Finite Group Databasebeta

← C5×#11505 #11934225

Subgroups — C5×#11505 #11934225

Order 1280.

814 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 118 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×#390C211yesmaximal, characteristic
2C5×#1463C212yesmaximal, complemented
3C5×#1318C214yesmaximal, complemented
4C23×C5×D4C411yescharacteristic
5C22×C5×C4⋊C4C2211yescharacteristic
6C22×C5×C22⋊C4—22no—
7C22×C42×C5C411yescharacteristic
8C5×#407—22no—
9C5×#390—22no—
10C5×#390C412yes—
11C5×#390C2212yes—
12C5×#324—22no—
13C5×#324C2214yescomplemented
14#11505C511yesmaximal, characteristic, direct product factor, Sylow
15C25×C5—21no—
16C22×C5×D4—24no—
17C22×C5×D4—21no—
18C22×C5×D4—41no—
19C22×C5×D4—41no—
20C22×C5×D4—42no—
21C22×C5×D4C2×C412yes—
22C23×C4×C5—21no—
23C23×C4×C5C2×C411yescharacteristic
24C23×C4×C5D412yes—
25C2×C5×M16—42no—
26C2×C5×C4⋊C4—41no—
27C2×C5×C4⋊C4—41no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4D412yes—
30C2×C5×C4⋊C4C2311yescharacteristic
31C2×C5×C22⋊C4—24no—
32C2×C5×C22⋊C4—24no—
33C2×C5×C22⋊C4—48no—
34C2×C42×C5—21no—
35C2×C42×C5—42no—
36C2×C42×C5C2×C412yes—
37C5×C22⋊C8—24no—
38C5×C22⋊C8—42no—
39C2×#390C2×C511yescharacteristic
40#1463C2×C512yescomplemented
41#1318C2×C514yescomplemented
42C24×C5—24no—
43C24×C5—22no—
44C24×C5—44no—
45C24×C5—42no—
46C24×C5—44no—
47C24×C5—41no—
48C24×C5—41no—
49C24×C5C22⋊C411yescharacteristic
50C2×C5×D4—24no—
51C2×C5×D4—22no—
52C2×C5×D4—42no—
53C2×C5×D4—42no—
54C2×C5×D4—48no—
55C2×C5×D4—48no—
56C2×C5×D4—42no—
57C2×C5×D4—42no—
58C2×C5×D4M1614yescomplemented
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5—24no—
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—22no—
67C22×C4×C5—42no—
68C22×C4×C5—42no—
69C22×C4×C5—44no—
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C2×D412yes—
74C5×M16—84no—
75C2×C5×C8—44no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—42no—
78C5×C4⋊C4—41no—
79C5×C22⋊C4—48no—
80C5×C22⋊C4—48no—
81C42×C5—42no—
82C42×C5—42no—
83C23×D4C4×C511yescharacteristic
84C22×C4⋊C4C22×C511yescharacteristic
85C22×C22⋊C4—22no—
86C22×C42C4×C511yescharacteristic
87#407—22no—
88#390—22no—
89#390C4×C512yes—
90#390C22×C512yes—
91#324—22no—
92#324C22×C514yescomplemented
93C23×C5—22no—
94C23×C5—22no—
95C23×C5—21no—
96C23×C5—21no—
97C23×C5—24no—
98C23×C5—44no—
99C23×C5—44no—
100C23×C5—44no—
101C23×C5—416no—
102C23×C5—44no—
103C23×C5—42no—
104C23×C5—42no—
105C23×C5—88no—
106C23×C5—82no—
107C23×C5—82no—
108C23×C5—82no—
109C23×C5—82no—
110C23×C5#9911yescharacteristic
111C23×C5#9911yescharacteristic
112C23×C5C2×C22⋊C411yescharacteristic
113C5×D4—44no—
114C5×D4—48no—
115C5×D4—44no—
116C2×C4×C5—24no—
117C2×C4×C5—24no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—24no—
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—48no—
126C2×C4×C5—42no—
127C2×C4×C5—44no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—42no—
131C2×C4×C5—82no—
132C2×C4×C5#10012yes—
133C2×C4×C5C2×M1612yes—
134C5×C8—84no—
135C25—21no—
136C22×D4—24no—
137C22×D4—21no—
138C22×D4—41no—
139C22×D4—41no—
140C22×D4—42no—
141C22×D4C2×C4×C512yes—
142C23×C4—21no—
143C23×C4C2×C4×C511yescharacteristic
144C23×C4C5×D412yes—
