Finite Group Databasebeta

← #10605810

Subgroups — #10605810

Order 640.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#683C211yesmaximal, characteristic
2C2×#4024C211yesmaximal, characteristic
3C5×#381C211yesmaximal, characteristic
4#65500C211yesmaximal, characteristic
5#65232C211yesmaximal, characteristic
6#65232C211yesmaximal, characteristic
7C22⋊C4×Dic5C211yesmaximal, characteristic
8#64949C212yesmaximal, complemented
9#64947C212yesmaximal, complemented
10#64939C212yesmaximal, complemented
11#64935C212yesmaximal, complemented
12C23×C4×C5C2211yescharacteristic
13C23×Dic5C2211yescharacteristic
14C23×Dic5C2211yescharacteristic
15C22×Dic10C2211yescharacteristic
16C2×C5×C22⋊C4C2211yescharacteristic
17C2×C5×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic5C2211yescharacteristic
19C2×C22⋊Dic5C2211yescharacteristic
20C2×C4⋊Dic5C2211yescharacteristic
21C2×#683—24no—
22C2×#683C2211yescharacteristic
23C2×#683C2211yescharacteristic
24C2×#683C2212yes—
25C2×#683C2212yes—
26C2×C4×Dic5C2212yes—
27#4024—24no—
28C5×#95C2212yes—
29C5×#95C2212yes—
30#3963C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#3963C2212yes—
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2503—51nomaximal, Sylow
38C24×C5C2311yescharacteristic
39C22×C4×C5—22no—
40C22×C4×C5—22no—
41C22×C4×C5—22no—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2312yes—
44C22×C4×C5C2311yescharacteristic
45C22×C4×C5C2312yes—
46C22×Dic5—24no—
47C22×Dic5—22no—
48C22×Dic5—22no—
49C22×Dic5—22no—
50C22×Dic5D414yes—
51C22×Dic5C2311yescharacteristic
52C22×Dic5C2312yes—
53C22×Dic5C2311yescharacteristic
54C22×Dic5C2312yes—
55C22×Dic5C2311yescharacteristic
56C22×Dic5C2311yescharacteristic
57C2×Dic10—22no—
58C2×Dic10—24no—
59C5×C22⋊C4—22no—
60C5×C22⋊C4—22no—
61C22⋊Dic5—22no—
62C22⋊Dic5—22no—
63C4⋊Dic5—22no—
64#683—22no—
65#683—22no—
66#683—24no—
67#683—24no—
68C4×Dic5—24no—
69C2×C22⋊Q8—51no—
70C22×C4⋊C4—51no—
71#400—52no—
72#400—52no—
73#391—52no—
74#382—52no—
75#381—51no—
76#381—51no—
77#381—51no—
78#381D511yescharacteristic
79C4×C22⋊C4—51no—
80C23×C5—22no—
81C23×C5—22no—
82C23×C5C2×D412yes—
83C23×C5#4112yes—
84C23×C5#4112yes—
85C23×C5C2411yescharacteristic
86C2×C4×C5—22no—
87C2×C4×C5—21no—
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×C5—44no—
97C2×Dic5—22no—
98C2×Dic5—28no—
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×Dic5—44no—
110C2×Dic5C2×D412yes—
111C2×Dic5C2×D412yes—
112C2×Dic5#4114yes—
113Dic10—44no—
114C22×Q8—51no—
115C23×C4—51no—
116C23×C4—51no—
117C23×C4C2×D511yescharacteristic
118C22⋊Q8—104no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—51no—
122C2×C4⋊C4—51no—
123C2×C4⋊C4—51no—
124C2×C4⋊C4—104no—
125C2×C22⋊C4—51no—
126C2×C22⋊C4—51no—
127C2×C22⋊C4C2×D511yescharacteristic
128C2×C22⋊C4C2×D511yescharacteristic
129C2×C42—52no—
130#95—52no—
131#95—52no—
132#95—52no—
133#95—52no—
134#95—52no—
135#95—52no—
136#95—52no—
137#95C2×D512yes—
138#95C2×D512yes—
139C22×C5—22no—
140C22×C5—22no—
141C22×C5—24no—
142C22×C5—24no—
143C22×C5#12414yes—
144C22×C5C22×D411yescharacteristic
145C22×C5C2×#4111yescharacteristic
146C22×C5C2×#4111yescharacteristic
147C22×C5C2×#4112yes—
148C22×C52−1+412yes—
149C4×C5—41no—
150C4×C5—42no—
151C4×C5—41no—
152C4×C5—42no—
153Dic5—22no—
154Dic5—41no—
155Dic5—42no—
156Dic5—41no—
157Dic5—42no—
158Dic5#12314yes—
159C24C22×D511yescharacteristic
160C2×Q8—102no—
161C2×Q8—104no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—51no—
166C22×C4—54no—
167C22×C4—51no—
168C22×C4—52no—
169C22×C4—51no—
170C22×C4—51no—
171C22×C4—52no—
172C22×C4—104no—
173C22×C4—102no—
174C22×C4—102no—
175C22×C4—102no—
176C22×C4C22×D512yes—
177C22×C4C22×D511yescharacteristic
178C22×C4C22×D511yescharacteristic
179C22×C4C22×D512yes—
180C4⋊C4—104no—
181C4⋊C4—104no—
182C4⋊C4—102no—
183C4⋊C4—102no—
184C4⋊C4—102no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—102no—
188C22⋊C4—102no—
189C42—104no—
190C2×C5—24no—
191C2×C5C2×#12311yescharacteristic
192C2×C5C2×#12411yescharacteristic
193C2×C5#53611yescharacteristic
194C2×C5#55212yes—
195C2×C5#55212yes—
196C23—22no—
197C23—22no—
198C23#70912yes—
199C23D4×D512yes—
200C23#71112yes—
201C23C23×D511yescharacteristic
202Q8—204no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—44no—
214C2×C4—52no—
215C2×C4—54no—
216C2×C4—52no—
217C2×C4—108no—
218C2×C4—102no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—101no—
222C2×C4—101no—
223C2×C4—102no—
224C2×C4—102no—
225C2×C4—102no—
226C2×C4—102no—
227C2×C4—102no—
228C2×C4—102no—
229C2×C4—204no—
230C5#250311yescharacteristic, complemented, Sylow
231C22—24no—
232C22—22no—
233C22—24no—
234C22—22no—
235C22#403114yes—
236C22C2×#70911yescharacteristic
237C22C2×D4×D511yescharacteristic
238C22C2×#71111yescharacteristic
239C22D5×#4112yes—
240C22#415012yes—
241C4—42no—
242C4—41no—
243C4—42no—
244C4—41no—
245C4—54no—
246C4—102no—
247C4—202no—
248C4—202no—
249C4—201no—
250C4—201no—
251C2—24no—
252C2C2×#403111yescharacteristic
253C2#6586512yes—
254C2#6598211yescharacteristic
255C2#6598412yes—
256C2D5×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#381C2
prime radicalC24×C5C23
hypercenter#381D5
hypocenterC5#2503
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
8. #64949C2semidirect
9. #64947C2semidirect
10. #64939C2semidirect
11. #64935C2semidirect
230. C5#2503semidirect

Maximal subgroups

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

subgroupindex
C22×#6832
C2×#40242
C5×#3812
#655002
#652322
C22⋊C4×Dic52
#649492
#649472
#649392
#649352
#25035