Finite Group Databasebeta

← #13102758

Subgroups — #13102758

Order 1600.

424 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 117 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#11717227C212yesmaximal, complemented
2#11717224C211yesmaximal, characteristic
3C52×#108C211yesmaximal, characteristic, complemented
4#11716692C212yesmaximal, complemented
5C8×#1039C211yesmaximal, characteristic, complemented
6#87900C2212yes—
7C52×M16C2212yes—
8C2×C52×C8C2211yescharacteristic
9C4×#1039C2211yescharacteristic
10C2×#6029C2211yescharacteristic
11#87802C411yescharacteristic, complemented
12#87801C411yescharacteristic, complemented
13#87800C412yescomplemented
14#87799—22no—
15C8×C5⋊D5—22no—
16#65184—56nomaximal
17C2×C4×C52C2311yescharacteristic
18C22⋊(C5⋊D5)—22no—
19C2×#1039—21no—
20C4⋊(C5⋊D5)C2×C412yes—
21C4×C5⋊D5—22no—
22#6045C2×C412yes—
23C52×C8—22no—
24C52×C8C2×C411yescharacteristic
25C52×C8C2×C411yescharacteristic
26#6029D411yescharacteristic
27#6029D411yescharacteristic
28#4053—512no—
29#4050—56no—
30C5×#108D516yescomplemented
31#3957—512no—
32C8×Dic5—56no—
33C22×C52#4111yescharacteristic
34C2×C5⋊D5—22no—
35C4×C52C22×C411yescharacteristic
36C4×C52C2×D411yescharacteristic
37#1039—22no—
38#1039—22no—
39#709—512no—
40C5×M16C2×D5112yes—
41C2×C5×C8C2×D516yes—
42C4×Dic5—56no—
43C2×#168—56no—
44Dic20—56no—
45D40—56no—
46#677—512no—
47#676—1012no—
48C8×D5—1012no—
49#443—251noSylow
50C2×C52—21no—
51C2×C52C4×D411yescharacteristic
52C5⋊D5—42no—
53C2×C4×C5C22×D516yes—
54C22⋊D5—1012no—
55C2×Dic5—106no—
56D20—512no—
57C4×D5—1012no—
58Dic10—512no—
59C5×C8—212no—
60C5×C8C4×D516yes—
61C5×C8C4×D516yes—
62#168—56no—
63#168—56no—
64#135—251no—
65#131—252no—
66#108C5⋊D511yescharacteristic, complemented
67#104—252no—
68C4×C8—251no—
69C52#44311yescharacteristic, complemented, Sylow
70C22×C5#71316yes—
71C2×D5—1012no—
72C4×C5C2×C4×D516yes—
73C4×C5D4×D516yes—
74Dic5—1012no—
75Dic5—1012no—
76#41—252no—
77Q16—251no—
78SD16—252no—
79D8—251no—
80M16—502no—
81M16C2×C5⋊D512yes—
82C2×C8—251no—
83C2×C8—502no—
84C2×C8C2×C5⋊D511yescharacteristic
85C42—251no—
86C2×C5—26no—
87C2×C5#403916yes—
88D5—2012no—
89Q8—252no—
90D4—252no—
91D4—502no—
92C2×C4—501no—
93C2×C4—502no—
94C2×C4C22×C5⋊D511yescharacteristic
95C8—22no—
96C8—251no—
97C8—251no—
98C8C4×C5⋊D511yescharacteristic
99C8C4×C5⋊D511yescharacteristic
100C5#6518416yescomplemented
101C22—502no—
102C22#8790411yescharacteristic
103C4—502no—
104C4—502no—
105C4C2×C4×C5⋊D511yescharacteristic
106C4D4×C5⋊D511yescharacteristic
107C2—21no—
108C2—1002no—
109C2#1171721311yescharacteristic
subgroupG/H
centerC4D4×C5⋊D5
commutatorC4×C52C22×C4
FrattiniC2×C4C22×C5⋊D5
FittingC52×#108C2
socleC2×C52C4×D4
prime radical#11717224C2
cosocleC2×C4×C52C23
hypercenter#108C5⋊D5
hypocenterC52#443
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #11717227C2semidirect
3. C52×#108C2semidirect
4. #11716692C2semidirect
5. C8×#1039C2semidirect
11. #87802C4semidirect
12. #87801C4semidirect
13. #87800C4semidirect
30. C5×#108D5semidirect
66. #108C5⋊D5semidirect
69. C52#443semidirect
100. C5#65184semidirect

Maximal subgroups

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

subgroupindex
#117172272
#117172242
C52×#1082
#117166922
C8×#10392
#651845