Finite Group Databasebeta

← #10609938

Subgroups — #10609938

Order 640.

388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 133 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×#400C211yesmaximal, characteristic
2#65268C211yesmaximal, characteristic
3#65266C211yesmaximal, characteristic
4#65261C212yesmaximal
5#64946C212yesmaximal
6#64941C212yesmaximal
7#64941C212yesmaximal
8#64937C212yesmaximal
9#64935C212yesmaximal
10C22×Dic10C2211yescharacteristic
11C2×C5×C4⋊C4C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic5C2211yescharacteristic
14C2×#683C2212yes—
15C2×#683C2212yes—
16C2×#683C2212yes—
17C2×#683C2212yes—
18C2×C4×Dic5C2212yes—
19C2×C4×Dic5C2212yes—
20C2×C4×Dic5C2211yescharacteristic
21C5×#95C2212yes—
22C5×#95C2212yes—
23C5×#95C2211yescharacteristic
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2211yescharacteristic
30#3963C2212yes—
31#2612—51nomaximal, Sylow
32C22×C4×C5C2311yescharacteristic
33C22×C4×C5C2311yescharacteristic
34C22×C4×C5C2312yes—
35C22×C4×C5C2312yes—
36C22×C4×C5C2311yescharacteristic
37C22×Dic5C2312yes—
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C2×Dic10—24no—
42C2×Dic10—41no—
43C5×C4⋊C4—41no—
44C5×C4⋊C4—41no—
45C4⋊Dic5—41no—
46#683—24no—
47#683—24no—
48#683—24no—
49#683—42no—
50C4×Dic5—24no—
51C4×Dic5—24no—
52C4×Dic5Q814yescomplemented
53#400D511yescharacteristic
54#398—52no—
55#395—51no—
56#391—52no—
57#389—52no—
58#387—52no—
59#387—52no—
60#382—51no—
61#376—52no—
62C23×C5C2411yescharacteristic
63C2×C4×C5—21no—
64C2×C4×C5—21no—
65C2×C4×C5—22no—
66C2×C4×C5—22no—
67C2×C4×C5—22no—
68C2×C4×C5—22no—
69C2×C4×C5—22no—
70C2×C4×C5—22no—
71C2×C4×C5—22no—
72C2×C4×C5—21no—
73C2×C4×C5—21no—
74C2×C4×C5—22no—
75C2×C4×C5C2×Q812yes—
76C2×Dic5—22no—
77C2×Dic5—22no—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5C2×Q814yes—
86C2×Dic5#4114yes—
87C2×Dic5#4114yes—
88Dic10—44no—
89C22×Q8—51no—
90C2×C4⋊C4—52no—
91C2×C4⋊C4—52no—
92C2×C4⋊C4—52no—
93C2×C4⋊C4—51no—
94C2×C4⋊C4—52no—
95C2×C4⋊C4C2×D511yescharacteristic
96C2×C4⋊C4C2×D511yescharacteristic
97C2×C42—51no—
98C2×C42—52no—
99C2×C42—52no—
100#95—52no—
101#95—52no—
102#95—52no—
103#95—52no—
104#95—52no—
105#95—51no—
106#95—52no—
107#95C2×D512yes—
108#95C2×D511yescharacteristic
109#95C2×D512yes—
110C22×C5C22×Q811yescharacteristic
111C22×C5C2×#4112yes—
112C22×C5C2×#4112yes—
113C22×C5H(5,𝔽2)11yescharacteristic
114C22×C52−1+411yescharacteristic
115C4×C5—22no—
116C4×C5—41no—
117C4×C5—41no—
118C4×C5—42no—
119C4×C5—42no—
120Dic5—24no—
121Dic5—24no—
122Dic5—24no—
123Dic5—42no—
124C2×Q8—104no—
125C2×Q8—201no—
126C22×C4—52no—
127C22×C4—52no—
128C22×C4—52no—
129C22×C4—52no—
130C22×C4C22×D511yescharacteristic
131C22×C4C22×D512yes—
132C22×C4C22×D511yescharacteristic
133C22×C4C22×D512yes—
134C22×C4C22×D511yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—104no—
138C4⋊C4—104no—
139C4⋊C4—104no—
140C4⋊C4—202no—
141C4⋊C4—201no—
142C42—54no—
143C42—104no—
144C42—104no—
145C2×C5#53312yes—
146C2×C5#54411yescharacteristic
147C2×C5#55111yescharacteristic
148C2×C5#55212yes—
149C2×C5#55511yescharacteristic
150C23C23×D511yescharacteristic
151Q8—204no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—54no—
165C2×C4—54no—
166C2×C4—54no—
167C2×C4—102no—
168C2×C4—102no—
169C2×C4—102no—
170C2×C4—102no—
171C2×C4—102no—
172C2×C4—102no—
173C2×C4—102no—
174C2×C4—102no—
175C2×C4—102no—
176C2×C4Q8×D512yes—
177C5#261211yescharacteristic, complemented, Sylow
178C22#414411yescharacteristic
179C22C2×Q8×D511yescharacteristic
180C22D5×#4112yes—
181C22D5×#4112yes—
182C22#415011yescharacteristic
183C4—22no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—42no—
188C4—104no—
189C4—104no—
190C4—104no—
191C4—202no—
192C2#6595711yescharacteristic
193C2#6599311yescharacteristic
194C2#6600411yescharacteristic
195C2#6602212yes—
196C2#6604212yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#400C2
hypercenter#400D5
hypocenterC5#2612
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C4×Dic5Q8semidirect
177. C5#2612semidirect

Maximal subgroups

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

subgroupindex
C5×#4002
#652682
#652662
#652612
#649462
#649412
#649372
#649352
#26125