Finite Group Databasebeta

← #13023792

Subgroups — #13023792

Order 1280.

320 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#10611249C211yesmaximal, characteristic
2#10603828C211yesmaximal, characteristic, complemented
3D5⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
4D4⋊#674C212yesmaximal, complemented
5#10598581C212yesmaximal, complemented
6#65891C411yescharacteristic
7C2×D5⋊C16—21no—
8C5×#436C411yescharacteristic
9#65416—21no—
10#65411—21no—
11D4×#168C2211yescharacteristic
12#65124C411yescharacteristic
13#65119C2211yescharacteristic
14#65014—21no—
15#65009—21no—
16C4×C8×D5C2211yescharacteristic
17#64968C411yescharacteristic
18#64888—21no—
19#64888—21no—
20#64887—21no—
21C4⋊#674C2212yes—
22C4×#674C2212yes—
23#11622—51nomaximal, Sylow
24C2×C5×M16—21no—
25C4×C5×D4C2×C411yescharacteristic
26#4084C811yescharacteristic
27#4082C811yescharacteristic
28C4×C22⋊D5—21no—
29#4072—21no—
30C22×#168—21no—
31C2×C8×D5D411yescharacteristic
32C2×C8×D5D411yescharacteristic
33#4043C811yescharacteristic
34#4036C811yescharacteristic
35#4029—21no—
36#4025—21no—
37C42×D5C2×C411yescharacteristic
38C4×Dic10C2×C411yescharacteristic
39C2×#674—22no—
40C2×#674—22no—
41D5⋊C16—42no—
42C5×C4⋊C8C2×C411yescharacteristic
43C5×C22⋊C8—21no—
44C4×C5×C8C2×C411yescharacteristic
45C22⋊#168—21no—
46#3952—21no—
47#3947—21no—
48#3947—21no—
49#3946—21no—
50#3946—21no—
51C8×Dic5—21no—
52C8×Dic5D411yescharacteristic
53C8×Dic5D411yescharacteristic
54C4⋊#168C2×C411yescharacteristic
55C4×#168C2311yescharacteristic
56#2966—51no—
57#2162—51no—
58C2×C4⋊C16—51no—
59Q8⋊C16—52no—
60D4⋊C16—52no—
61C2×C5×D4C2×C811yescharacteristic
62C22×C4×C5—21no—
63C2×C22⋊D5—21no—
64C2×C4×D5C22⋊C411yescharacteristic
65C2×C4×D5C2×C811yescharacteristic
66C2×C4×D5M1611yescharacteristic
67C2×Dic10C2×C811yescharacteristic
68C5×M16—42no—
69C2×C5×C8—21no—
70C2×C5×C8C22⋊C411yescharacteristic
71C2×C5×C8C22⋊C411yescharacteristic
72C5×C4⋊C4C2×C811yescharacteristic
73C5×C22⋊C4—21no—
74C42×C5C22×C411yescharacteristic
75C22⋊Dic5—21no—
76C22⋊Dic5—21no—
77C22⋊Dic5—21no—
78#685—21no—
79C4⋊Dic5—21no—
80C4⋊Dic5—21no—
81C4⋊Dic5C2×C811yescharacteristic
82#683—21no—
83#683—21no—
84C4×Dic5—21no—
85C4×Dic5C22⋊C411yescharacteristic
86C4×Dic5C2×C811yescharacteristic
87C4×Dic5M1611yescharacteristic
88C2×#168—21no—
89C2×#168—41no—
90C2×#168—41no—
91C2×#168C2×D411yescharacteristic
92C2×#168C2×D411yescharacteristic
93C8×D5—21no—
94C8×D5—21no—
95C8×D5—41no—
96#674—42no—
97#674—42no—
98#529—51no—
99C22×C16—101no—
100#446—51no—
101C8×Q8—51no—
102#436AGL(1,𝔽5)11yescharacteristic
103#435—101no—
104C8×D4—51no—
105C8×D4—101no—
106#433—101no—
107#432—51no—
108#405—101no—
109C2×C4×C8—51no—
110C4⋊C16—52no—
111C4⋊C16—101no—
112C4⋊C16—101no—
113C22⋊C16—101no—
114C4×C16—52no—
115C23×C5—21no—
116C22×D5C22⋊C811yescharacteristic
117C5×D4—22no—
118C2×C4×C5—21no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5C2×C22⋊C411yescharacteristic
122C2×C4×C5C22×C811yescharacteristic
123C2×C4×C5C2×M1611yescharacteristic
124C22⋊D5—42no—
125C2×Dic5—21no—
126C2×Dic5—21no—
127C2×Dic5C22⋊C811yescharacteristic
128C2×Dic5C22⋊C811yescharacteristic
129C2×Dic5C22⋊C811yescharacteristic
130C4×D5—22no—
131C4×D5—21no—
132C4×D5—21no—
133C4×D5—22no—
134Dic10—22no—
135C5×C8—21no—
136C5×C8—21no—
137C5×C8—41no—
138#168—21no—
