Finite Group Databasebeta

← #13023247

Subgroups — #13023247

Order 1280.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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#10615525C211yesmaximal, characteristic
2D5⋊(C22⋊C16)C212yesmaximal, complemented
3#10598831C212yesmaximal, complemented
4#10598782C212yesmaximal, complemented
5C2×C5×#131C411yescharacteristic
6#66162C411yescharacteristic
7C22×C8×D5C2211yescharacteristic
8C2×D5⋊C16—22no—
9#65523C2211yescharacteristic
10#65416—22no—
11#65415C411yescharacteristic
12#65408C2211yescharacteristic
13C8×C22⋊D5—22no—
14#65390C411yescharacteristic
15C22⋊#674C2214yes—
16#64887—22no—
17#11468—51nomaximal, Sylow
18C2×C5×#41C2×C411yescharacteristic
19C22×C4×D5C2×C411yescharacteristic
20C5×#131—42no—
21C2×C5×M16—21no—
22C2×C5×M16C2×C411yescharacteristic
23C22×C5×C8—21no—
24C22×C5×C8C2×C411yescharacteristic
25#4092C812yes—
26#4084C812yes—
27#4083—21no—
28#4081—21no—
29C4×C22⋊D5—22no—
30#4072C2×C411yescharacteristic
31C2×#681C2×C411yescharacteristic
32C22×#168C2311yescharacteristic
33C2×C8×D5—42no—
34C2×C8×D5D412yes—
35C2×C8×D5D412yes—
36C2×#674—24no—
37D5⋊C16—44no—
38C22⋊#168—22no—
39#3952—22no—
40#3947—21no—
41#3946—22no—
42C8×Dic5—21no—
43#2929—51no—
44C2×C22⋊C16—52no—
45#1323—52no—
46#1315—52no—
47C23×D5M1611yescharacteristic
48C5×#41—41no—
49C5×#41—41no—
50C2×C5×Q8C2×C811yescharacteristic
51C2×C5×D4—21no—
52C2×C5×D4C2×C811yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5C22×C411yescharacteristic
55C2×C22⋊D5—22no—
56C22×Dic5M1611yescharacteristic
57C2×C4×D5—41no—
58C2×C4×D5—41no—
59C2×C4×D5C22⋊C412yes—
60C2×C4×D5C2×C812yes—
61C5×M16—42no—
62C5×M16—41no—
63C2×C5×C8—22no—
64C2×C5×C8—21no—
65C2×C5×C8—42no—
66C2×C5×C8C22⋊C411yescharacteristic
67C2×C5×C8C22⋊C411yescharacteristic
68C22⋊Dic5—21no—
69C22⋊Dic5—22no—
70#685—22no—
71C4⋊Dic5C2×C812yes—
72#683—22no—
73C4×Dic5—21no—
74#681—41no—
75C2×#168—21no—
76C2×#168—41no—
77C2×#168C2×D412yes—
78C8×D5—24no—
79C8×D5—42no—
80#674—44no—
81C2×#131AGL(1,𝔽5)11yescharacteristic
82C23×C8—51no—
83#525—51no—
84C22×C16—102no—
85#435—102no—
86C8×D4—102no—
87#424—51no—
88#408—51no—
89#407—51no—
90#405—51no—
91C22⋊C16—54no—
92C22⋊C16—102no—
93C23×C5—21no—
94C23×C5C2×M1611yescharacteristic
95C22×D5—24no—
96C22×D5—41no—
97C22×D5C22⋊C812yes—
98C5×Q8—41no—
99C5×D4—41no—
100C5×D4—42no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5C2×C22⋊C411yescharacteristic
107C2×C4×C5C22×C811yescharacteristic
108C22⋊D5—44no—
109C2×Dic5—22no—
110C2×Dic5—41no—
111C2×Dic5C22⋊C812yes—
112C4×D5—22no—
113C4×D5—22no—
114C4×D5—42no—
115C5×C8—21no—
116C5×C8—41no—
117C5×C8#9912yes—
118#168—22no—
119#168—41no—
120C2×#41C2×AGL(1,𝔽5)11yescharacteristic
121C23×C4—51no—
122#131—42no—
123C2×M16—21no—
124C2×M16—51no—
