Finite Group Databasebeta

← #10609543

Subgroups — #10609543

Order 640.

582 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 137 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×#4044C211yesmaximal, characteristic, complemented
2C2×#4039C211yesmaximal, characteristic, complemented
3C5×#398C211yesmaximal, characteristic, complemented
4#65282C211yesmaximal, characteristic, complemented
5#65280C211yesmaximal, characteristic, complemented
6#65278C212yesmaximal, complemented
7#65277C212yesmaximal, complemented
8#64960C211yesmaximal, characteristic
9#64959C212yesmaximal, complemented
10#64954C212yesmaximal, complemented
11#64937C211yesmaximal, characteristic, complemented
12C22×D20C2211yescharacteristic
13C22×D20C2212yes—
14C22×C4×D5C2212yes—
15C2×C5×C4⋊C4C2211yescharacteristic
16C2×C5×C4⋊C4C2211yescharacteristic
17C2×C5×C4⋊C4C2212yes—
18C2×#685C2212yes—
19C2×#685C2211yescharacteristic
20C2×#685C2212yes—
21C2×#685C2211yescharacteristic
22C2×#685C2211yescharacteristic
23C2×#685C2212yes—
24C2×#685C2212yes—
25C2×#685C2212yes—
26C2×C4⋊Dic5C2211yescharacteristic
27C2×#683C2211yescharacteristic
28C2×C4×Dic5C2212yes—
29C2×C4×Dic5C2211yescharacteristic
30#4044—24no—
31#4039—24no—
32C5×#95C2211yescharacteristic
33C5×#95C2212yes—
34#3963C2211yescharacteristic
35#3963C2212yes—
36#3963C2212yes—
37#2603—51nomaximal, Sylow
38C23×D5C2311yescharacteristic
39C23×D5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×C4×C5C2312yes—
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×D20—24no—
50C2×D20—22no—
51C2×D20—24no—
52C2×D20—24no—
53C2×D20—42no—
54C2×C4×D5—24no—
55C2×C4×D5—42no—
56C2×C4×D5—42no—
57C5×C4⋊C4—22no—
58C5×C4⋊C4—22no—
59C5×C4⋊C4—42no—
60#685—24no—
61#685—22no—
62#685—24no—
63#685—24no—
64#685—22no—
65#685—22no—
66#685—42no—
67#685—42no—
68C4⋊Dic5—22no—
69#683—22no—
70C4×Dic5—24no—
71C4×Dic5D414yescomplemented
72C2×#126—51no—
73C2×C4×D4—51no—
74#398D511yescharacteristic, complemented
75#397—51no—
76#394—51no—
77#392—51no—
78#390—52no—
79#388—52no—
80#386—52no—
81#385—52no—
82#376—51no—
83C23×C5C2411yescharacteristic
84C22×D5—22no—
85C22×D5—22no—
86C22×D5—22no—
87C22×D5—22no—
88C22×D5—22no—
89C22×D5—22no—
90C22×D5—21no—
91C22×D5—22no—
92C22×D5—22no—
93C22×D5—21no—
94C22×D5—21no—
95C22×D5#4114yes—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—22no—
105C2×C4×C5—21no—
106C2×C4×C5—22no—
107C2×C4×C5C2×D412yes—
108C2×C4×C5#4114yes—
109C2×Dic5—22no—
110C2×Dic5—21no—
111C2×Dic5—21no—
112C2×Dic5—21no—
113C2×Dic5—22no—
114C2×Dic5—22no—
115C2×Dic5—22no—
116C2×Dic5—22no—
117C2×Dic5C2×D412yes—
118C2×Dic5C2×D412yes—
119D20—28no—
120D20—48no—
121C4×D5—48no—
122C22×D4—51no—
123C22×D4—52no—
124C23×C4—52no—
125#126—104no—
126C4×D4—104no—
127C2×C4⋊C4—51no—
128C2×C4⋊C4—51no—
129C2×C4⋊C4C2×D511yescharacteristic
130C2×C4⋊C4C2×D511yescharacteristic
131C2×C4⋊C4C2×D512yes—
132C2×C22⋊C4—52no—
133C2×C22⋊C4—51no—
134C2×C22⋊C4—51no—
135C2×C22⋊C4—51no—
136C2×C22⋊C4—52no—
137C2×C22⋊C4—52no—
138C2×C22⋊C4—52no—
139C2×C22⋊C4—52no—
140C2×C42—51no—
141C2×C42—52no—
