Finite Group Databasebeta

← #13086860

Subgroups — #13086860

Order 1440.

456 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 126 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×D5×C3⋊Dic3C211yesmaximal, characteristic
2C4×C3⋊Dic15C211yesmaximal, characteristic, complemented
3C5×#3750C211yesmaximal, characteristic, complemented
4C32×#685C211yesmaximal, characteristic
5#10623775C211yesmaximal, characteristic, complemented
6#10623770C211yesmaximal, characteristic
7Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#91394—34nomaximal
9C22×C32×D5C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16D5×C3⋊Dic3C414yescomplemented
17#64086—51nomaximal, Hall
18C2×D5×Dic3—34no—
19C4×Dic15—34no—
20C5×Dic3⋊C4—34no—
21C3×#685D314yes—
22Dic3⋊Dic5—34no—
23#6665—34no—
24Dic3×Dic5—34no—
25C22×C32×C5C2311yescharacteristic
26C2×C32×D5—21no—
27C2×C32×D5—21no—
28C2×C32×D5C2×C412yes—
29C32×C4×C5—21no—
30C3⋊Dic15—21no—
31C3⋊Dic15C2×C412yes—
32C5×C3⋊Dic3—21no—
33C5×C3⋊Dic3C2×C412yes—
34C32×Dic5—21no—
35#4038—91noHall
36C22×C3⋊Dic3—51no—
37C32×C22⋊C4—51no—
38#3757—51no—
39#3750—51no—
40#3750D511yescharacteristic, complemented
41C4×C3⋊Dic3—51no—
42C4×C3⋊Dic3—51no—
43C22×C3×D5C2×D314yes—
44C2×C3×C4×C5C2×D314yes—
45C2×Dic15—34no—
46C2×Dic15—34no—
47C2×C5×Dic3—34no—
48C2×C5×Dic3—34no—
49C2×C3×Dic5C2×D314yes—
50D5×Dic3—316no—
51#877—154no—
52C2×C32×C5C22×C411yescharacteristic
53C2×C32×C5#4111yescharacteristic
54C2×C32×C5#4111yescharacteristic
55C32×D5—22no—
56C2×C4×D5—91no—
57C5×C4⋊C4—91no—
58#685—91no—
59#685C3⋊D311yescharacteristic
60C4⋊Dic5—91no—
61C4×Dic5—91no—
62C4×Dic5—91no—
63C23×C32—51no—
64C2×C32×C4—51no—
65C2×C32×C4C2×D511yescharacteristic
66C2×C3⋊Dic3—51no—
67C2×C3⋊Dic3—54no—
68C2×C3⋊Dic3—51no—
69C2×C3⋊Dic3C2×D511yescharacteristic
70C2×C3⋊Dic3C2×D511yescharacteristic
71C22×C3×C5C22×D314yes—
72C2×C3×D5—24no—
73C2×C3×D5—24no—
74C2×C3×D5C4×D318yes—
75C3×C4×C5—24no—
76Dic15—38no—
77Dic15—64no—
78C3×Dic5—24no—
79C5×Dic3—38no—
80C5×Dic3—64no—
81C22×Dic3—154no—
82C3×C22⋊C4—54no—
83#217—154no—
84Dic3⋊C4—34no—
85Dic3⋊C4—154no—
86C4×Dic3—154no—
87C4×Dic3—154no—
88C32×C5#11711yescharacteristic, complemented, Hall
89C22×D5C2×C3⋊D311yescharacteristic
90C2×C4×C5—91no—
91C2×C4×C5—91no—
92C2×C4×C5C2×C3⋊D311yescharacteristic
93C2×Dic5—91no—
94C2×Dic5—91no—
95C2×Dic5C2×C3⋊D311yescharacteristic
96C4×D5—94no—
97C22×C32—52no—
98C22×C32—101no—
99C22×C32—101no—
100C22×C32C22×D511yescharacteristic
101C32×C4—21no—
102C32×C4—101no—
103C3⋊Dic3—21no—
104C3⋊Dic3—52no—
105C3⋊Dic3—101no—
106C3⋊Dic3C4×D512yes—
107#117—451noSylow
108C2×C3×C5C2×C4×D314yes—
109C2×C3×C5#23714yes—
110C2×C3×C5#23714yes—
111C3×D5—28no—
112C23×C3—54no—
113C2×C3×C4—54no—
114C2×C3×C4D3×D514yes—
115C2×Dic3—34no—
116C2×Dic3—34no—
117C2×Dic3—1516no—
118C2×Dic3—154no—
119C2×Dic3—154no—
120C22×C5C22×C3⋊D311yescharacteristic
121C2×D5—21no—
122C2×D5—21no—
123C2×D5C4×C3⋊D312yes—
124C4×C5—21no—
125C4×C5—92no—
126C4×C5—181no—
127Dic5—21no—
128Dic5—92no—
129Dic5—181no—
130C2×C32—102no—
131C2×C32C2×C4×D511yescharacteristic
132C2×C32#71111yescharacteristic
133C2×C32#71311yescharacteristic
134C22×C4—451no—
135C4⋊C4—91no—
136C4⋊C4—451no—
137C22⋊C4—51no—
138C22⋊C4—451no—
139C42—451no—
140C42—451no—
141C3×C5#87714yescomplemented
142C22×C3—58no—
143C22×C3—104no—
144C22×C3—104no—
145C22×C3C2×D3×D514yes—
146C3×C4—24no—
147C3×C4—104no—
148Dic3—38no—
149Dic3—64no—
150Dic3—158no—
151Dic3—304no—
152C2×C5C2×C4×C3⋊D311yescharacteristic
153C2×C5#383011yescharacteristic
154C2×C5#383011yescharacteristic
155D5—22no—
156C32#403811yescharacteristic, complemented, Sylow
157C23—51no—
158C2×C4—51no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—454no—
162C2×C4—451no—
163C2×C4—451no—
164C2×C4D5×C3⋊D311yescharacteristic
165C2×C3—108no—
166C2×C3#676614yes—
167C2×C3C4×D3×D514yes—
168C2×C3#678014yes—
169C5#6408611yescharacteristic, complemented, Sylow
170C22—52no—
171C22—101no—
172C22—101no—
173C22C2×D5×C3⋊D311yescharacteristic
174C4—21no—
175C4—92no—
176C4—101no—
177C4—181no—
178C4—452no—
179C4—901no—
180C3#9139414yescomplemented
181C2—102no—
182C2#1062414911yescharacteristic
183C2C4×D5×C3⋊D311yescharacteristic
184C2#1062416311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C32×D5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊Dic15C2semidirect
3. C5×#3750C2semidirect
5. #10623775C2semidirect
7. Dic5×C3⋊Dic3C2semidirect
16. D5×C3⋊Dic3C4semidirect
40. #3750D5semidirect
88. C32×C5#117semidirect
141. C3×C5#877semidirect
156. C32#4038semidirect
169. C5#64086semidirect
180. C3#91394semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C3⋊Dic32
C4×C3⋊Dic152
C5×#37502
C32×#6852
#106237752
#106237702
Dic5×C3⋊Dic32
#913943
#640865