Finite Group Databasebeta

← #13013867

Subgroups — #13013867

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#10604723C211yesmaximal, characteristic
2D5⋊(C22⋊C16)C211yesmaximal, characteristic
3D5×#341C211yesmaximal, characteristic
4C2×D5×M16—21no—
5C22×C8×D5C2211yescharacteristic
6#65765—21no—
7C2×#3994C412yes—
8C2×D5⋊C16—21no—
9C22⋊#674—21no—
10#64893—21no—
11#64887C412yescomplemented
12C5×#341C411yescharacteristic, complemented
13#64778—21no—
14#64772C411yescharacteristic, complemented
15#7259—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
23D5×M16—24no—
24D5×M16—42no—
25C2×#676—41no—
26C2×C8×D5—42no—
27C2×C8×D5—41no—
28C2×C8×D5C2×C411yescharacteristic
29C2×C8×D5C2×C411yescharacteristic
30C2×C8×D5D411yescharacteristic
31C2×C8×D5Q811yescharacteristic
32(C2×AGL(1,𝔽5))⋊C4—41no—
33C2×#674—22no—
34#3994—42no—
35D5⋊C16—42no—
36C2×C22⋊C16—51no—
37#1808—51no—
38C2×#341—51no—
39C23×D5SD1611yescharacteristic
40C22×AGL(1,𝔽5)—42no—
41C22×C4×C5C22⋊C411yescharacteristic
42C22×Dic5Q1611yescharacteristic
43C2×C4×D5—22no—
44C2×C4×D5—22no—
45C2×C4×D5C22⋊C411yescharacteristic
46C2×C4×D5C4⋊C411yescharacteristic
47C2×C4×D5D811yescharacteristic
48C2×C4×D5SD1611yescharacteristic
49C22⋊AGL(1,𝔽5)—82no—
50C4⋊AGL(1,𝔽5)—42no—
51C4⋊AGL(1,𝔽5)—42no—
52C5×M16—22no—
53C5×M16—41no—
54C2×C5×C8—41no—
55C2×C5×C8—41no—
56C2×C5×C8C4211yescharacteristic
57C2×C5×C8C4⋊C411yescharacteristic
58#681—22no—
59#681—41no—
60C2×#168—41no—
61C2×#168—41no—
62C2×#168C22⋊C411yescharacteristic
63C2×#168C4⋊C411yescharacteristic
64#676—44no—
65C8×D5—22no—
66C8×D5—22no—
67C8×D5—41no—
68C8×D5—41no—
69C8×D5—44no—
70#674—42no—
71C22×M16—101no—
72C23×C8—51no—
73C22×C16—101no—
74C2×#107—52no—
75#380—101no—
76C22⋊C16—52no—
77C22⋊C16—101no—
78#341—51no—
79#341—101no—
80#341AGL(1,𝔽5)11yescharacteristic, complemented
81#340—101no—
82C23×C5#10311yescharacteristic
83C22×D5—22no—
84C22×D5—22no—
85C22×D5—21no—
86C22×D5—21no—
87C22×D5#10211yescharacteristic
88C22×D5#10611yescharacteristic
89C2×AGL(1,𝔽5)—82no—
90C2×AGL(1,𝔽5)—82no—
91C2×AGL(1,𝔽5)—82no—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5#9511yescharacteristic
95C2×C4×C5#10211yescharacteristic
96C2×Dic5—22no—
97C2×Dic5#10311yescharacteristic
98C2×Dic5#10711yescharacteristic
99C4×D5—22no—
100C4×D5—21no—
101C4×D5—21no—
102C4×D5—22no—
103C4×D5#9912yes—
104C4×D5#10412yes—
105C5×C8—21no—
106C5×C8—21no—
107C5×C8—42no—
108#168—21no—
109#168—21no—
110#168—42no—
111C23×C4—51no—
112C2×M16—21no—
113C2×M16—104no—
114C2×M16—101no—
115C2×M16—201no—
116C2×M16—202no—
117C22×C8—51no—
118C22×C8—51no—
119C22×C8—51no—
120C22×C8—51no—
121C22×C8—51no—
122C22×C8—202no—
123C22×C8—201no—
124C22×C8C2×AGL(1,𝔽5)11yescharacteristic
