Finite Group Databasebeta

← #11986617

Subgroups — #11986617

Order 1280.

482 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C5×#1440C211yesmaximal, characteristic
2#10602332C212yesmaximal
3C22×C5×C22⋊C4C412yes—
4C22×C5×C22⋊C4C2211yescharacteristic
5C2×C5×#95—22no—
6#65496—22no—
7#64745—22no—
8#64745C414yescomplemented
9#7324—51nomaximal, Sylow
10C25×C5C2×C411yescharacteristic
11C23×C4×C5—22no—
12C23×C4×C5D412yes—
13C2×C5×C22⋊C4—42no—
14C2×C5×C22⋊C4—42no—
15C2×C5×C22⋊C4—44no—
16C2×C5×C22⋊C4C2×C412yes—
17C2×C5×C22⋊C4D411yescharacteristic
18C2×C5×C22⋊C4Q811yescharacteristic
19C2×#681—42no—
20C5×#95—44no—
21C22⋊#168—24no—
22C22⋊#168—42no—
23#1462—52no—
24#1440D511yescharacteristic
25C24×C5—22no—
26C24×C5—42no—
27C24×C5—42no—
28C24×C5—42no—
29C24×C5C4211yescharacteristic
30C24×C5C22⋊C411yescharacteristic
31C24×C5C4⋊C411yescharacteristic
32C22×C4×C5—22no—
33C22×C4×C5—22no—
34C22×C4×C5—24no—
35C22×C4×C5—42no—
36C22×C4×C5—42no—
37C22×C4×C5—42no—
38C22×C4×C5—42no—
39C22×C4×C5—42no—
40C22×C4×C5—42no—
41C22×C4×C5—42no—
42C22×C4×C5—42no—
43C22×C4×C5C22⋊C412yes—
44C22×C4×C5C4⋊C412yes—
45C5×C22⋊C4—42no—
46C5×C22⋊C4—41no—
47C5×C22⋊C4—41no—
48C5×C22⋊C4—44no—
49C5×C22⋊C4—44no—
50#681—82no—
51#681—82no—
52C2×#168—44no—
53C22×C22⋊C4Dic512yes—
54C22×C22⋊C4C2×D511yescharacteristic
55#407—102no—
56C2×#95—22no—
57#323—54no—
58#323—102no—
59C23×C5—22no—
60C23×C5—22no—
61C23×C5—22no—
62C23×C5—21no—
63C23×C5—21no—
64C23×C5—22no—
65C23×C5—22no—
66C23×C5—44no—
67C23×C5—44no—
68C23×C5—42no—
69C23×C5—42no—
70C23×C5—42no—
71C23×C5—42no—
72C23×C5—82no—
73C23×C5—82no—
74C23×C5—82no—
75C23×C5—82no—
76C23×C5#9511yescharacteristic
77C23×C5#9912yes—
78C2×C4×C5—22no—
79C2×C4×C5—22no—
80C2×C4×C5—42no—
81C2×C4×C5—42no—
82C2×C4×C5—42no—
83C2×C4×C5—42no—
84C2×C4×C5—44no—
85C2×C4×C5—44no—
86C2×C4×C5—44no—
87C2×C4×C5—82no—
88C2×C4×C5—82no—
89C2×C4×C5—82no—
90C2×C4×C5—82no—
91C2×C4×C5—82no—
92#168—84no—
93C25C2×Dic511yescharacteristic
94C23×C4—22no—
95C23×C4C22⋊D512yes—
96C2×M16—202no—
97C2×C22⋊C4—42no—
98C2×C22⋊C4—42no—
99C2×C22⋊C4—44no—
100C2×C22⋊C4Dic1011yescharacteristic
101C2×C22⋊C4C4×D512yes—
102C2×C22⋊C4D2011yescharacteristic
103C22⋊C8—104no—
104C22⋊C8—202no—
105#95—44no—
106C22×C5—22no—
107C22×C5—22no—
108C22×C5—22no—
109C22×C5—22no—
110C22×C5—22no—
111C22×C5—22no—
112C22×C5—22no—
113C22×C5—41no—
114C22×C5—41no—
115C22×C5—42no—
116C22×C5—42no—
117C22×C5—82no—
118C22×C5—82no—
119C22×C5—84no—
120C22×C5—84no—
121C22×C5#34211yescharacteristic
122C22×C5#34412yes—
123C22×C5AΣL(1,𝔽16)12yes—
124C22×C5#35212yes—
125C4×C5—42no—
126C4×C5—42no—
127C4×C5—84no—
128C24—22no—
129C24—42no—
130C24—42no—
131C24—42no—
132C24C4×Dic511yescharacteristic
133C24C4⋊Dic511yescharacteristic
134C24C22⋊Dic511yescharacteristic
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—24no—
138C22×C4—42no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4#68312yes—
147C22×C4#68512yes—
148M16—402no—
149M16—402no—
150C2×C8—204no—
151C22⋊C4—41no—
152C22⋊C4—42no—
153C22⋊C4—41no—
154C22⋊C4—44no—
155C22⋊C4—44no—
156C2×C5—22no—
157C2×C5—22no—
158C2×C5—22no—
159C2×C5—81no—
160C2×C5—81no—
161C2×C5#130611yescharacteristic
162C2×C5#139012yes—
163C23—22no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—44no—
171C23—44no—
172C23—42no—
173C23—42no—
174C23—42no—
175C23—42no—
176C23—82no—
177C23—82no—
178C23—82no—
179C23—82no—
180C23#396311yescharacteristic
181C23#396612yes—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—82no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C8—404no—
197C5#732411yescharacteristic, complemented, Sylow
198C22—22no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—42no—
208C22—42no—
209C22—82no—
210C22—82no—
211C22—84no—
212C22—84no—
213C22#6474611yescharacteristic
214C22#6475312yes—
215C22#6475612yes—
216C22#6475912yes—
217C4—42no—
218C4—42no—
219C4—84no—
220C2—22no—
221C2—22no—
222C2—22no—
223C2—81no—
224C2—81no—
225C2#1059812011yescharacteristic
226C2#1059812812yes—
subgroupG/H
centerC22#64746
commutatorC24×C5C42
FrattiniC22×C22⋊C4C2×D5
FittingC5×#1440C2
socleC22×C5#342
prime radicalC25×C5C2×C4
cosocleC22×C5×C22⋊C4C22
hypercenter#1440D5
hypocenterC5#7324
LCSG ▷ C24×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1440

Complements

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

NH ≅ G/Ntype
8. #64745C4semidirect
197. C5#7324semidirect

Maximal subgroups

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

subgroupindex
C5×#14402
#106023322
#73245