Finite Group Databasebeta

← #13014102

Subgroups — #13014102

Order 1280.

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

normal subgroups only

This group has 324 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#10600783C211yesmaximal, characteristic
2#10598818C212yesmaximal
3C23×Dic10C411yescharacteristic
4C5×#407C411yescharacteristic
5#65496C2211yescharacteristic
6C2×#3956—22no—
7#64912—22no—
8#7343—51nomaximal, Sylow
9C23×C4×C5C2×C411yescharacteristic
10C23×Dic5—21no—
11C22×Dic10—21no—
12C22×Dic10—44no—
13C22×Dic10—41no—
14C22×Dic10—41no—
15C22×Dic10C812yes—
16C2×C5×M16—21no—
17C2×#681D412yes—
18#3998—42no—
19C5×C22⋊C8—41no—
20C22⋊#168—41no—
21#3956—44no—
22#1784—51no—
23#1320—52no—
24C24×C5M1611yescharacteristic
25C22×C4×C5—21no—
26C22×C4×C5—21no—
27C22×C4×C5—42no—
28C22×C4×C5C22⋊C411yescharacteristic
29C22×C4×C5C2×C811yescharacteristic
30C22×Dic5—22no—
31C22×Dic5—44no—
32C22×Dic5—42no—
33C2×Dic10—24no—
34C2×Dic10—42no—
35C2×Dic10—48no—
36C2×Dic10—44no—
37C2×Dic10—41no—
38C2×Dic10—41no—
39C2×Dic10—42no—
40C2×Dic10—44no—
41C2×Dic10—44no—
42C5×M16—42no—
43C2×C5×C8—41no—
44#681—42no—
45C2×#168—22no—
46#674—82no—
47C23×Q8—51no—
48C2×#101—102no—
49#407—51no—
50#407AGL(1,𝔽5)11yescharacteristic
51#349—102no—
52C23×C5—21no—
53C23×C5—41no—
54C23×C5—42no—
55C23×C5C22⋊C811yescharacteristic
56C2×C4×C5—22no—
57C2×C4×C5—21no—
58C2×C4×C5—42no—
59C2×C4×C5—42no—
60C2×C4×C5—41no—
61C2×C4×C5#9911yescharacteristic
62C2×C4×C5#10011yescharacteristic
63C2×Dic5—24no—
64C2×Dic5—42no—
65C2×Dic5—48no—
66C2×Dic5—42no—
67Dic10—44no—
68Dic10—44no—
69Dic10—44no—
70Dic10—44no—
71C5×C8—81no—
72#168—42no—
73C22×Q8—52no—
74C22×Q8—101no—
75C22×Q8—201no—
76C22×Q8—201no—
77C22×Q8—204no—
78C23×C4—101no—
79C23×C4C2×AGL(1,𝔽5)11yescharacteristic
80C2×M16—21no—
81C2×M16—52no—
82M32—202no—
83#101—204no—
84C22⋊C8—41no—
85C22⋊C8—201no—
86C22×C5—22no—
87C22×C5—21no—
88C22×C5—41no—
89C22×C5—41no—
90C22×C5—42no—
91C22×C5—42no—
92C22×C5—41no—
93C22×C5#32311yescharacteristic
94C4×C5—21no—
95C4×C5—41no—
96C4×C5AΣL(1,𝔽16)12yes—
97Dic5—44no—
98C24#70011yescharacteristic
99C2×Q8—104no—
100C2×Q8—202no—
101C2×Q8—202no—
102C2×Q8—204no—
103C2×Q8—204no—
104C2×Q8—208no—
105C2×Q8—204no—
106C2×Q8—201no—
107C2×Q8—201no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—42no—
111C22×C4—102no—
112C22×C4—204no—
113C22×C4—202no—
114C22×C4D5⋊C811yescharacteristic
115C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
116M16—42no—
117M16—202no—
118C2×C8—41no—
119C2×C8—102no—
120C16—402no—
121C2×C5—21no—
122C2×C5—42no—
123C2×C5—41no—
124C2×C5#131611yescharacteristic
125C23—21no—
126C23—41no—
127C23—42no—
128C23#400311yescharacteristic
129Q8—204no—
130Q8—204no—
131Q8—204no—
132Q8—204no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—42no—
137C2×C4—41no—
138C2×C4—104no—
139C2×C4—202no—
140C2×C4—208no—
141C2×C4—202no—
142C2×C4#399911yescharacteristic
143C2×C4#401311yescharacteristic
144C8—81no—
145C8—202no—
146C5#734311yescharacteristic, complemented, Sylow
147C22—22no—
148C22—21no—
149C22—41no—
150C22—41no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22#6491511yescharacteristic
155C4—21no—
156C4—41no—
157C4—204no—
158C4#6486412yes—
159C2—21no—
160C2—42no—
161C2—41no—
162C2#1059870211yescharacteristic
subgroupG/H
centerC2#10598702
commutatorC22×C4×C5C2×C8
FrattiniC23×C4C2×AGL(1,𝔽5)
FittingC5×#407C4
socleC2×C5#1316
prime radicalC24×C5M16
cosocle#65496C22
hypercenter#407AGL(1,𝔽5)
hypocenterC5#7343
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
146. C5#7343semidirect

Maximal subgroups

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

subgroupindex
#106007832
#105988182
#73435