Finite Group Databasebeta

← #12008618

Subgroups — #12008618

Order 1280.

418 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 97 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×#65014C211yesmaximal, characteristic
2#10599886C212yesmaximal, complemented
3C5×#1314C211yesmaximal, characteristic, complemented
4#10598164C211yesmaximal, characteristic, complemented
5#10598013C212yesmaximal, complemented
6C2×C4×C22⋊D5C411yescharacteristic
7C23×#168C411yescharacteristic
8C22×C8×D5C411yescharacteristic
9C2×C5×C22⋊C8C2211yescharacteristic
10C2×#3952C2211yescharacteristic
11C2×#3946C411yescharacteristic
12C2×C8×Dic5C2211yescharacteristic
13#65014—22no—
14#65014—22no—
15C5×C22⋊C16C2212yes—
16C22⋊#672C2212yes—
17#64722—22no—
18#64721—22no—
19#11488—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C22×C22⋊D5C811yescharacteristic
22C22×C4×D5C2×C411yescharacteristic
23C22×C5×C8C2×C411yescharacteristic
24C22×C5×C8C2311yescharacteristic
25C2×C22⋊Dic5C811yescharacteristic
26C4×C22⋊D5—22no—
27C4×C22⋊D5—22no—
28C2×#685C811yescharacteristic
29C2×#683C811yescharacteristic
30C2×C4×Dic5C2×C411yescharacteristic
31C22×#168—21no—
32C22×#168—21no—
33C22×#168—42no—
34C22×#168C2×C411yescharacteristic
35C22×#168C2×C411yescharacteristic
36C2×C8×D5—21no—
37C2×C8×D5—21no—
38C2×C8×D5—42no—
39C2×C5×C16—22no—
40C5×C22⋊C8—22no—
41#3952—22no—
42#3946—22no—
43C8×Dic5D412yes—
44C8×Dic5D412yes—
45C2×#672—22no—
46C2×C8×D4—51no—
47#2163—52no—
48#1314—51no—
49#1314—52no—
50#1314D511yescharacteristic, complemented
51C24×C5C2×C811yescharacteristic
52C23×D5C2×C811yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—41no—
56C22×C4×C5—41no—
57C22×C4×C5C2×C811yescharacteristic
58C22×C4×C5C22×C411yescharacteristic
59C2×C22⋊D5—22no—
60C2×C22⋊D5—22no—
61C2×C22⋊D5—22no—
62C22×Dic5C2×C811yescharacteristic
63C22×Dic5C2×C811yescharacteristic
64C22×Dic5C2×C811yescharacteristic
65C2×C4×D5—21no—
66C2×C4×D5—21no—
67C2×C4×D5—41no—
68C2×C4×D5—41no—
69C2×C5×C8—21no—
70C2×C5×C8—41no—
71C2×C5×C8—41no—
72C2×C5×C8C2×D412yes—
73C22⋊Dic5—22no—
74#685—22no—
75#683—22no—
76C4×Dic5C22⋊C412yes—
77C4×Dic5M1612yes—
78C2×#168—22no—
79C2×#168—21no—
80C2×#168—42no—
81C2×#168—42no—
82C2×#168—41no—
83C2×#168C22⋊C411yescharacteristic
84C2×#168C22⋊C411yescharacteristic
85C8×D5—42no—
86C8×D5—42no—
87C5×C16—42no—
88#672—42no—
89C23×C8—51no—
90C23×C8—51no—
91C2×C4×D4—51no—
92C8×D4—102no—
93C8×D4—102no—
94C2×C4⋊C8—51no—
95C2×C22⋊C8—51no—
96C2×C22⋊C8C2×D511yescharacteristic
97C2×C4×C8—51no—
98C4⋊C16—102no—
99C22⋊C16—52no—
100C22⋊C16C2×D512yes—
101#346—102no—
102C23×C5—21no—
103C23×C5—21no—
104C23×C5—41no—
105C23×C5—41no—
106C23×C5M3212yes—
107C23×C5C22×C811yescharacteristic
108C22×D5—21no—
109C22×D5—21no—
110C22×D5—41no—
111C22×D5—41no—
112C22×D5M3212yes—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—42no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5C2×C22⋊C411yescharacteristic
121C2×C4×C5C2×M1611yescharacteristic
122C22⋊D5—28no—
123C2×Dic5—21no—
124C2×Dic5—21no—
125C2×Dic5—21no—
126C2×Dic5—41no—
127C2×Dic5—41no—
128C2×Dic5C22⋊C812yes—
129C2×Dic5C22⋊C812yes—
130C4×D5—42no—
131C4×D5—41no—
132C4×D5—41no—
133C5×C8—22no—
134C5×C8—41no—
135#168—21no—
136#168—41no—
137#168#10012yes—
138C22×D4—51no—
139C23×C4—51no—
140C23×C4C4×D511yescharacteristic
141C22×C8—51no—
142C22×C8—51no—
