Finite Group Databasebeta

← #10605971

Subgroups — #10605971

Order 640.

604 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 161 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×#4043C212yesmaximal, complemented
2C2×C4×D20C211yesmaximal, characteristic
3C2×C4×Dic10C211yesmaximal, characteristic, complemented
4C5×#382C211yesmaximal, characteristic, complemented
5#65276C212yesmaximal, complemented
6#64961C212yesmaximal
7#64959C214yesmaximal, complemented
8#64950C212yesmaximal, complemented
9C22×D20C2211yescharacteristic
10C22×C4×D5C2212yes—
11C22×Dic10C2211yescharacteristic
12C2×C5×C4⋊C4C2212yes—
13C2×C42×C5C2211yescharacteristic
14C2×#685C2212yes—
15C2×#685C2214yes—
16C2×#685C2214yes—
17C2×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊Dic5C2211yescharacteristic
19C2×C4⋊Dic5C2214yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2212yes—
22#4043—28no—
23C4×D20—24no—
24C4×Dic10—24no—
25C5×#95C2212yes—
26C5×#95C2212yes—
27#3963C2214yes—
28#2536—51nomaximal, Sylow
29C23×D5C2312yes—
30C22×C4×C5C2314yes—
31C22×C4×C5C2311yescharacteristic
32C22×C4×C5C2311yescharacteristic
33C22×C4×C5C2311yescharacteristic
34C22×Dic5C2312yes—
35C22×Dic5C2312yes—
36C22×Dic5C2312yes—
37C2×D20—24no—
38C2×D20—22no—
39C2×C4×D5—24no—
40C2×C4×D5—24no—
41C2×C4×D5—24no—
42C2×Dic10—22no—
43C2×Dic10—22no—
44C2×Dic10D414yescomplemented
45C5×C4⋊C4—24no—
46C42×C5D414yes—
47#685—28no—
48#685—24no—
49#685—28no—
50C4⋊Dic5—22no—
51C4⋊Dic5—22no—
52C4⋊Dic5—28no—
53#683—24no—
54C4×Dic5—24no—
55C2×C22⋊Q8—52no—
56C2×C4×Q8—51no—
57C2×C4×D4—51no—
58#398—52no—
59#394—52no—
60#388—54no—
61#382D511yescharacteristic, complemented
62#380—52no—
63C23×C5C2411yescharacteristic
64C22×D5—22no—
65C22×D5—22no—
66C22×D5—22no—
67C22×D5—22no—
68C22×D5—22no—
69C22×D5—22no—
70C22×D5#4114yes—
71C2×C4×C5—22no—
72C2×C4×C5—22no—
73C2×C4×C5—24no—
74C2×C4×C5—24no—
75C2×C4×C5—24no—
76C2×C4×C5C2×D412yes—
77C2×C4×C5C2×D412yes—
78C2×C4×C5C2×D412yes—
79C2×C4×C5C2×D412yes—
80C2×C4×C5#4112yes—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—24no—
87C2×Dic5—22no—
88C2×Dic5C2×D414yes—
89D20—28no—
90C4×D5—48no—
91Dic10—28no—
92C22×Q8—51no—
93C22×D4—51no—
94C23×C4—52no—
95C22⋊Q8—108no—
96C4×Q8—104no—
97C4×D4—104no—
98C2×C4⋊C4—51no—
99C2×C4⋊C4—51no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—54no—
102C2×C4⋊C4C2×D512yes—
103C2×C22⋊C4—52no—
104C2×C22⋊C4—54no—
105C2×C22⋊C4—54no—
106C2×C42—52no—
107C2×C42C2×D511yescharacteristic
108#95—54no—
109#95C2×D512yes—
110#95C2×D512yes—
111C22×C5C22×D411yescharacteristic
112C22×C5C22×D411yescharacteristic
113C22×C5C2×#4111yescharacteristic
114C22×C5C2×#4112yes—
115C22×C52−1+412yes—
116C2×D5—24no—
117C2×D5—24no—
118C2×D5—24no—
119C2×D5—42no—
120C2×D5—42no—
121C2×D5—42no—
122C2×D5—42no—
123C4×C5—22no—
124C4×C5—22no—
125C4×C5—44no—
126C4×C5#12114yes—
127Dic5—24no—
128Dic5—42no—
129Dic5—42no—
130C24—52no—
131C2×Q8—54no—
132C2×Q8—102no—
133C2×Q8—102no—
134C2×D4—104no—
135C2×D4—102no—
136C22×C4—52no—
137C22×C4—52no—
138C22×C4—52no—
139C22×C4—104no—
140C22×C4—104no—
141C22×C4—104no—
142C22×C4C22×D514yes—
143C22×C4C22×D511yescharacteristic
144C22×C4C22×D511yescharacteristic
145C22×C4C22×D511yescharacteristic
146C4⋊C4—24no—
147C4⋊C4—108no—
148C4⋊C4—102no—
149C4⋊C4—104no—
150C4⋊C4—102no—
151C22⋊C4—108no—
152C22⋊C4—108no—
153C22⋊C4—104no—
154C42—104no—
155C42D2014yes—
156C2×C5C2×#12111yescharacteristic
157C2×C5#52511yescharacteristic
158C2×C5#53611yescharacteristic
159C2×C5#54812yes—
160C2×C5#55212yes—
161D5—44no—
162C23—54no—
163C23—102no—
164C23—102no—
165C23—102no—
166C23—102no—
167C23—102no—
168C23—102no—
169C23C23×D511yescharacteristic
170Q8—108no—
171D4—108no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—54no—
178C2×C4—102no—
179C2×C4—102no—
180C2×C4—102no—
181C2×C4—102no—
182C2×C4—102no—
183C2×C4—102no—
184C2×C4—104no—
185C2×C4—208no—
186C2×C4C2×D2012yes—
187C2×C4C2×D2012yes—
188C2×C4C2×D2012yes—
189C2×C4D4×D512yes—
190C2×C4#71312yes—
191C5#253611yescharacteristic, complemented, Sylow
192C22—104no—
193C22—104no—
194C22—104no—
195C22—202no—
196C22—202no—
197C22—202no—
198C22—202no—
199C22C22×D2011yescharacteristic
200C22C2×D4×D511yescharacteristic
201C22C2×#71311yescharacteristic
202C22D5×#4112yes—
203C22#415012yes—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—104no—
208C4—202no—
209C4—202no—
210C4#404114yes—
211C2—204no—
212C2C2×#404111yescharacteristic
213C2#6585811yescharacteristic
214C2#6586011yescharacteristic
215C2#6601112yes—
216C2#6602812yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#382C2
prime radicalC22×D20C22
hypercenter#382D5
hypocenterC5#2536
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#4043C2semidirect
3. C2×C4×Dic10C2semidirect
4. C5×#382C2semidirect
5. #65276C2semidirect
7. #64959C2semidirect
8. #64950C2semidirect
44. C2×Dic10D4semidirect
61. #382D5semidirect
191. C5#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#40432
C2×C4×D202
C2×C4×Dic102
C5×#3822
#652762
#649612
#649592
#649502
#25365