Finite Group Databasebeta

← #13023214

Subgroups — #13023214

Order 1280.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×#65122C211yesmaximal, characteristic
2#10604709C212yesmaximal, complemented
3#10598760C212yesmaximal
4#10598690C212yesmaximal, complemented
5C2×C42×D5C411yescharacteristic
6C2×C5×C4⋊C8C411yescharacteristic
7C2×#3952C411yescharacteristic
8C2×#3952C2211yescharacteristic
9C2×C8×Dic5C411yescharacteristic
10C2×C8×Dic5C2211yescharacteristic
11C2×C4⋊#168C2211yescharacteristic
12#65122—22no—
13#65122—22no—
14C22⋊#674C2214yes—
15#64888—22no—
16#64885—22no—
17#11459—51nomaximal, Sylow
18C22×C4×D5C811yescharacteristic
19C22×C4×D5C811yescharacteristic
20C22×C4×D5C2×C411yescharacteristic
21C22×C5×C8C2×C411yescharacteristic
22C22×C5×C8C2×C411yescharacteristic
23C2×C42×C5C2×C411yescharacteristic
24C2×C4×Dic5C811yescharacteristic
25C2×C4×Dic5C811yescharacteristic
26C2×C4×Dic5C2×C411yescharacteristic
27C22×#168C2×C411yescharacteristic
28C22×#168C2311yescharacteristic
29C42×D5—21no—
30C42×D5—21no—
31C42×D5—21no—
32C42×D5—21no—
33C2×#674—24no—
34C5×C4⋊C8—22no—
35#3952—22no—
36#3952—22no—
37C8×Dic5—21no—
38C8×Dic5—21no—
39C8×Dic5D412yes—
40C8×Dic5D412yes—
41C4⋊#168—22no—
42C2×#431—51no—
43#2162—52no—
44#1322—52no—
45#1314—52no—
46C23×D5C2×C811yescharacteristic
47C22×C4×C5C2×C811yescharacteristic
48C22×C4×C5C2×C811yescharacteristic
49C22×C4×C5C22×C411yescharacteristic
50C22×Dic5C2×C811yescharacteristic
51C22×Dic5C2×C811yescharacteristic
52C22×Dic5C2×C811yescharacteristic
53C2×C4×D5—21no—
54C2×C4×D5—21no—
55C2×C4×D5—22no—
56C2×C4×D5—21no—
57C2×C4×D5—21no—
58C2×C4×D5—21no—
59C2×C4×D5—21no—
60C2×C4×D5—42no—
61C2×C4×D5—41no—
62C2×C4×D5—41no—
63C2×C4×D5C1614yescomplemented
64C2×C5×C8—21no—
65C2×C5×C8—41no—
66C2×C5×C8—41no—
67C2×C5×C8C22⋊C412yes—
68C42×C5—21no—
69C42×C5—21no—
70C4×Dic5—21no—
71C4×Dic5—21no—
72C4×Dic5—21no—
73C4×Dic5—21no—
74C4×Dic5C22⋊C411yescharacteristic
75C4×Dic5C22⋊C411yescharacteristic
76C4×Dic5M1611yescharacteristic
77C4×Dic5M1611yescharacteristic
78C2×#168—21no—
79C2×#168—41no—
80C2×#168—41no—
81C2×#168C2×D412yes—
82#674—44no—
83C22×C42—51no—
84#431—102no—
85#431—102no—
86C2×C4⋊C8—51no—
87C2×C4⋊C8AGL(1,𝔽5)11yescharacteristic
88C2×C22⋊C8—51no—
89C2×C22⋊C8—51no—
90C2×C4×C8—51no—
91C2×C4×C8—51no—
92C4⋊C16—102no—
93C22⋊C16—54no—
94C4×C16—102no—
95C23×C5C22×C811yescharacteristic
96C22×D5—21no—
97C22×D5—21no—
98C22×D5—41no—
99C22×D5—41no—
100C22×D5C2×C1612yes—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—41no—
107C2×C4×C5C2×C1612yes—
108C2×C4×C5C2×C22⋊C411yescharacteristic
109C2×C4×C5C2×M1611yescharacteristic
110C2×Dic5—22no—
111C2×Dic5—21no—
112C2×Dic5—41no—
113C2×Dic5C22⋊C811yescharacteristic
114C2×Dic5C22⋊C811yescharacteristic
115C2×Dic5C22⋊C811yescharacteristic
116C2×Dic5C22⋊C811yescharacteristic
117C2×Dic5C2×C1612yes—
118C2×Dic5M3212yes—
119C4×D5—24no—
120C4×D5—24no—
121C4×D5—42no—
122C4×D5—42no—
123C4×D5—41no—
124C4×D5—41no—
125C4×D5—42no—
126C5×C8—22no—
127C5×C8—41no—
128#168—22no—
129#168—41no—
130C23×C4—51no—
131C23×C4—51no—
132C23×C4—51no—
133C22×C8—51no—
134C22×C8—51no—
135C22×C8C2×AGL(1,𝔽5)11yescharacteristic
