Finite Group Databasebeta

← #13023242

Subgroups — #13023242

Order 1280.

438 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 98 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×#65014C211yesmaximal, characteristic
2#10604872C212yesmaximal, complemented
3#10598761C212yesmaximal, complemented
4#10598760C212yesmaximal, complemented
5C2×C4×C22⋊D5C411yescharacteristic
6C23×#168C2211yescharacteristic
7C22×C8×D5C411yescharacteristic
8C2×#3998—22no—
9C2×C5×C22⋊C8C411yescharacteristic
10C2×#3952C2211yescharacteristic
11C2×#3946C2211yescharacteristic
12C2×C8×Dic5C411yescharacteristic
13#65014—22no—
14#65014—22no—
15C22⋊#674—22no—
16C22⋊#674C2214yes—
17#11466—51nomaximal, Sylow
18C23×C4×C5C2×C411yescharacteristic
19C22×C22⋊D5C811yescharacteristic
20C22×C4×D5C2×C411yescharacteristic
21C22×C5×C8C2×C411yescharacteristic
22C22×C5×C8C2×C411yescharacteristic
23C2×C22⋊Dic5C811yescharacteristic
24C4×C22⋊D5—22no—
25C4×C22⋊D5—22no—
26C2×#685C811yescharacteristic
27C2×#683C811yescharacteristic
28C2×C4×Dic5C2×C411yescharacteristic
29C22×#168—42no—
30C22×#168C2×C411yescharacteristic
31C22×#168D412yes—
32C22×#168D412yes—
33C22×#168C2311yescharacteristic
34C2×C8×D5—21no—
35C2×C8×D5—21no—
36C2×C8×D5—42no—
37#3998—44no—
38C2×#674—24no—
39C5×C22⋊C8—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—41no—
51C22×C4×C5—41no—
52C22×C4×C5C22⋊C412yes—
53C22×C4×C5C2×C811yescharacteristic
54C22×C4×C5M1612yes—
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—21no—
63C2×C4×D5—21no—
64C2×C4×D5—41no—
65C2×C4×D5—41no—
66C2×C5×C8—21no—
67C2×C5×C8—21no—
68C2×C5×C8—41no—
69C2×C5×C8—41no—
70C22⋊Dic5—22no—
71#685—22no—
72#683—22no—
73C4×Dic5—21no—
74C4×Dic5—21no—
75C2×#168—24no—
76C2×#168—22no—
77C2×#168—42no—
78C2×#168—41no—
79C2×#168C22⋊C411yescharacteristic
80C2×#168C22⋊C411yescharacteristic
81C2×#168C2×D412yes—
82C8×D5—42no—
83C8×D5—42no—
84#674—44no—
85C23×C8—51no—
86C23×C8—51no—
87C2×C4×D4—51no—
88C2×M32—102no—
89C8×D4—102no—
90C8×D4—102no—
91C2×C4⋊C8—51no—
92C2×C22⋊C8—51no—
93C2×C22⋊C8AGL(1,𝔽5)11yescharacteristic
94C2×C4×C8—51no—
95C22⋊C16—54no—
96C22⋊C16—102no—
97C23×C5—21no—
98C23×C5—21no—
99C23×C5—41no—
100C23×C5—41no—
101C23×C5C22⋊C812yes—
102C23×C5C22×C811yescharacteristic
103C22×D5—21no—
104C22×D5—21no—
105C22×D5—41no—
106C22×D5—41no—
107C22×D5M3212yescomplemented
108C2×C4×C5—21no—
109C2×C4×C5—22no—
110C2×C4×C5—21no—
111C2×C4×C5—22no—
112C2×C4×C5—41no—
113C2×C4×C5—42no—
114C2×C4×C5C22⋊C812yes—
115C2×C4×C5C2×C22⋊C411yescharacteristic
116C2×C4×C5C2×M1611yescharacteristic
117C22⋊D5—28no—
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—21no—
121C2×Dic5—21no—
122C2×Dic5—41no—
123C2×Dic5—41no—
124C2×Dic5M3212yescomplemented
125C4×D5—42no—
126C4×D5—41no—
127C4×D5—41no—
128C5×C8—41no—
129C5×C8—41no—
130#168—22no—
131#168—21no—
132#168#9912yes—
133C22×D4—51no—
134C23×C4—51no—
