Finite Group Databasebeta

← #10600506

Subgroups — #10600506

Order 640.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#65834C211yesmaximal, characteristic
2C5×#398C211yesmaximal, characteristic
3#65260C212yesmaximal
4#64748C211yesmaximal, characteristic
5#64672C212yesmaximal
6C2×C5×C4⋊C4—21no—
7C2×C5×C4⋊C4C2211yescharacteristic
8C2×C5×C4⋊C4C2211yescharacteristic
9#4072—21no—
10#4070—21no—
11#4070C2212yes—
12#4036—22no—
13#4034—22no—
14C5×#95—21no—
15C5×#95C2211yescharacteristic
16C22⋊#168C2212yes—
17#3942—22no—
18#3940—22no—
19#1611—51nomaximal, Sylow
20C22×C4×C5—21no—
21C22×C4×C5—21no—
22C22×C4×C5D411yescharacteristic
23C22×C4×C5D411yescharacteristic
24C22×C4×C5C2311yescharacteristic
25C2×Dic10—21no—
26C2×Dic10D412yes—
27C5×C4⋊C4—22no—
28C5×C4⋊C4—22no—
29C5×C4⋊C4—42no—
30C22⋊Dic5—22no—
31C4⋊Dic5—21no—
32C4⋊Dic5—21no—
33C4⋊Dic5—21no—
34C4⋊Dic5D412yes—
35#683—22no—
36#683—22no—
37C4×Dic5—22no—
38C2×#168—22no—
39#544—51no—
40#483—52no—
41#398D511yescharacteristic
42#328—52no—
43#324—51no—
44C23×C5C2×D411yescharacteristic
45C2×C4×C5—21no—
46C2×C4×C5—21no—
47C2×C4×C5—22no—
48C2×C4×C5—21no—
49C2×C4×C5—41no—
50C2×C4×C5—41no—
51C2×C4×C5—41no—
52C2×C4×C5—41no—
53C2×C4×C5—41no—
54C2×C4×C5—41no—
55C2×C4×C5—41no—
56C2×C4×C5SD1612yes—
57C2×C4×C5C2×D412yes—
58C2×Dic5—22no—
59C2×Dic5—22no—
60Dic10—42no—
61Dic10—81no—
62#168—42no—
63C4⋊Q8—102no—
64#125—102no—
65C22⋊Q8—52no—
66C22⋊Q8—101no—
67#117—101no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4C2×D511yescharacteristic
70C2×C4⋊C4C2×D511yescharacteristic
71#106—102no—
72#103—102no—
73C22⋊C8—52no—
74#95—21no—
75#95C2×D511yescharacteristic
76C22×C5—21no—
77C22×C5—21no—
78C22×C5#12011yescharacteristic
79C22×C5C2×SD1611yescharacteristic
80C22×C5#13711yescharacteristic
81C4×C5—22no—
82C4×C5—22no—
83C4×C5—42no—
84C4×C5—41no—
85C4×C5—81no—
86Dic5—42no—
87Dic5—42no—
88C2×Q8—52no—
89C2×Q8—101no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4C22⋊D511yescharacteristic
93C22×C4C22⋊D511yescharacteristic
94C22×C4C22×D511yescharacteristic
95C2×C8—102no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—42no—
99C4⋊C4—52no—
100C4⋊C4—101no—
101C4⋊C4—101no—
102C4⋊C4—101no—
103C4⋊C4—102no—
104C4⋊C4—102no—
105C22⋊C4—102no—
106C42—102no—
107C2×C5—21no—
108C2×C5—21no—
109C2×C5#44811yescharacteristic
110C2×C5#45611yescharacteristic
111C2×C5#45811yescharacteristic
112C23C2×C22⋊D511yescharacteristic
113Q8—202no—
114Q8—401no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—102no—
127C2×C4—102no—
128C2×C4#68712yes—
129C2×C4D4×D512yes—
130C8—202no—
131C5#161111yescharacteristic, complemented, Sylow
132C22—21no—
133C22—21no—
134C22C2×#68711yescharacteristic
135C22#408311yescharacteristic
136C22#409711yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—81no—
142C4—202no—
143C4—202no—
144C2—21no—
145C2—21no—
146C2#6532911yescharacteristic
147C2#6534211yescharacteristic
148C2#6538411yescharacteristic
subgroupG/H
centerC22#4083
commutator, cosocleC22×C4×C5C23
FrattiniC22×C4C22×D5
FittingC5×#398C2
socleC22×C5#120
prime radicalC23×C5C2×D4
hypercenter#398D5
hypocenterC5#1611
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
131. C5#1611semidirect

Maximal subgroups

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

subgroupindex
#658342
C5×#3982
#652602
#647482
#646722
#16115