145C2×M16—42no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4C2×C4×C511yescharacteristic
149C2×C4⋊C4C5×D412yes—
150C2×C4⋊C4C23×C511yescharacteristic
151C2×C22⋊C4—24no—
152C2×C22⋊C4—24no—
153C2×C22⋊C4—48no—
154C2×C42—21no—
155C2×C42—42no—
156C2×C42C2×C4×C512yes—
157C22⋊C8—24no—
158C22⋊C8—42no—
159C22×C5—24no—
160C22×C5—24no—
161C22×C5—21no—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5—21no—
165C22×C5—21no—
166C22×C5—21no—
167C22×C5—48no—
168C22×C5—44no—
169C22×C5—84no—
170C22×C5—88no—
171C22×C5—88no—
172C22×C5—82no—
173C22×C5—82no—
174C22×C5#35312yes—
175C22×C5#35512yes—
176C22×C5#40711yescharacteristic
177C22×C5C2×#9911yescharacteristic
178C22×C5C2×#10011yescharacteristic
179C4×C5—22no—
180C4×C5—22no—
181C4×C5—44no—
182C4×C5—42no—
183C4×C5—42no—
184C24—24no—
185C24—22no—
186C24—44no—
187C24—42no—
188C24—44no—
189C24—41no—
190C24—41no—
191C24C5×C22⋊C411yescharacteristic
192C2×D4—24no—
193C2×D4—22no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—48no—
197C2×D4—48no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4C5×M1614yescomplemented
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—24no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—44no—
212C22×C4C5×C22⋊C411yescharacteristic
213C22×C4C5×C22⋊C412yes—
214C22×C4C22×C4×C511yescharacteristic
215C22×C4C2×C5×D412yes—
216M16—84no—
217C2×C8—44no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—41no—
221C22⋊C4—48no—
222C22⋊C4—48no—
223C42—42no—
224C42—42no—
225C2×C5—21no—
226C2×C5—21no—
227C2×C5—22no—
228C2×C5—22no—
229C2×C5—84no—
230C2×C5#146211yescharacteristic
231C2×C5C2×#35311yescharacteristic
232C2×C5C2×#35511yescharacteristic
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—24no—
238C23—44no—
239C23—44no—
240C23—44no—
241C23—416no—
242C23—44no—
243C23—42no—
244C23—42no—
245C23—88no—
246C23—82no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23C5×#9911yescharacteristic
251C23C5×#9911yescharacteristic
252C23C2×C5×C22⋊C411yescharacteristic
253D4—44no—
254D4—44no—
255D4—48no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—48no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4C5×#10012yes—
273C2×C4C2×C5×M1612yes—
274C8—84no—
275C5#1150511yescharacteristic, direct product factor, Sylow
276C22—24no—
277C22—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—48no—
285C22—44no—
286C22—84no—
287C22—88no—
288C22—88no—
289C22—82no—
290C22—82no—
291C22C5×#35312yes—
292C22C5×#35512yes—
293C22C5×#40711yescharacteristic
294C22C2×C5×#9911yescharacteristic
295C22C2×C5×#10011yescharacteristic
296C4—22no—
297C4—22no—
298C4—44no—
299C4—42no—
300C4—42no—
301C2—21no—
302C2—21no—
303C2—22no—
304C2—22no—
305C2—84no—
306C2C5×#146211yescharacteristic
307C2C2×C5×#35311yescharacteristic
308C2C2×C5×#35511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC23×C5×D4C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1463C2semidirect
3. C5×#1318C2semidirect
13. C5×#324C22semidirect
14. #11505C5direct (N × H)
40. #1463C2×C5semidirect
41. #1318C2×C5semidirect
58. C2×C5×D4M16semidirect
92. #324C22×C5semidirect
200. C2×D4C5×M16semidirect
275. C5#11505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3902
C5×#14632
C5×#13182
#115055