Finite Group Databasebeta

← #10608541

Subgroups — #10608541

Order 640.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#4090C211yesmaximal, characteristic, complemented
2C2×#4023C211yesmaximal, characteristic
3C5×#393C211yesmaximal, characteristic
4#65518C211yesmaximal, characteristic, complemented
5#65238C212yesmaximal
6#65236C211yesmaximal, characteristic
7#65231C212yesmaximal
8#64947C212yesmaximal, complemented
9#64945C211yesmaximal, characteristic, complemented
10#64939C211yesmaximal, characteristic, complemented
11#64936C212yesmaximal, complemented
12C22×C5×Q8C2211yescharacteristic
13C23×Dic5C2211yescharacteristic
14C22×Dic10C2211yescharacteristic
15C2×C5×C22⋊C4C2211yescharacteristic
16C2×C5×C22⋊C4C2212yes—
17C2×C22⋊Dic5C2211yescharacteristic
18C2×C22⋊Dic5C2212yes—
19#4090—24no—
20C2×C4⋊Dic5C2212yes—
21C2×#683C2211yescharacteristic
22C2×#683C2211yescharacteristic
23C2×#683C2212yes—
24C2×#683C2212yes—
25C2×#683C2212yes—
26C2×#683C2212yes—
27C2×C4×Dic5C2211yescharacteristic
28C2×C4×Dic5C2211yescharacteristic
29#4023—24no—
30C5×#95C2212yes—
31C5×#95C2211yescharacteristic
32#3963C2212yes—
33#3963C2212yes—
34#3963C2211yescharacteristic
35#3963C2212yes—
36#3963C2212yes—
37#2628—51nomaximal, Sylow
38C24×C5C2311yescharacteristic
39C2×C5×Q8—22no—
40C2×C5×Q8—42no—
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2312yes—
44C22×C4×C5C2311yescharacteristic
45C22×Dic5—22no—
46C22×Dic5—22no—
47C22×Dic5Q814yescomplemented
48C22×Dic5C2312yes—
49C22×Dic5C2312yes—
50C22×Dic5C2311yescharacteristic
51C22×Dic5C2311yescharacteristic
52C22×Dic5C2311yescharacteristic
53C22×Dic5C2311yescharacteristic
54C2×Dic10—22no—
55C2×Dic10—42no—
56C5×C22⋊C4—22no—
57C5×C22⋊C4—42no—
58C22⋊Dic5—22no—
59C22⋊Dic5—42no—
60C4⋊Dic5—42no—
61#683—22no—
62#683—22no—
63#683—24no—
64#683—24no—
65#683—24no—
66#683—42no—
67C4×Dic5—22no—
68C4×Dic5D414yes—
69C2×C4⋊Q8—51no—
70C2×#117—51no—
71#400—52no—
72#399—52no—
73#395—51no—
74#395—51no—
75#393—51no—
76#393D511yescharacteristic
77#389—52no—
78#382—51no—
79#380—52no—
80C23×C5—21no—
81C23×C5—21no—
82C23×C5—22no—
83C23×C5—22no—
84C23×C5C2×Q812yes—
85C23×C5C2411yescharacteristic
86C5×Q8—44no—
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×C5—22no—
94C2×C4×C5—22no—
95C2×C4×C5—22no—
96C2×C4×C5C2×D412yes—
97C2×Dic5—21no—
98C2×Dic5—21no—
99C2×Dic5—22no—
100C2×Dic5—28no—
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×Dic5C2×Q812yes—
112C2×Dic5C2×Q812yes—
113C2×Dic5#4112yes—
114Dic10—44no—
115C22×Q8—51no—
116C22×Q8C2×D511yescharacteristic
117C23×C4—51no—
118C4⋊Q8—104no—
119#117—104no—
120C2×C4⋊C4—51no—
121C2×C4⋊C4—51no—
122C2×C4⋊C4—52no—
123C2×C4⋊C4—52no—
124C2×C4⋊C4—52no—
125C2×C4⋊C4—52no—
126C2×C4⋊C4—52no—
127C2×C22⋊C4—51no—
128C2×C22⋊C4—52no—
