Finite Group Databasebeta

← #13023153

Subgroups — #13023153

Order 1280.

450 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 102 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×D5×C4⋊C8C211yesmaximal, characteristic
2#10604706C212yesmaximal
3#10598761C212yesmaximal, complemented
4#10598690C212yesmaximal, complemented
5C22×C8×D5C411yescharacteristic
6C22×C8×D5C2211yescharacteristic
7C2×C42×D5C411yescharacteristic
8C2×#3990—22no—
9C2×C5×C4⋊C8C411yescharacteristic
10C2×#3946C411yescharacteristic
11C2×#3946C2211yescharacteristic
12C2×C4⋊#168C2211yescharacteristic
13D5×C4⋊C8—22no—
14D5×C4⋊C8—22no—
15C22⋊#674C2214yes—
16#64887—22no—
17#11440—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
29C2×C8×D5—21no—
30C2×C8×D5—21no—
31C2×C8×D5—42no—
32C2×C8×D5—42no—
33C2×C8×D5D412yes—
34C2×C8×D5D412yes—
35C42×D5—21no—
36C42×D5—21no—
37C42×D5—21no—
38C42×D5—21no—
39C2×#674—24no—
40#3990—44no—
41C5×C4⋊C8—22no—
42#3946—22no—
43#3946—22no—
44C4⋊#168—22no—
45C22×C4⋊C8—51no—
46#2112—52no—
47#1322—52no—
48#1322—52no—
49C23×D5C2×C811yescharacteristic
50C22×C4×C5C2×C811yescharacteristic
51C22×C4×C5C2×C811yescharacteristic
52C22×C4×C5C22×C411yescharacteristic
53C22×Dic5C2×C811yescharacteristic
54C22×Dic5C2×C811yescharacteristic
55C22×Dic5C2×C811yescharacteristic
56C2×C4×D5—21no—
57C2×C4×D5—21no—
58C2×C4×D5—22no—
59C2×C4×D5—22no—
60C2×C4×D5—22no—
61C2×C4×D5—22no—
62C2×C4×D5—21no—
63C2×C4×D5—21no—
64C2×C4×D5—42no—
65C2×C4×D5C22⋊C411yescharacteristic
66C2×C4×D5C22⋊C411yescharacteristic
67C2×C4×D5M1611yescharacteristic
68C2×C4×D5M1611yescharacteristic
69C2×C5×C8—21no—
70C2×C5×C8—41no—
71C2×C5×C8—41no—
72C2×C5×C8C22⋊C412yes—
73C42×C5—21no—
74C42×C5—21no—
75C4×Dic5—21no—
76C4×Dic5—21no—
77C4×Dic5—21no—
78C4×Dic5—21no—
79C4×Dic5—21no—
80C4×Dic5—21no—
81C2×#168—21no—
82C2×#168—41no—
83C2×#168—41no—
84C2×#168C2×D412yes—
85C8×D5—24no—
86C8×D5—42no—
87C8×D5—42no—
88C8×D5—42no—
89#674—44no—
90C23×C8—51no—
91C23×C8—51no—
92C22×C42—51no—
93C2×M32—102no—
94C2×C4⋊C8—51no—
95C2×C4⋊C8—51no—
96C2×C4⋊C8—51no—
97C2×C4⋊C8—102no—
98C2×C4⋊C8—102no—
99C2×C4⋊C8AGL(1,𝔽5)11yescharacteristic
100C22⋊C16—54no—
101C22⋊C16—102no—
102C23×C5C22×C811yescharacteristic
103C22×D5—21no—
104C22×D5—21no—
105C22×D5—22no—
106C22×D5—22no—
107C22×D5C22⋊C811yescharacteristic
108C22×D5C22⋊C811yescharacteristic
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—41no—
115C2×C4×C5M3212yescomplemented
116C2×C4×C5C2×C22⋊C411yescharacteristic
117C2×C4×C5C2×M1611yescharacteristic
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—22no—
121C2×Dic5—21no—
122C2×Dic5—41no—
123C2×Dic5C22⋊C811yescharacteristic
124C2×Dic5C22⋊C811yescharacteristic
125C2×Dic5M3212yescomplemented
126C4×D5—24no—
127C4×D5—24no—
128C4×D5—22no—
129C4×D5—21no—
130C4×D5—21no—
131C4×D5—22no—
132C4×D5—42no—
133C4×D5—42no—
134C4×D5#9912yes—
135C4×D5#10112yes—
136C5×C8—22no—
137C5×C8—41no—
138#168—22no—
139#168—41no—
140C23×C4—51no—
141C23×C4—51no—
142C23×C4—51no—
143C22×C8—51no—
144C22×C8—52no—
145C22×C8—52no—
146C22×C8—51no—
147C22×C8—101no—
148C22×C8—101no—
149C22×C8—202no—
150C22×C8—202no—
151C22×C8C2×AGL(1,𝔽5)11yescharacteristic
152C22×C8C2×AGL(1,𝔽5)11yescharacteristic
