Finite Group Databasebeta

← #13018315

Subgroups — #13018315

Order 1280.

450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 94 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#10604885C212yesmaximal
3#10604699C212yesmaximal, complemented
4#10598776C212yesmaximal, complemented
5C2×C4×C22⋊D5C2211yescharacteristic
6C23×#168C411yescharacteristic
7C22×C8×D5C411yescharacteristic
8#65759C2214yes—
9C2×C5×C22⋊C8C411yescharacteristic
10C2×#3952C411yescharacteristic
11C2×#3946C2211yescharacteristic
12C2×C8×Dic5C2211yescharacteristic
13#65014—22no—
14#65014—22no—
15#64933—22no—
16#64915—22no—
17#64883—22no—
18#64882—22no—
19#8620—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C22×C22⋊D5Q811yescharacteristic
22C22×C4×D5C2×C411yescharacteristic
23C22×C5×C8C2×C411yescharacteristic
24C22×C5×C8C2×C411yescharacteristic
25C2×C22⋊Dic5D411yescharacteristic
26C4×C22⋊D5—22no—
27C4×C22⋊D5—22no—
28C2×#685D411yescharacteristic
29C2×#683Q811yescharacteristic
30C2×C4×Dic5C2311yescharacteristic
31C22×#168—21no—
32C22×#168—21no—
33C22×#168—42no—
34C22×#168C2×C411yescharacteristic
35C22×#168C2×C411yescharacteristic
36C2×C8×D5—21no—
37C2×C8×D5—21no—
38C2×C8×D5—42no—
39C22⋊#170—24no—
40#4002—24no—
41C4⋊#170—24no—
42C5×C22⋊C8—22no—
43#3952—22no—
44#3946—22no—
45C8×Dic5D412yes—
46C8×Dic5D412yes—
47C2×C8×D4—51no—
48#1568—52no—
49#1466—52no—
50#1290—52no—
51C24×C5C4⋊C411yescharacteristic
52C23×D5C4⋊C411yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—41no—
56C22×C4×C5—41no—
57C22×C4×C5C4⋊C411yescharacteristic
58C22×C4×C5C22×C411yescharacteristic
59C2×C22⋊D5—22no—
60C2×C22⋊D5—22no—
61C2×C22⋊D5—22no—
62C22×Dic5C4⋊C411yescharacteristic
63C22×Dic5C2×D411yescharacteristic
64C22×Dic5C2×Q811yescharacteristic
65C2×C4×D5—21no—
66C2×C4×D5—21no—
67C2×C4×D5—41no—
68C2×C4×D5—41no—
69C2×#170—44no—
70C2×C5×C8—21no—
71C2×C5×C8—41no—
72C2×C5×C8—41no—
73C2×C5×C8C22⋊C412yes—
74C22⋊Dic5—22no—
75#685—22no—
76#683—22no—
77C4×Dic5C2×D412yes—
78C4×Dic5#4112yes—
79C2×#168—22no—
80C2×#168—21no—
81C2×#168—42no—
82C2×#168—42no—
83C2×#168—41no—
84C2×#168C22⋊C411yescharacteristic
85C2×#168C22⋊C411yescharacteristic
86C8×D5—42no—
87C8×D5—42no—
88C23×C8—51no—
89C23×C8—51no—
90C2×C4×D4—51no—
91C8×D4—102no—
92C8×D4—102no—
93#432—54no—
94C2×C4⋊C8—51no—
95C2×C22⋊C8—51no—
96C2×C22⋊C8AGL(1,𝔽5)11yescharacteristic
97C2×C4×C8—51no—
98#335—102no—
99#334—102no—
100#323—102no—
101#323—102no—
102C23×C5—21no—
103C23×C5—21no—
104C23×C5—41no—
105C23×C5—41no—
106C23×C5#10812yes—
107C23×C5C2×C4⋊C411yescharacteristic
108C22×D5—21no—
109C22×D5—21no—
110C22×D5—41no—
111C22×D5—41no—
112C22×D5#10812yes—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—42no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5C2×C22⋊C411yescharacteristic
121C2×C4×C5#11711yescharacteristic
122C22⋊D5—28no—
123C2×Dic5—21no—
124C2×Dic5—21no—
125C2×Dic5—21no—
126C2×Dic5—41no—
127C2×Dic5—41no—
128C2×Dic5#12112yes—
129C2×Dic5C22⋊Q812yes—
130C4×D5—42no—
131C4×D5—41no—
132C4×D5—41no—
133#170—84no—
134C5×C8—22no—
135C5×C8—41no—
136#168—21no—
137#168—41no—
138#168#10012yes—
139C22×D4—51no—
140C23×C4—51no—
141C23×C4C2×AGL(1,𝔽5)11yescharacteristic
142C22×C8—51no—
143C22×C8—51no—
144C22×C8—101no—
145C22×C8—101no—
146C22×C8—101no—
147C22×C8—101no—
