Finite Group Databasebeta

← #12009199

Subgroups — #12009199

Order 1280.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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#10600077C211yesmaximal, characteristic, complemented
3#10599866C211yesmaximal, characteristic, complemented
4C5×#1330C211yesmaximal, characteristic, complemented
5#10598252C211yesmaximal, characteristic, complemented
6#10598050C211yesmaximal, characteristic, complemented
7#10598009C211yesmaximal, characteristic, complemented
8#65891C411yescharacteristic
9C5×#436C2211yescharacteristic
10#65416—21no—
11#65411—21no—
12D4×#168C411yescharacteristic
13C2×#3930—21no—
14#65124C411yescharacteristic
15#65119C411yescharacteristic
16#65014—21no—
17#65009—21no—
18C4×C8×D5C2211yescharacteristic
19#64968C2211yescharacteristic
20C5×C4⋊C16C2211yescharacteristic
21C5×#346C2211yescharacteristic
22#64727—21no—
23#64721—21no—
24#64721—21no—
25C4⋊#672C2211yescharacteristic
26#64681C2211yescharacteristic
27#11627—51nomaximal, Sylow
28C2×C5×M16—21no—
29C4×C5×D4C2×C411yescharacteristic
30#4084C811yescharacteristic
31#4082C811yescharacteristic
32C4×C22⋊D5—21no—
33#4072—21no—
34C22×#168—21no—
35C2×C8×D5D411yescharacteristic
36C2×C8×D5D411yescharacteristic
37#4043C811yescharacteristic
38#4036C811yescharacteristic
39#4029—21no—
40#4025—21no—
41C42×D5C2×C411yescharacteristic
42C4×Dic10C2×C411yescharacteristic
43C2×C5×C16—21no—
44C2×C5×C16—21no—
45C5×C4⋊C8C2×C411yescharacteristic
46C5×C22⋊C8—21no—
47C4×C5×C8C2311yescharacteristic
48C22⋊#168—21no—
49#3952—21no—
50#3947—21no—
51#3947—21no—
52#3946—21no—
53#3946—21no—
54C8×Dic5—21no—
55C8×Dic5D411yescharacteristic
56C8×Dic5D411yescharacteristic
57C2×#672—21no—
58C2×#672—21no—
59C4⋊#168C2×C411yescharacteristic
60C4×#168C2×C411yescharacteristic
61#3930—42no—
62#2966—51no—
63#2163—51no—
64#2150—51no—
65#1338—51no—
66#1338—51no—
67#1330—51no—
68#1330D511yescharacteristic, complemented
69C2×C5×D4C2×C811yescharacteristic
70C22×C4×C5—21no—
71C2×C22⋊D5—21no—
72C2×C4×D5C22⋊C411yescharacteristic
73C2×C4×D5C2×C811yescharacteristic
74C2×C4×D5M1611yescharacteristic
75C2×Dic10C2×C811yescharacteristic
76C5×M16—41no—
77C5×M16—41no—
78C2×C5×C8—21no—
79C2×C5×C8C2×D411yescharacteristic
80C2×C5×C8C2×D411yescharacteristic
81C5×C4⋊C4C2×C811yescharacteristic
82C5×C22⋊C4—21no—
83C42×C5C22×C411yescharacteristic
84C22⋊Dic5—21no—
85C22⋊Dic5—21no—
86C22⋊Dic5—21no—
87#685—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5—21no—
90C4⋊Dic5C2×C811yescharacteristic
91#683—21no—
92#683—21no—
93C4×Dic5—21no—
94C4×Dic5C22⋊C411yescharacteristic
95C4×Dic5C2×C811yescharacteristic
96C4×Dic5M1611yescharacteristic
97C2×#168—21no—
98C2×#168—42no—
99C2×#168C22⋊C411yescharacteristic
100C2×#168C22⋊C411yescharacteristic
101C8×D5—21no—
102C8×D5—21no—
103C8×D5—41no—
104C5×C16—41no—
105C5×C16—41no—
106#672—41no—
107#672—41no—
108#529—51no—
109C2×M32—101no—
110#446—51no—
111C8×Q8—51no—
112#436C2×D511yescharacteristic
113#435—101no—
114C8×D4—51no—
115C8×D4—101no—
116#433—101no—
117#432—51no—
118#405—101no—
119C2×C4×C8—51no—
120C4⋊C16—51no—
121C4⋊C16—101no—
122C4⋊C16—101no—
123C4⋊C16C2×D511yescharacteristic
124C22⋊C16—101no—
125#346—51no—
126#346C2×D511yescharacteristic
127C23×C5—21no—
128C22×D5C22⋊C811yescharacteristic
129C5×D4—41no—
130C2×C4×C5—21no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5C2×C22⋊C411yescharacteristic
134C2×C4×C5C22×C811yescharacteristic
135C2×C4×C5C2×M1611yescharacteristic
136C22⋊D5—42no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5C22⋊C811yescharacteristic
