Finite Group Databasebeta

← #13102925

Subgroups — #13102925

Order 1600.

584 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 111 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#11717520C211yesmaximal, characteristic, complemented
2C52×#124C211yesmaximal, characteristic, complemented
3#11717252C212yesmaximal, complemented
4#11716703C211yesmaximal, characteristic, complemented
5#11716672C212yesmaximal, complemented
6C2×C52×Q8C2211yescharacteristic
7C2×C52×D4C2211yescharacteristic
8#87904—22no—
9Q8×C5⋊D5—22no—
10#87900—22no—
11#87900C2212yes—
12C52×C22⋊C4—22no—
13C42×C52C2211yescharacteristic
14#87810—22no—
15#87809—22no—
16#87804C2212yes—
17#65351—56nomaximal
18C23×C52—21no—
19C52×Q8—22no—
20C52×D4—22no—
21C2×C4×C52—21no—
22C2×C4×C52D412yes—
23C2×C4×C52C2311yescharacteristic
24C22⋊(C5⋊D5)—22no—
25C4⋊(C5⋊D5)—22no—
26C4⋊(C5⋊D5)D412yes—
27C4×C5⋊D5—24no—
28C4×C5⋊D5—22no—
29#6045—22no—
30#6045D412yes—
31#6029—22no—
32#4147—56no—
33C5×#124D516yescomplemented
34#4078—512no—
35#3968—56no—
36#3937—512no—
37C22×C52—42no—
38C22×C52—41no—
39C22×C52C2×D411yescharacteristic
40C2×C5⋊D5—22no—
41C4×C52—22no—
42C4×C52—41no—
43C4×C52C2×D412yes—
44#1039—22no—
45C2×C5×Q8C2×D516yes—
46C2×C5×D4C2×D516yes—
47#713—1012no—
48Q8×D5—1012no—
49#709—512no—
50#709—1012no—
51C5×C22⋊C4—212no—
52C42×C5C2×D516yes—
53#687—1012no—
54#686—1012no—
55#681—512no—
56#454—251noSylow
57C2×C52—21no—
58C2×C52—81no—
59C2×C52#12011yescharacteristic
60C5⋊D5—42no—
61C23×C5—26no—
62C5×Q8—212no—
63C5×D4—212no—
64C2×C4×C5—26no—
65C2×C4×C5C22⋊D5112yes—
66C2×C4×C5C22×D516yes—
67C22⋊D5—1012no—
68D20—512no—
69D20—1012no—
70C4×D5—1024no—
71C4×D5—1012no—
72Dic10—512no—
73Dic10—1012no—
74#168—1012no—
752−1+4—251no—
76AGL(1,ℤ/8)—252no—
77#124C5⋊D511yescharacteristic, complemented
78#104—252no—
79#101—251no—
80C52#45411yescharacteristic, complemented, Sylow
81C22×C5—412no—
82C22×C5—46no—
83C22×C5C2×C22⋊D516yes—
84C2×D5—1012no—
85C4×C5—212no—
86C4×C5—46no—
87C4×C5D4×D5112yes—
88Dic5—1012no—
89#41—252no—
90#41—502no—
91#41—502no—
92C2×Q8—502no—
93C2×Q8C2×C5⋊D511yescharacteristic
94C2×D4C2×C5⋊D511yescharacteristic
95SD16—502no—
96D8—502no—
97M16—252no—
98C22⋊C4—22no—
99C42C2×C5⋊D511yescharacteristic
100C2×C5—26no—
101C2×C5—86no—
102C2×C5#408316yes—
103D5—2012no—
104C23—21no—
105Q8—22no—
106Q8—252no—
107Q8—502no—
108D4—22no—
109D4—252no—
110D4—502no—
111D4—502no—
112C2×C4—21no—
113C2×C4—504no—
114C2×C4—502no—
115C2×C4C22⋊(C5⋊D5)12yes—
116C2×C4C22×C5⋊D511yescharacteristic
117C8—502no—
118C5#6535116yescomplemented
119C22—42no—
120C22—41no—
121C22—502no—
122C22C2×C22⋊(C5⋊D5)11yescharacteristic
123C4—22no—
124C4—41no—
125C4—502no—
126C4D4×C5⋊D512yes—
127C2—21no—
128C2—81no—
129C2—1002no—
130C2#1171725711yescharacteristic
subgroupG/H
centerC2#11717257
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C22×C5⋊D5
FittingC52×#124C2
socleC2×C52#120
hypercenter#124C5⋊D5
hypocenterC52#454
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #11717520C2semidirect
2. C52×#124C2semidirect
3. #11717252C2semidirect
4. #11716703C2semidirect
5. #11716672C2semidirect
33. C5×#124D5semidirect
77. #124C5⋊D5semidirect
80. C52#454semidirect
118. C5#65351semidirect

Maximal subgroups

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

subgroupindex
#117175202
C52×#1242
#117172522
#117167032
#117166722
#653515