Finite Group Databasebeta

← #13104212

Subgroups — #13104212

Order 1600.

188 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 37 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#11717037C211yesmaximal, characteristic
3C4×#6034C211yesmaximal, characteristic
4#11716798C214yesmaximal
5C2×#6039—21no—
6C2×#6039C2212yes—
7C2×#6034C2212yes—
8C4×#1039C2211yescharacteristic
9C5×C4⋊Dic5—21no—
10C5×C4⋊Dic5—21no—
11#87781—21no—
12#87781C2212yes—
13C2×C4×C52D411yescharacteristic
14C2×#1039D411yescharacteristic
15C2×#1039C2311yescharacteristic
16C2×C5×Dic5—22no—
17C2×C5×Dic5—22no—
18#6039—24no—
19#6039—42no—
20#6034—22no—
21#4034—101no—
22#4034—101no—
23C4×#170—101no—
24C22×C52C2×D411yescharacteristic
25C4×C52Q1612yes—
26#1039SD1612yes—
27#1039#4112yes—
28C5×Dic5—42no—
29C5×Dic5—42no—
30C2×Dic10—102no—
31C2×Dic10—102no—
32C2×#170—102no—
33C5×C4⋊C4—101no—
34C5×C4⋊C4—101no—
35C4⋊Dic5—21no—
36C4⋊Dic5—21no—
37#683—102no—
38#683—102no—
39C4×Dic5—101no—
40C4×Dic5—101no—
41C4×Dic5—101no—
42#487—251nomaximal, Sylow
43C2×C52#12411yescharacteristic
44C2×C52C2×SD1611yescharacteristic
45C2×C52C2×Q1611yescharacteristic
46C2×C4×C5—21no—
47C2×C4×C5—21no—
48C2×C4×C5—21no—
49C2×C4×C5—102no—
50C2×C4×C5—102no—
51C2×Dic5—22no—
52C2×Dic5—22no—
53C2×Dic5—101no—
54C2×Dic5—101no—
55C2×Dic5—101no—
56C2×Dic5—101no—
57C2×Dic5—101no—
58C2×Dic5—101no—
59Dic10—204no—
60Dic10—204no—
61#170—104no—
62C4⋊Q8—251no—
63C4⋊Q8—251no—
64#103—254no—
65C4×C8—251no—
66C52#48711yescharacteristic, complemented, Sylow
67C22×C5—21no—
68C22×C5—21no—
69C22×C5—21no—
70C4×C5—22no—
71C4×C5—22no—
72C4×C5—22no—
73C4×C5—202no—
74C4×C5—202no—
75Dic5—42no—
76Dic5—42no—
77Dic5—102no—
78Dic5—102no—
79Dic5—102no—
80Dic5—102no—
81Dic5—102no—
82Dic5—102no—
83C2×Q8—252no—
84C2×Q8—501no—
85C2×C8—252no—
86C4⋊C4—101no—
87C4⋊C4—101no—
88C4⋊C4—252no—
89C4⋊C4—501no—
90C42—251no—
91C2×C5—21no—
92C2×C5—21no—
93C2×C5—21no—
94C2×C5—21no—
95C2×C5—21no—
96C2×C5—21no—
97C2×C5—21no—
98C2×C5—21no—
99C2×C5—21no—
100Q8—504no—
101Q8—1002no—
102C2×C4—102no—
103C2×C4—102no—
104C2×C4—251no—
105C2×C4—251no—
106C2×C4D52⋊C211yescharacteristic
107C8—502no—
108C5—21no—
109C5—21no—
110C5—21no—
111C22C2×D52⋊C211yescharacteristic
112C4—202no—
113C4—202no—
114C4—252no—
115C4—252no—
116C4#8783912yes—
117C2#1171737911yescharacteristic
118C2#1171738511yescharacteristic
119C2C2×#8783911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D52⋊C2
commutator, cosocleC2×#1039C23
FittingC2×C4×C52D4
socle, prime radicalC22×C52C2×D4
hypercenterC2×C4D52⋊C2
hypocenterC52#487
LCSG ▷ C2×#1039 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
66. C52#487semidirect

Maximal subgroups

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

subgroupindex
#117170372
C4×#60342
#117167982
#48725