Finite Group Databasebeta

← #10598934

Subgroups — #10598934

Order 640.

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

normal subgroups only

This group has 202 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
2#65275C211yesmaximal, characteristic
3#65011C212yesmaximal
4C5×#324C211yesmaximal, characteristic
5#64687C212yesmaximal
6C2×C5×C4⋊C4C2211yescharacteristic
7#4072—21no—
8C2×C4⋊Dic5C2211yescharacteristic
9#4070—21no—
10#4070C2212yes—
11#4036—22no—
12#4034—22no—
13C5×C22⋊C8C2212yes—
14#3963—21no—
15#3963—21no—
16#3963C2211yescharacteristic
17#3950—22no—
18#3948—22no—
19#1617—51nomaximal, Sylow
20C22×C4×C5D411yescharacteristic
21C22×C4×C5D411yescharacteristic
22C22×C4×C5C2311yescharacteristic
23C22×Dic5—21no—
24C22×Dic5—21no—
25C2×Dic10—21no—
26C2×Dic10D412yes—
27C2×C5×C8—22no—
28C5×C4⋊C4—22no—
29C22⋊Dic5—22no—
30C4⋊Dic5—21no—
31C4⋊Dic5—21no—
32C4⋊Dic5—21no—
33C4⋊Dic5—22no—
34C4⋊Dic5D412yes—
35#683—22no—
36#683—22no—
37C4×Dic5—22no—
38#544—51no—
39#484—52no—
40#400—51no—
41#328—52no—
42#324D511yescharacteristic
43C23×C5C2×D411yescharacteristic
44C2×C4×C5—21no—
45C2×C4×C5—21no—
46C2×C4×C5—21no—
47C2×C4×C5—41no—
48C2×C4×C5—41no—
49C2×C4×C5Q1612yes—
50C2×C4×C5C2×D412yes—
51C2×Dic5—22no—
52C2×Dic5—22no—
53C2×Dic5—41no—
54C2×Dic5—41no—
55C2×Dic5—42no—
56C2×Dic5—41no—
57C2×Dic5—41no—
58Dic10—42no—
59Dic10—81no—
60C5×C8—42no—
61C4⋊Q8—102no—
62#125—102no—
63C22⋊Q8—52no—
64C22⋊Q8—101no—
65#117—101no—
66C2×C4⋊C4—51no—
67C2×C4⋊C4C2×D511yescharacteristic
68#107—102no—
69#103—102no—
70C22⋊C8C2×D512yes—
71#95—51no—
72#95—101no—
73#95—101no—
74C22×C5—21no—
75C22×C5—21no—
76C22×C5#12011yescharacteristic
77C22×C5C2×Q1611yescharacteristic
78C22×C5#13711yescharacteristic
79C4×C5—22no—
80C4×C5—22no—
81C4×C5—41no—
82Dic5—42no—
83Dic5—42no—
84Dic5—81no—
85Dic5—81no—
86C2×Q8—52no—
87C2×Q8—101no—
88C22×C4—101no—
89C22×C4—101no—
90C22×C4D2011yescharacteristic
91C22×C4D2011yescharacteristic
92C22×C4C22×D511yescharacteristic
93C2×C8—22no—
94C4⋊C4—22no—
95C4⋊C4—52no—
96C4⋊C4—101no—
97C4⋊C4—101no—
98C4⋊C4—101no—
99C4⋊C4—102no—
100C4⋊C4—102no—
101C4⋊C4—102no—
102C22⋊C4—102no—
103C42—102no—
104C2×C5—21no—
105C2×C5—21no—
106C2×C5#45111yescharacteristic
107C2×C5#45411yescharacteristic
108C2×C5#45811yescharacteristic
109C23C2×D2011yescharacteristic
110Q8—202no—
111Q8—401no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—102no—
118C2×C4—102no—
119C2×C4—201no—
120C2×C4—201no—
121C2×C4—202no—
122C2×C4—201no—
123C2×C4—201no—
124C2×C4Dic2012yes—
125C2×C4D4×D512yes—
126C8—42no—
127C5#161711yescharacteristic, complemented, Sylow
128C22—21no—
129C22—21no—
130C22#402811yescharacteristic
131C22C2×Dic2011yescharacteristic
132C22#405511yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—202no—
137C4—202no—
138C4—401no—
139C4—401no—
140C2—21no—
141C2—21no—
142C2#6502811yescharacteristic
143C2#6503111yescharacteristic
144C2#6504211yescharacteristic
subgroupG/H
centerC22#4028
commutator, cosocleC22×C4×C5C23
FrattiniC22×C4C22×D5
FittingC5×#324C2
socleC22×C5#120
prime radicalC23×C5C2×D4
hypercenter#324D5
hypocenterC5#1617
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
127. C5#1617semidirect

Maximal subgroups

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

subgroupindex
#658342
#652752
#650112
C5×#3242
#646872
#16175