125C2×M16C2×AGL(1,𝔽5)11yescharacteristic
126C22×C8—21no—
127C22×C8—51no—
128C22×C8—52no—
129C22×C8—52no—
130C22×C8—202no—
131C22×C8C2×AGL(1,𝔽5)11yescharacteristic
132#123—101no—
133C22⋊Q8—52no—
134#121—52no—
135#120—101no—
136C4×D4—102no—
137#117—51no—
138C2×C16—104no—
139C2×C16—204no—
140C4⋊C8—102no—
141C22⋊C8—102no—
142C22⋊C8—102no—
143#97—101no—
144C4×C8—101no—
145C22×C5—22no—
146C22×C5—21no—
147C22×C5—42no—
148C22×C5—41no—
149C22×C5C2×C22⋊C811yescharacteristic
150C2×D5—22no—
151C2×D5—22no—
152C2×D5—44no—
153C2×D5#35014yes—
154C4×C5—21no—
155C4×C5—41no—
156C4×C5C2×#9911yescharacteristic
157C4×C5#41311yescharacteristic
158Dic5—22no—
159Dic5—42no—
160C24—51no—
161#41—41no—
162#41—41no—
163C2×Q8D5⋊C811yescharacteristic
164C2×D4—21no—
165C2×D4—102no—
166C2×D4D5⋊C811yescharacteristic
167C22×C4—21no—
168C22×C4—51no—
169C22×C4—52no—
170C22×C4—52no—
171C22×C4—201no—
172C22×C4—201no—
173C22×C4C22×AGL(1,𝔽5)11yescharacteristic
174M16—42no—
175M16—41no—
176M16—201no—
177C2×C8—22no—
178C2×C8—21no—
179C2×C8—42no—
180C2×C8—52no—
181C2×C8—104no—
182C2×C8—101no—
183C2×C8—202no—
184C2×C8—201no—
185C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
186C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
187C4⋊C4—52no—
188C4⋊C4—102no—
189C22⋊C4—102no—
190C22⋊C4—102no—
191C22⋊C4—101no—
192C42—101no—
193C16—204no—
194C2×C5—41no—
195C2×C5—81no—
196C2×C5#145911yescharacteristic
197C2×C5C2×#35012yes—
198D5—24no—
199C23—21no—
200C23—52no—
201C23—104no—
202C23—201no—
203C23D5⋊M1611yescharacteristic
204Q8—41no—
205D4—41no—
206D4—42no—
207D4—204no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—52no—
214C2×C4—102no—
215C2×C4—102no—
216C2×C4—102no—
217C2×C4—202no—
218C2×C4—201no—
219C2×C4C2×D5⋊C811yescharacteristic
220C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
221C8—21no—
222C8—41no—
223C8—102no—
224C8—201no—
225C8#401112yes—
226C5#1146811yescharacteristic, complemented, Sylow
227C22—21no—
228C22—22no—
229C22—41no—
230C22—42no—
231C22—54no—
232C22—102no—
233C22—102no—
234C22—204no—
235C22D5⋊(C22⋊C8)11yescharacteristic
236C4—21no—
237C4—41no—
238C4—102no—
239C4—202no—
240C4#6576111yescharacteristic
241C4C2×#401111yescharacteristic
242C2—41no—
243C2—81no—
244C2—104no—
245C2D5⋊#35012yes—
246C2#1060487811yescharacteristic
subgroupG/H
centerC2×C8C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#131C4
socleC22×C5C2×C22⋊C8
prime radical#66162C4
cosocleC22×#168C23
hypercenterC2×#131AGL(1,𝔽5)
hypocenterC5#11468
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. D5⋊(C22⋊C16)C2semidirect
3. #10598831C2semidirect
4. #10598782C2semidirect
226. C5#11468semidirect

Maximal subgroups

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

subgroupindex
#106155252
D5⋊(C22⋊C16)2
#105988312
#105987822
#114685