Finite Group Databasebeta

← #11989697

Subgroups — #11989697

Order 1280.

520 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 147 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#10611062C212yesmaximal
2#10610769C211yesmaximal, characteristic
3C5×#1307C211yesmaximal, characteristic, complemented
4#10598249C212yesmaximal, complemented
5#10598207C211yesmaximal, characteristic, complemented
6C2×C42×D5C2211yescharacteristic
7C5×#432C2212yes—
8C5×#423C2211yescharacteristic
9#65415C412yes—
10M16×Dic5C412yes—
11#65215C2212yes—
12#65213C2211yescharacteristic
13#65126—22no—
14#65124—22no—
15#65122—22no—
16#65122—22no—
17#65015C414yes—
18#65007C414yes—
19#64996—22no—
20#64994—22no—
21#8122—51nomaximal, Sylow
22C22×C4×D5C2×C411yescharacteristic
23C22×C4×D5C2×C412yes—
24C2×C5×M16C2×C412yes—
25C2×C42×C5C2311yescharacteristic
26C2×C4×Dic5C2×C411yescharacteristic
27C2×C4×Dic5C2×C412yes—
28C2×#681C2×C412yes—
29C2×#676—24no—
30C42×D5D412yes—
31C42×D5D412yes—
32C42×D5D412yes—
33C42×D5Q812yes—
34C5×C4⋊C8—22no—
35C5×C4⋊C8—22no—
36C5×C22⋊C8C2×C414yes—
37C5×#97—22no—
38C22⋊#168C2×C414yes—
39#3952—24no—
40#3952—24no—
41#3947—22no—
42#3946—24no—
43C8×Dic5—22no—
44C8×Dic5—24no—
45C4⋊#168—22no—
46C4⋊#168—22no—
47#3935—22no—
48#2920—51no—
49#2920—52no—
50#1307—52no—
51#1307—51no—
52#1307D511yescharacteristic, complemented
53C23×D5C4211yescharacteristic
54C22×C4×C5C22×C411yescharacteristic
55C22×C4×C5C22×C412yes—
56C22×Dic5C4212yes—
57C22×Dic5C4211yescharacteristic
58C2×C4×D5—44no—
59C2×C4×D5—41no—
60C2×C4×D5—41no—
61C2×C4×D5C22⋊C412yes—
62C2×C4×D5C22⋊C412yes—
63C2×C4×D5C22⋊C412yes—
64C2×C4×D5C4⋊C412yes—
65C2×C4×D5C4⋊C412yes—
66C2×C4×D5C4⋊C412yes—
67C5×M16—42no—
68C2×C5×C8—22no—
69C2×C5×C8—24no—
70C42×C5C2×D411yescharacteristic
71C42×C5C2×D412yes—
72C42×C5C2×Q811yescharacteristic
73C4×Dic5C22⋊C412yes—
74C4×Dic5C22⋊C411yescharacteristic
75C4×Dic5C22⋊C412yes—
76C4×Dic5C22⋊C411yescharacteristic
77C4×Dic5C4⋊C412yes—
78C4×Dic5C4⋊C412yes—
79C4×Dic5C4⋊C412yes—
80#681—42no—
81C2×#168—24no—
82C2×#168—22no—
83#676—48no—
84C22×C42—51no—
85#432—52no—
86#432—102no—
87#432—102no—
88#432C2×D512yes—
89#431—54no—
90#431—102no—
91#431—102no—
92#423—51no—
93#423—102no—
94#423C2×D511yescharacteristic
95#407—54no—
96#407—52no—
97C4×M16—52no—
98C4×M16—102no—
99C23×C5C2×C4211yescharacteristic
100C22×D5—41no—
101C22×D5—42no—
102C22×D5#9512yes—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—42no—
106C2×C4×C5C2×C22⋊C412yes—
107C2×C4×C5C2×C22⋊C411yescharacteristic
108C2×C4×C5C2×C4⋊C411yescharacteristic
109C2×C4×C5C2×C4⋊C412yes—
110C2×Dic5—24no—
111C2×Dic5—41no—
112C2×Dic5#9512yes—
113C2×Dic5#9512yes—
114C2×Dic5#9512yes—
115C4×D5—22no—
116C4×D5—22no—
117C4×D5—24no—
118C4×D5—24no—
119C4×D5—42no—
120C4×D5—42no—
121C4×D5—42no—
122C5×C8—44no—