129C2×C22⋊C4C2×D511yescharacteristic
130C2×C22⋊C4C2×D512yes—
131C2×C42—51no—
132C2×C42—51no—
133#95—52no—
134#95—52no—
135#95—51no—
136#95—52no—
137#95—52no—
138#95C2×D511yescharacteristic
139#95C2×D512yes—
140C22×C5—22no—
141C22×C5—24no—
142C22×C5—41no—
143C22×C5—41no—
144C22×C5—42no—
145C22×C5C22×D411yescharacteristic
146C22×C5C22×Q811yescharacteristic
147C22×C5C2×#4111yescharacteristic
148C22×C5H(5,𝔽2)12yes—
149C22×C52−1+412yes—
150C4×C5—22no—
151C4×C5—42no—
152C4×C5—41no—
153C4×C5—42no—
154Dic5—22no—
155Dic5—22no—
156Dic5—42no—
157Dic5—41no—
158Dic5—42no—
159Dic5C22⋊Q814yes—
160C24C22×D511yescharacteristic
161C2×Q8—22no—
162C2×Q8—42no—
163C2×Q8—102no—
164C2×Q8—202no—
165C22×C4—51no—
166C22×C4—54no—
167C22×C4—51no—
168C22×C4—51no—
169C22×C4—52no—
170C22×C4—52no—
171C22×C4—51no—
172C22×C4—102no—
173C22×C4—102no—
174C22×C4C22×D511yescharacteristic
175C22×C4C22×D512yes—
176C22×C4C22×D512yes—
177C22×C4C22×D511yescharacteristic
178C4⋊C4—102no—
179C4⋊C4—104no—
180C4⋊C4—104no—
181C4⋊C4—104no—
182C4⋊C4—102no—
183C4⋊C4—202no—
184C4⋊C4—202no—
185C22⋊C4—22no—
186C22⋊C4—42no—
187C22⋊C4—102no—
188C22⋊C4—202no—
189C42—54no—
190C42—102no—
191C2×C5—42no—
192C2×C5C2×C22⋊Q811yescharacteristic
193C2×C5#53511yescharacteristic
194C2×C5#53611yescharacteristic
195C2×C5#54212yes—
196C2×C5#54412yes—
197C23—21no—
198C23—22no—
199C23—21no—
200C23—22no—
201C23Q8×D512yes—
202C23C23×D511yescharacteristic
203Q8—44no—
204Q8—204no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—52no—
215C2×C4—52no—
216C2×C4—52no—
217C2×C4—52no—
218C2×C4—52no—
219C2×C4—108no—
220C2×C4—101no—
221C2×C4—101no—
222C2×C4—102no—
223C2×C4—101no—
224C2×C4—102no—
225C2×C4—102no—
226C2×C4—102no—
227C2×C4—102no—
228C2×C4—102no—
229C2×C4—102no—
230C2×C4—102no—
231C2×C4D4×D512yes—
232C5#262811yescharacteristic, complemented, Sylow
233C22—24no—
234C22—22no—
235C22—41no—
236C22—42no—
237C22—41no—
238C22C2×D4×D511yescharacteristic
239C22#414412yes—
240C22C2×Q8×D511yescharacteristic
241C22D5×#4111yescharacteristic
242C22#415012yes—
243C4—22no—
244C4—42no—
245C4—42no—
246C4—41no—
247C4—54no—
248C4—102no—
249C4—102no—
250C4—202no—
251C4—201no—
252C4—202no—
253C2—42no—
254C2#6592611yescharacteristic
255C2#6595712yes—
256C2D5×C22⋊Q811yescharacteristic
257C2#6600312yes—
258C2#6600911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#393C2
prime radicalC24×C5C23
hypercenter#393D5
hypocenterC5#2628
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#4090C2semidirect
4. #65518C2semidirect
8. #64947C2semidirect
9. #64945C2semidirect
10. #64939C2semidirect
11. #64936C2semidirect
47. C22×Dic5Q8semidirect
232. C5#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#40902
C2×#40232
C5×#3932
#655182
#652382
#652362
#652312
#649472
#649452
#649392
#649362
#26285