143C22×C8—101no—
144C22×C8—101no—
145C22×C8—101no—
146C22×C8—101no—
147C22×C8—202no—
148C22×C8—202no—
149C22×C8C4×D511yescharacteristic
150C22×C8C22×D511yescharacteristic
151C4×D4—102no—
152C4×D4—102no—
153C2×C4⋊C4—51no—
154C2×C22⋊C4—51no—
155C2×C22⋊C4—51no—
156C2×C42—51no—
157C2×C16—22no—
158C2×C16—102no—
159C4⋊C8—102no—
160C22⋊C8—22no—
161C22⋊C8—102no—
162C4×C8—52no—
163C4×C8—52no—
164C22×C5—21no—
165C22×C5—21no—
166C22×C5—22no—
167C22×C5—42no—
168C22×C5—42no—
169C22×C5—41no—
170C22×C5—41no—
171C22×C5C2×C22⋊C811yescharacteristic
172C22×C5C2×M3211yescharacteristic
173C22×C5C2×M3211yescharacteristic
174C2×D5—22no—
175C2×D5—42no—
176C2×D5—41no—
177C2×D5—41no—
178C2×D5—42no—
179C4×C5—21no—
180C4×C5—41no—
181C4×C5#41011yescharacteristic
182C4×C5C2×#10011yescharacteristic
183Dic5—22no—
184Dic5—22no—
185Dic5—41no—
186C24—51no—
187C24C8×D511yescharacteristic
188C2×D4—102no—
189C2×D4—102no—
190C2×D4—102no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—51no—
196C22×C4—51no—
197C22×C4—51no—
198C22×C4—101no—
199C22×C4—101no—
200C22×C4—201no—
201C22×C4—201no—
202C22×C4C8×D511yescharacteristic
203C22×C4C2×C4×D511yescharacteristic
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—51no—
208C2×C8—51no—
209C2×C8—102no—
210C2×C8—101no—
211C2×C8—202no—
212C2×C8—202no—
213C2×C8—202no—
214C2×C8—202no—
215C2×C8—201no—
216C2×C8D4×D512yes—
217C4⋊C4—102no—
218C22⋊C4—102no—
219C22⋊C4—102no—
220C42—52no—
221C42—52no—
222C16—42no—
223C16—202no—
224C2×C5—21no—
225C2×C5—21no—
226C2×C5—42no—
227C2×C5#146011yescharacteristic
228C2×C5#211211yescharacteristic
229C2×C5#211511yescharacteristic
230D5—42no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23—52no—
236C23—101no—
237C23—101no—
238C23—201no—
239C23—201no—
240C23#393012yes—
241C23C2×C8×D511yescharacteristic
242D4—108no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—52no—
251C2×C4—52no—
252C2×C4—101no—
253C2×C4—101no—
254C2×C4—101no—
255C2×C4—202no—
256C2×C4—201no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4D5×C22⋊C411yescharacteristic
261C2×C4D5×M1611yescharacteristic
262C8—22no—
263C8—41no—
264C8—52no—
265C8—101no—
266C8—201no—
267C5#1148811yescharacteristic, complemented, Sylow
268C22—21no—
269C22—21no—
270C22—22no—
271C22—42no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—102no—
276C22—202no—
277C22—202no—
278C22—201no—
279C22—201no—
280C22D5×C22⋊C811yescharacteristic
281C22C2×#393011yescharacteristic
282C22D5×M3211yescharacteristic
283C4—21no—
284C4—41no—
285C4—102no—
286C4—102no—
287C4—201no—
288C4#6502911yescharacteristic
289C4D5×#10011yescharacteristic
290C2—21no—
291C2—21no—
292C2—42no—
293C2—202no—
294C2#1059889411yescharacteristic
295C2#1059989911yescharacteristic
296C2#1059991211yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC23×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#1314C2
socleC22×C5C2×C22⋊C8
prime radicalC22×C22⋊D5C8
cosocleC22×C5×C8C23
hypercenter#1314D5
hypocenterC5#11488
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #10599886C2semidirect
3. C5×#1314C2semidirect
4. #10598164C2semidirect
5. #10598013C2semidirect
50. #1314D5semidirect
267. C5#11488semidirect

Maximal subgroups

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

subgroupindex
C2×#650142
#105998862
C5×#13142
#105981642
#105980132
#114885