Finite Group Databasebeta

← #10609862

Subgroups — #10609862

Order 640.

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

normal subgroups only

This group has 568 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×#4039C211yesmaximal, characteristic
2C2×#4033C211yesmaximal, characteristic, complemented
3C5×#400C211yesmaximal, characteristic, complemented
4#65280C211yesmaximal, characteristic
5#65271C211yesmaximal, characteristic, complemented
6#64964C212yesmaximal, complemented
7#64962C212yesmaximal, complemented
8#64961C211yesmaximal, characteristic
9#64955C212yesmaximal, complemented
10#64955C212yesmaximal, complemented
11#64937C211yesmaximal, characteristic, complemented
12C22×D20C2211yescharacteristic
13C22×C4×D5C2212yes—
14C22×Dic10C2211yescharacteristic
15C2×C5×C4⋊C4C2211yescharacteristic
16C2×C5×C4⋊C4C2211yescharacteristic
17C2×#685C2212yes—
18C2×#685C2212yes—
19C2×#685C2212yes—
20C2×#685C2212yes—
21C2×#685C2212yes—
22C2×#683C2211yescharacteristic
23C2×#683C2211yescharacteristic
24C2×C4×Dic5C2211yescharacteristic
25C2×C4×Dic5C2211yescharacteristic
26C2×C4×Dic5C2212yes—
27C2×C4×Dic5C2211yescharacteristic
28#4039—24no—
29#4033—24no—
30C5×#95C2211yescharacteristic
31C5×#95C2212yes—
32C5×#95C2212yes—
33#3963C2211yescharacteristic
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2398—51nomaximal, Sylow
38C23×D5C2312yes—
39C22×C4×C5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×Dic5C2312yes—
45C22×Dic5C2311yescharacteristic
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×D20—24no—
50C2×D20—22no—
51C2×C4×D5—24no—
52C2×C4×D5—24no—
53C2×C4×D5—24no—
54C2×Dic10—22no—
55C2×Dic10—22no—
56C2×Dic10—22no—
57C5×C4⋊C4—22no—
58C5×C4⋊C4—22no—
59#685—24no—
60#685—24no—
61#685—24no—
62#685—24no—
63#685—24no—
64#683—22no—
65#683—22no—
66C4×Dic5—22no—
67C4×Dic5—22no—
68C4×Dic5—24no—
69C4×Dic5D414yes—
70C2×C4×Q8—51no—
71C2×C4×D4—51no—
72#400—51no—
73#400D511yescharacteristic, complemented
74#397—52no—
75#394—51no—
76#394—51no—
77#393—52no—
78C4×C22⋊C4—52no—
79C4×C22⋊C4—52no—
80#376—51no—
81C23×C5C2411yescharacteristic
82C22×D5—22no—
83C22×D5—22no—
84C22×D5—22no—
85C22×D5—22no—
86C22×D5—22no—
87C22×D5—22no—
88C22×D5#4114yes—
89C2×C4×C5—21no—
90C2×C4×C5—21no—
91C2×C4×C5—22no—
92C2×C4×C5—21no—
93C2×C4×C5—22no—
94C2×C4×C5—22no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5C2×D412yes—
101C2×C4×C5#4112yes—
102C2×Dic5—21no—
103C2×Dic5—21no—
104C2×Dic5—21no—
105C2×Dic5—21no—
106C2×Dic5—21no—
107C2×Dic5—22no—
108C2×Dic5—22no—
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5C2×D412yes—
112C2×Dic5C2×D412yes—
113C2×Dic5#4112yes—
114C2×Dic5#4114yes—
115D20—28no—
116C4×D5—48no—
117Dic10—28no—
118C22×Q8—51no—
119C22×D4—51no—
120C23×C4—52no—
121C4×Q8—104no—
122C4×D4—104no—
123C2×C4⋊C4—51no—
124C2×C4⋊C4—51no—
125C2×C4⋊C4C2×D511yescharacteristic
126C2×C4⋊C4C2×D511yescharacteristic
127C2×C22⋊C4—52no—
128C2×C22⋊C4—52no—
129C2×C22⋊C4—52no—
130C2×C22⋊C4—52no—
