Finite Group Databasebeta

← #10609940

Subgroups — #10609940

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×#4038C211yesmaximal, characteristic
2C2×#4034C211yesmaximal, characteristic, complemented
3C5×#400C211yesmaximal, characteristic, complemented
4#65281C211yesmaximal, characteristic
5#65275C211yesmaximal, characteristic, complemented
6#64966C211yesmaximal, characteristic
7#64962C212yesmaximal
8#64956C212yesmaximal
9#64945C212yesmaximal, complemented
10#64939C211yesmaximal, characteristic, complemented
11#64936C212yesmaximal, complemented
12C22×C4×D5C2211yescharacteristic
13C22×Dic10C2212yes—
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2211yescharacteristic
16C2×#685C2211yescharacteristic
17C2×#685C2211yescharacteristic
18C2×#685C2212yes—
19C2×#685C2212yes—
20C2×C4⋊Dic5C2211yescharacteristic
21C2×C4⋊Dic5C2211yescharacteristic
22C2×C4⋊Dic5C2212yes—
23C2×#683C2212yes—
24C2×#683C2212yes—
25C2×#683C2212yes—
26C2×C4×Dic5C2211yescharacteristic
27C2×C4×Dic5C2211yescharacteristic
28#4038—24no—
29#4034—24no—
30C5×#95C2212yes—
31C5×#95C2211yescharacteristic
32C5×#95C2212yes—
33#3963C2211yescharacteristic
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2628—51nomaximal, Sylow
38C23×D5C2311yescharacteristic
39C22×C4×C5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×Dic5C2312yes—
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×C4×D5—22no—
50C2×C4×D5—22no—
51C2×C4×D5Q814yescomplemented
52C2×Dic10—24no—
53C2×Dic10—42no—
54C2×Dic10—42no—
55C5×C4⋊C4—22no—
56C5×C4⋊C4—22no—
57#685—22no—
58#685—22no—
59#685—42no—
60#685—42no—
61C4⋊Dic5—22no—
62C4⋊Dic5—22no—
63C4⋊Dic5—42no—
64#683—24no—
65#683—24no—
66#683—42no—
67C4×Dic5—22no—
68C4×Dic5D414yes—
69C2×C4⋊Q8—51no—
70C2×#117—51no—
71#400—51no—
72#400D511yescharacteristic, complemented
73#399—51no—
74#399—51no—
75#395—52no—
76#393—52no—
77#389—52no—
78#382—51no—
79#380—52no—
80C23×C5C2411yescharacteristic
81C22×D5—21no—
82C22×D5—21no—
83C22×D5—22no—
84C22×D5—22no—
85C22×D5C2×Q812yes—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—22no—
89C2×C4×C5—21no—
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—22no—
97C2×C4×C5C2×D412yes—
98C2×C4×C5C2×Q812yes—
99C2×Dic5—22no—
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5—22no—
103C2×Dic5—22no—
104C2×Dic5—22no—
105C2×Dic5—22no—
106C2×Dic5—22no—
107C2×Dic5—22no—
108C2×Dic5C2×D412yes—
109C2×Dic5C2×D412yes—
110C2×Dic5C2×Q812yes—
111C2×Dic5#4112yes—
112C4×D5—28no—
113Dic10—48no—
114C22×Q8—52no—
115C23×C4—51no—
116C4⋊Q8—104no—
117#117—104no—
118C2×C4⋊C4—51no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—51no—
121C2×C4⋊C4—52no—
122C2×C4⋊C4—52no—
123C2×C4⋊C4—52no—
124C2×C4⋊C4C2×D511yescharacteristic
125C2×C4⋊C4C2×D511yescharacteristic
126C2×C22⋊C4—51no—
127C2×C22⋊C4—51no—
128C2×C22⋊C4—52no—
129C2×C22⋊C4—52no—
130C2×C42—51no—
131C2×C42—51no—
132#95—52no—
133#95—52no—
134#95—51no—
135#95—52no—
136#95C2×D512yes—
137#95C2×D511yescharacteristic
138#95C2×D512yes—
139C22×C5C22×D411yescharacteristic
140C22×C5C22×Q811yescharacteristic
141C22×C5C2×#4111yescharacteristic
142C22×C5H(5,𝔽2)12yes—
143C22×C52−1+412yes—
144C2×D5—22no—
145C2×D5—24no—
146C2×D5—41no—
147C2×D5—41no—
148C2×D5—42no—
149C4×C5—22no—
150C4×C5—22no—
151C4×C5—42no—
152C4×C5—41no—
153C4×C5—42no—
154Dic5—22no—
155Dic5—42no—
156Dic5—41no—
157Dic5—42no—
158Dic5C22⋊Q814yes—
159C24—51no—
160C2×Q8—104no—
161C2×Q8—202no—
162C2×Q8—202no—
163C22×C4—51no—
164C22×C4—51no—
165C22×C4—54no—
166C22×C4—52no—
167C22×C4—52no—
168C22×C4—51no—
169C22×C4—102no—
170C22×C4—102no—
171C22×C4C22×D511yescharacteristic
172C22×C4C22×D512yes—
173C22×C4C22×D512yes—
174C22×C4C22×D511yescharacteristic
175C22×C4C22×D511yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—102no—
179C4⋊C4—104no—
180C4⋊C4—104no—
181C4⋊C4—102no—
182C4⋊C4—202no—
183C4⋊C4—202no—
184C22⋊C4—102no—
185C22⋊C4—102no—
186C22⋊C4—202no—
187C22⋊C4—202no—
188C42—54no—
189C42—102no—
190C2×C5C2×C22⋊Q811yescharacteristic
191C2×C5#53511yescharacteristic
192C2×C5#53611yescharacteristic
193C2×C5#54212yes—
194C2×C5#54412yes—
195D5—42no—
196C23—52no—
197C23—101no—
198C23—101no—
199C23—102no—
200C23—102no—
201C23C23×D511yescharacteristic
202Q8—208no—
203C2×C4—21no—
204C2×C4—21no—
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—108no—
219C2×C4—102no—
220C2×C4—101no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—102no—
225C2×C4—102no—
226C2×C4—102no—
227C2×C4—102no—
228C2×C4D4×D512yes—
229C2×C4Q8×D512yes—
230C5#262811yescharacteristic, complemented, Sylow
231C22—102no—
232C22—104no—
233C22—201no—
234C22—201no—
235C22—202no—
236C22C2×D4×D511yescharacteristic
237C22C2×Q8×D511yescharacteristic
238C22D5×#4111yescharacteristic
239C22#414912yes—
240C22#415012yes—
241C4—22no—
242C4—22no—
243C4—41no—
244C4—42no—
245C4—42no—
246C4—54no—
247C4—102no—
248C4—202no—
249C4—201no—
250C4—202no—
251C2—202no—
252C2D5×C22⋊Q811yescharacteristic
253C2#6598211yescharacteristic
254C2#6600811yescharacteristic
255C2#6602312yes—
256C2#6604412yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#400C2
prime radicalC23×D5C23
hypercenter#400D5
hypocenterC5#2628
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#4034C2semidirect
3. C5×#400C2semidirect
5. #65275C2semidirect
9. #64945C2semidirect
10. #64939C2semidirect
11. #64936C2semidirect
51. C2×C4×D5Q8semidirect
72. #400D5semidirect
230. C5#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#40382
C2×#40342
C5×#4002
#652812
#652752
#649662
#649622
#649562
#649452
#649392
#649362
#26285