Finite Group Databasebeta

← #13085596

Subgroups — #13085596

Order 1440.

148 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C2×C5×#627C211yesmaximal, characteristic
2C2×#67126C211yesmaximal, characteristic
3#10623832C211yesmaximal, characteristic
4C2×C5×C3⋊Dic3C2211yescharacteristic
5C2×C3×Dic15—21no—
6C2×C3×C5×Dic3—21no—
7C5×#627—21no—
8C5×#627C412yescomplemented
9#67126—21no—
10#63740—51nomaximal, Hall
11C2×C5×Dic6—61no—
12Dic3⋊Dic5—61no—
13C22×C32×C5D411yescharacteristic
14C5×C3⋊Dic3C2×C411yescharacteristic
15C5×C3⋊Dic3D411yescharacteristic
16C3×Dic15—41no—
17C3×C5×Dic3—22no—
18#3967—91nomaximal, Hall
19C2×#627D511yescharacteristic
20C2×#622—51no—
21#3724—51no—
22C2×C3×C4×C5—61no—
23C2×Dic15—21no—
24C2×C5×Dic3—21no—
25C2×C5×Dic3—61no—
26C2×C5×Dic3—61no—
27C5×Dic6—62no—
28C5×Dic6—62no—
29C2×C3×Dic5—61no—
30C2×C32×C5C22⋊C411yescharacteristic
31C2×C32×C5SD1611yescharacteristic
32C2×C32×C5Q1611yescharacteristic
33C2×C5×Q8—91no—
34C4⋊Dic5—91no—
35C2×#168—91no—
36C2×C3⋊Dic3C2×D511yescharacteristic
37C2×C3×Dic3—21no—
38C2×C3×Dic3—101no—
39#627—21no—
40#627Dic512yescomplemented
41#622—101no—
42C22×C3×C5—21no—
43C22×C3×C5—21no—
44C3×C4×C5—62no—
45Dic15—41no—
46C3×Dic5—121no—
47C5×Dic3—22no—
48C5×Dic3—61no—
49C5×Dic3—61no—
50C5×Dic3—61no—
51C5×Dic3—61no—
52C2×Dic6—61no—
53Dic3⋊C4—301no—
54C32×C5#10311yescharacteristic, complemented, Hall
55C5×Q8—92no—
56C5×Q8—181no—
57C2×C4×C5—61no—
58C2×C4×C5—91no—
59C2×Dic5—61no—
60#168—181no—
61C22×C32C22⋊D511yescharacteristic
62C3⋊Dic3C2×Dic511yescharacteristic
63C3⋊Dic3C22⋊D511yescharacteristic
64C3×Dic3—22no—
65C3×Dic3—201no—
66#103—451noSylow
67C2×C3×C5—21no—
68C2×C3×C5—21no—
69C2×C3×C5—21no—
70C2×C3×C5—21no—
71C2×C3×C5—21no—
72C2×C3×C5—21no—
73C2×C3×C4—61no—
74C2×C3×C4—301no—
75C2×Dic3—21no—
76C2×Dic3—61no—
77C2×Dic3—61no—
78C2×Dic3—101no—
79Dic6—62no—
80Dic6—62no—
81C22×C5GO+(4,𝔽2)11yescharacteristic
82C4×C5—62no—
83C4×C5—91no—
84C4×C5—91no—
85Dic5—121no—
86C2×C32#68811yescharacteristic
87C2×C32#68911yescharacteristic
88C2×C32C22⋊Dic511yescharacteristic
89C2×Q8—91no—
90C2×C8—451no—
91C4⋊C4—451no—
92C3×C5—21no—
93C3×C5—21no—
94C22×C3—21no—
95C22×C3—21no—
96C3×C4—62no—
97C3×C4—601no—
98Dic3—22no—
99Dic3—61no—
100Dic3—61no—
101Dic3—61no—
102Dic3—61no—
103Dic3—201no—
104C2×C5D32⋊C411yescharacteristic
105C2×C5#377511yescharacteristic
106C2×C5#377611yescharacteristic
107C32#396711yescharacteristic, complemented, Sylow
108Q8—92no—
109Q8—181no—
110C2×C4—61no—
111C2×C4—91no—
112C2×C4—301no—
113C8—901no—
114C2×C3—21no—
115C2×C3—21no—
116C2×C3—21no—
117C2×C3—21no—
118C2×C3—21no—
119C2×C3—21no—
120C5#6374011yescharacteristic, complemented, Sylow
121C22D32⋊D511yescharacteristic
122C4—62no—
123C4—91no—
124C4—91no—
125C4—601no—
126C3—21no—
127C3—21no—
128C2D32⋊Dic511yescharacteristic
129C2#1062400711yescharacteristic
130C2#1062400911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32⋊D5
commutatorC5×C3⋊Dic3C2×C4
Fitting, socle, prime radicalC22×C32×C5D4
cosocleC2×C5×C3⋊Dic3C22
hypocenterC32×C5#103
LCSG ▷ C5×C3⋊Dic3 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
8. C5×#627C4semidirect
40. #627Dic5semidirect
54. C32×C5#103semidirect
107. C32#3967semidirect
120. C5#63740semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6272
C2×#671262
#106238322
#637405
#39679