Finite Group Databasebeta

← #12008523

Subgroups — #12008523

Order 1280.

454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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×#65123C211yesmaximal, characteristic
2D5×C22⋊C16C212yesmaximal, complemented
3C5×#1322C211yesmaximal, characteristic, complemented
4#10598200C211yesmaximal, characteristic, complemented
5#10598013C212yesmaximal, complemented
6C22×C8×D5C411yescharacteristic
7C22×C8×D5C2211yescharacteristic
8C2×C4×D20C411yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×#3952C411yescharacteristic
11C2×#3952C2211yescharacteristic
12C2×C4×#168C411yescharacteristic
13C2×D5×C16—22no—
14#65123—22no—
15#65123—22no—
16C5×C22⋊C16C2212yes—
17C22⋊#672C2212yes—
18#64727—22no—
19#11465—51nomaximal, Sylow
20C22×D20C811yescharacteristic
21C22×C4×D5C2×C411yescharacteristic
22C22×C4×D5C2×C411yescharacteristic
23C22×C5×C8C2×C411yescharacteristic
24C22×C5×C8C2311yescharacteristic
25C2×C42×C5C2×C411yescharacteristic
26C2×#685C811yescharacteristic
27C2×#685C811yescharacteristic
28C2×C4⋊Dic5C811yescharacteristic
29C22×#168C2×C411yescharacteristic
30C22×#168C2×C411yescharacteristic
31C2×C8×D5—21no—
32C2×C8×D5—21no—
33C2×C8×D5—42no—
34C2×C8×D5—42no—
35C2×C8×D5D412yes—
36C2×C8×D5D412yes—
37C4×D20—22no—
38C4×D20—22no—
39C2×C5×C16—22no—
40C5×C4⋊C8—22no—
41#3952—22no—
42#3952—22no—
43C2×#672—22no—
44C4×#168—21no—
45C4×#168—21no—
46D5×C16—44no—
47C2×C8×D4—51no—
48C2×C22⋊C16—52no—
49#1322—51no—
50#1322D511yescharacteristic, complemented
51#1314—52no—
52C23×D5C2×C811yescharacteristic
53C23×D5C2×C811yescharacteristic
54C22×C4×C5C2×C811yescharacteristic
55C22×C4×C5C2×C811yescharacteristic
56C22×C4×C5C22×C411yescharacteristic
57C22×Dic5C2×C811yescharacteristic
58C22×Dic5C2×C811yescharacteristic
59C2×D20—22no—
60C2×D20—22no—
61C2×D20C1614yescomplemented
62C2×C4×D5—21no—
63C2×C4×D5—21no—
64C2×C4×D5—41no—
65C2×C4×D5—41no—
66C2×C4×D5—41no—
67C2×C4×D5—41no—
68C2×C4×D5C22⋊C412yes—
69C2×C4×D5M1612yes—
70C2×C5×C8—21no—
71C2×C5×C8—41no—
72C2×C5×C8—41no—
73C2×C5×C8C2×D412yes—
74C42×C5—21no—
75C42×C5—21no—
76#685—22no—
77#685—22no—
78C4⋊Dic5—22no—
79C2×#168—22no—
80C2×#168—21no—
81C2×#168—41no—
82C2×#168C22⋊C411yescharacteristic
83C2×#168C22⋊C411yescharacteristic
84C8×D5—24no—
85C8×D5—42no—
86C8×D5—42no—
87C8×D5—42no—
88C5×C16—42no—
89#672—42no—
90C23×C8—51no—
91C23×C8—51no—
92C2×C4×D4—51no—
93C22×C16—102no—
94C8×D4—102no—
95C8×D4—102no—
96C2×C4⋊C8C2×D511yescharacteristic
97C2×C22⋊C8—51no—
98C2×C22⋊C8—51no—
99C2×C4×C8—51no—
100C22⋊C16—52no—
101C22⋊C16—102no—
102C22⋊C16C2×D512yes—
103C23×C5C22×C811yescharacteristic
104C22×D5—21no—
105C22×D5—21no—
106C22×D5—41no—
107C22×D5—41no—
108C22×D5—41no—
109C22×D5—41no—
110C22×D5C22⋊C812yes—
111C22×D5C2×C1612yes—
112C22×D5C2×C1612yescomplemented
113C22×D5M3212yes—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—41no—
120C2×C4×C5C2×C1612yescomplemented
121C2×C4×C5C2×C22⋊C411yescharacteristic
122C2×C4×C5C2×M1611yescharacteristic
123C2×Dic5—21no—
124C2×Dic5—41no—
125C2×Dic5—41no—
126C2×Dic5C22⋊C812yes—
127D20—28no—
128C4×D5—22no—
129C4×D5—22no—
130C4×D5—42no—
131C4×D5—42no—
132C4×D5—41no—
133C4×D5—41no—
134C5×C8—22no—
135C5×C8—41no—
136#168—21no—
137#168—41no—
138#168#9912yes—
139C22×D4—51no—
140C23×C4—51no—
141C23×C4—51no—
142C22×C8—51no—
143C22×C8—52no—
144C22×C8—52no—
145C22×C8—51no—
146C22×C8—101no—
147C22×C8—101no—
148C22×C8—202no—
149C22×C8—202no—