153C2×C42—51no—
154C2×C42—51no—
155C2×C42—51no—
156C2×C42—101no—
157C2×C42—101no—
158C2×C42—101no—
159C2×C42—101no—
160C2×C42C2×AGL(1,𝔽5)11yescharacteristic
161M32—204no—
162C2×C16—104no—
163C4⋊C8—22no—
164C4⋊C8—102no—
165C4⋊C8—102no—
166C4⋊C8—102no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5C2×C22⋊C811yescharacteristic
170C22×C5C2×M3211yescharacteristic
171C22×C5C2×M3211yescharacteristic
172C2×D5—24no—
173C2×D5—24no—
174C2×D5—21no—
175C2×D5—21no—
176C2×D5—21no—
177C2×D5—21no—
178C2×D5#32412yes—
179C2×D5#34912yes—
180C4×C5—22no—
181C4×C5—21no—
182C4×C5—41no—
183C4×C5C2×#9911yescharacteristic
184C4×C5C2×#10111yescharacteristic
185Dic5—22no—
186Dic5—21no—
187Dic5—41no—
188Dic5#32412yes—
189C24—51no—
190C22×C4—51no—
191C22×C4—51no—
192C22×C4—51no—
193C22×C4—51no—
194C22×C4—51no—
195C22×C4—51no—
196C22×C4—51no—
197C22×C4—102no—
198C22×C4—102no—
199C22×C4—102no—
200C22×C4—101no—
201C22×C4—101no—
202C22×C4—101no—
203C22×C4—101no—
204C22×C4—102no—
205C22×C4—202no—
206C22×C4D5⋊C811yescharacteristic
207C22×C4D5⋊C811yescharacteristic
208C22×C4C22×AGL(1,𝔽5)11yescharacteristic
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—52no—
213C2×C8—104no—
214C2×C8—101no—
215C2×C8—202no—
216C2×C8—202no—
217C2×C8—202no—
218C2×C8—201no—
219C2×C8—201no—
220C2×C8C22⋊AGL(1,𝔽5)12yes—
221C42—21no—
222C42—21no—
223C42—101no—
224C42—101no—
225C42—101no—
226C42—101no—
227C42—101no—
228C42—101no—
229C16—204no—
230C2×C5—21no—
231C2×C5—21no—
232C2×C5C2×#32411yescharacteristic
233C2×C5#211211yescharacteristic
234C2×C5C2×#34911yescharacteristic
235D5—22no—
236D5—22no—
237C23—51no—
238C23—51no—
239C23—102no—
240C23—102no—
241C23—101no—
242C23—101no—
243C23C2×D5⋊C811yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—51no—
251C2×C4—52no—
252C2×C4—52no—
253C2×C4—52no—
254C2×C4—51no—
255C2×C4—102no—
256C2×C4—102no—
257C2×C4—104no—
258C2×C4—104no—
259C2×C4—102no—
260C2×C4—101no—
261C2×C4—101no—
262C2×C4—101no—
263C2×C4—101no—
264C2×C4—101no—
265C2×C4—202no—
266C2×C4—202no—
267C2×C4—201no—
268C2×C4#399012yescomplemented
269C2×C4D5⋊M1611yescharacteristic
270C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
271C8—22no—
272C8—41no—
273C8—102no—
274C8—201no—
275C5#1144011yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—52no—
279C22—52no—
280C22—104no—
281C22—104no—
282C22—101no—
283C22—101no—
284C22—101no—
285C22—101no—
286C22C2×#399011yescharacteristic
287C22D5⋊M3211yescharacteristic
288C22D5⋊(C22⋊C8)11yescharacteristic
289C4—21no—
290C4—22no—
291C4—41no—
292C4—52no—
293C4—101no—
294C4—102no—
295C4—201no—
296C4D5⋊#9911yescharacteristic
297C4D5⋊#10111yescharacteristic
298C2—21no—
299C2—21no—
300C2—102no—
301C2—102no—
302C2D5⋊#32411yescharacteristic
303C2#1060470611yescharacteristic
304C2D5⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
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#11440
LCSG ▷ C23×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
3. #10598761C2semidirect
4. #10598690C2semidirect
115. C2×C4×C5M32semidirect
125. C2×Dic5M32semidirect
268. C2×C4#3990semidirect
275. C5#11440semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊C82
#106047062
#105987612
#105986902
#114405