Finite Group Databasebeta

← #13087712

Subgroups — #13087712

Order 1440.

334 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 75 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×#67158C211yesmaximal, characteristic, complemented
2C2×#67157C211yesmaximal, characteristic
3C4×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#6714C212yesmaximal, complemented
5#10623829C212yesmaximal, complemented
6#91353—32nomaximal
7C22×C3×D15C2212yes—
8C2×C32×C4×C5C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic15C2212yes—
12#67158—22no—
13#67157—22no—
14#63915—51nomaximal, Hall
15C2×#1204—32no—
16C2×#1202—32no—
17#6714D312yescomplemented
18C4×C5×Dic3—32no—
19C4×C5×Dic3—61no—
20C3×#685—32no—
21#6667—32no—
22#6665—32no—
23C22×C32×C5C2311yescharacteristic
24C2×C3×D15—22no—
25C2×C3×D15—22no—
26C2×C3×D15—22no—
27C32×C4×C5—21no—
28C5×C3⋊Dic3—21no—
29C5×C3⋊Dic3D412yes—
30C3×Dic15—22no—
31#4021—91noHall
32C2×#627—51no—
33C2×#625—51no—
34C4×C3⋊Dic3D511yescharacteristic, complemented
35C3×(C2×D3)⋊C4—52no—
36(C2×D3)⋊Dic3—52no—
37C22×D15C2×D312yes—
38C22×C3×D5—32no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5C2×D312yes—
41C2×Dic15C2×D312yes—
42C2×C5×Dic3—32no—
43C2×C5×Dic3—32no—
44C2×C5×Dic3—61no—
45C2×C5×Dic3—61no—
46C2×C3×Dic5—32no—
47#1204—64no—
48#1202—64no—
49#885—152no—
50C2×C32×C5C2×D411yescharacteristic
51C2×C32×C5#4111yescharacteristic
52C2×C32×C5#4111yescharacteristic
53C3×D15—42no—
54C2×D20—91no—
55C2×Dic10—91no—
56C42×C5—91no—
57#685—32no—
58#685—92no—
59C22×C3×D3—52no—
60C2×C32×C4C2×D511yescharacteristic
61C2×C3⋊Dic3C2×D511yescharacteristic
62C2×C3⋊Dic3C2×D511yescharacteristic
63C2×C3×Dic3—52no—
64#627—102no—
65#625—102no—
66C22×C3×C5—21no—
67C22×C3×C5C22×D312yes—
68C2×D15—22no—
69C2×D15—22no—
70C2×D15—22no—
71C2×C3×D5—62no—
72C2×C3×D5—62no—
73C2×C3×D5—62no—
74C3×C4×C5—22no—
75C3×C4×C5—22no—
76Dic15—22no—
77C3×Dic5—62no—
78C5×Dic3—34no—
79C5×Dic3—62no—
80C5×Dic3—62no—
81C5×Dic3—62no—
82C2×#67—152no—
83C2×Dic6—152no—
84C3×C22⋊C4—152no—
85#217—152no—
86(C2×D3)⋊C4—52no—
87(C2×D3)⋊C4—152no—
88C4×Dic3—32no—
89C4×Dic3—61no—
90C32×C5#12411yescharacteristic, complemented, Hall
91C22×D5—32no—
92C2×C4×C5—91no—
93C2×C4×C5—91no—
94C2×C4×C5D3211yescharacteristic
95C2×Dic5—32no—
96D20—182no—
97Dic10—182no—
98C22×C32C22×D511yescharacteristic
99C2×C3×D3—102no—
100C2×C3×D3—102no—
101C2×C3×D3—102no—
102C32×C4—21no—
103C3⋊Dic3—21no—
104C3⋊Dic3D2012yes—
105C3×Dic3—102no—
106#124—451noSylow
107C2×C3×C5—21no—
108C2×C3×C5—21no—
109C2×C3×C5—21no—
110C2×C3×C5#23512yes—
111C2×C3×C5D3×D412yes—
112C2×C3×C5#23712yes—
113D15—42no—
114C3×D5—122no—
115C23×C3—152no—
116C22×D3—52no—
117C2×C3×C4—21no—
118C2×C3×C4—152no—
119C2×C3×C4D3×D512yes—
120#67—304no—
121C2×Dic3—32no—
122C2×Dic3—32no—
123C2×Dic3—52no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126Dic6—304no—
127C22×C5C2×D3211yescharacteristic
128C2×D5—62no—
129C2×D5—62no—
130C2×D5—62no—
131C4×C5—21no—
132C4×C5—92no—
133C4×C5—181no—
134Dic5—62no—
135C2×C32C2×D2011yescharacteristic
136C2×C32#70911yescharacteristic
137C2×C32#70911yescharacteristic
138C3×D3—202no—
139C2×Q8—451no—
140C2×D4—451no—
141C22⋊C4—152no—
142C22⋊C4—452no—
143C42—91no—
144C3×C5—21no—
145C3×C5#88512yescomplemented
146C22×C3—21no—
147C22×C3—302no—
148C22×C3—302no—
149C22×C3—302no—
150C22×C3C2×D3×D512yes—
151C2×D3—102no—
152C2×D3—102no—
153C2×D3—102no—
154C3×C4—22no—
155C3×C4—22no—
156C3×C4—302no—
157Dic3—34no—
158Dic3—62no—
159Dic3—62no—
160Dic3—62no—
161Dic3—102no—
162C2×C5#379811yescharacteristic
163C2×C5#380211yescharacteristic
164C2×C5#380511yescharacteristic
165D5—122no—
166C32#402111yescharacteristic, complemented, Sylow
167C23—152no—
168Q8—902no—
169D4—902no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—152no—
173C2×C4(C3⋊D3)⋊D511yescharacteristic
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—602no—
178C2×C3#677112yes—
179C2×C3D3×D2012yes—
180C2×C3#677912yes—
181D3—202no—
182C5#6391511yescharacteristic, complemented, Sylow
183C22—302no—
184C22—302no—
185C22—302no—
186C22C2×(C3⋊D3)⋊D511yescharacteristic
187C4—21no—
188C4—92no—
189C4—181no—
190C4—302no—
191C3—21no—
192C3#9135312yescomplemented
193C2—602no—
194C2#1062422311yescharacteristic
195C2#1062422711yescharacteristic
196C2#1062422911yescharacteristic
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC2×#67157C2
hypercenterC2×C4(C3⋊D3)⋊D5
hypocenterC32×C5#124
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#67158C2semidirect
3. C4×C5×C3⋊Dic3C2semidirect
4. C3×#6714C2semidirect
5. #10623829C2semidirect
17. #6714D3semidirect
34. C4×C3⋊Dic3D5semidirect
90. C32×C5#124semidirect
145. C3×C5#885semidirect
166. C32#4021semidirect
182. C5#63915semidirect
192. C3#91353semidirect

Maximal subgroups

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

subgroupindex
C2×#671582
C2×#671572
C4×C5×C3⋊Dic32
C3×#67142
#106238292
#913533
#639155