Finite Group Databasebeta

← #13023239

Subgroups — #13023239

Order 1280.

438 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 96 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×C8×C22⋊D5C211yesmaximal, characteristic
2#10604706C212yesmaximal, complemented
3#10598817C212yesmaximal, complemented
4#10598761C212yesmaximal, complemented
5C23×C5×C8C411yescharacteristic
6C2×C4×C22⋊D5C411yescharacteristic
7C22×C8×D5C2211yescharacteristic
8C2×#3990—22no—
9C2×C22⋊#168C2211yescharacteristic
10C8×C22⋊D5—22no—
11C8×C22⋊D5—22no—
12C2×#3952C411yescharacteristic
13C2×#3946C2211yescharacteristic
14C2×C8×Dic5C411yescharacteristic
15C22⋊#674C2214yes—
16#64887—22no—
17#11466—51nomaximal, Sylow
18C23×C4×C5C2×C411yescharacteristic
19C22×C22⋊D5C811yescharacteristic
20C22×C4×D5C2×C411yescharacteristic
21C22×C5×C8—21no—
22C22×C5×C8—21no—
23C22×C5×C8—42no—
24C22×C5×C8C2×C411yescharacteristic
25C22×C5×C8C2×C411yescharacteristic
26C2×C22⋊Dic5C811yescharacteristic
27C4×C22⋊D5—22no—
28C4×C22⋊D5—22no—
29C2×#685C811yescharacteristic
30C2×#683C811yescharacteristic
31C2×C4×Dic5C2×C411yescharacteristic
32C22×#168C2×C411yescharacteristic
33C22×#168C2311yescharacteristic
34C2×C8×D5—42no—
35C2×C8×D5D412yes—
36C2×C8×D5D412yes—
37C2×#674—24no—
38#3990—44no—
39C22⋊#168—22no—
40#3952—22no—
41#3946—22no—
42C8×Dic5—21no—
43C8×Dic5—21no—
44C2×C8×D4—51no—
45#2112—52no—
46#1322—52no—
47#1314—52no—
48C24×C5C2×C811yescharacteristic
49C23×D5C2×C811yescharacteristic
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5—41no—
53C22×C4×C5—41no—
54C22×C4×C5C2×C811yescharacteristic
55C22×C4×C5C22×C411yescharacteristic
56C2×C22⋊D5—22no—
57C2×C22⋊D5—22no—
58C2×C22⋊D5—22no—
59C22×Dic5C2×C811yescharacteristic
60C22×Dic5C2×C811yescharacteristic
61C22×Dic5C2×C811yescharacteristic
62C2×C4×D5—41no—
63C2×C4×D5—41no—
64C2×C4×D5C22⋊C412yes—
65C2×C4×D5M1612yes—
66C2×C5×C8—22no—
67C2×C5×C8—21no—
68C2×C5×C8—42no—
69C2×C5×C8—42no—
70C2×C5×C8—41no—
71C2×C5×C8C22⋊C411yescharacteristic
72C2×C5×C8C22⋊C411yescharacteristic
73C22⋊Dic5—22no—
74#685—22no—
75#683—22no—
76C4×Dic5—21no—
77C4×Dic5—21no—
78C2×#168—21no—
79C2×#168—41no—
80C2×#168—41no—
81C2×#168C2×D412yes—
82C8×D5—24no—
83C8×D5—42no—
84#674—44no—
85C23×C8—51no—
86C23×C8AGL(1,𝔽5)11yescharacteristic
87C2×C4×D4—51no—
88C2×M32—102no—
89C8×D4—102no—
90C8×D4—102no—
91C2×C4⋊C8—51no—
92C2×C22⋊C8—51no—
93C2×C22⋊C8—51no—
94C2×C4×C8—51no—
95C22⋊C16—54no—
96C22⋊C16—102no—
97C23×C5—21no—
98C23×C5—21no—
99C23×C5—41no—
100C23×C5—41no—
101C23×C5M3212yescomplemented
102C23×C5C22×C811yescharacteristic
103C22×D5—21no—
104C22×D5—21no—
105C22×D5—41no—
106C22×D5—41no—
107C22×D5C22⋊C812yes—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—42no—
112C2×C4×C5—41no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5C2×C22⋊C411yescharacteristic
116C2×C4×C5C2×M1611yescharacteristic
117C22⋊D5—28no—
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—21no—
121C2×Dic5—41no—
122C2×Dic5—41no—
123C2×Dic5C22⋊C812yes—
124C2×Dic5M3212yescomplemented
125C4×D5—22no—
126C4×D5—22no—
127C4×D5—42no—
128C5×C8—21no—
129C5×C8—41no—
130C5×C8#9912yes—
131#168—22no—
132#168—41no—
133C22×D4—51no—
134C23×C4—51no—
135C23×C4C2×AGL(1,𝔽5)11yescharacteristic
136C22×C8—21no—
137C22×C8—21no—
138C22×C8—42no—
139C22×C8—51no—
140C22×C8—52no—
141C22×C8—52no—
