Finite Group Databasebeta

← #13086805

Subgroups — #13086805

Order 1440.

336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C4×C3⋊Dic15C211yesmaximal, characteristic
2C5×#3750C211yesmaximal, characteristic
3C32×#683C211yesmaximal, characteristic
4#10623775C211yesmaximal, characteristic
5#10623774C211yesmaximal, characteristic
6#10623774C211yesmaximal, characteristic
7#10623773C211yesmaximal, characteristic
8#91382—34nomaximal
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3⋊Dic15C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C32×Dic5C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16#64098—51nomaximal, Hall
17C4×Dic15—34no—
18C5×Dic3⋊C4—34no—
19C3×#683D314yes—
20Dic3⋊Dic5—34no—
21#6669—34no—
22#6669—34no—
23#6668—34no—
24C22×C32×C5C2311yescharacteristic
25C32×C4×C5—21no—
26C3⋊Dic15—21no—
27C3⋊Dic15Q812yes—
28C5×C3⋊Dic3—21no—
29C5×C3⋊Dic3—21no—
30C32×Dic5—21no—
31C32×Dic5—21no—
32#4035—91noHall
33C32×C4⋊C4—51no—
34C4⋊(C3⋊Dic3)—51no—
35#3750—51no—
36#3750—51no—
37#3750—51no—
38#3750D511yescharacteristic
39C4×C3⋊Dic3—51no—
40C2×C3×C4×C5C2×D314yes—
41C2×Dic15—34no—
42C2×Dic15—34no—
43C2×C5×Dic3—34no—
44C2×C5×Dic3—34no—
45C2×C3×Dic5C2×D314yes—
46C2×C3×Dic5C2×D314yes—
47#889—154no—
48C2×C32×C5C2×Q811yescharacteristic
49C2×C32×C5#4111yescharacteristic
50C2×C32×C5#4111yescharacteristic
51C5×C4⋊C4—91no—
52C4⋊Dic5—91no—
53#683—91no—
54#683—91no—
55#683—91no—
56#683C3⋊D311yescharacteristic
57C4×Dic5—91no—
58C2×C32×C4—51no—
59C2×C32×C4—51no—
60C2×C32×C4C2×D511yescharacteristic
61C2×C3⋊Dic3—51no—
62C2×C3⋊Dic3—51no—
63C2×C3⋊Dic3C2×D511yescharacteristic
64C2×C3⋊Dic3C2×D511yescharacteristic
65C22×C3×C5C22×D314yes—
66C3×C4×C5—24no—
67Dic15—38no—
68Dic15—64no—
69C3×Dic5—24no—
70C3×Dic5—24no—
71C5×Dic3—64no—
72C5×Dic3—64no—
73C3×C4⋊C4—54no—
74C4⋊Dic3—154no—
75Dic3⋊C4—34no—
76Dic3⋊C4—154no—
77Dic3⋊C4—154no—
78Dic3⋊C4—154no—
79C4×Dic3—154no—
80C32×C5#12511yescharacteristic, complemented, Hall
81C2×C4×C5—91no—
82C2×C4×C5—91no—
83C2×C4×C5C2×C3⋊D311yescharacteristic
84C2×Dic5—91no—
85C2×Dic5—91no—
86C2×Dic5C2×C3⋊D311yescharacteristic
87C2×Dic5C2×C3⋊D311yescharacteristic
88C22×C32C22×D511yescharacteristic
89C32×C4—21no—
90C32×C4—101no—
91C32×C4—101no—
92C3⋊Dic3—21no—
93C3⋊Dic3—21no—
94C3⋊Dic3—52no—
95C3⋊Dic3—101no—
96#125—451noSylow
97C2×C3×C5#23514yes—
98C2×C3×C5#23714yes—
99C2×C3×C5D3×Q814yes—
100C2×C3×C4—54no—
101C2×C3×C4—54no—
102C2×C3×C4D3×D514yes—
103C2×Dic3—34no—
104C2×Dic3—34no—
105C2×Dic3—154no—
106C2×Dic3—154no—
107C22×C5C22×C3⋊D311yescharacteristic
108C4×C5—21no—
109C4×C5—181no—
110C4×C5—181no—
111Dic5—21no—
112Dic5—21no—
113Dic5—92no—
114Dic5—181no—
115C2×C32#70911yescharacteristic
116C2×C32#71111yescharacteristic
117C2×C32Q8×D511yescharacteristic
118C4⋊C4—51no—
119C4⋊C4—91no—
120C4⋊C4—451no—
121C4⋊C4—451no—
122C4⋊C4—451no—
123C4⋊C4—451no—
124C42—451no—
125C3×C5#88914yescomplemented
126C22×C3C2×D3×D514yes—
127C3×C4—24no—
128C3×C4—104no—
129C3×C4—104no—
130Dic3—64no—
131Dic3—64no—
132Dic3—158no—
133Dic3—304no—
134C2×C5#382811yescharacteristic
135C2×C5#383011yescharacteristic
136C2×C5Q8×C3⋊D311yescharacteristic
137C32#403511yescharacteristic, complemented, Sylow
138C2×C4—51no—
139C2×C4—51no—
140C2×C4—91no—
141C2×C4—91no—
142C2×C4—451no—
143C2×C4—451no—
144C2×C4D5×C3⋊D311yescharacteristic
145C2×C3D15⋊Q814yes—
146C2×C3#677114yes—
147C2×C3#678014yes—
148C5#6409811yescharacteristic, complemented, Sylow
149C22C2×D5×C3⋊D311yescharacteristic
150C4—21no—
151C4—101no—
152C4—101no—
153C4—181no—
154C4—181no—
155C4—452no—
156C4—901no—
157C3#9138214yescomplemented
158C2#1062415311yescharacteristic
159C2#1062415411yescharacteristic
160C2#1062416311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, prime radical, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#125
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
80. C32×C5#125semidirect
125. C3×C5#889semidirect
137. C32#4035semidirect
148. C5#64098semidirect
157. C3#91382semidirect

Maximal subgroups

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

subgroupindex
C4×C3⋊Dic152
C5×#37502
C32×#6832
#106237752
#106237742
#106237732
#913823
#640985