Finite Group Databasebeta

← D5×#3750 #13086858

Subgroups — D5×#3750 #13086858

Order 1440.

552 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 174 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×C32×C4×D5C211yesmaximal, characteristic
2C2×D5×C3⋊Dic3C211yesmaximal, characteristic
3C2×D5×C3⋊Dic3C211yesmaximal, characteristic
4#10623906C211yesmaximal, characteristic, complemented
5C5×#3750C211yesmaximal, characteristic, complemented
6#10623775C211yesmaximal, characteristic, complemented
7#10623774C211yesmaximal, characteristic, complemented
8D5×Dic3⋊C4—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
16C32×C4×D5—22no—
17D5×C3⋊Dic3—22no—
18D5×C3⋊Dic3C414yescomplemented
19C2×#3750—51nomaximal, Hall
20C2×C3×C4×D5D314yes—
21C2×D5×Dic3—34no—
22C2×D5×Dic3—34no—
23#6712—34no—
24C5×Dic3⋊C4—34no—
25Dic3⋊Dic5—34no—
26#6669—34no—
27C22×C32×C5C2311yescharacteristic
28C2×C32×D5C2×C412yes—
29C2×C32×D5D412yes—
30C2×C32×D5Q812yes—
31C32×C4×C5—21no—
32C3⋊Dic15—21no—
33C3⋊Dic15C2×C412yescomplemented
34C5×C3⋊Dic3—21no—
35C5×C3⋊Dic3C2×C412yescomplemented
36C32×Dic5—21no—
37D5×C4⋊C4—91noHall
38C22×C32×C4—51no—
39C22×C3⋊Dic3—51no—
40C22×C3⋊Dic3—51no—
41#3750—51no—
42#3750—51no—
43#3750—51no—
44#3750D511yescharacteristic, direct product factor
45C22×C3×D5C2×D314yes—
46C2×C3×C4×C5C2×D314yes—
47C2×Dic15—34no—
48C2×Dic15—34no—
49C2×C5×Dic3—34no—
50C2×C5×Dic3—34no—
51C2×C3×Dic5C2×D314yes—
52C3×C4×D5—28no—
53D5×Dic3—316no—
54D5×Dic3—68no—
55C2×Dic3⋊C4—154no—
56C2×C32×C5C22×C411yescharacteristic
57C2×C32×C5C2×D411yescharacteristic
58C2×C32×C5C2×Q811yescharacteristic
59C32×D5C4⋊C414yescomplemented
60C2×C4×D5—91no—
61C2×C4×D5—91no—
62C2×C4×D5C3⋊D311yescharacteristic
63C5×C4⋊C4—91no—
64C4⋊Dic5—91no—
65#683—91no—
66#683—91no—
67C23×C32—51no—
68C2×C32×C4—51no—
69C2×C32×C4—102no—
70C2×C32×C4C2×D511yescharacteristic
71C2×C3⋊Dic3—51no—
72C2×C3⋊Dic3—54no—
73C2×C3⋊Dic3—51no—
74C2×C3⋊Dic3—102no—
75C2×C3⋊Dic3C2×D511yescharacteristic
76C2×C3⋊Dic3C2×D511yescharacteristic
77C22×C3×C5C22×D314yes—
78C2×C3×D5Dic618yes—
79C2×C3×D5C4×D318yes—
80C2×C3×D5#6718yes—
81C3×C4×C5—24no—
82Dic15—38no—
83Dic15—64no—
84C3×Dic5—24no—
85C5×Dic3—38no—
86C5×Dic3—64no—
87C22×C3×C4—54no—
88C22×Dic3—154no—
89C22×Dic3—154no—
90Dic3⋊C4—34no—
91Dic3⋊C4—154no—
92Dic3⋊C4—154no—
93Dic3⋊C4—154no—
94C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
95C22×D5C2×C3⋊D311yescharacteristic
96C2×C4×C5—91no—
97C2×C4×C5—91no—
98C2×C4×C5C2×C3⋊D311yescharacteristic
99C2×Dic5—91no—
100C2×Dic5—91no—
101C2×Dic5C2×C3⋊D311yescharacteristic
102C4×D5—22no—
103C4×D5—94no—
104C4×D5—182no—
105C22×C32—52no—
106C22×C32—52no—
107C22×C32—52no—
