Finite Group Databasebeta

← #13013783

Subgroups — #13013783

Order 1280.

292 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 64 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#10604722C211yesmaximal, characteristic
2D5⋊(C22⋊C16)C211yesmaximal, characteristic
3#10599732C211yesmaximal, characteristic
4C22×C8×D5C2211yescharacteristic
5#65765—21no—
6C2×#3993—21no—
7C2×D5⋊C16C412yescomplemented
8#65415—21no—
9C2×#3954—21no—
10C22⋊#674—21no—
11#64893C412yes—
12#64887—21no—
13C5×#341C411yescharacteristic, complemented
14#64772C411yescharacteristic, complemented
15#7232—51nomaximal, Sylow
16C22×C4×D5D411yescharacteristic
17C2×C22⋊AGL(1,𝔽5)—41no—
18C2×C4⋊AGL(1,𝔽5)—22no—
19C2×C5×M16—21no—
20C22×C5×C8C2×C411yescharacteristic
21C2×#681—21no—
22C22×#168D411yescharacteristic
23C2×C8×D5—42no—
24C2×C8×D5C2×C411yescharacteristic
25C2×C8×D5C2×C411yescharacteristic
26C2×C8×D5D411yescharacteristic
27C2×C8×D5Q811yescharacteristic
28(C2×AGL(1,𝔽5))⋊C4—41no—
29C2×#674—22no—
30#3993—42no—
31D5⋊C16—42no—
32#3954—42no—
33#3952—41no—
34#3952—41no—
35C2×C22⋊C16—51no—
36#1810—51no—
37#1807—51no—
38C23×D5SD1611yescharacteristic
39C22×AGL(1,𝔽5)—42no—
40C22×C4×C5C22⋊C411yescharacteristic
41C22×Dic5Q1611yescharacteristic
42C2×C4×D5—41no—
43C2×C4×D5—41no—
44C2×C4×D5C22⋊C411yescharacteristic
45C2×C4×D5C4⋊C411yescharacteristic
46C2×C4×D5D811yescharacteristic
47C2×C4×D5SD1611yescharacteristic
48C22⋊AGL(1,𝔽5)—82no—
49C4⋊AGL(1,𝔽5)—42no—
50C4⋊AGL(1,𝔽5)—42no—
51C5×M16—41no—
52C5×M16—41no—
53C2×C5×C8—41no—
54C2×C5×C8—41no—
55C2×C5×C8C4211yescharacteristic
56C2×C5×C8C4⋊C411yescharacteristic
57#681—41no—
58#681—41no—
59C2×#168—22no—
60C2×#168—41no—
61C2×#168C22⋊C411yescharacteristic
62C2×#168C4⋊C411yescharacteristic
63C8×D5—22no—
64C8×D5—22no—
65C8×D5—41no—
66C8×D5—41no—
67#674—42no—
68C23×C8—51no—
69C22×C16—52no—
70C2×#108—101no—
71C2×#106—101no—
72#407—101no—
73#380—101no—
74C22⋊C16—101no—
75C22⋊C16—101no—
76#341—51no—
77#341AGL(1,𝔽5)11yescharacteristic, complemented
78#340—52no—
79C23×C5#10311yescharacteristic
80C22×D5—22no—
81C22×D5—22no—
82C22×D5—41no—
83C22×D5#10211yescharacteristic
84C22×D5#10611yescharacteristic
85C2×AGL(1,𝔽5)—82no—
86C2×AGL(1,𝔽5)—82no—
87C2×AGL(1,𝔽5)—82no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5#9511yescharacteristic
91C2×C4×C5#10211yescharacteristic
92C2×Dic5—41no—
93C2×Dic5#10311yescharacteristic
94C2×Dic5#10711yescharacteristic
95C4×D5—21no—
96C4×D5—21no—
97C4×D5—21no—
98C4×D5—21no—
99C4×D5—41no—
100C4×D5—41no—
101C5×C8—21no—
102C5×C8—21no—
103C5×C8—81no—
104#168—21no—
105#168—81no—
106#168#9912yes—
107C23×C4—51no—
108C2×M16—21no—
109C2×M16—101no—
110C22×C8—51no—
111C22×C8—51no—
112C22×C8—51no—
113C22×C8—51no—
114C22×C8—51no—
