Finite Group Databasebeta

← #13098520

Subgroups — #13098520

Order 1600.

213 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C25×2−1+4C211yesmaximal, characteristic
2#11716511C212yesmaximal, complemented
3#11716506C211yesmaximal, characteristic, complemented
4#11716385C212yesmaximal, complemented
5#11716383C211yesmaximal, characteristic, complemented
6#41×C25—22no—
7#41×C25—22no—
8#41×C25C2212yes—
9C2×Q8×C25—22no—
10C2×Q8×C25C2211yescharacteristic
11C2×Dic50C2211yescharacteristic
12#87723—22no—
13#87721—22no—
14#87718—22no—
15C4×Dic25C2211yescharacteristic
16#87716C2212yes—
17#65535—51nomaximal
18Q8×C25—22no—
19Q8×C25—22no—
20Q8×C25D412yes—
21D4×C25—22no—
22D4×C25—22no—
23D4×C25D412yes—
24C2×C4×C25—24no—
25C2×C4×C25—22no—
26C2×C4×C25D412yes—
27C2×C4×C25C2311yescharacteristic
28C2×Dic25—21no—
29C2×Dic25—21no—
30Dic50—22no—
31#6014—22no—
32C5×2−1+4D511yescharacteristic
33#4097—52no—
34#4090—51no—
35#3969—52no—
36#3968—51no—
37C22×C25—22no—
38C22×C25C2×D411yescharacteristic
39C4×C25—22no—
40C4×C25—22no—
41C4×C25C2×D412yes—
42Dic25—22no—
43Dic25—41no—
44C5×#41—22no—
45C5×#41—22no—
46C5×#41C2×D512yes—
47C2×C5×Q8—22no—
48C2×C5×Q8C2×D511yescharacteristic
49C2×Dic10—51no—
50#689—102no—
51#687—102no—
52#683—102no—
53C4×Dic5—51no—
54#681—52no—
55#456—251noSylow
56C2×C25—21no—
57C2×C25—42no—
58C2×C25#12011yescharacteristic
59C5×Q8—22no—
60C5×Q8—22no—
61C5×Q8C22⋊D512yes—
62C5×D4—22no—
63C5×D4—22no—
64C5×D4C22⋊D512yes—
65C2×C4×C5—24no—
66C2×C4×C5—22no—
67C2×C4×C5C22⋊D512yes—
68C2×C4×C5C22×D511yescharacteristic
69C2×Dic5—101no—
70C2×Dic5—101no—
71Dic10—102no—
72#168—102no—
732−1+4D2511yescharacteristic
74#137—252no—
75C4⋊Q8—251no—
76#104—252no—
77#101—251no—
78C25#45611yescharacteristic, complemented, Sylow
79C22×C5—22no—
80C22×C5C2×C22⋊D511yescharacteristic
81C4×C5—22no—
82C4×C5—22no—
83C4×C5C2×C22⋊D512yes—
84Dic5—102no—
85Dic5—201no—
86#41—22no—
87#41—22no—
88#41C2×D2512yes—
89C2×Q8—22no—
90C2×Q8—251no—
91C2×Q8C2×D2511yescharacteristic
92Q16—502no—
93SD16—502no—
94M16—252no—
95C4⋊C4—502no—
96C42—251no—
97C2×C5—21no—
98C2×C5—42no—
99C2×C5#409911yescharacteristic
100Q8—22no—
101Q8—22no—
102Q8—502no—
103Q8C22⋊D2512yes—
104D4—22no—
105D4—22no—
106D4C22⋊D2512yes—
107C2×C4—24no—
108C2×C4—22no—
109C2×C4—501no—
110C2×C4—501no—
111C2×C4C22⋊D2512yes—
112C2×C4C22×D2511yescharacteristic
113C8—502no—
114C5#6553511yescharacteristic
115C22—22no—
116C22C2×C22⋊D2511yescharacteristic
117C4—22no—
118C4—22no—
119C4—502no—
120C4—1001no—
121C4C2×C22⋊D2512yes—
122C2—21no—
123C2—42no—
124C2#1171651511yescharacteristic
subgroupG/H
centerC2#11716515
commutator, cosocleC2×C4×C25C23
FrattiniC2×C4×C5C22×D5
FittingC25×2−1+4C2
socleC2×C5#4099
prime radicalC5×2−1+4D5
hypercenter2−1+4D25
hypocenterC25#456
LCSG ▷ C2×C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C2×C4 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
2. #11716511C2semidirect
3. #11716506C2semidirect
4. #11716385C2semidirect
5. #11716383C2semidirect
78. C25#456semidirect

Maximal subgroups

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

subgroupindex
C25×2−1+42
#117165112
#117165062
#117163852
#117163832
#655355