Finite Group Databasebeta

← #13013663

Subgroups — #13013663

Order 1280.

292 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 70 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#10604719C211yesmaximal, characteristic
2C2×#64887C211yesmaximal, characteristic
3#10599899C211yesmaximal, characteristic
4C22×C8×D5C2211yescharacteristic
5C4×C22⋊AGL(1,𝔽5)C411yescharacteristic
6D5⋊(C22⋊C8)C411yescharacteristic
7C22×#674C412yescomplemented
8C2×#3992—21no—
9C2×#3930—21no—
10(C2×AGL(1,𝔽5))⋊C8—21no—
11#64887—21no—
12#64887—21no—
13C5×C22⋊C16C411yescharacteristic, complemented
14C22⋊#672C411yescharacteristic, complemented
15#64727—21no—
16#7200—51nomaximal, Sylow
17C22×C4×D5C2×C411yescharacteristic
18C2×C22⋊AGL(1,𝔽5)—21no—
19C2×C4×AGL(1,𝔽5)—21no—
20C2×D5⋊C8—21no—
21C22×C5×C8C2×C411yescharacteristic
22C22×#168C2×C411yescharacteristic
23C2×C8×D5—42no—
24C2×C8×D5D411yescharacteristic
25C2×C8×D5D411yescharacteristic
26C2×C8×D5D411yescharacteristic
27C2×C8×D5Q811yescharacteristic
28C22⋊#170—21no—
29(C2×AGL(1,𝔽5))⋊C4C812yes—
30#4003C812yes—
31C2×#674—22no—
32C2×#674—42no—
33#3992—42no—
34C2×C5×C16—21no—
35C2×#672—21no—
36#3930—42no—
37#2112—51no—
38C2×C22⋊C16—51no—
39#1752—51no—
40C23×D5M1611yescharacteristic
41C22×AGL(1,𝔽5)—22no—
42C22×C4×C5C4211yescharacteristic
43C22×Dic5M1611yescharacteristic
44C2×C4×D5—41no—
45C2×C4×D5—41no—
46C2×C4×D5C22⋊C411yescharacteristic
47C2×C4×D5C4⋊C411yescharacteristic
48C2×C4×D5C2×C811yescharacteristic
49C2×C4×D5C2×C811yescharacteristic
50C22⋊AGL(1,𝔽5)—41no—
51C22⋊AGL(1,𝔽5)—41no—
52C2×#170—22no—
53C4×AGL(1,𝔽5)—41no—
54C4×AGL(1,𝔽5)—41no—
55D5⋊C8—41no—
56D5⋊C8—41no—
57C2×C5×C8—41no—
58C2×C5×C8C22⋊C411yescharacteristic
59C2×C5×C8C4⋊C411yescharacteristic
60C2×#168—22no—
61C2×#168C22⋊C411yescharacteristic
62C2×#168C4⋊C411yescharacteristic
63C8×D5—22no—
64C8×D5—22no—
65C8×D5—41no—
66C8×D5—41no—
67#674—42no—
68C5×C16—41no—
69#672—41no—
70C23×C8—51no—
71C2×M32—101no—
72C22×C16—52no—
73C2×C22⋊C8—51no—
74C2×#97—101no—
75C4×C22⋊C4—51no—
76C22⋊C16—51no—
77C22⋊C16—101no—
78C22⋊C16—101no—
79C22⋊C16—101no—
80C22⋊C16AGL(1,𝔽5)11yescharacteristic, complemented
81#336—101no—
82C23×C5#9711yescharacteristic
83C22×D5—21no—
84C22×D5—21no—
85C22×D5—22no—
86C22×D5—41no—
87C22×D5C22⋊C811yescharacteristic
88C22×D5C4⋊C811yescharacteristic
89C2×AGL(1,𝔽5)—42no—
90C2×AGL(1,𝔽5)—42no—
91C2×AGL(1,𝔽5)—42no—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5#9511yescharacteristic
95C2×C4×C5C4×C811yescharacteristic
96C2×Dic5—41no—
97C2×Dic5C22⋊C811yescharacteristic
98C2×Dic5C4⋊C811yescharacteristic
99C4×D5—21no—
100C4×D5—21no—
101C4×D5—21no—
102C4×D5—21no—
103C4×D5—41no—
104C4×D5—41no—
105#170—42no—
106C5×C8—21no—
107C5×C8—21no—
108#168—21no—
109#168#9912yes—
110C23×C4—51no—
111C22×C8—51no—
112C22×C8—51no—
113C22×C8—51no—
114C22×C8—51no—
115C22×C8—51no—
116C22×C8—101no—
117C22×C8—202no—
118C22×C8C2×AGL(1,𝔽5)11yescharacteristic
