Finite Group Databasebeta

← #13104160

Subgroups — #13104160

Order 1600.

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

normal subgroups only

This group has 190 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#11717381C211yesmaximal, characteristic
2#11716921C212yesmaximal, complemented
3C8×#1044C211yesmaximal, characteristic, complemented
4#11716791C211yesmaximal, characteristic, complemented
5#11716789C212yesmaximal, complemented
6#87873C2212yes—
7C4×#1044C2211yescharacteristic
8#87862C2211yescharacteristic
9#87839C411yescharacteristic, complemented
10#87838C412yescomplemented
11#87837C411yescharacteristic, complemented
12C8×C5⋊D5C2211yescharacteristic
13C5×C8×D5—22no—
14#87769C2212yes—
15#87768—22no—
16C2×#1044—21no—
17C4×C5⋊D5C2311yescharacteristic
18C4×C5×D5—22no—
19#6039C2×C412yes—
20#6038—22no—
21#6037C2×C412yes—
22#6034C2×C411yescharacteristic
23#6034C2×C411yescharacteristic
24C52×C8D411yescharacteristic
25#6029D411yescharacteristic
26C5×#168—22no—
27#4047—102no—
28C8×AGL(1,𝔽5)—101no—
29C2×C5⋊D5#4111yescharacteristic
30C2×C5×D5—22no—
31#1044—22no—
32C4×C52C2×D411yescharacteristic
33#1039C22×C411yescharacteristic
34C5×Dic5—22no—
35#709—102no—
36C4×AGL(1,𝔽5)—101no—
37D5⋊C8—101no—
38C2×C5×C8—102no—
39#681—102no—
40#676—102no—
41#676—102no—
42C8×D5—22no—
43C8×D5—101no—
44C8×D5—102no—
45#443—251nomaximal, Sylow
46C2×C52C4×D411yescharacteristic
47C5⋊D5—21no—
48C5×D5—42no—
49C2×AGL(1,𝔽5)—102no—
50C2×C4×C5—102no—
51C22⋊D5—102no—
52C22⋊D5—102no—
53D20—102no—
54C4×D5—22no—
55C4×D5—102no—
56C4×D5—101no—
57Dic10—102no—
58#170—101no—
59#170—101no—
60C5×C8—22no—
61C5×C8—21no—
62C5×C8—102no—
63#168—22no—
64#168—101no—
65#168—102no—
66#135—251no—
67#131—252no—
68#108—251no—
69#104—252no—
70C4×C8—251no—
71C52#44311yescharacteristic, complemented, Sylow
72C22×C5—102no—
73C2×D5—22no—
74C2×D5—101no—
75C2×D5—102no—
76AGL(1,𝔽5)—104no—
77C4×C5—22no—
78C4×C5—21no—
79C4×C5—102no—
80Dic5—22no—
81Dic5—101no—
82Dic5—102no—
83#41—252no—
84Q16—251no—
85SD16—252no—
86D8—251no—
87M16—252no—
88M16—502no—
89C2×C8—102no—
90C2×C8—251no—
91C2×C8—251no—
92C42—251no—
93C2×C5—22no—
94C2×C5—21no—
95C2×C5—202no—
96D5—42no—
97D5—102no—
98D5—202no—
99Q8—252no—
100D4—252no—
101D4—502no—
102C2×C4—102no—
103C2×C4—251no—
104C2×C4—501no—
105C8—102no—
106C8—251no—
107C8—251no—
108C8—251no—
109C8D52⋊C211yescharacteristic
110C5—22no—
111C5—21no—
112C22—102no—
113C22—251no—
114C4—102no—
115C4—251no—
116C4—502no—
117C4C2×D52⋊C211yescharacteristic
118C2—202no—
119C2—501no—
120C2C4×D52⋊C211yescharacteristic
subgroupG/H
center, hypercenterC8D52⋊C2
commutator#1039C22×C4
FrattiniC4C2×D52⋊C2
FittingC52×C8D4
socleC2×C52C4×D4
prime radical#11717381C2
cosocleC4×C5⋊D5C23
hypocenterC52#443
LCSG ▷ #1039 ▷ C2×C52 ▷ C52
UCSC1 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #11716921C2semidirect
3. C8×#1044C2semidirect
4. #11716791C2semidirect
5. #11716789C2semidirect
9. #87839C4semidirect
10. #87838C4semidirect
11. #87837C4semidirect
71. C52#443semidirect

Maximal subgroups

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

subgroupindex
#117173812
#117169212
C8×#10442
#117167912
#117167892
#44325