Finite Group Databasebeta

← #12008651

Subgroups — #12008651

Order 1280.

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

normal subgroups only

This group has 292 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#10610807C211yesmaximal, characteristic
2#10599886C211yesmaximal, characteristic
3#10599885C211yesmaximal, characteristic
4C5×#1323C211yesmaximal, characteristic
5#10598209C211yesmaximal, characteristic
6#10598016C211yesmaximal, characteristic
7#10598016C211yesmaximal, characteristic
8#65851C411yescharacteristic
9C5×#424C2211yescharacteristic
10#65411C411yescharacteristic
11#65407C411yescharacteristic
12#65391C2211yescharacteristic
13C2×C8×Dic5C2211yescharacteristic
14#65286C411yescharacteristic
15#65119—21no—
16#65119—21no—
17#65117—21no—
18#65117—21no—
19C5×C22⋊C16C2211yescharacteristic
20C5×C22⋊C16C2211yescharacteristic
21C22⋊#672C2211yescharacteristic
22C22⋊#672C2211yescharacteristic
23#64722—21no—
24#64721—21no—
25#64721—21no—
26C16×Dic5—21no—
27#11498—51nomaximal, Sylow
28C2×C5×M16C2×C411yescharacteristic
29C22×C5×C8C2311yescharacteristic
30C5×#117C2×C411yescharacteristic
31#4072C2×C411yescharacteristic
32C2×C4×Dic5C2×C411yescharacteristic
33C2×#681C2×C411yescharacteristic
34C22×#168C2×C411yescharacteristic
35#4036C811yescharacteristic
36#4036C811yescharacteristic
37#4034C811yescharacteristic
38#4034C811yescharacteristic
39#4024—21no—
40#4024—21no—
41C4×Dic10—21no—
42C4×Dic10—21no—
43C2×C5×C16—21no—
44C2×C5×C16—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47#3947—21no—
48#3946—21no—
49#3946—21no—
50#3946—21no—
51#3946—21no—
52C8×Dic5—21no—
53C8×Dic5D411yescharacteristic
54C8×Dic5D411yescharacteristic
55C8×Dic5D411yescharacteristic
56C8×Dic5D411yescharacteristic
57C2×#672—21no—
58C2×#672—21no—
59#3935—21no—
60C4×#168—21no—
61#2960—51no—
62#2163—51no—
63#2162—51no—
64#1323—51no—
65#1323—51no—
66#1323—51no—
67#1323D511yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×Dic5M1611yescharacteristic
70C22×Dic5M1611yescharacteristic
71C2×Dic10—21no—
72C2×Dic10—21no—
73C5×M16—41no—
74C2×C5×C8—21no—
75C2×C5×C8—41no—
76C2×C5×C8C2×D411yescharacteristic
77C2×C5×C8C2×D411yescharacteristic
78C5×C4⋊C4C2×C811yescharacteristic
79C5×C4⋊C4C2×C811yescharacteristic
80C5×C22⋊C4—21no—
81C42×C5—21no—
82C22⋊Dic5—21no—
83C4⋊Dic5—21no—
84C4⋊Dic5—21no—
85C4⋊Dic5C2×C811yescharacteristic
86C4⋊Dic5C2×C811yescharacteristic
87#683—21no—
88#683—21no—
89#683—21no—
90#683—21no—
91C4×Dic5—21no—
92C4×Dic5C22⋊C411yescharacteristic
93C4×Dic5C22⋊C411yescharacteristic
94C4×Dic5C2×C811yescharacteristic
95C4×Dic5C2×C811yescharacteristic
96#681—41no—
97C2×#168—22no—
98C2×#168—21no—
99C2×#168C22⋊C411yescharacteristic
100C2×#168C22⋊C411yescharacteristic
101C5×C16—41no—
102C5×C16—41no—
103#672—41no—
104#672—41no—
105#533—51no—
106#446—101no—
107#446—101no—
108C8×Q8—101no—
109C8×Q8—101no—
110#424—51no—
111#424C2×D511yescharacteristic
112#423—51no—
113#405—51no—
114#405—51no—
115C2×C4×C8—51no—
116C4⋊C16—101no—
117C4⋊C16—101no—
118C22⋊C16—51no—
119C22⋊C16—51no—
120C22⋊C16C2×D511yescharacteristic
121C22⋊C16C2×D511yescharacteristic
122#346—101no—
123C4×C16—101no—
124C23×C5C2×M1611yescharacteristic
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5C2×C22⋊C411yescharacteristic
