Finite Group Databasebeta

← #13086935

Subgroups — #13086935

Order 1440.

468 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4×C3⋊D15C211yesmaximal, characteristic, complemented
2C2×#67140C211yesmaximal, characteristic
3C5×#3752C211yesmaximal, characteristic, complemented
4C32×#683C211yesmaximal, characteristic, complemented
5#10623775C211yesmaximal, characteristic, complemented
6#10623772C211yesmaximal, characteristic, complemented
7#10623771C211yesmaximal, characteristic, complemented
8#91355—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C5×C3⋊D3C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C4×C3⋊D15—22no—
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67140—22no—
18#64103—51nomaximal, Hall
19C2×C4×D15—34no—
20C2×#1203—34no—
21C5×(C2×D3)⋊C4—34no—
22C3×#683D314yescomplemented
23Dic3⋊Dic5—34no—
24#6667—34no—
25(C2×D3)⋊Dic5—34no—
26C22×C32×C5C2311yescharacteristic
27C2×C3⋊D15—21no—
28C2×C3⋊D15—21no—
29C2×C3⋊D15D412yes—
30C2×C5×C3⋊D3—21no—
31C2×C5×C3⋊D3—21no—
32C2×C5×C3⋊D3—21no—
33C32×C4×C5—21no—
34C3⋊Dic15—21no—
35C5×C3⋊Dic3—21no—
36C32×Dic5—21no—
37C32×Dic5—21no—
38#4029—91noHall
39C2×C4⋊(C3⋊D3)—51no—
40C2×C4×C3⋊D3—51no—
41C32×C4⋊C4—51no—
42#3752—51no—
43#3752—51no—
44#3752D511yescharacteristic, complemented
45#3750—51no—
46C22×D15—34no—
47C22×C5×D3—34no—
48C2×C3×C4×C5C2×D314yes—
49C2×Dic15—34no—
50C4×D15—68no—
51C2×C5×Dic3—34no—
52C2×C3×Dic5C2×D314yes—
53C2×C3×Dic5C2×D314yes—
54#1203—68no—
55#894—154no—
56C2×C32×C5C2×D411yescharacteristic
57C2×C32×C5#4111yescharacteristic
58C2×C32×C5#4111yescharacteristic
59C3⋊D15—22no—
60C5×C3⋊D3—41no—
61C2×C22⋊D5—91no—
62C2×C4×D5—91no—
63C5×C22⋊C4—91no—
64C22⋊Dic5—91no—
65#685—91no—
66C4⋊Dic5—91no—
67#683C3⋊D311yescharacteristic, complemented
68C22×C3⋊D3—51no—
69C22×C3⋊D3C2×D511yescharacteristic
70C2×C32×C4—51no—
71C2×C32×C4—51no—
72C2×C32×C4C2×D511yescharacteristic
73C2×C3⋊Dic3—51no—
74C2×C3⋊Dic3C2×D511yescharacteristic
75C4⋊(C3⋊D3)—102no—
76C4×C3⋊D3—102no—
77C22×C3×C5C22×D314yes—
78C2×D15—38no—
79C2×D15—64no—
80C2×D15—64no—
81C2×C5×D3—64no—
82C2×C5×D3—64no—
83C2×C5×D3—64no—
84C3×C4×C5—24no—
85Dic15—64no—
86C3×Dic5—24no—
87C3×Dic5—24no—
88C5×Dic3—64no—
89C2×D12—154no—
90C2×C4×D3—154no—
91C3×C4⋊C4—54no—
92(C2×D3)⋊C4—34no—
93(C2×D3)⋊C4—154no—
94(C2×D3)⋊C4—154no—
95Dic3⋊C4—154no—
96C32×C5#12311yescharacteristic, complemented, Hall
97C23×C5—91no—
98C22×D5—91no—
99C2×C4×C5—91no—
100C2×C4×C5C2×C3⋊D311yescharacteristic
101C22⋊D5—182no—
102C2×Dic5—91no—
103C2×Dic5C2×C3⋊D311yescharacteristic
104C2×Dic5C2×C3⋊D311yescharacteristic
105C4×D5—182no—
