Finite Group Databasebeta

← #10608536

Subgroups — #10608536

Order 640.

492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×Dic5C211yesmaximal, characteristic, complemented
2C2×#4023C211yesmaximal, characteristic
3C5×#393C211yesmaximal, characteristic
4#65518C211yesmaximal, characteristic, complemented
5#65242C211yesmaximal, characteristic
6#65239C212yesmaximal
7#65234C212yesmaximal
8#64950C211yesmaximal, characteristic, complemented
9#64944C212yesmaximal, complemented
10#64943C212yesmaximal, complemented
11#64940C211yesmaximal, characteristic, complemented
12C22×C5×Q8C2211yescharacteristic
13C23×Dic5C2211yescharacteristic
14C2×C5×C22⋊C4C2211yescharacteristic
15C2×C5×C22⋊C4C2212yes—
16C2×C22⋊Dic5C2211yescharacteristic
17C2×C22⋊Dic5C2212yes—
18Q8×Dic5—24no—
19C2×C4⋊Dic5C2212yes—
20C2×C4⋊Dic5C2211yescharacteristic
21C2×C4⋊Dic5C2212yes—
22C2×#683C2211yescharacteristic
23C2×#683C2211yescharacteristic
24C2×#683C2212yes—
25C2×C4×Dic5C2211yescharacteristic
26C2×C4×Dic5C2212yes—
27C2×C4×Dic5C2211yescharacteristic
28#4023—24no—
29C5×#95C2211yescharacteristic
30C5×#95C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#3963C2211yescharacteristic
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2599—51nomaximal, Sylow
38C24×C5C2311yescharacteristic
39C2×C5×Q8—22no—
40C2×C5×Q8—24no—
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×C4×C5C2312yes—
45C22×Dic5—22no—
46C22×Dic5—22no—
47C22×Dic5—22no—
48C22×Dic5C2312yes—
49C22×Dic5C2311yescharacteristic
50C22×Dic5C2312yes—
51C22×Dic5C2311yescharacteristic
52C22×Dic5C2311yescharacteristic
53C22×Dic5C2311yescharacteristic
54C5×C22⋊C4—22no—
55C5×C22⋊C4—24no—
56C22⋊Dic5—24no—
57C22⋊Dic5—22no—
58C4⋊Dic5—22no—
59C4⋊Dic5—24no—
60C4⋊Dic5—24no—
61#683—22no—
62#683—24no—
63#683—22no—
64C4×Dic5—22no—
65C4×Dic5—24no—
66C4×Dic5D414yes—
67C2×C4×Q8—51no—
68C2×#117—51no—
69#398—51no—
70#397—51no—
71#395—51no—
72#393D511yescharacteristic
73#388—52no—
74#387—52no—
75#387—52no—
76#385—52no—
77#383—51no—
78C23×C5—21no—
79C23×C5—22no—
80C23×C5—21no—
81C23×C5—22no—
82C23×C5#4112yes—
83C23×C5C2411yescharacteristic
84C5×Q8—28no—
85C2×C4×C5—22no—
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—22no—
93C2×C4×C5C2×D412yes—
94C2×C4×C5#4114yes—
95C2×Dic5—28no—
96C2×Dic5—21no—
97C2×Dic5—21no—
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5—22no—
101C2×Dic5—21no—
102C2×Dic5—22no—
103C2×Dic5—22no—
104C2×Dic5—22no—
105C2×Dic5—22no—
106C2×Dic5—22no—
107C2×Dic5—22no—
108C2×Dic5—22no—
109C2×Dic5C2×D412yes—
110C2×Dic5C2×D412yes—
111C2×Dic5#4112yes—
112C22×Q8C2×D511yescharacteristic
113C23×C4—51no—
114C4×Q8—104no—
115#117—104no—
116C2×C4⋊C4—51no—
117C2×C4⋊C4—51no—
118C2×C4⋊C4—52no—
119C2×C4⋊C4—51no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—52no—
122C2×C22⋊C4—51no—
123C2×C22⋊C4—52no—
124C2×C22⋊C4C2×D511yescharacteristic
125C2×C22⋊C4C2×D512yes—
126C2×C42—51no—
127C2×C42—51no—
128C2×C42—52no—
129#95—52no—
130#95—52no—
131#95—51no—
132#95—52no—
133#95—52no—
134#95—52no—
135#95C2×D511yescharacteristic
136#95C2×D512yes—
137C22×C5—22no—
138C22×C5—24no—
139C22×C5—41no—
140C22×C5—41no—
141C22×C5—42no—
142C22×C5C22×D411yescharacteristic
143C22×C5C2×#4112yes—
144C22×C5C2×#4111yescharacteristic
145C22×C5C2×#4111yescharacteristic
146C22×C52−1+412yes—
147C4×C5—22no—
148C4×C5—24no—
149C4×C5—41no—
150C4×C5—42no—
151Dic5—22no—
152Dic5—22no—
153Dic5—22no—
154Dic5—41no—
155Dic5—42no—
156Dic5—42no—
157C24C22×D511yescharacteristic
158C2×Q8—22no—
159C2×Q8—24no—
160C22×C4—51no—
161C22×C4—51no—
162C22×C4—51no—
163C22×C4—52no—
164C22×C4—51no—
165C22×C4—52no—
166C22×C4—102no—
167C22×C4—102no—
168C22×C4—102no—
169C22×C4C22×D512yes—
170C22×C4C22×D511yescharacteristic
171C22×C4C22×D511yescharacteristic
172C22×C4C22×D512yes—
173C4⋊C4—102no—
174C4⋊C4—104no—
175C4⋊C4—104no—
176C4⋊C4—102no—
177C4⋊C4—102no—
178C4⋊C4—104no—
179C22⋊C4—22no—
180C22⋊C4—24no—
181C22⋊C4—102no—
182C22⋊C4—104no—
183C42—54no—
184C42—102no—
185C42—104no—
186C2×C5—42no—
187C2×C5#52511yescharacteristic
188C2×C5#52511yescharacteristic
189C2×C5#53611yescharacteristic
190C2×C5#55212yes—
191C2×C5#55612yes—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#71312yes—
197C23C23×D511yescharacteristic
198Q8—28no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—52no—
208C2×C4—52no—
209C2×C4—52no—
210C2×C4—108no—
211C2×C4—101no—
212C2×C4—101no—
213C2×C4—101no—
214C2×C4—101no—
215C2×C4—102no—
216C2×C4—101no—
217C2×C4—102no—
218C2×C4—102no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4D4×D512yes—
225C2×C4#71114yes—
226C5#259911yescharacteristic, complemented, Sylow
227C22—22no—
228C22—24no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22C2×D4×D511yescharacteristic
233C22C2×#71112yes—
234C22C2×#71311yescharacteristic
235C22D5×#4111yescharacteristic
236C22#415012yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—102no—
242C4—102no—
243C4—102no—
244C4—201no—
245C4—202no—
246C4—202no—
247C2—42no—
248C2#6592011yescharacteristic
249C2#6596111yescharacteristic
250C2#6597612yes—
251C2#6600512yes—
252C2#6600911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#393C2
prime radicalC24×C5C23
hypercenter#393D5
hypocenterC5#2599
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic5C2semidirect
4. #65518C2semidirect
8. #64950C2semidirect
9. #64944C2semidirect
10. #64943C2semidirect
11. #64940C2semidirect
226. C5#2599semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic52
C2×#40232
C5×#3932
#655182
#652422
#652392
#652342
#649502
#649442
#649432
#649402
#25995