Finite Group Databasebeta

← #13086811

Subgroups — #13086811

Order 1440.

360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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#10623908C211yesmaximal, characteristic
2C5×#3750C211yesmaximal, characteristic, complemented
3C32×C4×Dic5C211yesmaximal, characteristic, complemented
4#10623775C211yesmaximal, characteristic, complemented
5#10623774C211yesmaximal, characteristic, complemented
6#10623772C211yesmaximal, characteristic
7#10623772C211yesmaximal, characteristic
8#91387—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C32×Dic5C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16#64085—51nomaximal, Hall
17#6714—34no—
18C5×Dic3⋊C4—34no—
19C3×C4×Dic5D314yescomplemented
20Dic3⋊Dic5—34no—
21#6669—34no—
22#6667—34no—
23#6667—34no—
24C22×C32×C5C2311yescharacteristic
25C2×C3⋊D15—21no—
26C2×C3⋊D15—21no—
27C2×C3⋊D15—21no—
28C32×C4×C5—21no—
29C3⋊Dic15—21no—
30C5×C3⋊Dic3—21no—
31C5×C3⋊Dic3—21no—
32C32×Dic5—21no—
33C32×Dic5—21no—
34#4044—91noHall
35C32×C42—51no—
36#3752—51no—
37#3752—51no—
38#3752—51no—
39#3750—51no—
40#3750—51no—
41#3750D511yescharacteristic, complemented
42C22×D15—34no—
43C2×C3×C4×C5C2×D314yes—
44C2×Dic15—34no—
45C2×C5×Dic3—34no—
46C2×C5×Dic3—34no—
47C2×C3×Dic5C2×D314yes—
48C2×C3×Dic5C2×D314yes—
49#876—154no—
50C2×C32×C5#4111yescharacteristic
51C2×C32×C5#4111yescharacteristic
52C2×C32×C5#4111yescharacteristic
53C3⋊D15—41no—
54C5×C4⋊C4—91no—
55#685—91no—
56#685—91no—
57#685—91no—
58C4⋊Dic5—91no—
59#683—91no—
60C4×Dic5C3⋊D311yescharacteristic, complemented
61C22×C3⋊D3—51no—
62C2×C32×C4—51no—
63C2×C32×C4—51no—
64C2×C32×C4C2×D511yescharacteristic
65C2×C3⋊Dic3—51no—
66C2×C3⋊Dic3C2×D511yescharacteristic
67C2×C3⋊Dic3C2×D511yescharacteristic
68C22×C3×C5C22×D314yes—
69C2×D15—64no—
70C2×D15—64no—
71C2×D15—64no—
72C3×C4×C5—24no—
73Dic15—64no—
74C3×Dic5—24no—
75C3×Dic5—24no—
76C5×Dic3—64no—
77C5×Dic3—64no—
78C3×C42—54no—
79(C2×D3)⋊C4—154no—
80(C2×D3)⋊C4—154no—
81(C2×D3)⋊C4—154no—
82Dic3⋊C4—34no—
83Dic3⋊C4—154no—
84Dic3⋊C4—154no—
85C32×C5#12611yescharacteristic, complemented, Hall
86C22×D5—91no—
87C2×C4×C5—91no—
88C2×C4×C5—91no—
89C2×C4×C5C2×C3⋊D311yescharacteristic
90C2×Dic5—91no—
91C2×Dic5C2×C3⋊D311yescharacteristic
92C2×Dic5C2×C3⋊D311yescharacteristic
93C22×C32C22×D511yescharacteristic
94C2×C3⋊D3—101no—
95C2×C3⋊D3—101no—
96C2×C3⋊D3—101no—
97C32×C4—21no—
98C32×C4—101no—
99C32×C4—101no—
100C3⋊Dic3—21no—
101C3⋊Dic3—21no—
102C3⋊Dic3—101no—
103#126—451noSylow
104C2×C3×C5#23514yes—
105C2×C3×C5#23514yes—
106C2×C3×C5#23514yes—
107D15—124no—
108C22×D3—154no—
109C2×C3×C4—54no—
110C2×C3×C4—54no—
111C2×C3×C4D3×D514yes—
112C2×Dic3—34no—
113C2×Dic3—34no—
114C2×Dic3—154no—
115C22×C5C22×C3⋊D311yescharacteristic
116C2×D5—181no—
117C2×D5—181no—
118C2×D5—181no—
119C4×C5—21no—
120C4×C5—181no—
121C4×C5—181no—
122Dic5—21no—
123Dic5—21no—
124Dic5—181no—
125C2×C32#70911yescharacteristic
126C2×C32#71111yescharacteristic
127C2×C32#71311yescharacteristic
128C3⋊D3—201no—
129C4⋊C4—91no—
130C4⋊C4—451no—
131C4⋊C4—451no—
132C22⋊C4—451no—
133C22⋊C4—451no—
134C22⋊C4—451no—
135C42—51no—
136C3×C5#87614yescomplemented
137C22×C3C2×D3×D514yes—
138C2×D3—304no—
139C2×D3—304no—
140C2×D3—304no—
141C3×C4—24no—
142C3×C4—104no—
143C3×C4—104no—
144Dic3—64no—
145Dic3—64no—
146Dic3—304no—
147C2×C5#382811yescharacteristic
148C2×C5#382811yescharacteristic
149C2×C5#382811yescharacteristic
150D5—361no—
151C32#404411yescharacteristic, complemented, Sylow
152C23—451no—
153C2×C4—51no—
154C2×C4—51no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—451no—
158C2×C4D5×C3⋊D311yescharacteristic
159C2×C3#677114yes—
160C2×C3#677314yes—
161C2×C3#678214yes—
162D3—604no—
163C5#6408511yescharacteristic, complemented, Sylow
164C22—901no—
165C22—901no—
166C22—901no—
167C22C2×D5×C3⋊D311yescharacteristic
168C4—21no—
169C4—101no—
170C4—101no—
171C4—181no—
172C4—181no—
173C4—901no—
174C3#9138714yescomplemented
175C2—1801no—
176C2#1062415411yescharacteristic
177C2#1062415611yescharacteristic
178C2#1062416511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC22×C3⋊D15C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#126
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C5×#3750C2semidirect
3. C32×C4×Dic5C2semidirect
4. #10623775C2semidirect
5. #10623774C2semidirect
19. C3×C4×Dic5D3semidirect
41. #3750D5semidirect
60. C4×Dic5C3⋊D3semidirect
85. C32×C5#126semidirect
136. C3×C5#876semidirect
151. C32#4044semidirect
163. C5#64085semidirect
174. C3#91387semidirect

Maximal subgroups

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

subgroupindex
#106239082
C5×#37502
C32×C4×Dic52
#106237752
#106237742
#106237722
#913873
#640855