Finite Group Databasebeta

← #13023162

Subgroups — #13023162

Order 1280.

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

normal subgroups only

This group has 382 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
1D5×#424C211yesmaximal, characteristic
2#10604706C212yesmaximal
3#10598782C212yesmaximal, complemented
4#10598726C212yesmaximal, complemented
5C2×D5×M16C411yescharacteristic
6C22×C8×D5C2211yescharacteristic
7D5×#117C411yescharacteristic
8C2×#3990—22no—
9C5×#424C411yescharacteristic
10#65408C2211yescharacteristic
11#65391C411yescharacteristic
12#65288C2211yescharacteristic
13#65128—22no—
14D5×C4⋊C8—22no—
15C22⋊#674C2214yes—
16#64887—22no—
17#11443—51nomaximal, Sylow
18C22×C4×D5C2×C411yescharacteristic
19C2×C5×M16C2×C411yescharacteristic
20C22×C5×C8C2×C411yescharacteristic
21C5×#117C2×C411yescharacteristic
22#4072C2×C411yescharacteristic
23C2×#681C2×C411yescharacteristic
24C22×#168C2311yescharacteristic
25D5×M16—42no—
26C2×#676—21no—
27C2×C8×D5—21no—
28C2×C8×D5—42no—
29C2×C8×D5D412yes—
30C2×C8×D5D412yes—
31#4038C812yes—
32D5×C4⋊C4C812yes—
33D5×C22⋊C4—21no—
34#4023—21no—
35#4018—21no—
36C42×D5—21no—
37C2×#674—24no—
38#3990—44no—
39C5×C4⋊C8—22no—
40#3946—22no—
41#3946—22no—
42C4⋊#168—22no—
43C2×#424—51no—
44#2112—52no—
45#1323—52no—
46#1323—52no—
47C23×D5M1611yescharacteristic
48C22×C4×C5C22×C411yescharacteristic
49C22×Dic5M1611yescharacteristic
50C2×C4×D5—22no—
51C2×C4×D5—22no—
52C2×C4×D5—22no—
53C2×C4×D5C22⋊C411yescharacteristic
54C2×C4×D5C22⋊C411yescharacteristic
55C2×C4×D5C2×C811yescharacteristic
56C2×C4×D5C2×C811yescharacteristic
57C5×M16—41no—
58C2×C5×C8—21no—
59C2×C5×C8—41no—
60C2×C5×C8C22⋊C412yes—
61C5×C4⋊C4C2×C812yes—
62C5×C22⋊C4—21no—
63C42×C5—21no—
64C22⋊Dic5—21no—
65#685—22no—
66C4⋊Dic5C2×C812yes—
67#683—22no—
68C4×Dic5—21no—
69C4×Dic5—22no—
70#681—41no—
71C2×#168—21no—
72C2×#168—41no—
73C2×#168C2×D412yes—
74#676—42no—
75C8×D5—24no—
76C8×D5—42no—
77C8×D5—42no—
78#674—44no—
79C22×M16—51no—
80C23×C8—51no—
81C2×#117—51no—
82C2×M32—102no—
83#424—51no—
84#424—51no—
85#424—51no—
86#424—102no—
87#424AGL(1,𝔽5)11yescharacteristic
88C2×C4⋊C8—102no—
89C22⋊C16—54no—
90C22⋊C16—102no—
91C23×C5C2×M1611yescharacteristic
92C22×D5—22no—
93C22×D5—42no—
94C22×D5C22⋊C811yescharacteristic
95C22×D5C22⋊C811yescharacteristic
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5C2×C22⋊C411yescharacteristic
100C2×C4×C5C22×C811yescharacteristic
101C2×Dic5—22no—
102C2×Dic5—22no—
103C2×Dic5C22⋊C811yescharacteristic
104C2×Dic5C22⋊C811yescharacteristic
105C4×D5—22no—
106C4×D5—21no—
107C4×D5—21no—
108C4×D5—22no—
109C4×D5—44no—
110C4×D5#9912yes—
111C4×D5#10112yes—
112C5×C8—22no—
113C5×C8—41no—
114#168—22no—
115#168—41no—