125C2×C4⋊C4—102no—
126C2×C22⋊C4—201no—
127C2×C16—102no—
128C2×C16—202no—
129#107—202no—
130#95—201no—
131C22×C5—21no—
132C22×C5—21no—
133C22×C5—21no—
134C22×C5#34011yescharacteristic
135C2×D5—21no—
136C2×D5—21no—
137C2×D5—21no—
138C2×D5—42no—
139C2×D5—42no—
140C2×D5#32712yes—
141C2×D5#35912yes—
142C2×D5#36111yescharacteristic
143C2×D5#36211yescharacteristic
144AGL(1,𝔽5)—162no—
145C4×C5—21no—
146C4×C5#33911yescharacteristic
147C4×C5#34211yescharacteristic
148Dic5—21no—
149Dic5#32812yes—
150C24—51no—
151C22×C4—51no—
152C22×C4—51no—
153C22×C4—51no—
154C22×C4—51no—
155C22×C4—51no—
156C22×C4—102no—
157C22×C4—102no—
158C22×C4—202no—
159C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
160M16—22no—
161M16—41no—
162M16—102no—
163M16—204no—
164M16—201no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—51no—
168C2×C8—51no—
169C2×C8—102no—
170C2×C8—102no—
171C2×C8—201no—
172C2×C8—201no—
173C2×C8—204no—
174C2×C8—201no—
175C2×C8—201no—
176C2×C8C4×AGL(1,𝔽5)11yescharacteristic
177C2×C8C4⋊AGL(1,𝔽5)11yescharacteristic
178C4⋊C4—202no—
179C4⋊C4—202no—
180C22⋊C4—402no—
181C16—202no—
182C2×C5—41no—
183C2×C5#129411yescharacteristic
184C2×C5#138211yescharacteristic
185C2×C5#138711yescharacteristic
186D5—41no—
187D5#134912yes—
188D5#135012yes—
189C23—51no—
190C23—51no—
191C23—101no—
192C23—102no—
193C23—102no—
194C23—101no—
195C23#400911yescharacteristic
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—51no—
199C2×C4—52no—
200C2×C4—52no—
201C2×C4—51no—
202C2×C4—102no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4—101no—
206C2×C4—101no—
207C2×C4—402no—
208C2×C4—402no—
209C2×C4—402no—
210C2×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
211C2×C4#400711yescharacteristic
212C8—21no—
213C8—21no—
214C8—42no—
215C8—101no—
216C8—101no—
217C8—202no—
218C5#725911yescharacteristic, complemented, Sylow
219C22—21no—
220C22—21no—
221C22—21no—
222C22—52no—
223C22—52no—
224C22—51no—
225C22—51no—
226C22—101no—
227C22—101no—
228C22—101no—
229C22—202no—
230C22—202no—
231C22#6487411yescharacteristic
232C4—21no—
233C4—52no—
234C4—101no—
235C4—802no—
236C4#6486211yescharacteristic
237C4#6486611yescharacteristic
238C2—41no—
239C2—52no—
240C2—52no—
241C2—201no—
242C2#1059850411yescharacteristic
243C2#1059862611yescharacteristic
244C2#1059862911yescharacteristic
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#7259
LCSG ▷ C2×C5×C8 ▷ C2×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
11. #64887C4semidirect
12. C5×#341C4semidirect
14. #64772C4semidirect
80. #341AGL(1,𝔽5)semidirect
218. C5#7259semidirect

Maximal subgroups

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

subgroupindex
#106047232
D5⋊(C22⋊C16)2
D5×#3412
#72595