Finite Group Databasebeta

← #13013868

Subgroups — #13013868

Order 1280.

342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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#10604730C211yesmaximal, characteristic
2#10604723C211yesmaximal, characteristic
3D5×C22⋊C16C211yesmaximal, characteristic
4C2×D5⋊M16—21no—
5C22×C8×D5C2211yescharacteristic
6#65765—21no—
7C2×#3994C412yes—
8C2×D5×C16—21no—
9#64896—21no—
10#64896C412yescomplemented
11#64893—21no—
12C5×C22⋊C16C411yescharacteristic, complemented
13C22⋊#672C411yescharacteristic, complemented
14#64727—21no—
15#7259—51nomaximal, Sylow
16C22×C4×D5D411yescharacteristic
17C2×C22⋊AGL(1,𝔽5)—41no—
18C2×#704—41no—
19C2×C4⋊AGL(1,𝔽5)—22no—
20D5⋊M16—24no—
21D5⋊M16—42no—
22C2×#700—22no—
23C2×D5⋊C8—41no—
24C22×C5×C8C2×C411yescharacteristic
25C22×#168Q811yescharacteristic
26C2×C8×D5—42no—
27C2×C8×D5C2×C411yescharacteristic
28C2×C8×D5C2×C411yescharacteristic
29C2×C8×D5D411yescharacteristic
30C2×C8×D5D411yescharacteristic
31(C2×AGL(1,𝔽5))⋊C4—41no—
32#3994—42no—
33C2×C5×C16—21no—
34C2×#672—21no—
35D5×C16—42no—
36C2×C22⋊C16—51no—
37#1808—51no—
38C2×#341—51no—
39C23×D5SD1611yescharacteristic
40C22×AGL(1,𝔽5)—42no—
41C22×C4×C5C4⋊C411yescharacteristic
42C22×Dic5SD1611yescharacteristic
43C2×C4×D5—22no—
44C2×C4×D5—22no—
45C2×C4×D5C22⋊C411yescharacteristic
46C2×C4×D5C22⋊C411yescharacteristic
47C2×C4×D5D811yescharacteristic
48C2×C4×D5Q1611yescharacteristic
49C22⋊AGL(1,𝔽5)—82no—
50#704—44no—
51C2×#170—42no—
52C4⋊AGL(1,𝔽5)—42no—
53C4⋊AGL(1,𝔽5)—42no—
54#700—24no—
55#700—42no—
56D5⋊C8—44no—
57C2×C5×C8—41no—
58C2×C5×C8C4211yescharacteristic
59C2×C5×C8C22⋊C411yescharacteristic
60C2×#168—41no—
61C2×#168C4⋊C411yescharacteristic
62C2×#168C4⋊C411yescharacteristic
63C8×D5—22no—
64C8×D5—22no—
65C8×D5—41no—
66C8×D5—41no—
67C5×C16—41no—
68#672—41no—
69C22×M16—101no—
70C23×C8—51no—
71C22×C16—101no—
72C2×#107—52no—
73#380—101no—
74C22⋊C16—51no—
75C22⋊C16—101no—
76C22⋊C16AGL(1,𝔽5)11yescharacteristic, complemented
77#341—52no—
78#341—101no—
79#340—101no—
80C23×C5#10611yescharacteristic
81C22×D5—22no—
82C22×D5—22no—
83C22×D5—21no—
84C22×D5—21no—
85C22×D5#10211yescharacteristic
86C22×D5#10311yescharacteristic
87C2×AGL(1,𝔽5)—82no—
88C2×AGL(1,𝔽5)—82no—
89C2×AGL(1,𝔽5)—82no—
90C2×C4×C5—21no—
91C2×C4×C5—21no—
92C2×C4×C5#9511yescharacteristic
93C2×C4×C5#10711yescharacteristic
94C2×Dic5—22no—
95C2×Dic5#10211yescharacteristic
96C2×Dic5#10311yescharacteristic
97C4×D5—22no—
98C4×D5—21no—
99C4×D5—21no—
100C4×D5—22no—
101C4×D5#9912yes—
102C4×D5#10412yes—
103#170—44no—
104C5×C8—21no—
105C5×C8—21no—
106#168—21no—
107#168—21no—
108C23×C4—51no—
109C2×M16—102no—
110C2×M16—104no—
111C2×M16—201no—
112C2×M16—202no—
113C22×C8—51no—
114C22×C8—51no—
115C22×C8—51no—
116C22×C8—51no—
117C22×C8—51no—
118C22×C8—202no—
119C22×C8—201no—
120C22×C8C2×AGL(1,𝔽5)11yescharacteristic