106C22×C32C22×D511yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—21no—
110C2×C3⋊D3—52no—
111C2×C3⋊D3—101no—
112C2×C3⋊D3—101no—
113C32×C4—21no—
114C32×C4—101no—
115C32×C4—101no—
116C3⋊Dic3—21no—
117C3⋊Dic3—101no—
118#123—451noSylow
119C2×C3×C5#23514yes—
120C2×C3×C5D3×D414yes—
121C2×C3×C5#23914yes—
122D15—68no—
123C5×D3—124no—
124C22×D3—34no—
125C22×D3—154no—
126C2×C3×C4—54no—
127C2×C3×C4—54no—
128C2×C3×C4D3×D514yes—
129C2×Dic3—34no—
130C2×Dic3—154no—
131D12—308no—
132C4×D3—308no—
133C22×C5—181no—
134C22×C5—181no—
135C22×C5—181no—
136C22×C5C22×C3⋊D311yescharacteristic
137C2×D5—92no—
138C2×D5—181no—
139C2×D5—181no—
140C4×C5—21no—
141C4×C5—181no—
142Dic5—21no—
143Dic5—21no—
144Dic5—181no—
145C2×C32#70911yescharacteristic
146C2×C32D4×D511yescharacteristic
147C2×C32#71111yescharacteristic
148C3⋊D3—41no—
149C3⋊D3—102no—
150C2×D4—451no—
151C22×C4—451no—
152C4⋊C4—51no—
153C4⋊C4—451no—
154C22⋊C4—91no—
155C22⋊C4—451no—
156C22⋊C4—451no—
157C3×C5#89414yescomplemented
158C22×C3C2×D3×D514yes—
159C2×D3—64no—
160C2×D3—64no—
161C2×D3—64no—
162C2×D3—158no—
163C2×D3—304no—
164C2×D3—304no—
165C3×C4—24no—
166C3×C4—104no—
167C3×C4—104no—
168Dic3—64no—
169Dic3—304no—
170C2×C5—361no—
171C2×C5#382811yescharacteristic
172C2×C5D4×C3⋊D311yescharacteristic
173C2×C5#383211yescharacteristic
174D5—182no—
175C32#402911yescharacteristic, complemented, Sylow
176C23—91no—
177C23—451no—
178D4—902no—
179C2×C4—51no—
180C2×C4—51no—
181C2×C4—91no—
182C2×C4—451no—
183C2×C4—902no—
184C2×C4D5×C3⋊D311yescharacteristic
185C2×C3#676814yes—
186C2×C3#677114yes—
187C2×C3#679014yes—
188D3—124no—
189D3—308no—
190C5#6410311yescharacteristic, complemented, Sylow
191C22—181no—
192C22—181no—
193C22—181no—
194C22—452no—
195C22—901no—
196C22—901no—
197C22C2×D5×C3⋊D311yescharacteristic
198C4—21no—
199C4—101no—
200C4—101no—
201C4—181no—
202C4—901no—
203C3#9135514yescomplemented
204C2—361no—
205C2—902no—
206C2#1062415111yescharacteristic
207C2#1062415411yescharacteristic
208C2#1062417311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC2×#67140C2
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#123
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×C4×C3⋊D15C2semidirect
3. C5×#3752C2semidirect
4. C32×#683C2semidirect
5. #10623775C2semidirect
6. #10623772C2semidirect
7. #10623771C2semidirect
22. C3×#683D3semidirect
44. #3752D5semidirect
67. #683C3⋊D3semidirect
96. C32×C5#123semidirect
157. C3×C5#894semidirect
175. C32#4029semidirect
190. C5#64103semidirect
203. C3#91355semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D152
C2×#671402
C5×#37522
C32×#6832
#106237752
#106237722
#106237712
#913553
#641035