Finite Group Databasebeta

← #13100724

Subgroups — #13100724

Order 1600.

264 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 62 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#11717208C211yesmaximal, characteristic
2#11716985C211yesmaximal, characteristic
3C5×#3942C212yesmaximal
4#11716607C212yesmaximal
5#11716594C211yesmaximal, characteristic
6C2×#6045—21no—
7C2×C5×Dic10C2212yes—
8C52×C4⋊C4C2211yescharacteristic
9C4⋊#1039C2211yescharacteristic
10#87806—21no—
11C4×#1039C2211yescharacteristic
12C2×C5×#168C2212yes—
13#87781—21no—
14#87781—21no—
15#65081—52nomaximal
16C2×C4×C52—21no—
17C2×C4×C52C2311yescharacteristic
18C2×#1039—21no—
19C2×#1039D411yescharacteristic
20C2×#1039D411yescharacteristic
21#6045—42no—
22C2×C5×Dic5—22no—
23C5×Dic10—22no—
24C5×Dic10—22no—
25C5×#168—22no—
26#4090—52no—
27#4034—52no—
28#4034—102no—
29C5×#103—52no—
30#3967—52no—
31#3948—52no—
32C8×Dic5—52no—
33#3942D512yes—
34C22×C52C2×D411yescharacteristic
35C4×C52—41no—
36C4×C52#4112yes—
37#1039—41no—
38#1039SD1612yes—
39#1039Q1612yes—
40C5×Dic5—42no—
41C2×C5×Q8—52no—
42C2×Dic10—102no—
43C2×Dic10—104no—
44C2×Dic10C2×D512yes—
45C2×C5×C8—52no—
46C5×C4⋊C4—22no—
47C5×C4⋊C4C2×D512yes—
48C4⋊Dic5—52no—
49C4⋊Dic5—102no—
50#683—102no—
51#683—102no—
52#683—102no—
53#683—104no—
54C4×Dic5—52no—
55C4×Dic5—102no—
56C2×#168C2×D512yes—
57#487—251noSylow
58C2×C52#12411yescharacteristic
59C2×C52C2×SD1611yescharacteristic
60C2×C52C2×Q1611yescharacteristic
61C5×Q8—102no—
62C5×Q8—102no—
63C2×C4×C5—24no—
64C2×C4×C5—22no—
65C2×C4×C5—22no—
66C2×C4×C5—102no—
67C2×C4×C5C22×D512yes—
68C2×Dic5—22no—
69C2×Dic5—52no—
70C2×Dic5—52no—
71C2×Dic5—102no—
72C2×Dic5—102no—
73C2×Dic5—104no—
74C2×Dic5—102no—
75Dic10—22no—
76Dic10—22no—
77Dic10—204no—
78Dic10—208no—
79C5×C8—102no—
80#168—22no—
81C4⋊Q8—251no—
82C4⋊Q8—251no—
83#103—52no—
84#103—252no—
85C4×C8—251no—
86C52#48711yescharacteristic, complemented, Sylow
87C22×C5—22no—
88C22×C5D4×D512yes—
89C4×C5—24no—
90C4×C5—44no—
91C4×C5—42no—
92C4×C5—202no—
93C4×C5#70912yes—
94C4×C5#71112yes—
95Dic5—42no—
96Dic5—54no—
97Dic5—54no—
98Dic5—104no—
99Dic5—104no—
100Dic5—204no—
101Dic5—202no—
102C2×Q8—52no—
103C2×Q8—501no—
104C2×C8—52no—
105C4⋊C4—251no—
106C4⋊C4—501no—
107C4⋊C4—501no—
108C4⋊C4—501no—
109C4⋊C4D5211yescharacteristic
110C42—251no—
111C2×C5—22no—
112C2×C5—22no—
113C2×C5—22no—
114C2×C5#403112yes—
115C2×C5D5×SD1612yes—
116C2×C5D5×Q1612yes—
117Q8—102no—
118Q8—102no—
119Q8—1002no—
120C2×C4—21no—
121C2×C4—102no—
122C2×C4—251no—
123C2×C4—251no—
124C2×C4—501no—
125C2×C4C2×D5211yescharacteristic
126C8—102no—
127C5—22no—
128C5#6508112yescomplemented
129C22#8788611yescharacteristic
130C4—41no—
131C4—202no—
132C4—252no—
133C4—252no—
134C4—1001no—
135C4#8787012yes—
136C2#1171703111yescharacteristic
137C2#1171704811yescharacteristic
138C2#1171706211yescharacteristic
subgroupG/H
centerC22#87886
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC52×C4⋊C4C22
socle, prime radicalC22×C52C2×D4
hypercenterC4⋊C4D52
hypocenterC52#487
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
86. C52#487semidirect
128. C5#65081semidirect

Maximal subgroups

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

subgroupindex
#117172082
#117169852
C5×#39422
#117166072
#117165942
#650815