121C2×C4⋊C4—102no—
122C2×C22⋊C4—201no—
123C2×C16—21no—
124C2×C16—101no—
125C2×C16—202no—
126#107—202no—
127#95—201no—
128C22×C5—21no—
129C22×C5—21no—
130C22×C5—21no—
131C22×C5#34011yescharacteristic
132C2×D5—21no—
133C2×D5—21no—
134C2×D5—21no—
135C2×D5—42no—
136C2×D5—42no—
137C2×D5#32712yes—
138C2×D5#35912yes—
139C2×D5#36111yescharacteristic
140C2×D5#36211yescharacteristic
141AGL(1,𝔽5)—162no—
142C4×C5—21no—
143C4×C5#33911yescharacteristic
144C4×C5#34211yescharacteristic
145Dic5—21no—
146Dic5#32812yes—
147C24—51no—
148C22×C4—51no—
149C22×C4—51no—
150C22×C4—51no—
151C22×C4—51no—
152C22×C4—51no—
153C22×C4—102no—
154C22×C4—102no—
155C22×C4—202no—
156C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
157M16—104no—
158M16—202no—
159M16—204no—
160C2×C8—41no—
161C2×C8—51no—
162C2×C8—51no—
163C2×C8—102no—
164C2×C8—102no—
165C2×C8—201no—
166C2×C8—201no—
167C2×C8—201no—
168C2×C8—202no—
169C2×C8—204no—
170C2×C8C4×AGL(1,𝔽5)11yescharacteristic
171C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
172C4⋊C4—202no—
173C4⋊C4—202no—
174C22⋊C4—402no—
175C16—41no—
176C16—201no—
177C2×C5—41no—
178C2×C5#129411yescharacteristic
179C2×C5#138211yescharacteristic
180C2×C5#138711yescharacteristic
181D5—41no—
182D5#134912yes—
183D5#135012yes—
184C23—51no—
185C23—51no—
186C23—101no—
187C23—102no—
188C23—102no—
189C23—101no—
190C23#399311yescharacteristic
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—51no—
194C2×C4—52no—
195C2×C4—52no—
196C2×C4—51no—
197C2×C4—102no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—101no—
201C2×C4—101no—
202C2×C4—402no—
203C2×C4—402no—
204C2×C4—402no—
205C2×C4#399411yescharacteristic
206C2×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
207C8—21no—
208C8—21no—
209C8—101no—
210C8—101no—
211C8—204no—
212C5#725911yescharacteristic, complemented, Sylow
213C22—21no—
214C22—21no—
215C22—21no—
216C22—52no—
217C22—51no—
218C22—51no—
219C22—52no—
220C22—101no—
221C22—101no—
222C22—101no—
223C22—202no—
224C22—202no—
225C22#6489311yescharacteristic
226C4—21no—
227C4—52no—
228C4—101no—
229C4—802no—
230C4#6486611yescharacteristic
231C4#6490011yescharacteristic
232C2—41no—
233C2—52no—
234C2—52no—
235C2—201no—
236C2#1059855211yescharacteristic
237C2#1059866511yescharacteristic
238C2#1059867411yescharacteristic
subgroupG/H
centerC22#64893
commutatorC2×C5×C8C42
FrattiniC22×C8C2×AGL(1,𝔽5)
FittingC5×C22⋊C16C4
socleC22×C5#340
prime radicalC23×D5SD16
cosocleC22×C8×D5C22
hypercenterC22⋊C16AGL(1,𝔽5)
hypocenterC5#7259
LCSG ▷ C2×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
10. #64896C4semidirect
12. C5×C22⋊C16C4semidirect
13. C22⋊#672C4semidirect
76. C22⋊C16AGL(1,𝔽5)semidirect
212. C5#7259semidirect

Maximal subgroups

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

subgroupindex
#106047302
#106047232
D5×C22⋊C162
#72595