119C2×C22⋊C4—101no—
120C2×C42—101no—
121M32—202no—
122C2×C16—21no—
123C2×C16—102no—
124C2×C16—101no—
125C2×C16—202no—
126C22⋊C8—52no—
127C22⋊C8—101no—
128#97—202no—
129#95—52no—
130C22×C5—21no—
131C22×C5—21no—
132C22×C5#33611yescharacteristic
133C22×C5#34711yescharacteristic
134C22×C5#34711yescharacteristic
135C2×D5—21no—
136C2×D5—21no—
137C2×D5—21no—
138C2×D5—21no—
139C2×D5—21no—
140C2×D5—42no—
141C2×D5—42no—
142C2×D5#35012yes—
143AGL(1,𝔽5)—82no—
144C4×C5—21no—
145C4×C5#34211yescharacteristic
146C4×C5#34411yescharacteristic
147Dic5—21no—
148Dic5—21no—
149C24—51no—
150C22×C4—51no—
151C22×C4—51no—
152C22×C4—51no—
153C22×C4—51no—
154C22×C4—51no—
155C22×C4—102no—
156C22×C4—201no—
157C22×C4—201no—
158C22×C4C4×AGL(1,𝔽5)11yescharacteristic
159C2×C8—41no—
160C2×C8—51no—
161C2×C8—51no—
162C2×C8—102no—
163C2×C8—102no—
164C2×C8—102no—
165C2×C8—102no—
166C2×C8—201no—
167C2×C8—201no—
168C2×C8—201no—
169C2×C8—201no—
170C2×C8C4⋊AGL(1,𝔽5)11yescharacteristic
171C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
172C22⋊C4—201no—
173C22⋊C4—201no—
174C42—201no—
175C42—201no—
176C16—41no—
177C16—201no—
178C16—202no—
179C2×C5—21no—
180C2×C5—21no—
181C2×C5#128211yescharacteristic
182C2×C5#137511yescharacteristic
183C2×C5#137911yescharacteristic
184D5—22no—
185D5—41no—
186C23—51no—
187C23—51no—
188C23—102no—
189C23—101no—
190C23—101no—
191C23—201no—
192C23#399211yescharacteristic
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—51no—
196C2×C4—51no—
197C2×C4—101no—
198C2×C4—101no—
199C2×C4—101no—
200C2×C4—101no—
201C2×C4—201no—
202C2×C4—201no—
203C2×C4—201no—
204C2×C4—202no—
205C2×C4—202no—
206C2×C4—202no—
207C2×C4C8×AGL(1,𝔽5)11yescharacteristic
208C2×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
209C8—21no—
210C8—21no—
211C8—52no—
212C8—101no—
213C8—202no—
214C5#720011yescharacteristic, complemented, Sylow
215C22—21no—
216C22—21no—
217C22—52no—
218C22—101no—
219C22—101no—
220C22—101no—
221C22—101no—
222C22—101no—
223C22—202no—
224C22—202no—
225C22#6484511yescharacteristic
226C22#6484611yescharacteristic
227C22(C2×AGL(1,𝔽5))⋊C811yescharacteristic
228C4—21no—
229C4—101no—
230C4—101no—
231C4—402no—
232C4#6486611yescharacteristic
233C4#6490211yescharacteristic
234C2—21no—
235C2—21no—
236C2—102no—
237C2—201no—
238C2#1059855911yescharacteristic
239C2#1059866011yescharacteristic
240C2#1059867311yescharacteristic
subgroupG/H
centerC2×C4(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C4×C8
FrattiniC22×C8C2×AGL(1,𝔽5)
FittingC5×C22⋊C16C4
socleC22×C5#336
prime radicalC23×D5M16
cosocleC22×C8×D5C22
hypercenterC22⋊C16AGL(1,𝔽5)
hypocenterC5#7200
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
7. C22×#674C4semidirect
13. C5×C22⋊C16C4semidirect
14. C22⋊#672C4semidirect
80. C22⋊C16AGL(1,𝔽5)semidirect
214. C5#7200semidirect

Maximal subgroups

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

subgroupindex
#106047192
C2×#648872
#105998992
#72005