Finite Group Databasebeta

← C5×#11532 #11934252

Subgroups — C5×#11532 #11934252

Order 1280.

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

normal subgroups only

This group has 412 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×C4⋊Q8C211yesmaximal, characteristic
2C5×#1467C212yesmaximal
3C5×#1325C212yesmaximal
4C5×#1319C212yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#432—22no—
9C5×#391C411yescharacteristic
10C5×#391C2211yescharacteristic
11C5×#389—22no—
12C5×#384C2211yescharacteristic
13C4×C5×C4⋊C4—22no—
14C43×C5C411yescharacteristic
15C5×#324—22no—
16C5×#324C2214yes—
17#11532C511yesmaximal, characteristic, direct product factor, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×C5×Q8C2×C411yescharacteristic
20C5×C4⋊Q8—22no—
21C5×C4⋊Q8—22no—
22C4×C5×Q8—41no—
23C4×C5×Q8—41no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4C2311yescharacteristic
32C2×C42×C5—21no—
33C2×C42×C5—21no—
34C2×C42×C5—21no—
35C2×C42×C5C2×C411yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5D412yes—
39C5×C4⋊C8—42no—
40C5×C22⋊C8—24no—
41C5×#97—42no—
42C5×#95—22no—
43C5×#95—22no—
44C4×C4⋊Q8C2×C511yescharacteristic
45#1467C2×C512yes—
46#1325C2×C512yes—
47#1319C2×C512yes—
48C2×C5×Q8—21no—
49C2×C5×Q8—21no—
50C2×C5×Q8—21no—
51C2×C5×Q8—41no—
52C2×C5×Q8—41no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8M1612yes—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5C22⋊C412yes—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D412yes—
65C2×C5×C8—44no—
66C5×C4⋊C4—28no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—41no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—44no—
71C5×C4⋊C4—42no—
72C42×C5—24no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—22no—
76C42×C5—22no—
77C42×C5—21no—
78C42×C5—41no—
79C42×C5—42no—
80C42×C5—41no—
81C42×C5—41no—
82C42×C5M1612yes—
83C2×C4⋊Q8C4×C511yescharacteristic
84C2×C4×Q8C4×C511yescharacteristic
85C2×C4×Q8C22×C511yescharacteristic
86#432—22no—
87#391C4×C511yescharacteristic
88#391C22×C511yescharacteristic
89#389—22no—
90#384C22×C511yescharacteristic
91C4×C4⋊C4—22no—
92C43C4×C511yescharacteristic
93#324—22no—
94#324C22×C514yes—
95C23×C5C2×C22⋊C411yescharacteristic
96C5×Q8—42no—
97C5×Q8—42no—
98C5×Q8—42no—
99C5×Q8—42no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—22no—
109C2×C4×C5—21no—
110C2×C4×C5—22no—
111C2×C4×C5—22no—
112C2×C4×C5—22no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—41no—
121C2×C4×C5#9911yescharacteristic
122C2×C4×C5#9911yescharacteristic
123C2×C4×C5C2×M1611yescharacteristic
124C2×C4×C5C2×M1611yescharacteristic
125C5×C8—84no—
126C22×Q8C2×C4×C511yescharacteristic
127C22×Q8C2×C4×C511yescharacteristic
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C2×C4×C511yescharacteristic
138C2×C4⋊C4C5×D412yes—
139C2×C4⋊C4C23×C511yescharacteristic
140C2×C42—21no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42C2×C4×C511yescharacteristic
144C2×C42C2×C4×C511yescharacteristic
145C2×C42C2×C4×C511yescharacteristic
146C2×C42C5×D412yes—
147C4⋊C8—42no—
148C22⋊C8—24no—
149#97—42no—
150#95—22no—
151#95—22no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5#40711yescharacteristic
155C22×C5C2×#9911yescharacteristic
156C22×C5#41311yescharacteristic
157C4×C5—24no—
158C4×C5—21no—
159C4×C5—21no—
160C4×C5—21no—
161C4×C5—42no—
162C4×C5—42no—
163C4×C5—41no—
164C4×C5—42no—
165C4×C5—42no—
166C4×C5—81no—
167C4×C5#35612yes—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8C5×M1612yes—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4C5×C22⋊C412yes—
181C22×C4C5×C22⋊C411yescharacteristic
182C22×C4C5×C22⋊C411yescharacteristic
183C22×C4C22×C4×C511yescharacteristic
184C22×C4C2×C5×D412yes—
185C2×C8—44no—
186C4⋊C4—28no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—44no—
192C42—24no—
193C42—21no—
194C42—22no—
195C42—22no—
196C42—21no—
197C42—21no—
198C42—41no—
199C42—42no—
200C42—41no—
201C42—41no—
202C42C5×M1612yes—
203C2×C5—21no—
204C2×C5—21no—
205C2×C5#146511yescharacteristic
206C2×C5#212611yescharacteristic
207C2×C5C2×#35611yescharacteristic
208C23C2×C5×C22⋊C411yescharacteristic
209Q8—42no—
210Q8—42no—
211Q8—42no—
212Q8—42no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4C5×#9911yescharacteristic
235C2×C4C5×#9911yescharacteristic
236C2×C4C2×C5×M1611yescharacteristic
237C2×C4C2×C5×M1611yescharacteristic
238C8—84no—
239C5#1153211yescharacteristic, direct product factor, Sylow
240C22—21no—
241C22—21no—
242C22C5×#40711yescharacteristic
243C22C2×C5×#9911yescharacteristic
244C22C5×#41311yescharacteristic
245C4—24no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—41no—
252C4—42no—
253C4—42no—
254C4—81no—
255C4C5×#35612yes—
256C2—21no—
257C2—21no—
258C2C5×#146511yescharacteristic
259C2C5×#212611yescharacteristic
260C2C2×C5×#35611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC23×C5C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
17. #11532C5direct (N × H)
239. C5#11532direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×C4⋊Q82
C5×#14672
C5×#13252
C5×#13192
#115325