Finite Group Databasebeta

← #14514567

Subgroups — #14514567

Order 1920.

552 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 21 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
1C3×C4×C24⋊C5C211yesmaximal, characteristic
2C3⋊#66245C212yesmaximal
3(C24⋊C5)⋊Q8—31nomaximal, Hall
4C2×C3×C24⋊C5C2211yescharacteristic
5#84031—51nomaximal, Hall
6C4×C24⋊C5D311yescharacteristic
7#66245—32no—
8C3×C24⋊C5Q811yescharacteristic, complemented
9C24×C3×C4D511yescharacteristic
10C2×#924—53no—
11#5247—52no—
12#5212—53no—
13#5210—56no—
14C2×C24⋊C5C2×D311yescharacteristic
15#2848—151noSylow
16Dic30—161nomaximal
17C25×C3C2×D511yescharacteristic
18C23×C3×C4—53no—
19C23×C3×C4—53no—
20C22×Dic6—51no—
21C2×#217—56no—
22C2×#217—56no—
23C2×C4⋊Dic3—53no—
24#924—106no—
25#924—106no—
26C2×Dic3⋊C4—56no—
27C3⋊#95—56no—
28C24⋊C5Dic611yescharacteristic, complemented
29C24×C4D1511yescharacteristic
30C2×C22⋊Q8—153no—
31#385—156no—
32#380—153no—
33#379—152no—
34C3×C4×C5—161no—
35Dic15—162no—
36C24×C3—53no—
37C24×C3—53no—
38C24×C3Dic1011yescharacteristic, complemented
39C22×C3×C4—51no—
40C22×C3×C4—56no—
41C22×C3×C4—56no—
42C22×C3×C4—53no—
43C22×C3×C4—106no—
44C22×Dic3—56no—
45C22×Dic3—52no—
46C2×Dic6—103no—
47C2×Dic6—103no—
48#217—1012no—
49#217—1012no—
50C4⋊Dic3—103no—
51C4⋊Dic3—103no—
52Dic3⋊C4—1012no—
53Dic10—481no—
54C25C2×D1511yescharacteristic
55C22×Q8—151no—
56C23×C4—53no—
57C23×C4—53no—
58C22⋊Q8—306no—
59C22⋊Q8—306no—
60C2×C4⋊C4—153no—
61C2×C4⋊C4—156no—
62C2×C22⋊C4—156no—
63C2×C22⋊C4—156no—
64#95—156no—
65C2×C3×C5—161no—
66C23×C3—53no—
67C23×C3—51no—
68C23×C3—56no—
69C23×C3—56no—
70C23×C3—53no—
71C23×C3—106no—
72C2×C3×C4—53no—
73C2×C3×C4—53no—
74C2×C3×C4—56no—
75C2×C3×C4—106no—
76C2×Dic3—106no—
77C2×Dic3—106no—
78C2×Dic3—1012no—
79Dic6—203no—
80Dic6—201no—
81C4×C5—161no—
82Dic5—482no—
83C24—53no—
84C24—53no—
85C24Dic3011yescharacteristic, complemented
86C2×Q8—303no—
87C2×Q8—303no—
88C22×C4—51no—
89C22×C4—56no—
90C22×C4—56no—
91C22×C4—53no—
92C22×C4—106no—
93C22×C4—156no—
94C22×C4—152no—
95C4⋊C4—3012no—
96C4⋊C4—303no—
97C4⋊C4—303no—
98C22⋊C4—3012no—
99C22⋊C4—3012no—
100C3×C5—161noHall
101C22×C3—56no—
102C22×C3—56no—
103C22×C3—53no—
104C22×C3—51no—
105C22×C3—53no—
106C22×C3—106no—
107C3×C4—53no—
108C3×C4(C24⋊C5)⋊C211yescharacteristic
109Dic3—206no—
110Dic3—202no—
111C2×C5—161no—
112C23—53no—
113C23—51no—
114C23—56no—
115C23—56no—
116C23—53no—
117C23—106no—
118Q8—603no—
119Q8—601no—
120C2×C4—53no—
121C2×C4—53no—
122C2×C4—56no—
123C2×C4—106no—
124C2×C4—306no—
125C2×C4—306no—
126C2×C4—3012no—
127C2×C3—53no—
128C2×C3—53no—
129C2×C3C2×(C24⋊C5)⋊C211yescharacteristic
130C5—161noSylow
131C22—56no—
132C22—56no—
133C22—53no—
134C22—51no—
135C22—53no—
136C22—106no—
137C4—53no—
138C4—606no—
139C4—602no—
140C4C3⋊((C24⋊C5)⋊C2)11yescharacteristic
141C3(C24⋊C5)⋊Q811yescharacteristic, complemented, Sylow
142C2—53no—
143C2—53no—
144C2C2×C3⋊((C24⋊C5)⋊C2)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×C3⋊((C24⋊C5)⋊C2)
commutator, prime radical, cosocleC2×C3×C24⋊C5C22
FittingC24×C3×C4D5
socleC25×C3C2×D5
hypercenterC4C3⋊((C24⋊C5)⋊C2)
hypocenterC3×C24⋊C5Q8
LCSG ▷ C2×C3×C24⋊C5 ▷ C3×C24⋊C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
8. C3×C24⋊C5Q8semidirect
28. C24⋊C5Dic6semidirect
38. C24×C3Dic10semidirect
85. C24Dic30semidirect
141. C3(C24⋊C5)⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C24⋊C52
C3⋊#662452
(C24⋊C5)⋊Q83
#840315
Dic3016