140C2×Dic5C22⋊C811yescharacteristic
141C2×Dic5C22⋊C811yescharacteristic
142C4×D5—21no—
143C4×D5—21no—
144C4×D5—41no—
145C4×D5—41no—
146Dic10—41no—
147C5×C8—21no—
148C5×C8—41no—
149C5×C8AGL(1,ℤ/8)11yescharacteristic
150C5×C8#13711yescharacteristic
151#168—21no—
152#168—21no—
153#168—41no—
154C2×M16—21no—
155C22×C8—51no—
156C22×C8—51no—
157C22×C8—101no—
158#126—101no—
159#125—51no—
160#124—51no—
161#123—101no—
162C22⋊Q8—51no—
163#121—51no—
164C4×Q8—51no—
165C4×D4—101no—
166C4×D4C4×D511yescharacteristic
167#117—101no—
168C2×C42—51no—
169M32—202no—
170C2×C16—21no—
171C2×C16—21no—
172C2×C16—101no—
173C2×C16—101no—
174C4⋊C8—51no—
175C4⋊C8—101no—
176C4⋊C8—101no—
177C4⋊C8C4×D511yescharacteristic
178C22⋊C8—21no—
179C22⋊C8—101no—
180C22⋊C8—101no—
181#97—101no—
182#97—101no—
183C4×C8—51no—
184C4×C8—51no—
185C4×C8—51no—
186C4×C8—101no—
187C4×C8C22×D511yescharacteristic
188C22×C5—41no—
189C22×C5—41no—
190C22×C5—41no—
191C22×C5C2×C22⋊C811yescharacteristic
192C2×D5—21no—
193C2×D5—21no—
194C2×D5—21no—
195C4×C5—21no—
196C4×C5—21no—
197C4×C5—41no—
198C4×C5#41711yescharacteristic
199C4×C5#42111yescharacteristic
200Dic5—21no—
201Dic5—21no—
202Dic5—21no—
203Dic5—41no—
204Dic5—41no—
205C2×Q8—51no—
206C2×D4—101no—
207C2×D4C8×D511yescharacteristic
208C22×C4—21no—
209C22×C4—51no—
210C22×C4—51no—
211C22×C4—51no—
212M16—41no—
213M16—41no—
214C2×C8—21no—
215C2×C8—51no—
216C2×C8—51no—
217C2×C8—101no—
218C2×C8—101no—
219C2×C8—101no—
220C2×C8—201no—
221C2×C8—202no—
222C2×C8D4×D511yescharacteristic
223C2×C8D4×D511yescharacteristic
224C4⋊C4—51no—
225C4⋊C4—101no—
226C4⋊C4—101no—
227C4⋊C4—101no—
228C4⋊C4—101no—
229C4⋊C4C8×D511yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—101no—
232C22⋊C4—101no—
233C22⋊C4—101no—
234C22⋊C4—101no—
235C42—51no—
236C42—51no—
237C42—51no—
238C42—101no—
239C42C2×C4×D511yescharacteristic
240C16—41no—
241C16—41no—
242C16—201no—
243C16—201no—
244C2×C5—81no—
245C2×C5#147711yescharacteristic
246C2×C5#211511yescharacteristic
247C2×C5#211711yescharacteristic
248D5—41no—
249C23—21no—
250C23—51no—
251Q8—201no—
252D4—41no—
253D4—202no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—51no—
258C2×C4—51no—
259C2×C4—51no—
260C2×C4—101no—
261C2×C4—101no—
262C2×C4—101no—
263C2×C4—101no—
264C2×C4—201no—
265C2×C4—201no—
266C2×C4D5×C22⋊C411yescharacteristic
267C2×C4C2×C8×D511yescharacteristic
268C2×C4D5×M1611yescharacteristic
269C8—21no—
270C8—41no—
271C8—101no—
272C8—101no—
273C8—201no—
274C8#405711yescharacteristic
275C8#406111yescharacteristic
276C5#1162711yescharacteristic, complemented, Sylow
277C22—41no—
278C22—41no—
279C22—41no—
280C22—101no—
281C22—101no—
282C22—101no—
283C22D5×C22⋊C811yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—101no—
288C4—101no—
289C4—101no—
290C4—201no—
291C4—201no—
292C4#6506011yescharacteristic
293C4#6511011yescharacteristic
294C2—81no—
295C2—201no—
296C2#1059895911yescharacteristic
297C2#1059991211yescharacteristic
298C2#1059991811yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C22×C8
FrattiniC4×C8C22×D5
FittingC5×#1330C2
socleC22×C5C2×C22⋊C8
prime radical#4084C8
cosocleC4×C5×C8C23
hypercenter#1330D5
hypocenterC5#11627
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #10600077C2semidirect
3. #10599866C2semidirect
4. C5×#1330C2semidirect
5. #10598252C2semidirect
6. #10598050C2semidirect
7. #10598009C2semidirect
68. #1330D5semidirect
276. C5#11627semidirect

Maximal subgroups

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

subgroupindex
#106112492
#106000772
#105998662
C5×#13302
#105982522
#105980502
#105980092
#116275