135C23×C4C2×AGL(1,𝔽5)11yescharacteristic
136C22×C8—52no—
137C22×C8—51no—
138C22×C8—52no—
139C22×C8—51no—
140C22×C8—101no—
141C22×C8—101no—
142C22×C8—202no—
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—22no—
156C22⋊C8—102no—
157C4×C8—101no—
158C4×C8—101no—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5—22no—
162C22×C5—22no—
163C22×C5—22no—
164C22×C5—42no—
165C22×C5—42no—
166C22×C5C2×C22⋊C811yescharacteristic
167C22×C5C2×M3211yescharacteristic
168C22×C5C2×M3211yescharacteristic
169C2×D5—22no—
170C2×D5—42no—
171C2×D5—41no—
172C2×D5—41no—
173C2×D5—42no—
174C4×C5—21no—
175C4×C5—22no—
176C4×C5C2×#9911yescharacteristic
177C4×C5#41311yescharacteristic
178Dic5—22no—
179Dic5—41no—
180Dic5—41no—
181C24—51no—
182C24D5⋊C811yescharacteristic
183C2×D4—102no—
184C2×D4—102no—
185C2×D4—102no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—51no—
189C22×C4—51no—
190C22×C4—51no—
191C22×C4—101no—
192C22×C4—101no—
193C22×C4—201no—
194C22×C4—201no—
195C22×C4D5⋊C811yescharacteristic
196C22×C4#70012yes—
197C22×C4C22⋊AGL(1,𝔽5)12yes—
198C22×C4C22×AGL(1,𝔽5)11yescharacteristic
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—51no—
204C2×C8—51no—
205C2×C8—52no—
206C2×C8—104no—
207C2×C8—102no—
208C2×C8—202no—
209C2×C8—202no—
210C2×C8—201no—
211C2×C8—202no—
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#400312yes—
235C23C2×D5⋊C811yescharacteristic
236D4—108no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—52no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—101no—
247C2×C4—101no—
248C2×C4—202no—
249C2×C4—201no—
250C2×C4—201no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4#400312yes—
254C2×C4C2×#70011yescharacteristic
255C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
256C8—41no—
257C8—41no—
258C8—52no—
259C8—102no—
260C8—101no—
261C5#1146611yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—42no—
268C22—42no—
269C22—102no—
270C22—202no—
271C22—202no—
272C22—201no—
273C22—201no—
274C22D5⋊M3211yescharacteristic
275C22D5⋊M3211yescharacteristic
276C22C2×#400311yescharacteristic
277C4—21no—
278C4—22no—
279C4—102no—
280C4—201no—
281C4—201no—
282C4D5⋊#9911yescharacteristic
283C4#6577711yescharacteristic
284C2—21no—
285C2—21no—
286C2—42no—
287C2—202no—
288C2#1060420111yescharacteristic
289C2#1060470511yescharacteristic
290C2#1060475011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C22⋊C8C4
socleC22×C5C2×C22⋊C8
prime radicalC22×C22⋊D5C8
cosocleC22×#168C23
hypercenterC2×C22⋊C8AGL(1,𝔽5)
hypocenterC5#11466
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10604872C2semidirect
3. #10598761C2semidirect
4. #10598760C2semidirect
107. C22×D5M32semidirect
124. C2×Dic5M32semidirect
261. C5#11466semidirect

Maximal subgroups

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

subgroupindex
C2×#650142
#106048722
#105987612
#105987602
#114665