142#95—52no—
143#95—51no—
144#95—52no—
145#95C2×D511yescharacteristic
146#95C2×D512yes—
147C22×C5C22×D411yescharacteristic
148C22×C5C2×#4112yes—
149C22×C5C2×#4112yes—
150C22×C5H(5,𝔽2)11yescharacteristic
151C22×C5H(5,𝔽2)11yescharacteristic
152C2×D5—24no—
153C2×D5—24no—
154C2×D5—24no—
155C2×D5—42no—
156C2×D5—42no—
157C2×D5—42no—
158C2×D5—42no—
159C2×D5—41no—
160C2×D5—41no—
161C2×D5—41no—
162C2×D5—42no—
163C2×D5—42no—
164C4×C5—22no—
165C4×C5—24no—
166C4×C5—41no—
167C4×C5—42no—
168C4×C5—41no—
169Dic5—22no—
170Dic5—22no—
171Dic5—41no—
172Dic5—42no—
173C24—52no—
174C24—51no—
175C2×D4—104no—
176C2×D4—104no—
177C2×D4—102no—
178C2×D4—104no—
179C2×D4—202no—
180C22×C4—51no—
181C22×C4—51no—
182C22×C4—52no—
183C22×C4—51no—
184C22×C4—104no—
185C22×C4—202no—
186C22×C4—202no—
187C22×C4C22×D512yes—
188C22×C4C22×D511yescharacteristic
189C22×C4C22×D511yescharacteristic
190C22×C4C22×D511yescharacteristic
191C22×C4C22×D512yes—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—102no—
196C4⋊C4—102no—
197C22⋊C4—104no—
198C22⋊C4—102no—
199C22⋊C4—102no—
200C22⋊C4—104no—
201C22⋊C4—102no—
202C22⋊C4—104no—
203C22⋊C4—202no—
204C22⋊C4—202no—
205C42—54no—
206C42—104no—
207C2×C5#52511yescharacteristic
208C2×C5#53211yescharacteristic
209C2×C5#53511yescharacteristic
210C2×C5#55112yes—
211C2×C5#55312yes—
212D5—44no—
213D5—81no—
214C23—54no—
215C23—102no—
216C23—102no—
217C23—102no—
218C23—102no—
219C23—102no—
220C23—102no—
221C23—101no—
222C23—101no—
223C23—102no—
224C23—102no—
225C23—101no—
226C23C23×D511yescharacteristic
227D4—108no—
228D4—208no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—52no—
241C2×C4—52no—
242C2×C4—101no—
243C2×C4—102no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—208no—
251C2×C4D4×D512yes—
252C2×C4#71314yes—
253C5#260311yescharacteristic, complemented, Sylow
254C22—104no—
255C22—104no—
256C22—104no—
257C22—202no—
258C22—202no—
259C22—202no—
260C22—202no—
261C22—201no—
262C22—201no—
263C22—202no—
264C22—201no—
265C22—202no—
266C22C2×D4×D511yescharacteristic
267C22#414411yescharacteristic
268C22C2×#71312yes—
269C22D5×#4112yes—
270C22#414911yescharacteristic
271C4—24no—
272C4—22no—
273C4—42no—
274C4—41no—
275C4—41no—
276C4—102no—
277C4—102no—
278C4—201no—
279C4—202no—
280C2—204no—
281C2—401no—
282C2#6594111yescharacteristic
283C2#6597112yes—
284C2#6599011yescharacteristic
285C2#6602912yes—
286C2#6605911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#398C2
prime radical#64960C2
hypercenter#398D5
hypocenterC5#2603
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#4044C2semidirect
2. C2×#4039C2semidirect
3. C5×#398C2semidirect
4. #65282C2semidirect
5. #65280C2semidirect
6. #65278C2semidirect
7. #65277C2semidirect
9. #64959C2semidirect
10. #64954C2semidirect
11. #64937C2semidirect
71. C4×Dic5D4semidirect
74. #398D5semidirect
253. C5#2603semidirect

Maximal subgroups

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

subgroupindex
C2×#40442
C2×#40392
C5×#3982
#652822
#652802
#652782
#652772
#649602
#649592
#649542
#649372
#26035