Finite Group Databasebeta

← #11746293

Subgroups — #11746293

Order 960.

136 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 37 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#91824C211yesmaximal, characteristic
2C3×C5×#99C211yesmaximal, characteristic
3#91117C211yesmaximal, characteristic
4#64692—31nomaximal, Hall
5C2×C3×C5×D4C2211yescharacteristic
6C22×Dic15C411yescharacteristic, complemented
7C3×C5×C22⋊C4—21no—
8#6719—21no—
9#6719C411yescharacteristic, complemented
10#6712—21no—
11#6710—21no—
12#4472—51nomaximal, Hall
13#4081—31no—
14C5×#99D311yescharacteristic
15#3965—31no—
16C23×C3×C5C2×C411yescharacteristic
17C23×C3×C5D411yescharacteristic
18C3×C5×D4—41no—
19C2×C3×C4×C5—41no—
20C2×C3×C4×C5D411yescharacteristic
21C2×Dic15—21no—
22C2×Dic15—21no—
23C2×Dic15—41no—
24C3⋊#168—41no—
25#935—51no—
26C3×#99D511yescharacteristic
27#833—51no—
28C2×C5×D4C2×D311yescharacteristic
29C22×Dic5—31no—
30C5×C22⋊C4—21no—
31C22⋊Dic5—31no—
32C22⋊Dic5—61no—
33#683—61no—
34#681—61no—
35#352—151noSylow
36C22×C3×C5—21no—
37C22×C3×C5—21no—
38C22×C3×C5—41no—
39C22×C3×C5—41no—
40C22×C3×C5C22⋊C411yescharacteristic
41C3×C4×C5—21no—
42C3×C4×C5—81no—
43Dic15—41no—
44Dic15—41no—
45C2×C3×D4C2×D511yescharacteristic
46C22×Dic3—51no—
47C3×C22⋊C4—21no—
48#217—51no—
49#217—101no—
50Dic3⋊C4—101no—
51#208—101no—
52C23×C5C4×D311yescharacteristic
53C23×C5#6711yescharacteristic
54C5×D4—41no—
55C2×C4×C5—41no—
56C2×C4×C5D1211yescharacteristic
57C2×Dic5—61no—
58C2×Dic5—61no—
59C2×Dic5—121no—
60#168—121no—
61#123—151no—
62#100—151no—
63#99D1511yescharacteristic
64C2×C3×C5—21no—
65C2×C3×C5—41no—
66C2×C3×C5—41no—
67C2×C3×C5#9911yescharacteristic
68C23×C3C4×D511yescharacteristic
69C23×C3C22⋊D511yescharacteristic
70C3×D4—41no—
71C2×C3×C4—41no—
72C2×C3×C4D2011yescharacteristic
73C2×Dic3—101no—
74C2×Dic3—101no—
75C2×Dic3—201no—
76C3⋊C8—201no—
77C22×C5—21no—
78C22×C5—21no—
79C22×C5—41no—
80C22×C5—41no—
81C22×C5(C2×D3)⋊C411yescharacteristic
82C4×C5—21no—
83C4×C5—81no—
84Dic5—121no—
85Dic5—121no—
86C2×D4C2×D1511yescharacteristic
87C22×C4—151no—
88M16—301no—
89C4⋊C4—301no—
90C22⋊C4—21no—
91C22⋊C4—151no—
92C22⋊C4—301no—
93C3×C5#35211yescharacteristic, complemented, Hall
94C22×C3—21no—
95C22×C3—21no—
96C22×C3—41no—
97C22×C3—41no—
98C22×C3#68511yescharacteristic
99C3×C4—21no—
100C3×C4—81no—
101Dic3—201no—
102Dic3—201no—
103C2×C5—21no—
104C2×C5—41no—
105C2×C5—41no—
106C2×C5#80611yescharacteristic
107C23C4×D1511yescharacteristic
108C23#122011yescharacteristic
109D4—41no—
110C2×C4—41no—
111C2×C4—301no—
112C2×C4—301no—
113C2×C4—601no—
114C2×C4D6011yescharacteristic
115C8—601no—
116C2×C3—21no—
117C2×C3—41no—
118C2×C3—41no—
119C2×C3#393811yescharacteristic
120C5#447211yescharacteristic, complemented, Sylow
121C22—21no—
122C22—21no—
123C22—41no—
124C22—41no—
125C22#671411yescharacteristic
126C4—21no—
127C4—81no—
128C4—601no—
129C4—601no—
130C3#6469211yescharacteristic, complemented, Sylow
131C2—21no—
132C2—41no—
133C2—41no—
134C2#9109011yescharacteristic
subgroupG/H
centerC2#91090
commutatorC23×C3×C5C2×C4
FrattiniC2×D4C2×D15
FittingC3×C5×#99C2
socleC2×C3×C5#99
prime radical, cosocleC2×C3×C5×D4C22
hypercenter#99D15
hypocenterC3×C5#352
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
6. C22×Dic15C4semidirect
9. #6719C4semidirect
93. C3×C5#352semidirect
120. C5#4472semidirect
130. C3#64692semidirect

Maximal subgroups

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

subgroupindex
#918242
C3×C5×#992
#911172
#646923
#44725