Finite Group Databasebeta

← #13104248

Subgroups — #13104248

Order 1600.

160 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 29 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#11716940C212yesmaximal, complemented
2C2×#87765C211yesmaximal, characteristic, complemented
3#11716794C211yesmaximal, characteristic, complemented
4#11716793C212yesmaximal, complemented
5#11716792C211yesmaximal, characteristic, complemented
6C5×#709—22no—
7C2×#6029C2211yescharacteristic
8#87775C2212yes—
9#87772—22no—
10#87770C2212yes—
11#87765C2211yescharacteristic
12#87765C2211yescharacteristic
13C2×C4×C52D411yescharacteristic
14C5×C22⋊D5—42no—
15C5×D20—22no—
16C4×C5×D5—42no—
17C5×Dic10—22no—
18#6029D411yescharacteristic
19#6029C2311yescharacteristic
20#4096—102no—
21C2×#674—101no—
22C22×C52D811yescharacteristic
23C2×C5×D5—42no—
24C4×C52D811yescharacteristic
25C4×C52C2×D411yescharacteristic
26C5×Dic5—42no—
27C5×#41—102no—
28#709—22no—
29#689—102no—
30#688—102no—
31#687—102no—
32#686—102no—
33C2×#168—102no—
34C2×#168—101no—
35#674—101no—
36#674—101no—
37#508—251nomaximal, Sylow
38C2×C52—21no—
39C2×C52C2×D811yescharacteristic
40C5×D5—82no—
41C5×Q8—102no—
42C5×D4—102no—
43C5×D4—202no—
44C2×C4×C5—21no—
45C2×C4×C5—22no—
46C2×C4×C5—202no—
47C22⋊D5—42no—
48D20—22no—
49C4×D5—42no—
50Dic10—22no—
51#168—101no—
52#168—102no—
53#168—101no—
54#168—102no—
55#135—252no—
56Q32—251no—
57SD32—252no—
58D16—251no—
59C2×C16—251no—
60C52#50811yescharacteristic, complemented, Sylow
61C22×C5—21no—
62C22×C5—22no—
63C22×C5—202no—
64C2×D5—42no—
65C4×C5—22no—
66C4×C5—21no—
67C4×C5—22no—
68C4×C5—21no—
69C4×C5—202no—
70Dic5—42no—
71#41—102no—
72Q16—252no—
73SD16—502no—
74D8—252no—
75C2×C8—251no—
76C16—251no—
77C16—251no—
78C2×C5—22no—
79C2×C5—22no—
80C2×C5—21no—
81C2×C5—42no—
82C2×C5—402no—
83D5—82no—
84Q8—102no—
85D4—102no—
86D4—202no—
87C2×C4—202no—
88C2×C4D52⋊C211yescharacteristic
89C8—251no—
90C8—251no—
91C5—22no—
92C5—21no—
93C22—202no—
94C22#8783711yescharacteristic
95C4—202no—
96C4#8783711yescharacteristic
97C4C2×D52⋊C211yescharacteristic
98C2—21no—
99C2—402no—
100C2C2×#8783711yescharacteristic
subgroupG/H
centerC4#87837
commutator, cosocle#6029C23
FrattiniC4C2×D52⋊C2
FittingC2×C4×C52D4
socleC2×C52C2×D8
hypercenterC2×C4D52⋊C2
hypocenterC52#508
LCSG ▷ #6029 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11716940C2semidirect
2. C2×#87765C2semidirect
3. #11716794C2semidirect
4. #11716793C2semidirect
5. #11716792C2semidirect
60. C52#508semidirect

Maximal subgroups

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

subgroupindex
#117169402
C2×#877652
#117167942
#117167932
#117167922
#50825