131C2×C22⋊C4—52no—
132C2×C42—51no—
133C2×C42—51no—
134C2×C42—51no—
135C2×C42—52no—
136#95—52no—
137#95—51no—
138#95—52no—
139#95—52no—
140#95C2×D511yescharacteristic
141#95C2×D512yes—
142#95C2×D512yes—
143C22×C5C22×D411yescharacteristic
144C22×C5C2×#4111yescharacteristic
145C22×C5C2×#4112yes—
146C22×C5C2×#4111yescharacteristic
147C22×C5C2×#4112yes—
148C2×D5—24no—
149C2×D5—24no—
150C2×D5—24no—
151C2×D5—42no—
152C2×D5—42no—
153C2×D5—42no—
154C2×D5—42no—
155C4×C5—22no—
156C4×C5—22no—
157C4×C5—41no—
158C4×C5—42no—
159C4×C5—42no—
160Dic5—22no—
161Dic5—22no—
162Dic5—41no—
163Dic5—42no—
164Dic5#12414yes—
165C24—52no—
166C2×Q8—102no—
167C2×Q8—102no—
168C2×Q8—102no—
169C2×D4—104no—
170C2×D4—102no—
171C22×C4—51no—
172C22×C4—51no—
173C22×C4—51no—
174C22×C4—52no—
175C22×C4—51no—
176C22×C4—104no—
177C22×C4—104no—
178C22×C4—104no—
179C22×C4C22×D512yes—
180C22×C4C22×D512yes—
181C22×C4C22×D511yescharacteristic
182C22×C4C22×D511yescharacteristic
183C22×C4C22×D511yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—102no—
187C4⋊C4—102no—
188C22⋊C4—104no—
189C22⋊C4—104no—
190C22⋊C4—104no—
191C22⋊C4—104no—
192C22⋊C4—104no—
193C42—54no—
194C42—102no—
195C42—102no—
196C42—104no—
197C2×C5#52511yescharacteristic
198C2×C5#52511yescharacteristic
199C2×C5C2×#12411yescharacteristic
200C2×C5#52912yes—
201C2×C5#52912yes—
202D5—44no—
203C23—54no—
204C23—102no—
205C23—102no—
206C23—102no—
207C23—102no—
208C23—102no—
209C23—102no—
210C23C23×D511yescharacteristic
211Q8—108no—
212D4—108no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—52no—
225C2×C4—54no—
226C2×C4—52no—
227C2×C4—52no—
228C2×C4—101no—
229C2×C4—101no—
230C2×C4—101no—
231C2×C4—101no—
232C2×C4—101no—
233C2×C4—102no—
234C2×C4—102no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—208no—
238C2×C4D4×D512yes—
239C2×C4#71312yes—
240C5#239811yescharacteristic, complemented, Sylow
241C22—104no—
242C22—104no—
243C22—104no—
244C22—202no—
245C22—202no—
246C22—202no—
247C22—202no—
248C22C2×D4×D511yescharacteristic
249C22C2×#71311yescharacteristic
250C22D5×#4111yescharacteristic
251C22D5×#4112yes—
252C22D5×#4112yes—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—42no—
258C4—54no—
259C4—102no—
260C4—102no—
261C4—201no—
262C4—202no—
263C2—204no—
264C2#6596111yescharacteristic
265C2#6599011yescharacteristic
266C2D5×#12411yescharacteristic
267C2#6602512yes—
268C2#6604012yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#400C2
prime radicalC22×D20C22
hypercenter#400D5
hypocenterC5#2398
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#4033C2semidirect
3. C5×#400C2semidirect
5. #65271C2semidirect
6. #64964C2semidirect
7. #64962C2semidirect
9. #64955C2semidirect
10. #64955C2semidirect
11. #64937C2semidirect
73. #400D5semidirect
240. C5#2398semidirect

Maximal subgroups

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

subgroupindex
C2×#40392
C2×#40332
C5×#4002
#652802
#652712
#649642
#649622
#649612
#649552
#649372
#23985