Finite Group Databasebeta

← #13103389

Subgroups — #13103389

Order 1600.

190 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 36 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#11717395C211yesmaximal, characteristic
2#11717371C212yesmaximal, complemented
3#11716806C211yesmaximal, characteristic, complemented
4#11716799C212yesmaximal, complemented
5#11716777C211yesmaximal, characteristic, complemented
6#87880C2212yes—
7#87867C2212yes—
8C2×#6034C2211yescharacteristic
9C2×#6033C2211yescharacteristic
10#87839C411yescharacteristic, complemented
11#87838C412yescomplemented
12#87837C411yescharacteristic, complemented
13#87834—22no—
14D5⋊#170—22no—
15Dic52C2211yescharacteristic
16C2×#1039C2311yescharacteristic
17C5×C22⋊D5—22no—
18C2×C5×Dic5—21no—
19#6039C2×C412yes—
20#6037C2×C412yes—
21D5×Dic5—22no—
22#6034—22no—
23#6034C2×C411yescharacteristic
24#6034C2×C411yescharacteristic
25#6033D411yescharacteristic
26#6033D411yescharacteristic
27#4131—102no—
28C4×#170—101no—
29C22×C52#4111yescharacteristic
30C2×C5×D5—22no—
31#1039C22×C411yescharacteristic
32#1039C2×D411yescharacteristic
33C5×Dic5—22no—
34C5×Dic5—22no—
35#711—102no—
36#704—102no—
37#704—102no—
38C2×#170—102no—
39C2×#170—101no—
40C2×#170—101no—
41C2×#170—102no—
42#700—102no—
43D5⋊C8—102no—
44C4×Dic5—101no—
45#443—251nomaximal, Sylow
46C2×C52—21no—
47C2×C52C4×D411yescharacteristic
48C5×D5—42no—
49C5×D4—102no—
50C2×C4×C5—101no—
51C22⋊D5—22no—
52C22⋊D5—102no—
53C2×Dic5—21no—
54C2×Dic5—101no—
55C2×Dic5—102no—
56C2×Dic5—102no—
57C4×D5—102no—
58Dic10—102no—
59#170—102no—
60#170—102no—
61#170—101no—
62#170—101no—
63#170—101no—
64#170—101no—
65#170—102no—
66#170—102no—
67#135—251no—
68#131—252no—
69#108—251no—
70#104—252no—
71C4×C8—251no—
72C52#44311yescharacteristic, complemented, Sylow
73C22×C5—21no—
74C22×C5—22no—
75C22×C5—102no—
76C2×D5—22no—
77C4×C5—102no—
78C4×C5—102no—
79Dic5—22no—
80Dic5—22no—
81Dic5—101no—
82Dic5—102no—
83Dic5—102no—
84Dic5—101no—
85#41—252no—
86Q16—251no—
87SD16—252no—
88D8—251no—
89M16—252no—
90M16—502no—
91C2×C8—251no—
92C2×C8—251no—
93C2×C8—502no—
94C42—251no—
95C2×C5—21no—
96C2×C5—21no—
97C2×C5—22no—
98C2×C5—21no—
99C2×C5—42no—
100C2×C5—202no—
101D5—42no—
102Q8—252no—
103D4—102no—
104D4—252no—
105C2×C4—101no—
106C2×C4—251no—
107C2×C4—502no—
108C8—251no—
109C8—251no—
110C8—251no—
111C8—251no—
112C8—502no—
113C5—22no—
114C5—21no—
115C22—102no—
116C22(D5⋊AGL(1,𝔽5))⋊C211yescharacteristic
117C4—102no—
118C4—102no—
119C4—251no—
120C4—251no—
121C2—21no—
122C2—202no—
123C2#1171730711yescharacteristic
subgroupG/H
centerC2#11717307
commutator#1039C22×C4
Frattini, hypercenterC22(D5⋊AGL(1,𝔽5))⋊C2
FittingC22×C52#41
socleC2×C52C4×D4
prime radical#11717395C2
cosocleC2×#1039C23
hypocenterC52#443
LCSG ▷ #1039 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #11717371C2semidirect
3. #11716806C2semidirect
4. #11716799C2semidirect
5. #11716777C2semidirect
10. #87839C4semidirect
11. #87838C4semidirect
12. #87837C4semidirect
72. C52#443semidirect

Maximal subgroups

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

subgroupindex
#117173952
#117173712
#117168062
#117167992
#117167772
#44325