150C22×C8C4×D511yescharacteristic
151C22×C8C22×D511yescharacteristic
152C4×D4—102no—
153C4×D4—102no—
154C2×C4⋊C4—51no—
155C2×C22⋊C4—51no—
156C2×C22⋊C4—51no—
157C2×C42C4×D511yescharacteristic
158C2×C16—22no—
159C2×C16—102no—
160C2×C16—204no—
161C4⋊C8—22no—
162C22⋊C8—102no—
163C22⋊C8—102no—
164C4×C8—101no—
165C4×C8—101no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5C2×C22⋊C811yescharacteristic
169C22×C5C22×C1611yescharacteristic
170C22×C5C2×M3211yescharacteristic
171C2×D5—22no—
172C2×D5—22no—
173C2×D5—22no—
174C2×D5—42no—
175C2×D5—42no—
176C2×D5—42no—
177C2×D5—41no—
178C2×D5—41no—
179C2×D5—42no—
180C2×D5C22⋊C1614yes—
181C4×C5—22no—
182C4×C5—21no—
183C4×C5—41no—
184C4×C5C2×#9911yescharacteristic
185C4×C5#41311yescharacteristic
186Dic5—22no—
187Dic5—41no—
188C24—51no—
189C24—51no—
190C2×D4—54no—
191C2×D4—102no—
192C2×D4—102no—
193C22×C4—51no—
194C22×C4—52no—
195C22×C4—52no—
196C22×C4—51no—
197C22×C4—101no—
198C22×C4—101no—
199C22×C4—201no—
200C22×C4—201no—
201C22×C4—201no—
202C22×C4—201no—
203C22×C4C8×D511yescharacteristic
204C22×C4C8×D511yescharacteristic
205C22×C4C2×C4×D511yescharacteristic
206C2×C8—21no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—51no—
210C2×C8—51no—
211C2×C8—104no—
212C2×C8—102no—
213C2×C8—101no—
214C2×C8—202no—
215C2×C8—202no—
216C2×C8—202no—
217C2×C8—201no—
218C2×C8D4×D512yes—
219C4⋊C4—102no—
220C22⋊C4—102no—
221C22⋊C4—102no—
222C42—21no—
223C42—21no—
224C16—42no—
225C16—202no—
226C2×C5—21no—
227C2×C5—21no—
228C2×C5#145911yescharacteristic
229C2×C5C2×C22⋊C1611yescharacteristic
230C2×C5#211511yescharacteristic
231D5—24no—
232D5—42no—
233C23—52no—
234C23—52no—
235C23—52no—
236C23—52no—
237C23—101no—
238C23—101no—
239C23—201no—
240C23—201no—
241C23—201no—
242C23—201no—
243C23C2×C8×D511yescharacteristic
244D4—108no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—52no—
252C2×C4—102no—
253C2×C4—102no—
254C2×C4—101no—
255C2×C4—202no—
256C2×C4—202no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4—201no—
261C2×C4D5×C1612yescomplemented
262C2×C4D5×C22⋊C411yescharacteristic
263C2×C4D5×M1611yescharacteristic
264C8—22no—
265C8—41no—
266C8—52no—
267C8—101no—
268C8—201no—
269C5#1146511yescharacteristic, complemented, Sylow
270C22—21no—
271C22—21no—
272C22—54no—
273C22—102no—
274C22—102no—
275C22—102no—
276C22—202no—
277C22—202no—
278C22—202no—
279C22—202no—
280C22—201no—
281C22—201no—
282C22D5×C22⋊C811yescharacteristic
283C22C2×D5×C1611yescharacteristic
284C22D5×M3211yescharacteristic
285C4—21no—
286C4—22no—
287C4—41no—
288C4—102no—
289C4—201no—
290C4D5×#9911yescharacteristic
291C4#6504011yescharacteristic
292C2—21no—
293C2—21no—
294C2—104no—
295C2—202no—
296C2#1059893611yescharacteristic
297C2D5×C22⋊C1611yescharacteristic
298C2#1059991211yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC22×C5C22×C16
FrattiniC22×C8C22×D5
FittingC5×#1322C2
socleC22×C5C2×C22⋊C8
prime radicalC22×D20C8
cosocleC22×C5×C8C23
hypercenter#1322D5
hypocenterC5#11465
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. D5×C22⋊C16C2semidirect
3. C5×#1322C2semidirect
4. #10598200C2semidirect
5. #10598013C2semidirect
50. #1322D5semidirect
61. C2×D20C16semidirect
112. C22×D5C2×C16semidirect
120. C2×C4×C5C2×C16semidirect
261. C2×C4D5×C16semidirect
269. C5#11465semidirect

Maximal subgroups

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

subgroupindex
C2×#651232
D5×C22⋊C162
C5×#13222
#105982002
#105980132
#114655