Finite Group Databasebeta

← #13106535

Subgroups — #13106535

Order 1600.

598 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C5×#4149C212yesmaximal, complemented
2#11717268C211yesmaximal, characteristic, complemented
3#11716941C216yesmaximal, complemented
4#11716940C213yesmaximal, complemented
5C2×#87770C213yesmaximal, complemented
6C52×#41C2211yescharacteristic
7C5×#713—22no—
8C5×D4×D5—26no—
9C5×#709C2216yescomplemented
10C2×C5×D20C2216yescomplemented
11#87804C2213yescomplemented
12C2×#6029C2213yescomplemented
13#87775C2211yescharacteristic, complemented
14#87772C2216yescomplemented
15#87770C2213yescomplemented
16#87770C2216yescomplemented
17#66169—52nomaximal
18C22×C5×D5—26no—
19C52×Q8D411yescharacteristic
20C52×D4D413yes—
21C2×C4×C52C2313yes—
22C5×C22⋊D5—26no—
23C5×D20—26no—
24C5×D20C2316yes—
25C4×C5×D5—26no—
26C5×Dic10C2312yes—
27#6029C2311yescharacteristic
28#6029C2313yes—
29C5×H(5,𝔽2)—52no—
30#4149D512yescomplemented
31#4096—56no—
32#4095—56no—
33#4094—52no—
34#4094—102no—
35#4078—56no—
36C2×#686—56no—
37C22×C52C2×D413yes—
38C2×C5×D5—26no—
39C2×C5×D5—86no—
40C4×C52C2×D413yes—
41C4×C52C2411yescharacteristic
42C5×Dic5—22no—
43C5×#41—22no—
44C5×#41—56no—
45C5×#41—102no—
46C5×#41C2×D512yes—
47C2×C5×D4—56no—
48C2×C5×D4—106no—
49#713—22no—
50D4×D5—26no—
51#709C2×D516yescomplemented
52C2×D20C2×D516yescomplemented
53#689—52no—
54#688—56no—
55#687—56no—
56#686—56no—
57#686—512no—
58#681—56no—
59#681—106no—
60C2×#168—56no—
61C2×#168—106no—
62#576—251noSylow
63C2×C52—23no—
64C2×C52C22×D411yescharacteristic
65C5×D5—46no—
66C23×C5—106no—
67C22×D5—26no—
68C5×Q8—22no—
69C5×Q8—52no—
70C5×Q8C22⋊D512yes—
71C5×D4—26no—
72C5×D4—56no—
73C5×D4—106no—
74C5×D4—106no—
75C5×D4C22⋊D516yes—
76C2×C4×C5—26no—
77C2×C4×C5—106no—
78C2×C4×C5C22×D516yes—
79C22⋊D5—26no—
80D20—26no—
81D20C22×D516yes—
82C4×D5—26no—
83Dic10C22×D512yes—
84#168—52no—
85#168—56no—
86#168—102no—
87#168—106no—
88H(5,𝔽2)—52no—
89AGL(1,ℤ/8)—256no—
90#135—253no—
91C2×D8—253no—
92#131—251no—
93C52#57611yescharacteristic, complemented, Sylow
94C22×C5—26no—
95C22×C5—106no—
96C22×C5—406no—
97C22×C5C2×C22⋊D516yes—
98C2×D5—26no—
99C2×D5—86no—
100C4×C5—26no—
101C4×C5—22no—
102C4×C5—102no—
103C4×C5C2×C22⋊D516yes—
104C4×C5C23×D512yes—
105Dic5—22no—
106#41—56no—
107#41—102no—
108#41D5211yescharacteristic
109C2×D4—56no—
110C2×D4—106no—
111Q16—251no—
112SD16—256no—
113D8—253no—
114D8—256no—
115M16—253no—
116C2×C8—253no—
117C2×C5—26no—
118C2×C5—22no—
119C2×C5—46no—
120C2×C5—206no—
121C2×C5C22×C22⋊D512yes—
122D5—46no—
123C23—106no—
124Q8—52no—
125Q8#603711yescharacteristic
126D4—56no—
127D4—106no—
128D4—106no—
129D4#603713yes—
130C2×C4—106no—
131C2×C4C2×D5213yes—
132C8—251no—
133C8—253no—
134C5—22no—
135C5#6616912yescomplemented
136C22—106no—
137C22—406no—
138C22C2×#603713yes—
139C4—102no—
140C4C2×#603713yes—
141C4C22×D5211yescharacteristic
142C2—23no—
143C2—206no—
144C2C22×#603711yescharacteristic
subgroupG/H
centerC2C22×#6037
commutator, cosocleC4×C52C24
FrattiniC4C22×D52
FittingC52×#41C22
socleC2×C52C22×D4
hypercenter#41D52
hypocenterC52#576
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C5×#4149C2semidirect
2. #11717268C2semidirect
3. #11716941C2semidirect
4. #11716940C2semidirect
5. C2×#87770C2semidirect
9. C5×#709C22semidirect
10. C2×C5×D20C22semidirect
11. #87804C22semidirect
12. C2×#6029C22semidirect
13. #87775C22semidirect
14. #87772C22semidirect
15. #87770C22semidirect
16. #87770C22semidirect
30. #4149D5semidirect
51. #709C2×D5semidirect
52. C2×D20C2×D5semidirect
93. C52#576semidirect
135. C5#66169semidirect

Maximal subgroups

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

subgroupindex
C5×#41492
#117172682
#117169412
#117169402
C2×#877702
#661695