148C22×C8—202no—
149C22×C8—202no—
150C22×C8C2×AGL(1,𝔽5)11yescharacteristic
151C22×C8C2×AGL(1,𝔽5)11yescharacteristic
152C4×D4—102no—
153C4×D4—102no—
154C2×C4⋊C4—51no—
155C2×C22⋊C4—51no—
156C2×C22⋊C4—51no—
157C2×C42—51no—
158C4⋊C8—102no—
159C4⋊C8—104no—
160C22⋊C8—22no—
161C22⋊C8—102no—
162C22⋊C8—104no—
163#97—104no—
164C4×C8—52no—
165C4×C8—52no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—22no—
169C22×C5—42no—
170C22×C5—42no—
171C22×C5—41no—
172C22×C5—41no—
173C22×C5#38011yescharacteristic
174C22×C5C2×#10811yescharacteristic
175C22×C5C2×#10811yescharacteristic
176C2×D5—22no—
177C2×D5—42no—
178C2×D5—41no—
179C2×D5—41no—
180C2×D5—42no—
181C4×C5—21no—
182C4×C5—41no—
183C4×C5C2×#10011yescharacteristic
184C4×C5#41311yescharacteristic
185Dic5—22no—
186Dic5—22no—
187Dic5—41no—
188C24—51no—
189C24C4⋊AGL(1,𝔽5)11yescharacteristic
190C2×D4—102no—
191C2×D4—102no—
192C2×D4—102no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—51no—
198C22×C4—51no—
199C22×C4—51no—
200C22×C4—101no—
201C22×C4—101no—
202C22×C4—201no—
203C22×C4—201no—
204C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
205C22×C4C22×AGL(1,𝔽5)11yescharacteristic
206C2×C8—21no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—51no—
210C2×C8—51no—
211C2×C8—102no—
212C2×C8—101no—
213C2×C8—202no—
214C2×C8—202no—
215C2×C8—202no—
216C2×C8—202no—
217C2×C8—201no—
218C2×C8—204no—
219C2×C8C22⋊AGL(1,𝔽5)12yes—
220C4⋊C4—102no—
221C22⋊C4—102no—
222C22⋊C4—102no—
223C42—52no—
224C42—52no—
225C2×C5—21no—
226C2×C5—21no—
227C2×C5—42no—
228C2×C5#180011yescharacteristic
229C2×C5#181011yescharacteristic
230C2×C5#181211yescharacteristic
231D5—42no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—52no—
237C23—101no—
238C23—101no—
239C23—201no—
240C23—201no—
241C23#399612yes—
242C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
243D4—108no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—52no—
252C2×C4—52no—
253C2×C4—101no—
254C2×C4—101no—
255C2×C4—101no—
256C2×C4—202no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4—201no—
261C2×C4#413011yescharacteristic
262C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C8—22no—
264C8—41no—
265C8—52no—
266C8—101no—
267C8—201no—
268C8—404no—
269C5#862011yescharacteristic, complemented, Sylow
270C22—21no—
271C22—21no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—102no—
278C22—202no—
279C22—202no—
280C22—201no—
281C22—201no—
282C22C2×#399611yescharacteristic
283C22D5⋊#10811yescharacteristic
284C22#6576511yescharacteristic
285C4—21no—
286C4—41no—
287C4—102no—
288C4—102no—
289C4—201no—
290C4#6577711yescharacteristic
291C4D5⋊#10011yescharacteristic
292C2—21no—
293C2—21no—
294C2—42no—
295C2—202no—
296C2#1060424611yescharacteristic
297C2#1060473211yescharacteristic
298C2#1060476511yescharacteristic
subgroupG/H
centerC22#65765
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C22⋊C8C4
socleC22×C5#380
prime radicalC22×C22⋊D5Q8
cosocleC2×C4×Dic5C23
hypercenterC2×C22⋊C8AGL(1,𝔽5)
hypocenterC5#8620
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10604699C2semidirect
4. #10598776C2semidirect
269. C5#8620semidirect

Maximal subgroups

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

subgroupindex
C2×#650142
#106048852
#106046992
#105987762
#86205