Finite Group Databasebeta

← #10608369

Subgroups — #10608369

Order 640.

476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C5×#391C211yesmaximal, characteristic, complemented
2#65520C212yesmaximal, complemented
3#65280C211yesmaximal, characteristic
4#65275C211yesmaximal, characteristic, complemented
5C4×#685C212yesmaximal, complemented
6#64959C212yesmaximal, complemented
7#64954C212yesmaximal
8#64953C212yesmaximal, complemented
9#64940C212yesmaximal, complemented
10C22×C5×Q8C2211yescharacteristic
11C22×D20C2211yescharacteristic
12C22×C4×D5C2212yes—
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C42×C5C2211yescharacteristic
15C2×#685C2212yes—
16C2×#685C2212yes—
17C2×#685C2212yes—
18C2×#685C2212yes—
19C2×#685C2212yes—
20C2×C4⋊Dic5C2211yescharacteristic
21C2×C4×Dic5C2212yes—
22C5×#95C2212yes—
23C5×#95C2212yes—
24#3963C2211yescharacteristic
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2211yescharacteristic
30#3963C2212yes—
31#2572—51nomaximal, Sylow
32C23×D5C2312yes—
33C2×C5×Q8—22no—
34C2×C5×Q8—41no—
35C2×C5×Q8—41no—
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2312yes—
39C22×C4×C5C2311yescharacteristic
40C22×C4×C5C2312yes—
41C22×Dic5C2312yes—
42C22×Dic5C2312yes—
43C22×Dic5C2312yes—
44C2×D20—24no—
45C2×D20—41no—
46C2×C4×D5—24no—
47C2×C4×D5—24no—
48C2×C4×D5—42no—
49C5×C4⋊C4—41no—
50C42×C5—41no—
51#685—24no—
52#685—24no—
53#685—24no—
54#685—42no—
55#685—42no—
56C4⋊Dic5—41no—
57C4×Dic5—24no—
58#400—51no—
59#394—51no—
60#393—52no—
61#391D511yescharacteristic, complemented
62#388—52no—
63#386—52no—
64#383—52no—
65#381—52no—
66C4×C22⋊C4—52no—
67C23×C5C2411yescharacteristic
68C22×D5—22no—
69C22×D5—22no—
70C22×D5—22no—
71C22×D5—22no—
72C22×D5—22no—
73C22×D5—22no—
74C22×D5#4114yes—
75C5×Q8—44no—
76C2×C4×C5—22no—
77C2×C4×C5—22no—
78C2×C4×C5—21no—
79C2×C4×C5—21no—
80C2×C4×C5—22no—
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5—21no—
84C2×C4×C5—22no—
85C2×C4×C5—22no—
86C2×C4×C5—21no—
87C2×C4×C5#4112yes—
88C2×C4×C5#4114yes—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—22no—
95C2×Dic5—22no—
96C2×Dic5—22no—
97C2×Dic5—22no—
98D20—44no—
99C4×D5—48no—
100C22×Q8C2×D511yescharacteristic
101C22×D4—51no—
102C23×C4—52no—
103C2×C4⋊C4—51no—
104C2×C4⋊C4C2×D511yescharacteristic
105C2×C22⋊C4—52no—
106C2×C22⋊C4—52no—
107C2×C22⋊C4—52no—
108C2×C22⋊C4—52no—
109C2×C22⋊C4—52no—
110C2×C42—52no—
111C2×C42C2×D511yescharacteristic
112#95—52no—
113#95—52no—
114#95—51no—
115#95—52no—
116#95—51no—
117#95—52no—
118#95—52no—
119#95C2×D512yes—
120#95C2×D512yes—
121C22×C5C2×#4111yescharacteristic
122C22×C5C2×#4112yes—
123C22×C5C2×#4112yes—
124C22×C5H(5,𝔽2)11yescharacteristic
125C22×C5H(5,𝔽2)11yescharacteristic
126C2×D5—24no—
127C2×D5—24no—
128C2×D5—24no—
129C2×D5—42no—
130C2×D5—42no—
131C2×D5—42no—
132C2×D5—42no—
133C4×C5—22no—
134C4×C5—24no—
135C4×C5—42no—
136C4×C5—41no—
137C4×C5—41no—
138Dic5—42no—
139Dic5—42no—
140Dic5—42no—
141C24—52no—
142C2×Q8—22no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×D4—104no—
146C2×D4—201no—
147C22×C4—52no—
148C22×C4—52no—
149C22×C4—52no—
150C22×C4—104no—
151C22×C4—104no—
152C22×C4—202no—
153C22×C4C22×D511yescharacteristic
154C22×C4C22×D512yes—
155C22×C4C22×D511yescharacteristic
156C22×C4C22×D511yescharacteristic
157C22×C4C22×D512yes—
158C4⋊C4—41no—
159C4⋊C4—201no—
160C22⋊C4—104no—
161C22⋊C4—104no—
162C22⋊C4—104no—
163C22⋊C4—202no—
164C22⋊C4—202no—
165C42—41no—
166C42—104no—
167C2×C5#52912yes—
168C2×C5#53811yescharacteristic
169C2×C5#55112yes—
170C2×C5#55111yescharacteristic
171C2×C5#55511yescharacteristic
172D5—44no—
173C23—54no—
174C23—102no—
175C23—102no—
176C23—102no—
177C23—102no—
178C23—102no—
179C23—102no—
180C23C23×D511yescharacteristic
181Q8—44no—
182D4—204no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—102no—
195C2×C4—102no—
196C2×C4—102no—
197C2×C4—102no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—102no—
202C2×C4—102no—
203C2×C4—208no—
204C2×C4#70912yes—
205C2×C4#71314yes—
206C5#257211yescharacteristic, complemented, Sylow
207C22—104no—
208C22—104no—
209C22—104no—
210C22—202no—
211C22—202no—
212C22—202no—
213C22—202no—
214C22C2×#70911yescharacteristic
215C22#414411yescharacteristic
216C22#414411yescharacteristic
217C22C2×#71312yes—
218C22D5×#4112yes—
219C4—22no—
220C4—24no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—202no—
225C4—202no—
226C4—202no—
227C2—204no—
228C2#6582811yescharacteristic
229C2#6591412yes—
230C2#6597112yes—
231C2#6601311yescharacteristic
232C2#6606811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#391C2
prime radicalC22×D20C22
hypercenter#391D5
hypocenterC5#2572
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C5×#391C2semidirect
2. #65520C2semidirect
4. #65275C2semidirect
5. C4×#685C2semidirect
6. #64959C2semidirect
8. #64953C2semidirect
9. #64940C2semidirect
61. #391D5semidirect
206. C5#2572semidirect

Maximal subgroups

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

subgroupindex
C5×#3912
#655202
#652802
#652752
C4×#6852
#649592
#649542
#649532
#649402
#25725