Finite Group Databasebeta

← #13098370

Subgroups — #13098370

Order 1600.

213 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 51 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#11716566C211yesmaximal, characteristic
2C25×C4⋊Q8C211yesmaximal, characteristic, complemented
3#11716505C212yesmaximal, complemented
4#11716383C211yesmaximal, characteristic, complemented
5#11716353C212yesmaximal, complemented
6C2×Q8×C25C2211yescharacteristic
7C2×Q8×C25C2211yescharacteristic
8#87748—22no—
9Q8×D25—22no—
10#87744—22no—
11#87744C2212yes—
12C4⋊C4×C25—22no—
13C42×C25C2211yescharacteristic
14#87724—22no—
15#87723—22no—
16#87716C2212yes—
17#65384—51nomaximal
18Q8×C25—22no—
19Q8×C25—22no—
20C2×C4×C25—21no—
21C2×C4×C25—21no—
22C2×C4×C25D412yes—
23C2×C4×C25C2311yescharacteristic
24C22⋊D25—22no—
25D100—22no—
26D100D412yes—
27C4×D25—24no—
28C4×D25—22no—
29Dic50—22no—
30Dic50D412yes—
31#6014—22no—
32#4147—51no—
33C5×C4⋊Q8D511yescharacteristic
34#4088—52no—
35#3968—51no—
36#3937—52no—
37C22×C25C2×D411yescharacteristic
38C2×D25—22no—
39C4×C25—22no—
40C4×C25—22no—
41C4×C25—41no—
42C4×C25C2×D412yes—
43Dic25—22no—
44C2×C5×Q8C2×D511yescharacteristic
45C2×C5×Q8C2×D511yescharacteristic
46#713—102no—
47Q8×D5—102no—
48#709—52no—
49#709—102no—
50C5×C4⋊C4—22no—
51C42×C5C2×D511yescharacteristic
52#689—102no—
53#688—102no—
54#681—52no—
55#456—251noSylow
56C2×C25—21no—
57C2×C25#12011yescharacteristic
58D25—42no—
59C5×Q8—22no—
60C5×Q8—22no—
61C2×C4×C5—21no—
62C2×C4×C5—21no—
63C2×C4×C5C22⋊D512yes—
64C2×C4×C5C22×D511yescharacteristic
65C22⋊D5—102no—
66D20—52no—
67D20—102no—
68C4×D5—104no—
69C4×D5—102no—
70Dic10—52no—
71Dic10—102no—
72#168—102no—
732−1+4—251no—
74#137—252no—
75C4⋊Q8D2511yescharacteristic, complemented
76#104—252no—
77#101—251no—
78C25#45611yescharacteristic, complemented, Sylow
79C22×C5C2×C22⋊D511yescharacteristic
80C2×D5—102no—
81C4×C5—22no—
82C4×C5—22no—
83C4×C5—41no—
84C4×C5D4×D512yes—
85Dic5—102no—
86#41—252no—
87#41—502no—
88#41—502no—
89C2×Q8—502no—
90C2×Q8C2×D2511yescharacteristic
91C2×Q8C2×D2511yescharacteristic
92Q16—502no—
93SD16—502no—
94M16—252no—
95C4⋊C4—22no—
96C42C2×D2511yescharacteristic
97C2×C5—21no—
98C2×C5#408311yescharacteristic
99D5—202no—
100Q8—22no—
101Q8—22no—
102Q8—252no—
103Q8—502no—
104D4—252no—
105D4—502no—
106D4—502no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—504no—
110C2×C4—502no—
111C2×C4C22⋊D2512yes—
112C2×C4C22×D2511yescharacteristic
113C8—502no—
114C5#6538411yescharacteristic
115C22—502no—
116C22C2×C22⋊D2511yescharacteristic
117C4—22no—
118C4—22no—
119C4—41no—
120C4—502no—
121C4D4×D2512yes—
122C2—21no—
123C2—1002no—
124C2#1171649911yescharacteristic
subgroupG/H
centerC2#11716499
commutator, cosocleC2×C4×C25C23
FrattiniC2×C4×C5C22×D5
FittingC25×C4⋊Q8C2
socleC2×C5#4083
prime radical#11716566C2
hypercenterC4⋊Q8D25
hypocenterC25#456
LCSG ▷ C2×C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C25×C4⋊Q8C2semidirect
3. #11716505C2semidirect
4. #11716383C2semidirect
5. #11716353C2semidirect
75. C4⋊Q8D25semidirect
78. C25#456semidirect

Maximal subgroups

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

subgroupindex
#117165662
C25×C4⋊Q82
#117165052
#117163832
#117163532
#653845