no—
105C23×C5C2×C22⋊C411yescharacteristic
106C5×D4—42no—
107C5×D4—42no—
108C5×D4—42no—
109C5×D4—42no—
110C5×D4—88no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—22no—
114C2×C4×C5—21no—
115C2×C4×C5—22no—
116C2×C4×C5—41no—
117C2×C4×C5—44no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—42no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—42no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—82no—
128C2×C4×C5—84no—
129C2×C4×C5#9912yes—
130C2×C4×C5C2×M1611yescharacteristic
131C2×C4×C5C2×M1611yescharacteristic
132C5×C8—84no—
133C22×D4—22no—
134C22×D4C2×C4×C511yescharacteristic
135C22×D4C2×C4×C511yescharacteristic
136C23×C4—21no—
137C23×C4C5×D412yes—
138C2×M16—42no—
139#127—22no—
140#127—22no—
141C4×D4—42no—
142C4×D4—42no—
143C2×C4⋊C4C2×C4×C511yescharacteristic
144C2×C4⋊C4C23×C511yescharacteristic
145C2×C22⋊C4—21no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4C5×D412yes—
149C2×C42C2×C4×C511yescharacteristic
150C2×C42C2×C4×C511yescharacteristic
151C2×C42C2×C4×C511yescharacteristic
152C22⋊C8—24no—
153C22⋊C8—42no—
154#95—21no—
155#95—21no—
156#95—22no—
157C22×C5—21no—
158C22×C5—21no—
159C22×C5—44no—
160C22×C5—44no—
161C22×C5—42no—
162C22×C5—42no—
163C22×C5—42no—
164C22×C5—42no—
165C22×C5—82no—
166C22×C5—82no—
167C22×C5—81no—
168C22×C5—81no—
169C22×C5#40711yescharacteristic
170C22×C5C2×#9911yescharacteristic
171C22×C5#41311yescharacteristic
172C4×C5—22no—
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—42no—
176C4×C5—42no—
177C4×C5—41no—
178C4×C5—81no—
179C4×C5—81no—
180C24—21no—
181C24C5×C22⋊C412yes—
182C2×D4—28no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—82no—
191C2×D4—82no—
192C2×D4C5×M1612yescomplemented
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—82no—
200C22×C4—82no—
201C22×C4C5×C22⋊C411yescharacteristic
202C22×C4C5×C22⋊C411yescharacteristic
203C22×C4C22×C4×C511yescharacteristic
204C22×C4C2×C5×D412yes—
205M16—84no—
206C2×C8—44no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—82no—
212C22⋊C4—82no—
213C42—21no—
214C42—22no—
215C42—41no—
216C42C5×M1612yescomplemented
217C2×C5—21no—
218C2×C5—21no—
219C2×C5—82no—
220C2×C5—82no—
221C2×C5#146511yescharacteristic
222C2×C5#212711yescharacteristic
223C2×C5#213411yescharacteristic
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—41no—
233C23—41no—
234C23C2×C5×C22⋊C411yescharacteristic
235D4—42no—
236D4—42no—
237D4—42no—
238D4—42no—
239D4—88no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—44no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—82no—
257C2×C4—84no—
258C2×C4C5×#9912yes—
259C2×C4C2×C5×M1611yescharacteristic
260C2×C4C2×C5×M1611yescharacteristic
261C8—84no—
262C5#1153311yescharacteristic, direct product factor, Sylow
263C22—21no—
264C22—21no—
265C22—44no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—82no—
272C22—82no—
273C22—81no—
274C22—81no—
275C22C5×#40711yescharacteristic
276C22C2×C5×#9911yescharacteristic
277C22C5×#41311yescharacteristic
278C4—22no—
279C4—21no—
280C4—21no—
281C4—42no—
282C4—42no—
283C4—41no—
284C4—81no—
285C4—81no—
286C2—21no—
287C2—21no—
288C2—82no—
289C2—82no—
290C2C5×#146511yescharacteristic
291C2C5×#212711yescharacteristic
292C2C5×#213411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC2×C5×#127C4
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
2. C5×#1465C2semidirect
3. C5×#1324C2semidirect
4. C5×#1318C2semidirect
17. #11533C5direct (N × H)
43. #1465C2×C5semidirect
44. #1324C2×C5semidirect
45. #1318C2×C5semidirect
58. C2×C5×D4M16semidirect
82. C42×C5M16semidirect
192. C2×D4C5×M16semidirect
216. C42C5×M16semidirect
262. C5#11533direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23282
C5×#14652
C5×#13242
C5×#13182
#115335