130C2×C4×C5C22×C811yescharacteristic
131C2×Dic5—22no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—41no—
135C2×Dic5C22⋊C811yescharacteristic
136C2×Dic5C22⋊C811yescharacteristic
137C2×Dic5C22⋊C811yescharacteristic
138C2×Dic5C22⋊C811yescharacteristic
139Dic10—42no—
140Dic10—42no—
141C5×C8—21no—
142C5×C8—21no—
143C5×C8—41no—
144#168—21no—
145#168—41no—
146#168#10112yes—
147C2×M16—51no—
148C2×M16C4×D511yescharacteristic
149C22×C8—51no—
150C22×C8C22×D511yescharacteristic
151C4⋊Q8—51no—
152C4⋊Q8—51no—
153#125—51no—
154#125—51no—
155C22⋊Q8—101no—
156C22⋊Q8—101no—
157C4×Q8—101no—
158C4×Q8—101no—
159#117—51no—
160#117C4×D511yescharacteristic
161C2×C42—51no—
162C2×C16—21no—
163C2×C16—21no—
164C2×C16—101no—
165C2×C16—101no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—101no—
169C4⋊C8—101no—
170C4⋊C8—101no—
171C4⋊C8—101no—
172#97—101no—
173#97—101no—
174C4×C8—51no—
175C4×C8—51no—
176C4×C8—51no—
177C4×C8—51no—
178C4×C8—101no—
179C4×C8—101no—
180C22×C5—21no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5C2×C22⋊C811yescharacteristic
184C4×C5—21no—
185C4×C5—41no—
186C4×C5—41no—
187C4×C5#41011yescharacteristic
188C4×C5C2×#10111yescharacteristic
189Dic5—21no—
190Dic5—21no—
191Dic5—21no—
192Dic5—41no—
193Dic5—41no—
194Dic5#35012yes—
195C2×Q8—101no—
196C2×Q8—101no—
197C22×C4—51no—
198C22×C4—51no—
199C22×C4C2×C4×D511yescharacteristic
200M16—41no—
201M16—201no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—51no—
205C2×C8—51no—
206C2×C8—102no—
207C2×C8—101no—
208C2×C8D4×D511yescharacteristic
209C2×C8D4×D511yescharacteristic
210C4⋊C4—51no—
211C4⋊C4—51no—
212C4⋊C4—101no—
213C4⋊C4—101no—
214C4⋊C4—101no—
215C4⋊C4—101no—
216C4⋊C4—101no—
217C4⋊C4—101no—
218C4⋊C4C8×D511yescharacteristic
219C4⋊C4C8×D511yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—101no—
222C42—21no—
223C42—51no—
224C42—51no—
225C42—51no—
226C42—51no—
227C42—101no—
228C16—41no—
229C16—41no—
230C16—201no—
231C16—201no—
232C2×C5—41no—
233C2×C5#146111yescharacteristic
234C2×C5C2×#35011yescharacteristic
235C2×C5#211711yescharacteristic
236C23D5×M1611yescharacteristic
237Q8—202no—
238Q8—202no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—51no—
244C2×C4—51no—
245C2×C4—51no—
246C2×C4—51no—
247C2×C4—102no—
248C2×C4—101no—
249C2×C4—101no—
250C2×C4—201no—
251C2×C4D5×C22⋊C411yescharacteristic
252C2×C4C2×C8×D511yescharacteristic
253C8—21no—
254C8—21no—
255C8—41no—
256C8—52no—
257C8—101no—
258C8—201no—
259C5#1149811yescharacteristic, complemented, Sylow
260C22—21no—
261C22—21no—
262C22—21no—
263C22D5×C22⋊C811yescharacteristic
264C4—21no—
265C4—41no—
266C4—41no—
267C4—52no—
268C4—101no—
269C4—101no—
270C4—101no—
271C4—201no—
272C4—201no—
273C4#6502911yescharacteristic
274C4D5×#10111yescharacteristic
275C2—41no—
276C2#1059891811yescharacteristic
277C2D5×#35011yescharacteristic
278C2#1059991811yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#1323C2
socleC22×C5C2×C22⋊C8
prime radicalC23×C5C2×M16
cosocleC22×C5×C8C23
hypercenter#1323D5
hypocenterC5#11498
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
259. C5#11498semidirect

Maximal subgroups

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

subgroupindex
#106108072
#105998862
#105998852
C5×#13232
#105982092
#105980162
#114985