136C22×C8C2×AGL(1,𝔽5)11yescharacteristic
137C2×C42—51no—
138C2×C42—51no—
139C2×C42—51no—
140C2×C42—101no—
141C2×C42—101no—
142C2×C42—101no—
143C2×C42—101no—
144C2×C42C2×AGL(1,𝔽5)11yescharacteristic
145C2×C16—104no—
146C4⋊C8—22no—
147C4⋊C8—102no—
148C22⋊C8—102no—
149C22⋊C8—102no—
150C4×C8—52no—
151C4×C8—52no—
152C4×C8—101no—
153C4×C8—101no—
154C22×C5—21no—
155C22×C5—21no—
156C22×C5C2×C22⋊C811yescharacteristic
157C22×C5C22×C1611yescharacteristic
158C22×C5C2×M3211yescharacteristic
159C2×D5—22no—
160C2×D5—42no—
161C2×D5—41no—
162C2×D5—41no—
163C2×D5—42no—
164C4×C5—22no—
165C4×C5—21no—
166C4×C5—41no—
167C4×C5#41011yescharacteristic
168C4×C5#41311yescharacteristic
169Dic5—21no—
170Dic5—41no—
171Dic5C22⋊C1612yes—
172Dic5C22⋊C1612yes—
173Dic5#34912yes—
174C24—51no—
175C22×C4—51no—
176C22×C4—51no—
177C22×C4—54no—
178C22×C4—51no—
179C22×C4—101no—
180C22×C4—101no—
181C22×C4—102no—
182C22×C4—101no—
183C22×C4—101no—
184C22×C4—101no—
185C22×C4—101no—
186C22×C4—201no—
187C22×C4—201no—
188C22×C4—202no—
189C22×C4D5⋊C811yescharacteristic
190C22×C4D5⋊C811yescharacteristic
191C22×C4C22×AGL(1,𝔽5)11yescharacteristic
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—52no—
196C2×C8—101no—
197C2×C8—201no—
198C2×C8—201no—
199C2×C8C22⋊AGL(1,𝔽5)12yes—
200C42—21no—
201C42—21no—
202C42—51no—
203C42—51no—
204C42—51no—
205C42—51no—
206C42—101no—
207C42—101no—
208C42—101no—
209C42—101no—
210C16—204no—
211C2×C5—21no—
212C2×C5—21no—
213C2×C5#145811yescharacteristic
214C2×C5C2×C22⋊C1611yescharacteristic
215C2×C5C2×#34911yescharacteristic
216D5—42no—
217C23—52no—
218C23—101no—
219C23—101no—
220C23—201no—
221C23—201no—
222C23C2×D5⋊C811yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—52no—
230C2×C4—52no—
231C2×C4—51no—
232C2×C4—51no—
233C2×C4—51no—
234C2×C4—51no—
235C2×C4—104no—
236C2×C4—104no—
237C2×C4—102no—
238C2×C4—101no—
239C2×C4—202no—
240C2×C4—202no—
241C2×C4—202no—
242C2×C4—201no—
243C2×C4—201no—
244C2×C4—201no—
245C2×C4D5⋊C1612yes—
246C2×C4D5⋊M1611yescharacteristic
247C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
248C8—22no—
249C8—41no—
250C8—102no—
251C8—201no—
252C5#1145911yescharacteristic, complemented, Sylow
253C22—21no—
254C22—21no—
255C22—102no—
256C22—202no—
257C22—202no—
258C22—201no—
259C22—201no—
260C22C2×D5⋊C1611yescharacteristic
261C22D5⋊M3211yescharacteristic
262C22D5⋊(C22⋊C8)11yescharacteristic
263C4—21no—
264C4—22no—
265C4—41no—
266C4—52no—
267C4—52no—
268C4—52no—
269C4—101no—
270C4—201no—
271C4#6577711yescharacteristic
272C4#6578511yescharacteristic
273C2—21no—
274C2—21no—
275C2—202no—
276C2#1060428911yescharacteristic
277C2D5⋊(C22⋊C16)11yescharacteristic
278C2D5⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C16
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC22×C5C2×C22⋊C8
prime radicalC23×D5C2×C8
cosocleC22×#168C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5#11459
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10604709C2semidirect
4. #10598690C2semidirect
63. C2×C4×D5C16semidirect
252. C5#11459semidirect

Maximal subgroups

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

subgroupindex
C2×#651222
#106047092
#105987602
#105986902
#114595