139#168—41no—
140#168AGL(1,ℤ/8)11yescharacteristic
141#168#13711yescharacteristic
142C2×M16—21no—
143C22×C8—51no—
144C22×C8—51no—
145C22×C8—101no—
146#126—101no—
147#125—51no—
148#124—51no—
149#123—101no—
150C22⋊Q8—51no—
151#121—51no—
152C4×Q8—51no—
153C4×D4—101no—
154C4×D4C2×AGL(1,𝔽5)11yescharacteristic
155#117—101no—
156C2×C42—51no—
157C2×C16—102no—
158C2×C16—102no—
159C2×C16—202no—
160C4⋊C8—51no—
161C4⋊C8—101no—
162C4⋊C8—101no—
163C4⋊C8C2×AGL(1,𝔽5)11yescharacteristic
164C22⋊C8—21no—
165C22⋊C8—101no—
166C22⋊C8—101no—
167#97—101no—
168#97—101no—
169C4×C8—51no—
170C4×C8—51no—
171C4×C8—51no—
172C4×C8—101no—
173C4×C8C2×AGL(1,𝔽5)11yescharacteristic
174C22×C5—41no—
175C22×C5—41no—
176C22×C5—41no—
177C22×C5C2×C22⋊C811yescharacteristic
178C2×D5—21no—
179C2×D5—21no—
180C2×D5#35012yes—
181C4×C5—21no—
182C4×C5—41no—
183C4×C5#41711yescharacteristic
184C4×C5#42111yescharacteristic
185C4×C5#50412yes—
186Dic5—21no—
187Dic5—21no—
188Dic5—21no—
189Dic5—41no—
190Dic5—41no—
191C2×Q8—51no—
192C2×D4—101no—
193C2×D4D5⋊C811yescharacteristic
194C22×C4—21no—
195C22×C4—51no—
196C22×C4—51no—
197C22×C4—51no—
198M16—42no—
199C2×C8—21no—
200C2×C8—51no—
201C2×C8—51no—
202C2×C8—101no—
203C2×C8—101no—
204C2×C8—101no—
205C2×C8—201no—
206C2×C8—201no—
207C2×C8—201no—
208C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
209C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
210C4⋊C4—51no—
211C4⋊C4—101no—
212C4⋊C4—101no—
213C4⋊C4—101no—
214C4⋊C4—101no—
215C4⋊C4D5⋊C811yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—101no—
218C22⋊C4—101no—
219C22⋊C4—101no—
220C22⋊C4—101no—
221C42—51no—
222C42—51no—
223C42—51no—
224C42—101no—
225C42C22×AGL(1,𝔽5)11yescharacteristic
226C16—202no—
227C16—202no—
228C2×C5—81no—
229C2×C5#147711yescharacteristic
230C2×C5#211311yescharacteristic
231C2×C5C2×#35011yescharacteristic
232D5—22no—
233C23—21no—
234C23—51no—
235Q8—102no—
236D4—22no—
237D4—202no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—51no—
242C2×C4—51no—
243C2×C4—51no—
244C2×C4—102no—
245C2×C4—101no—
246C2×C4—102no—
247C2×C4—101no—
248C2×C4—101no—
249C2×C4—101no—
250C2×C4C2×D5⋊C811yescharacteristic
251C2×C4D5⋊M1611yescharacteristic
252C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
253C8—21no—
254C8—21no—
255C8—41no—
256C8—51no—
257C8—51no—
258C8—101no—
259C8—201no—
260C5#1162211yescharacteristic, complemented, Sylow
261C22—41no—
262C22—41no—
263C22—41no—
264C22—52no—
265C22—101no—
266C22—101no—
267C22D5⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—41no—
270C4—101no—
271C4—101no—
272C4—101no—
273C4—201no—
274C4—201no—
275C4#6572512yes—
276C4#6576911yescharacteristic
277C4#6579311yescharacteristic
278C2—81no—
279C2—102no—
280C2#1060440211yescharacteristic
281C2#1060474311yescharacteristic
282C2D5⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC42C22×AGL(1,𝔽5)
FittingC5×#436C4
socleC22×C5C2×C22⋊C8
prime radical#4084C8
cosocleC4×#168C23
hypercenter#436AGL(1,𝔽5)
hypocenterC5#11622
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #10603828C2semidirect
3. D5⋊(C4⋊C16)C2semidirect
4. D4⋊#674C2semidirect
5. #10598581C2semidirect
260. C5#11622semidirect

Maximal subgroups

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

subgroupindex
#106112492
#106038282
D5⋊(C4⋊C16)2
D4⋊#6742
#105985812
#116225