Finite Group Databasebeta

← #13104226

Subgroups — #13104226

Order 1600.

188 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 41 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#11717037C211yesmaximal, characteristic
2#11716985C211yesmaximal, characteristic
3C4×#6034C211yesmaximal, characteristic
4#11716800C214yesmaximal
5C2×C5×Dic10—21no—
6C2×#6039—21no—
7C2×#6034C2212yes—
8C4×#1039C2211yescharacteristic
9C5×C4⋊Dic5—21no—
10#87781—21no—
11#87781C2212yes—
12#87781C2212yes—
13C2×C4×C52D411yescharacteristic
14C2×#1039D411yescharacteristic
15C2×#1039C2311yescharacteristic
16C2×C5×Dic5—22no—
17C2×C5×Dic5—22no—
18C5×Dic10—42no—
19#6039—42no—
20#6034Q814yescomplemented
21#4090—101no—
22#4034—101no—
23C4×#170—101no—
24C22×C52C2×D411yescharacteristic
25C4×C52SD1612yes—
26#1039SD1612yes—
27#1039C2×Q812yes—
28C5×Dic5—42no—
29C5×Dic5—42no—
30C2×C5×Q8—101no—
31C2×Dic10—21no—
32C2×Dic10—102no—
33C2×#170—102no—
34C5×C4⋊C4—101no—
35C4⋊Dic5—21no—
36#683—102no—
37#683—102no—
38#683—102no—
39C4×Dic5—101no—
40C4×Dic5—101no—
41C4×Dic5—101no—
42#498—251nomaximal, Sylow
43C2×C52C4⋊Q811yescharacteristic
44C2×C52C2×SD1611yescharacteristic
45C2×C52C2×SD1611yescharacteristic
46C5×Q8—202no—
47C2×C4×C5—21no—
48C2×C4×C5—21no—
49C2×C4×C5—21no—
50C2×C4×C5—102no—
51C2×C4×C5—102no—
52C2×Dic5—22no—
53C2×Dic5—22no—
54C2×Dic5—101no—
55C2×Dic5—101no—
56C2×Dic5—101no—
57C2×Dic5—101no—
58C2×Dic5—101no—
59C2×Dic5—101no—
60Dic10—42no—
61Dic10—204no—
62#170—104no—
63C4⋊Q8—251no—
64C4⋊Q8—251no—
65#106—254no—
66C4×C8—251no—
67C52#49811yescharacteristic, complemented, Sylow
68C22×C5—21no—
69C22×C5—21no—
70C22×C5—21no—
71C4×C5—22no—
72C4×C5—22no—
73C4×C5—22no—
74C4×C5—202no—
75C4×C5—202no—
76Dic5—42no—
77Dic5—42no—
78Dic5—102no—
79Dic5—102no—
80Dic5—102no—
81Dic5—102no—
82Dic5—102no—
83Dic5—102no—
84C2×Q8—101no—
85C2×Q8—501no—
86C2×C8—252no—
87C4⋊C4—101no—
88C4⋊C4—252no—
89C4⋊C4—252no—
90C4⋊C4—501no—
91C42—251no—
92C2×C5—21no—
93C2×C5—21no—
94C2×C5—21no—
95C2×C5—21no—
96C2×C5—21no—
97C2×C5—21no—
98C2×C5—21no—
99C2×C5—21no—
100C2×C5—21no—
101Q8—202no—
102Q8—1002no—
103C2×C4—102no—
104C2×C4—102no—
105C2×C4—251no—
106C2×C4—251no—
107C2×C4D52⋊C211yescharacteristic
108C8—254no—
109C5—21no—
110C5—21no—
111C5—21no—
112C22C2×D52⋊C211yescharacteristic
113C4—202no—
114C4—202no—
115C4—252no—
116C4—252no—
117C4#8783812yes—
118C2#1171738011yescharacteristic
119C2#1171738511yescharacteristic
120C2C2×#8783811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D52⋊C2
commutator, cosocleC2×#1039C23
FittingC2×C4×C52D4
socle, prime radicalC22×C52C2×D4
hypercenterC2×C4D52⋊C2
hypocenterC52#498
LCSG ▷ C2×#1039 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
20. #6034Q8semidirect
67. C52#498semidirect

Maximal subgroups

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

subgroupindex
#117170372
#117169852
C4×#60342
#117168002
#49825