Finite Group Databasebeta

← #13086134

Subgroups — #13086134

Order 1440.

342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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×#67157C211yesmaximal, characteristic
2C2×#67141C211yesmaximal, characteristic, complemented
3#10623811C212yesmaximal, complemented
4C5×Dic32C211yesmaximal, characteristic, complemented
5C3×#6667C212yesmaximal, complemented
6#91353—32nomaximal
7C22×C3×D15C2212yes—
8C2×C3⋊Dic15C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12#67157—22no—
13#67141—22no—
14#63913—51nomaximal, Hall
15C2×#1204—32no—
16C2×#1204—61no—
17C2×#1202—32no—
18#6714—32no—
19C4×C5×Dic3—32no—
20C3×#685—32no—
21#6667D312yescomplemented
22#6665—32no—
23C22×C32×C5C2311yescharacteristic
24C2×C3×D15—22no—
25C2×C3×D15—22no—
26C2×C3×D15—22no—
27C3⋊Dic15—21no—
28C5×C3⋊Dic3D412yes—
29C3×C5×Dic3—22no—
30C32×Dic5—21no—
31#4021—91noHall
32C2×#634—51no—
33C2×#625—51no—
34C3×(C2×D3)⋊C4—52no—
35(C2×D3)⋊Dic3—52no—
36Dic32D511yescharacteristic, complemented
37C22×D15C2×D312yes—
38C22×C3×D5—32no—
39C2×C3×C4×C5—32no—
40C2×Dic15—32no—
41C2×Dic15—61no—
42C2×C5×Dic3—32no—
43C2×C5×Dic3—61no—
44C2×C5×Dic3C2×D312yes—
45C2×C3×Dic5—21no—
46C2×C3×Dic5C2×D312yes—
47#1204—64no—
48#1204—64no—
49#1202—64no—
50#885—152no—
51C2×C32×C5C2×D411yescharacteristic
52C2×C32×C5#4112yes—
53C3×D15—42no—
54C2×D20—91no—
55C2×Dic10—91no—
56C42×C5—91no—
57#685—32no—
58#685—92no—
59C22×C3×D3—52no—
60C2×C32×C4—51no—
61C2×C3⋊Dic3—51no—
62C2×C3⋊Dic3C2×D511yescharacteristic
63#634—102no—
64C2×C3×Dic3C2×D512yes—
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—62no—
75Dic15—62no—
76Dic15—62no—
77C3×Dic5—22no—
78C3×Dic5—22no—
79C5×Dic3—22no—
80C5×Dic3—34no—
81C5×Dic3—62no—
82C2×#67—152no—
83C2×Dic6—152no—
84C2×Dic6—301no—
85C3×C22⋊C4—152no—
86#217—152no—
87(C2×D3)⋊C4—52no—
88(C2×D3)⋊C4—152no—
89C4×Dic3—32no—
90C32×C5#12411yescharacteristic, complemented, Hall
91C22×D5—32no—
92C2×C4×C5—32no—
93C2×C4×C5—91no—
94C2×Dic5—91no—
95C2×Dic5D3211yescharacteristic
96D20—182no—
97Dic10—182no—
98C22×C32C22×D511yescharacteristic
99C2×C3×D3—102no—
100C2×C3×D3—102no—
101C2×C3×D3—102no—
102C32×C4—101no—
103C3⋊Dic3—101no—
104C3⋊Dic3D2012yes—
105C3×Dic3—22no—
106#124—451noSylow
107C2×C3×C5—22no—
108C2×C3×C5—21no—
109C2×C3×C5#23512yes—
110C2×C3×C5D3×D412yes—
111C2×C3×C5#23712yes—
112D15—42no—
113C3×D5—122no—
114C23×C3—152no—
115C22×D3—52no—
116C2×C3×C4—32no—
117C2×C3×C4—52no—
118C2×C3×C4—101no—
119#67—304no—
120C2×Dic3—32no—
121C2×Dic3—61no—
122C2×Dic3—152no—
123C2×Dic3—301no—
124C2×Dic3D3×D512yes—
125Dic6—304no—
126Dic6—304no—
127C22×C5C2×D3211yescharacteristic
128C2×D5—62no—
129C2×D5—62no—
130C2×D5—62no—
131C4×C5—62no—
132C4×C5—92no—
133Dic5—21no—
134Dic5—181no—
135C2×C32C2×D2011yescharacteristic
136C2×C32#70912yes—
137C3×D3—202no—
138C2×Q8—451no—
139C2×D4—451no—
140C22⋊C4—152no—
141C22⋊C4—452no—
142C42—91no—
143C3×C5—21no—
144C3×C5#88512yescomplemented
145C22×C3—21no—
146C22×C3—302no—
147C22×C3—302no—
148C22×C3—302no—
149C22×C3C2×D3×D512yes—
150C2×D3—102no—
151C2×D3—102no—
152C2×D3—102no—
153C3×C4—62no—
154C3×C4—102no—
155C3×C4—102no—
156Dic3—22no—
157Dic3—34no—
158Dic3—62no—
159Dic3—302no—
160Dic3—302no—
161C2×C5#379512yes—
162C2×C5#381111yescharacteristic
163D5—122no—
164C32#402111yescharacteristic, complemented, Sylow
165C23—152no—
166Q8—902no—
167D4—902no—
168C2×C4—32no—
169C2×C4—51no—
170C2×C4—91no—
171C2×C4—451no—
172C2×C3—21no—
173C2×C3—22no—
174C2×C3—602no—
175C2×C3#677112yes—
176C2×C3D3×D2012yes—
177C2×C3#677912yes—
178D3—202no—
179C5#6391311yescharacteristic, complemented, Sylow
180C22—302no—
181C22—302no—
182C22—302no—
183C22D32×D511yescharacteristic
184C4—62no—
185C4—92no—
186C4—101no—
187C4—901no—
188C3—21no—
189C3#9135312yescomplemented
190C2—602no—
191C2#1062403111yescharacteristic
192C2#1062405312yes—
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67157C2
hypocenterC32×C5#124
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×#67141C2semidirect
3. #10623811C2semidirect
4. C5×Dic32C2semidirect
5. C3×#6667C2semidirect
21. #6667D3semidirect
36. Dic32D5semidirect
90. C32×C5#124semidirect
144. C3×C5#885semidirect
164. C32#4021semidirect
179. C5#63913semidirect
189. C3#91353semidirect

Maximal subgroups

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

subgroupindex
C2×#671572
C2×#671412
#106238112
C5×Dic322
C3×#66672
#913533
#639135