142C22×C8—51no—
143C22×C8—202no—
144C22×C8C2×AGL(1,𝔽5)11yescharacteristic
145C22×C8C2×AGL(1,𝔽5)11yescharacteristic
146C4×D4—102no—
147C4×D4—102no—
148C2×C4⋊C4—51no—
149C2×C22⋊C4—51no—
150C2×C22⋊C4—51no—
151C2×C42—51no—
152M32—204no—
153C2×C16—104no—
154C4⋊C8—102no—
155C22⋊C8—102no—
156C22⋊C8—102no—
157C4×C8—101no—
158C4×C8—101no—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5—22no—
162C22×C5—42no—
163C22×C5—42no—
164C22×C5—41no—
165C22×C5—41no—
166C22×C5C2×C22⋊C811yescharacteristic
167C22×C5C2×M3211yescharacteristic
168C22×C5C2×M3211yescharacteristic
169C2×D5—22no—
170C2×D5—22no—
171C2×D5—22no—
172C2×D5—42no—
173C2×D5—42no—
174C4×C5—21no—
175C4×C5—41no—
176C4×C5C2×#9911yescharacteristic
177C4×C5#41311yescharacteristic
178Dic5—22no—
179Dic5—22no—
180Dic5—41no—
181C24—51no—
182C24D5⋊C811yescharacteristic
183C2×D4—102no—
184C2×D4—102no—
185C2×D4—102no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—51no—
191C22×C4—51no—
192C22×C4—52no—
193C22×C4—52no—
194C22×C4—51no—
195C22×C4—201no—
196C22×C4—201no—
197C22×C4D5⋊C811yescharacteristic
198C22×C4C22×AGL(1,𝔽5)11yescharacteristic
199C2×C8—22no—
200C2×C8—21no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—41no—
204C2×C8—52no—
205C2×C8—104no—
206C2×C8—101no—
207C2×C8—202no—
208C2×C8—201no—
209C2×C8—201no—
210C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
211C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
212C4⋊C4—102no—
213C22⋊C4—102no—
214C22⋊C4—102no—
215C42—101no—
216C42—101no—
217C16—204no—
218C2×C5—21no—
219C2×C5—21no—
220C2×C5—42no—
221C2×C5#145911yescharacteristic
222C2×C5#211211yescharacteristic
223C2×C5#211511yescharacteristic
224D5—42no—
225C23—21no—
226C23—21no—
227C23—41no—
228C23—41no—
229C23—52no—
230C23—101no—
231C23—101no—
232C23—201no—
233C23—201no—
234C23#399012yescomplemented
235C23C2×D5⋊C811yescharacteristic
236D4—108no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—52no—
245C2×C4—52no—
246C2×C4—101no—
247C2×C4—101no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—101no—
251C2×C4—202no—
252C2×C4—201no—
253C2×C4—201no—
254C2×C4D5⋊M1611yescharacteristic
255C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
256C8—21no—
257C8—41no—
258C8—102no—
259C8—201no—
260C8#401112yes—
261C5#1146611yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—22no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—102no—
270C22—102no—
271C22—102no—
272C22—202no—
273C22—202no—
274C22C2×#399011yescharacteristic
275C22D5⋊M3211yescharacteristic
276C22D5⋊(C22⋊C8)11yescharacteristic
277C4—21no—
278C4—41no—
279C4—102no—
280C4—102no—
281C4—201no—
282C4#6576111yescharacteristic
283C4C2×#401111yescharacteristic
284C2—21no—
285C2—21no—
286C2—42no—
287C2—202no—
288C2#1060470611yescharacteristic
289C2#1060471311yescharacteristic
290C2#1060487811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC22×C5C2×C22⋊C8
prime radicalC22×C22⋊D5C8
cosocleC22×#168C23
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5#11466
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #10604706C2semidirect
3. #10598817C2semidirect
4. #10598761C2semidirect
101. C23×C5M32semidirect
124. C2×Dic5M32semidirect
234. C23#3990semidirect
261. C5#11466semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D52
#106047062
#105988172
#105987612
#114665