Finite Group Databasebeta

← #10608592

Subgroups — #10608592

Order 640.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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×#393C211yesmaximal, characteristic
2#65518C212yesmaximal, complemented
3#65238C211yesmaximal, characteristic
4#65237C212yesmaximal
5#65232C211yesmaximal, characteristic
6#65231C212yesmaximal
7#64948C212yesmaximal, complemented
8#64946C212yesmaximal, complemented
9#64946C212yesmaximal, complemented
10C22×C5×Q8C2211yescharacteristic
11C23×Dic5C2211yescharacteristic
12C2×C5×C22⋊C4C2212yes—
13C2×C5×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic5C2212yes—
15C2×C22⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊Dic5C2212yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×#683C2212yes—
22C2×#683C2212yes—
23C5×#95C2211yescharacteristic
24C5×#95C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2211yescharacteristic
29#3963C2212yes—
30#3963C2212yes—
31#2841—51nomaximal, Sylow
32C24×C5C2311yescharacteristic
33C2×C5×Q8—41no—
34C2×C5×Q8—42no—
35C22×C4×C5C2312yes—
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2312yes—
39C22×Dic5—41no—
40C22×Dic5—41no—
41C22×Dic5Q814yescomplemented
42C22×Dic5C2312yes—
43C22×Dic5C2312yes—
44C22×Dic5C2312yes—
45C22×Dic5C2312yes—
46C5×C22⋊C4—42no—
47C5×C22⋊C4—41no—
48C22⋊Dic5—42no—
49C22⋊Dic5—41no—
50C4⋊Dic5—41no—
51C4⋊Dic5—42no—
52#683—42no—
53#683—42no—
54#683—42no—
55#683—42no—
56#683—42no—
57#400—52no—
58#399—51no—
59#398—52no—
60#398—52no—
61#396—52no—
62#395—52no—
63#393D511yescharacteristic
64#381—51no—
65#380—52no—
66C23×C5—22no—
67C23×C5—21no—
68C23×C5—21no—
69C23×C5—22no—
70C23×C5C2×Q812yes—
71C23×C5C2411yescharacteristic
72C5×Q8—44no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
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×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—44no—
95C2×Dic5C2×Q814yes—
96C22×Q8C2×D511yescharacteristic
97C23×C4—51no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—52no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—52no—
102C2×C4⋊C4—52no—
103C2×C4⋊C4—52no—
104C2×C4⋊C4—51no—
105C2×C22⋊C4—52no—
106C2×C22⋊C4—51no—
107C2×C22⋊C4C2×D512yes—
108C2×C22⋊C4C2×D511yescharacteristic
109#95—52no—
110#95—52no—
111#95—52no—
112#95—52no—
113#95—52no—
114#95—51no—
115#95C2×D511yescharacteristic
116#95C2×D512yes—
117C22×C5—22no—
118C22×C5—24no—
119C22×C5—41no—
120C22×C5—42no—
121C22×C5—41no—
122C22×C5C22×Q811yescharacteristic
123C22×C5H(5,𝔽2)11yescharacteristic
124C22×C5H(5,𝔽2)12yes—
125C22×C5H(5,𝔽2)11yescharacteristic
126C22×C52−1+412yes—
127C4×C5—42no—
128C4×C5—41no—
129C4×C5—42no—
130C4×C5—41no—
131Dic5—24no—
132Dic5—42no—
133Dic5—42no—
134Dic5—42no—
135C24C22×D511yescharacteristic
136C2×Q8—42no—
137C2×Q8—41no—
138C22×C4—52no—
139C22×C4—54no—
140C22×C4—52no—
141C22×C4—52no—
142C22×C4—52no—
143C22×C4—201no—
144C22×C4—201no—
145C22×C4C22×D511yescharacteristic
146C22×C4C22×D512yes—
147C22×C4C22×D511yescharacteristic
148C22×C4C22×D512yes—
149C4⋊C4—202no—
150C4⋊C4—202no—
151C4⋊C4—202no—
152C4⋊C4—202no—
153C4⋊C4—202no—
154C4⋊C4—201no—
155C4⋊C4—202no—
156C22⋊C4—42no—
157C22⋊C4—41no—
158C22⋊C4—202no—
159C22⋊C4—201no—
160C2×C5—42no—
161C2×C5#54311yescharacteristic
162C2×C5#54412yes—
163C2×C5#56011yescharacteristic
164C2×C5#56212yes—
165C2×C5#56311yescharacteristic
166C23—22no—
167C23—21no—
168C23—21no—
169C23—22no—
170C23Q8×D512yes—
171C23C23×D511yescharacteristic
172Q8—44no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—54no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4—102no—
187C2×C4—102no—
188C2×C4—102no—
189C2×C4—102no—
190C2×C4—102no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4—204no—
196C5#284111yescharacteristic, complemented, Sylow
197C22—24no—
198C22—22no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22#414412yes—
203C22#414411yescharacteristic
204C22C2×Q8×D511yescharacteristic
205C22#414911yescharacteristic
206C22#415012yes—
207C4—42no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—104no—
212C4—202no—
213C4—202no—
214C4—202no—
215C2—42no—
216C2#6592911yescharacteristic
217C2#6595712yes—
218C2#6596811yescharacteristic
219C2#6600611yescharacteristic
220C2#6601812yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#393C2
prime radicalC24×C5C23
hypercenter#393D5
hypocenterC5#2841
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #65518C2semidirect
7. #64948C2semidirect
8. #64946C2semidirect
9. #64946C2semidirect
41. C22×Dic5Q8semidirect
196. C5#2841semidirect

Maximal subgroups

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

subgroupindex
C5×#3932
#655182
#652382
#652372
#652322
#652312
#649482
#649462
#28415