115C22×C8—202no—
116C22×C8C2×AGL(1,𝔽5)11yescharacteristic
117C2×C4⋊C4—102no—
118C2×C22⋊C4—201no—
119C2×C16—102no—
120C2×C16—202no—
121#108—202no—
122#106—202no—
123C22⋊C8—201no—
124C22⋊C8—201no—
125#95—201no—
126C22×C5—21no—
127C22×C5—21no—
128C22×C5—21no—
129C22×C5#34011yescharacteristic
130C2×D5—21no—
131C2×D5—21no—
132C2×D5—21no—
133C2×D5—21no—
134C2×D5—44no—
135C2×D5#35912yes—
136C2×D5#36512yes—
137AGL(1,𝔽5)—162no—
138C4×C5—21no—
139C4×C5H(3,ℤ/4)11yescharacteristic
140C4×C5#34211yescharacteristic
141Dic5—21no—
142Dic5—21no—
143C24—51no—
144C22×C4—51no—
145C22×C4—51no—
146C22×C4—51no—
147C22×C4—51no—
148C22×C4—51no—
149C22×C4—201no—
150C22×C4—201no—
151C22×C4—202no—
152C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
153M16—41no—
154M16—41no—
155M16—201no—
156M16—201no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—51no—
160C2×C8—51no—
161C2×C8—102no—
162C2×C8—102no—
163C2×C8—102no—
164C2×C8—201no—
165C2×C8—201no—
166C2×C8—201no—
167C2×C8C4×AGL(1,𝔽5)11yescharacteristic
168C2×C8C4⋊AGL(1,𝔽5)11yescharacteristic
169C4⋊C4—202no—
170C4⋊C4—202no—
171C22⋊C4—402no—
172C16—202no—
173C2×C5—41no—
174C2×C5#128911yescharacteristic
175C2×C5#138211yescharacteristic
176C2×C5#138311yescharacteristic
177D5—22no—
178D5—22no—
179C23—51no—
180C23—51no—
181C23—102no—
182C23—102no—
183C23—201no—
184C23#400911yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—51no—
188C2×C4—51no—
189C2×C4—101no—
190C2×C4—101no—
191C2×C4—101no—
192C2×C4—101no—
193C2×C4—201no—
194C2×C4—201no—
195C2×C4—201no—
196C2×C4—402no—
197C2×C4—402no—
198C2×C4—402no—
199C2×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
200C2×C4#400711yescharacteristic
201C8—21no—
202C8—21no—
203C8—52no—
204C8—81no—
205C8—101no—
206C8—401no—
207C5#723211yescharacteristic, complemented, Sylow
208C22—21no—
209C22—21no—
210C22—21no—
211C22—52no—
212C22—52no—
213C22—101no—
214C22—101no—
215C22—101no—
216C22—101no—
217C22—204no—
218C22#6487411yescharacteristic
219C4—21no—
220C4—101no—
221C4—101no—
222C4—802no—
223C4#6486311yescharacteristic
224C4#6486611yescharacteristic
225C2—41no—
226C2—102no—
227C2—102no—
228C2#1059850611yescharacteristic
229C2#1059862611yescharacteristic
230C2#1059862711yescharacteristic
subgroupG/H
centerC22#64874
commutatorC2×C5×C8C42
FrattiniC22×C8C2×AGL(1,𝔽5)
FittingC5×#341C4
socleC22×C5#340
prime radicalC23×D5SD16
cosocleC22×C8×D5C22
hypercenter#341AGL(1,𝔽5)
hypocenterC5#7232
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
7. C2×D5⋊C16C4semidirect
13. C5×#341C4semidirect
14. #64772C4semidirect
77. #341AGL(1,𝔽5)semidirect
207. C5#7232semidirect

Maximal subgroups

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

subgroupindex
#106047222
D5⋊(C22⋊C16)2
#105997322
#72325