Finite Group Databasebeta

← #13087783

Subgroups — #13087783

Order 1440.

350 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×C5×C3⋊Dic3C211yesmaximal, characteristic
2C2×#67158C211yesmaximal, characteristic, complemented
3C3×#6719C212yesmaximal
4#10623832C211yesmaximal, characteristic, complemented
5#10623831C212yesmaximal, complemented
6#91575—32nomaximal
7C23×C32×C5C2211yescharacteristic
8C2×C5×C3⋊Dic3—22no—
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic15C2212yes—
12C2×C3×Dic15C2212yes—
13#67158—22no—
14#63982—51nomaximal, Hall
15C22×C5×Dic3—32no—
16C22×C5×Dic3—61no—
17C2×#1204—32no—
18#6719D312yes—
19C3×C22⋊Dic5—32no—
20Dic3⋊Dic5—32no—
21#6669—32no—
22#6668—32no—
23C22×C32×C5—21no—
24C22×C32×C5—21no—
25C22×C32×C5Q812yescomplemented
26C22×C32×C5C2311yescharacteristic
27C5×C3⋊Dic3—21no—
28C5×C3⋊Dic3D412yes—
29C3×Dic15—22no—
30C3×Dic15—22no—
31#4070—91noHall
32C22×C3⋊Dic3D511yescharacteristic
33C2×#627—51no—
34C3×#217—52no—
35#3724—51no—
36Dic3⋊Dic3—52no—
37C23×C3×C5—21no—
38C23×C3×C5C2×D312yes—
39C2×Dic15C2×D312yes—
40C2×Dic15C2×D312yes—
41C2×C5×Dic3—32no—
42C2×C5×Dic3—32no—
43C2×C5×Dic3—64no—
44C2×C5×Dic3—61no—
45C2×C5×Dic3—61no—
46C2×C5×Dic3—64no—
47C2×C3×Dic5—32no—
48C2×C3×Dic5—32no—
49#1204—64no—
50#878—152no—
51C2×C32×C5—22no—
52C2×C32×C5C2×D411yescharacteristic
53C2×C32×C5C2×Q811yescharacteristic
54C2×C32×C5#4111yescharacteristic
55C22×C4×C5—91no—
56C2×Dic10—91no—
57C22⋊Dic5—32no—
58C4⋊Dic5—91no—
59#683—92no—
60C23×C32C2×D511yescharacteristic
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3C2×D511yescharacteristic
63C2×C3⋊Dic3C2×D511yescharacteristic
64C2×C3×Dic3—52no—
65C2×C3×Dic3—52no—
66#627—102no—
67C22×C3×C5—22no—
68C22×C3×C5—22no—
69C22×C3×C5—22no—
70C22×C3×C5—22no—
71C22×C3×C5—22no—
72C22×C3×C5—21no—
73C22×C3×C5Dic614yescomplemented
74C22×C3×C5C22×D312yes—
75Dic15—22no—
76Dic15—22no—
77C3×Dic5—62no—
78C3×Dic5—62no—
79C5×Dic3—34no—
80C5×Dic3—62no—
81C5×Dic3—62no—
82C5×Dic3—62no—
83C22×Dic3—32no—
84C22×Dic3—61no—
85C2×Dic6—152no—
86C3×C22⋊C4—152no—
87#217—52no—
88C4⋊Dic3—152no—
89Dic3⋊C4—152no—
90Dic3⋊C4—152no—
91C32×C5C22⋊Q811yescharacteristic, complemented, Hall
92C23×C5D3211yescharacteristic
93C2×C4×C5—91no—
94C2×C4×C5—91no—
95C2×C4×C5—182no—
96C2×Dic5—32no—
97C2×Dic5—32no—
98Dic10—182no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32Dic1012yescomplemented
102C22×C32C22×D511yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3C22⋊D512yes—
105C3×Dic3—102no—
106C3×Dic3—102no—
107C22⋊Q8—451noSylow
108C2×C3×C5—24no—
109C2×C3×C5—24no—
110C2×C3×C5—21no—
111C2×C3×C5—21no—
112C2×C3×C5—21no—
113C2×C3×C5C2×Dic612yes—
114C2×C3×C5D3×D412yes—
115C2×C3×C5#23712yes—
116C23×C3—21no—
117C23×C3D3×D512yes—
118C2×C3×C4—152no—
119C2×C3×C4—152no—
120C2×Dic3—32no—
121C2×Dic3—32no—
122C2×Dic3—52no—
123C2×Dic3—52no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128Dic6—304no—
129C22×C5—21no—
130C22×C5—21no—
131C22×C5#62712yescomplemented
132C22×C5C2×D3211yescharacteristic
133C4×C5—92no—
134C4×C5—181no—
135Dic5—62no—
136Dic5—62no—
137C2×C32—22no—
138C2×C32C2×Dic1011yescharacteristic
139C2×C32#70911yescharacteristic
140C2×C32C2×C22⋊D511yescharacteristic
141C2×Q8—451no—
142C22×C4—91no—
143C4⋊C4—452no—
144C4⋊C4—451no—
145C22⋊C4—152no—
146C3×C5—21no—
147C3×C5#87812yescomplemented
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—21no—
154C22×C3#120414yescomplemented
155C22×C3C2×D3×D512yes—
156C3×C4—302no—
157C3×C4—302no—
158Dic3—34no—
159Dic3—62no—
160Dic3—62no—
161Dic3—62no—
162Dic3—102no—
163Dic3—102no—
164C2×C5—22no—
165C2×C5#380511yescharacteristic
166C2×C5C2×#62711yescharacteristic
167C2×C5#381111yescharacteristic
168C32#407011yescharacteristic, complemented, Sylow
169C23(C3⋊D3)⋊D511yescharacteristic
170Q8—902no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—152no—
174C2×C4—152no—
175C2×C4—182no—
176C2×C3—24no—
177C2×C3—24no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3#677912yes—
182C2×C3C2×#120412yes—
183C2×C3D3×C22⋊D512yes—
184C5#6398211yescharacteristic, complemented, Sylow
185C22—21no—
186C22—21no—
187C22#6715812yescomplemented
188C22C2×(C3⋊D3)⋊D511yescharacteristic
189C4—92no—
190C4—181no—
191C4—302no—
192C4—302no—
193C3—21no—
194C3#9157512yescomplemented
195C2—22no—
196C2#1062422911yescharacteristic
197C2C2×#6715811yescharacteristic
198C2#1062423611yescharacteristic
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutator, socle, cosocleC22×C32×C5C23
Fitting, prime radicalC23×C32×C5C22
hypercenterC23(C3⋊D3)⋊D5
hypocenterC32×C5C22⋊Q8
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#67158C2semidirect
4. #10623832C2semidirect
5. #10623831C2semidirect
25. C22×C32×C5Q8semidirect
73. C22×C3×C5Dic6semidirect
91. C32×C5C22⋊Q8semidirect
101. C22×C32Dic10semidirect
131. C22×C5#627semidirect
147. C3×C5#878semidirect
154. C22×C3#1204semidirect
168. C32#4070semidirect
184. C5#63982semidirect
187. C22#67158semidirect
194. C3#91575semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C3⋊Dic32
C2×#671582
C3×#67192
#106238322
#106238312
#915753
#639825