116C23×C4—51no—
117C2×M16—51no—
118C2×M16—101no—
119C2×M16—202no—
120C2×M16C2×AGL(1,𝔽5)11yescharacteristic
121C22×C8—51no—
122C22×C8—52no—
123C22×C8—52no—
124C22×C8—101no—
125C22×C8—202no—
126C22×C8C2×AGL(1,𝔽5)11yescharacteristic
127#117—51no—
128#117—52no—
129#117—101no—
130#117—101no—
131#117C2×AGL(1,𝔽5)11yescharacteristic
132C2×C4⋊C4—52no—
133C2×C22⋊C4—101no—
134C2×C42—101no—
135M32—204no—
136C2×C16—104no—
137C4⋊C8—22no—
138C4⋊C8—102no—
139C4⋊C8—102no—
140C4⋊C8—102no—
141C22×C5—22no—
142C22×C5—21no—
143C22×C5C2×C22⋊C811yescharacteristic
144C2×D5—22no—
145C2×D5—22no—
146C2×D5—21no—
147C2×D5—44no—
148C2×D5#32412yes—
149C4×C5—21no—
150C4×C5—42no—
151C4×C5C2×#9911yescharacteristic
152C4×C5C2×#10111yescharacteristic
153Dic5—21no—
154Dic5—42no—
155Dic5#32412yes—
156C24—51no—
157C22×C4—51no—
158C22×C4—51no—
159C22×C4—51no—
160C22×C4—51no—
161C22×C4—51no—
162C22×C4—102no—
163C22×C4—102no—
164C22×C4—102no—
165C22×C4C22×AGL(1,𝔽5)11yescharacteristic
166M16—41no—
167M16—202no—
168M16—201no—
169C2×C8—21no—
170C2×C8—41no—
171C2×C8—52no—
172C2×C8—104no—
173C2×C8—101no—
174C2×C8—202no—
175C2×C8—202no—
176C2×C8—201no—
177C2×C8C22⋊AGL(1,𝔽5)12yes—
178C4⋊C4—52no—
179C4⋊C4—102no—
180C4⋊C4D5⋊C812yes—
181C22⋊C4—21no—
182C22⋊C4—102no—
183C22⋊C4—101no—
184C42—21no—
185C42—102no—
186C42—101no—
187C16—204no—
188C2×C5—41no—
189C2×C5C2×#32411yescharacteristic
190C2×C5#211712yes—
191D5—22no—
192D5—41no—
193C23—51no—
194C23—51no—
195C23—102no—
196C23—202no—
197C23D5⋊M1611yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—51no—
202C2×C4—52no—
203C2×C4—52no—
204C2×C4—51no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—101no—
209C2×C4—101no—
210C2×C4—102no—
211C2×C4—204no—
212C2×C4C2×D5⋊C811yescharacteristic
213C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
214C8—22no—
215C8—41no—
216C8—102no—
217C8—201no—
218C5#1144311yescharacteristic, complemented, Sylow
219C22—21no—
220C22—22no—
221C22—52no—
222C22—102no—
223C22—101no—
224C22—102no—
225C22—204no—
226C22D5⋊(C22⋊C8)11yescharacteristic
227C4—21no—
228C4—42no—
229C4—52no—
230C4—101no—
231C4—202no—
232C4D5⋊#9911yescharacteristic
233C4D5⋊#10111yescharacteristic
234C2—41no—
235C2—102no—
236C2—201no—
237C2D5⋊#32411yescharacteristic
238C2#1060477612yes—
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#424C4
socleC22×C5C2×C22⋊C8
prime radicalC23×D5M16
cosocleC22×#168C23
hypercenter#424AGL(1,𝔽5)
hypocenterC5#11443
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #10598782C2semidirect
4. #10598726C2semidirect
218. C5#11443semidirect

Maximal subgroups

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

subgroupindex
D5×#4242
#106047062
#105987822
#105987262
#114435