108C22×C32C22×D511yescharacteristic
109C32×C4—21no—
110C32×C4—101no—
111C3⋊Dic3—21no—
112C3⋊Dic3—52no—
113C3⋊Dic3—101no—
114C3⋊Dic3C4×D512yescomplemented
115C2×C4⋊C4—451noSylow
116C2×C3×C5C2×Dic614yes—
117C2×C3×C5C2×C4×D314yes—
118C2×C3×C5C2×#6714yes—
119C3×D5Dic3⋊C4116yescomplemented
120C23×C3—54no—
121C2×C3×C4—54no—
122C2×C3×C4—108no—
123C2×C3×C4D3×D514yes—
124C2×Dic3—34no—
125C2×Dic3—34no—
126C2×Dic3—1516no—
127C2×Dic3—154no—
128C2×Dic3—154no—
129C2×Dic3—308no—
130C22×C5C22×C3⋊D311yescharacteristic
131C2×D5#63412yes—
132C2×D5C4×C3⋊D312yes—
133C2×D5#63812yes—
134C4×C5—21no—
135C4×C5—92no—
136C4×C5—181no—
137Dic5—21no—
138Dic5—92no—
139Dic5—181no—
140C2×C32—54no—
141C2×C32C2×C4×D511yescharacteristic
142C2×C32D4×D511yescharacteristic
143C2×C32Q8×D511yescharacteristic
144C22×C4—51no—
145C22×C4—451no—
146C22×C4—451no—
147C4⋊C4—91no—
148C4⋊C4—451no—
149C4⋊C4—451no—
150C4⋊C4—451no—
151C3×C5C2×Dic3⋊C414yescomplemented
152C22×C3—58no—
153C22×C3—58no—
154C22×C3—58no—
155C22×C3C2×D3×D514yes—
156C3×C4—24no—
157C3×C4—104no—
158Dic3—38no—
159Dic3—64no—
160Dic3—158no—
161Dic3—304no—
162C2×C5C2×#63411yescharacteristic
163C2×C5C2×C4×C3⋊D311yescharacteristic
164C2×C5C2×#63811yescharacteristic
165D5#375014yesdirect product factor
166C32D5×C4⋊C411yescharacteristic, complemented, Sylow
167C23—51no—
168C2×C4—51no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—102no—
172C2×C4—454no—
173C2×C4—451no—
174C2×C4—451no—
175C2×C4—902no—
176C2×C4D5×C3⋊D311yescharacteristic
177C2×C3—516no—
178C2×C3D5×Dic614yes—
179C2×C3C4×D3×D514yes—
180C2×C3D5×#6714yes—
181C5C2×#375011yescharacteristic, complemented, Sylow
182C22—52no—
183C22—52no—
184C22—52no—
185C22C2×D5×C3⋊D311yescharacteristic
186C4—21no—
187C4—92no—
188C4—101no—
189C4—181no—
190C4—452no—
191C4—901no—
192C3D5×Dic3⋊C414yescomplemented
193C2—54no—
194C2D5×#63411yescharacteristic
195C2C4×D5×C3⋊D311yescharacteristic
196C2D5×#63811yescharacteristic
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×C5C2×C4⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10623906C2semidirect
5. C5×#3750C2semidirect
6. #10623775C2semidirect
7. #10623774C2semidirect
18. D5×C3⋊Dic3C4semidirect
33. C3⋊Dic15C2×C4semidirect
35. C5×C3⋊Dic3C2×C4semidirect
44. #3750D5direct (N × H)
59. C32×D5C4⋊C4semidirect
94. C32×C5C2×C4⋊C4semidirect
114. C3⋊Dic3C4×D5semidirect
119. C3×D5Dic3⋊C4semidirect
151. C3×C5C2×Dic3⋊C4semidirect
165. D5#3750direct (N × H)
166. C32D5×C4⋊C4semidirect
181. C5C2×#3750semidirect
192. C3D5×Dic3⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D52
C2×D5×C3⋊Dic32
#106239062
C5×#37502
#106237752
#106237742
D5×Dic3⋊C43
C2×#37505