123C5×C8—42no—
124#168—44no—
125#168—42no—
126C23×C4—52no—
127C23×C4—51no—
128C2×M16—52no—
129C2×M16—104no—
130C2×M16C4×D512yes—
131C2×C42—51no—
132C2×C42—52no—
133C2×C42—52no—
134C2×C42—52no—
135C2×C42—52no—
136C2×C42—52no—
137C2×C42C22×D511yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8—104no—
141C4⋊C8—102no—
142C4⋊C8—102no—
143C22⋊C8—54no—
144C22⋊C8—104no—
145C22⋊C8—104no—
146C22⋊C8C4×D514yes—
147#97—22no—
148#97—102no—
149#97—102no—
150C4×C8—102no—
151C4×C8—104no—
152C22×C5—21no—
153C22×C5—22no—
154C22×C5C2×#9511yescharacteristic
155C2×D5—22no—
156C2×D5—22no—
157C2×D5—22no—
158C2×D5—44no—
159C4×C5—21no—
160C4×C5—22no—
161C4×C5—22no—
162C4×C5#41311yescharacteristic
163C4×C5#41311yescharacteristic
164Dic5—22no—
165Dic5—22no—
166Dic5#34414yes—
167C24—51no—
168C22×C4—52no—
169C22×C4—51no—
170C22×C4—52no—
171C22×C4—52no—
172C22×C4—52no—
173C22×C4—52no—
174C22×C4—52no—
175C22×C4—52no—
176C22×C4—201no—
177C22×C4—201no—
178C22×C4—204no—
179C22×C4C2×C4×D511yescharacteristic
180C22×C4C2×C4×D512yes—
181M16—42no—
182M16—208no—
183M16—202no—
184C2×C8—24no—
185C2×C8—22no—
186C2×C8—104no—
187C2×C8—102no—
188C42—51no—
189C42—52no—
190C42—51no—
191C42—52no—
192C42—52no—
193C42—52no—
194C42—52no—
195C42D4×D511yescharacteristic
196C42D4×D512yes—
197C42Q8×D511yescharacteristic
198C2×C5—41no—
199C2×C5#174211yescharacteristic
200C2×C5C2×#34412yes—
201D5—42no—
202C23—52no—
203C23—201no—
204C23—202no—
205C23C42×D511yescharacteristic
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—42no—
209C2×C4—52no—
210C2×C4—52no—
211C2×C4—52no—
212C2×C4—104no—
213C2×C4—104no—
214C2×C4—104no—
215C2×C4—102no—
216C2×C4—102no—
217C2×C4—202no—
218C2×C4—202no—
219C2×C4—202no—
220C2×C4—201no—
221C2×C4D5×C22⋊C412yes—
222C2×C4D5×C22⋊C411yescharacteristic
223C2×C4D5×C4⋊C411yescharacteristic
224C2×C4D5×C4⋊C412yes—
225C8—44no—
226C8—42no—
227C8—204no—
228C8—202no—
229C5#812211yescharacteristic, complemented, Sylow
230C22—21no—
231C22—22no—
232C22—102no—
233C22—102no—
234C22—102no—
235C22—204no—
236C22D5×#9511yescharacteristic
237C4—21no—
238C4—22no—
239C4—22no—
240C4—54no—
241C4—102no—
242C4—102no—
243C4#6503411yescharacteristic
244C4#6504011yescharacteristic
245C2—41no—
246C2—202no—
247C2#1059978211yescharacteristic
248C2D5×#34412yes—
subgroupG/H
centerC22D5×#95
commutatorC23×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1307C2
socleC22×C5C2×#95
prime radicalC23×D5C42
cosocleC2×C42×C5C23
hypercenter#1307D5
hypocenterC5#8122
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
3. C5×#1307C2semidirect
4. #10598249C2semidirect
5. #10598207C2semidirect
52. #1307D5semidirect
229. C5#8122semidirect

Maximal subgroups

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

subgroupindex
#106110622
#106107692
C5×#13072
#105982492
#105982072
#81225