Finite Group Databasebeta

← #13098521

Subgroups — #13098521

Order 1600.

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

normal subgroups only

This group has 219 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, complemented
2#11716512C212yesmaximal, complemented
3#11716509C211yesmaximal, 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×D100C2211yescharacteristic
12#87724—22no—
13#87722—22no—
14#87720—22no—
15C4×Dic25C2211yescharacteristic
16#87716C2212yes—
17#65534—51nomaximal
18C22×D25—21no—
19Q8×C25—22no—
20Q8×C25—22no—
21Q8×C25D412yes—
22D4×C25—22no—
23D4×C25—22no—
24D4×C25D412yes—
25C2×C4×C25—24no—
26C2×C4×C25—22no—
27C2×C4×C25D412yes—
28C2×C4×C25C2311yescharacteristic
29C2×Dic25—21no—
30D100—22no—
31#6014—22no—
32C5×2−1+4D511yescharacteristic
33#4095—52no—
34#4093—51no—
35#3969—52no—
36#3968—51no—
37C22×C25—22no—
38C22×C25C2×D411yescharacteristic
39C2×D25—42no—
40C2×D25—41no—
41C4×C25—22no—
42C4×C25—22no—
43C4×C25C2×D412yes—
44Dic25—41no—
45C5×#41—22no—
46C5×#41—22no—
47C5×#41C2×D512yes—
48C2×C5×Q8—22no—
49C2×C5×Q8C2×D511yescharacteristic
50C2×D20—51no—
51#688—102no—
52#686—102no—
53#685—102no—
54C4×Dic5—51no—
55#681—52no—
56#454—251noSylow
57C2×C25—21no—
58C2×C25—42no—
59C2×C25#12011yescharacteristic
60D25—81no—
61C22×D5—101no—
62C5×Q8—22no—
63C5×Q8—22no—
64C5×Q8C22⋊D512yes—
65C5×D4—22no—
66C5×D4—22no—
67C5×D4C22⋊D512yes—
68C2×C4×C5—24no—
69C2×C4×C5—22no—
70C2×C4×C5C22⋊D512yes—
71C2×C4×C5C22×D511yescharacteristic
72C2×Dic5—101no—
73D20—102no—
74#168—102no—
752−1+4D2511yescharacteristic, complemented
76AGL(1,ℤ/8)—252no—
77#124—251no—
78#104—252no—
79#101—251no—
80C25#45411yescharacteristic, complemented, Sylow
81C22×C5—22no—
82C22×C5C2×C22⋊D511yescharacteristic
83C2×D5—202no—
84C2×D5—201no—
85C4×C5—22no—
86C4×C5—22no—
87C4×C5C2×C22⋊D512yes—
88Dic5—201no—
89#41—22no—
90#41—22no—
91#41C2×D2512yes—
92C2×Q8—22no—
93C2×Q8C2×D2511yescharacteristic
94C2×D4—251no—
95SD16—502no—
96D8—502no—
97M16—252no—
98C22⋊C4—502no—
99C42—251no—
100C2×C5—21no—
101C2×C5—42no—
102C2×C5#409911yescharacteristic
103D5—401no—
104C23—501no—
105Q8—22no—
106Q8—22no—
107Q8C22⋊D2512yes—
108D4—22no—
109D4—22no—
110D4—502no—
111D4C22⋊D2512yes—
112C2×C4—24no—
113C2×C4—22no—
114C2×C4—501no—
115C2×C4C22⋊D2512yes—
116C2×C4C22×D2511yescharacteristic
117C8—502no—
118C5#6553411yescharacteristic
119C22—22no—
120C22—1002no—
121C22—1001no—
122C22C2×C22⋊D2511yescharacteristic
123C4—22no—
124C4—22no—
125C4—1001no—
126C4C2×C22⋊D2512yes—
127C2—21no—
128C2—42no—
129C2—2001no—
130C2#1171651511yescharacteristic
subgroupG/H
centerC2#11716515
commutator, cosocleC2×C4×C25C23
FrattiniC2×C4×C5C22×D5
FittingC25×2−1+4C2
socleC2×C5#4099
hypercenter2−1+4D25
hypocenterC25#454
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
1. C25×2−1+4C2semidirect
2. #11716512C2semidirect
3. #11716509C2semidirect
4. #11716385C2semidirect
5. #11716383C2semidirect
75. 2−1+4D25semidirect
80. C25#454semidirect

Maximal subgroups

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

subgroupindex
C25×2−1+42
#117165122
#117165092
#117163852
#117163832
#655345