Finite Group Databasebeta

← C5×#11520 #11934240

Subgroups — C5×#11520 #11934240

Order 1280.

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

normal subgroups only

This group has 418 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
1C5×#2317C211yesmaximal, characteristic
2C5×#1464C211yesmaximal, characteristic
3C5×#1464C211yesmaximal, characteristic
4C5×#1326C214yesmaximal
5C2×C5×#117C411yescharacteristic
6C2×C5×#117C2211yescharacteristic
7C22×C5×C4⋊C4C411yescharacteristic
8C5×#432—21no—
9C5×#432—21no—
10C5×#389—21no—
11C5×#389—21no—
12C5×#385C412yes—
13C5×#385C2212yes—
14C5×#384—21no—
15C5×#382—21no—
16C5×#324—21no—
17C5×#324—21no—
18C5×#323C2212yes—
19C5×#323C2212yes—
20#11520C511yesmaximal, characteristic, direct product factor, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C412yes—
23C5×#117—24no—
24C5×#117—41no—
25C5×#117—41no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—41no—
32C2×C5×C4⋊C4—41no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C22⋊C4C2×C412yes—
36C2×C5×C22⋊C4C2×C411yescharacteristic
37C2×C5×C22⋊C4C2311yescharacteristic
38C2×C42×C5—21no—
39C2×C42×C5D411yescharacteristic
40C2×C42×C5D411yescharacteristic
41C5×C4⋊C8—41no—
42C5×C4⋊C8—41no—
43C5×C22⋊C8—22no—
44C5×C22⋊C8—22no—
45C5×#97—41no—
46C5×#97—41no—
47C5×#95—22no—
48C5×#95—22no—
49#2317C2×C511yescharacteristic
50#1464C2×C511yescharacteristic
51#1464C2×C511yescharacteristic
52#1326C2×C514yes—
53C24×C5C22×C411yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—42no—
61C22×C4×C5—82no—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C2×C5×C8—42no—
69C2×C5×C8—42no—
70C5×C4⋊C4—24no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—82no—
77C5×C4⋊C4—82no—
78C5×C22⋊C4—22no—
79C5×C22⋊C4—41no—
80C5×C22⋊C4—41no—
81C5×C22⋊C4M1614yes—
82C42×C5—24no—
83C42×C5—21no—
84C42×C5—21no—
85C42×C5—21no—
86C42×C5—21no—
87C2×#117C4×C511yescharacteristic
88C2×#117C22×C511yescharacteristic
89C22×C4⋊C4C4×C511yescharacteristic
90#432—21no—
91#432—21no—
92#389—21no—
93#389—21no—
94#385C4×C512yes—
95#385C22×C512yes—
96#384—21no—
97#382—21no—
98#324—21no—
99#324—21no—
100#323C22×C512yes—
101#323C22×C512yes—
102C23×C5—21no—
103C23×C5—21no—
104C23×C5—41no—
105C23×C5—41no—
106C23×C5C2×C22⋊C411yescharacteristic
107C23×C5C2×M1612yes—
108C2×C4×C5—24no—
109C2×C4×C5—24no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—24no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—84no—
129C2×C4×C5#9911yescharacteristic
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#10112yes—
132C5×C8—82no—
133C5×C8—82no—
134C23×C4C2×C4×C511yescharacteristic
135C23×C4C2×C4×C512yes—
136#117—24no—
137#117—41no—
138#117—41no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4C5×D411yescharacteristic
147C2×C4⋊C4C5×D411yescharacteristic
148C2×C22⋊C4C2×C4×C512yes—
149C2×C22⋊C4C2×C4×C511yescharacteristic
150C2×C22⋊C4C23×C511yescharacteristic
151C2×C42—21no—
152C2×C42C5×D411yescharacteristic
153C2×C42C5×D411yescharacteristic
154C4⋊C8—41no—
155C4⋊C8—41no—
156C22⋊C8—22no—
157C22⋊C8—22no—
158#97—41no—
159#97—41no—
160#95—22no—
161#95—22no—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5—22no—
165C22×C5—42no—
166C22×C5—42no—
167C22×C5—41no—
168C22×C5—41no—
169C22×C5#40711yescharacteristic
170C22×C5C2×#9911yescharacteristic
171C22×C5C2×#10111yescharacteristic
172C4×C5—21no—
173C4×C5—21no—
174C4×C5—22no—
175C4×C5—44no—
176C4×C5—41no—
177C4×C5—41no—
178C4×C5—41no—
179C4×C5—41no—
180C4×C5—82no—
181C24C22×C4×C511yescharacteristic
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—42no—
189C22×C4—82no—
190C22×C4C5×C22⋊C411yescharacteristic
191C22×C4C5×C22⋊C411yescharacteristic
192C22×C4C5×C22⋊C411yescharacteristic
193C22×C4C5×C22⋊C411yescharacteristic
194C22×C4C2×C5×D411yescharacteristic
195C22×C4C2×C5×D411yescharacteristic
196C2×C8—42no—
197C2×C8—42no—
198C4⋊C4—24no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C22⋊C4—22no—
207C22⋊C4—41no—
208C22⋊C4—41no—
209C22⋊C4C5×M1614yes—
210C42—24no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C2×C5—21no—
216C2×C5—21no—
217C2×C5—42no—
218C2×C5#146311yescharacteristic
219C2×C5#212211yescharacteristic
220C2×C5#212311yescharacteristic
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×C5×C22⋊C411yescharacteristic
226C23C2×C5×M1612yes—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—24no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—84no—
248C2×C4C5×#9911yescharacteristic
249C2×C4C5×#9911yescharacteristic
250C2×C4C5×#10112yes—
251C8—82no—
252C8—82no—
253C5#1152011yescharacteristic, direct product factor, Sylow
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22C5×#40711yescharacteristic
262C22C2×C5×#9911yescharacteristic
263C22C2×C5×#10111yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—44no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2C5×#146311yescharacteristic
277C2C5×#212211yescharacteristic
278C2C5×#212311yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC24×C5C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
20. #11520C5direct (N × H)
253. C5#11520direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23172
C5×#14642
C5×#13262
#115205