Finite Group Databasebeta

← C32×#4085 #13087857

Subgroups — C32×#4085 #13087857

Order 1440.

564 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 210 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×C5×D4C211yesmaximal, characteristic, complemented
2C2×C32×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×C32×Dic5C211yesmaximal, characteristic, complemented
5C32×C22⋊Dic5C211yesmaximal, characteristic, complemented
6C32×#685C211yesmaximal, characteristic, complemented
7C32×#683C211yesmaximal, characteristic, complemented
8C3×#4085C314yesmaximal, direct product factor
9C23×C32×C5C2211yescharacteristic
10C23×C32×C5C2211yescharacteristic
11C22×C32×D5C2211yescharacteristic
12C32×C5×D4—22no—
13C2×C32×C4×C5C2211yescharacteristic
14C32×C22⋊D5—22no—
15C32×C22⋊D5—22no—
16C2×C32×Dic5—22no—
17C2×C32×Dic5C2211yescharacteristic
18C2×C32×Dic5C2211yescharacteristic
19C2×C32×Dic5C2211yescharacteristic
20C32×#121—51nomaximal, Hall
21C2×C3×C5×D4C2×C314yescomplemented
22C2×C3×C22⋊D5C2×C314yescomplemented
23C2×C3×C22⋊D5C2×C314yescomplemented
24C22×C3×Dic5C2×C314yescomplemented
25C3×C22⋊Dic5C2×C314yescomplemented
26C3×#685C2×C314yescomplemented
27C3×#683C2×C314yescomplemented
28C22×C32×C5—21no—
29C22×C32×C5—21no—
30C22×C32×C5—21no—
31C22×C32×C5—21no—
32C22×C32×C5—21no—
33C22×C32×C5D412yescomplemented
34C22×C32×C5C2311yescharacteristic
35C2×C32×D5—21no—
36C2×C32×D5—21no—
37C2×C32×D5—21no—
38C32×C4×C5—21no—
39C32×Dic5—21no—
40C32×Dic5—21no—
41C32×Dic5D412yescomplemented
42#4085C3211yescharacteristic, direct product factor, Hall
43C2×C32×D4—51no—
44C2×C32×D4—51no—
45C2×C32×D4D511yescharacteristic, complemented
46C22×C32×C4—51no—
47C32×C4⋊C4—51no—
48C32×C22⋊C4—51no—
49C32×C22⋊C4—51no—
50C23×C3×C5C22×C314yes—
51C23×C3×C5C22×C314yes—
52C22×C3×D5C22×C314yes—
53C3×C5×D4—28no—
54C2×C3×C4×C5C22×C314yes—
55C3×C22⋊D5—28no—
56C3×C22⋊D5—28no—
57C2×C3×Dic5—28no—
58C2×C3×Dic5C22×C314yes—
59C2×C3×Dic5C22×C314yes—
60C2×C3×Dic5C22×C314yes—
61C3×#121—54no—
62C2×C32×C5—22no—
63C2×C32×C5—41no—
64C2×C32×C5C2×D411yescharacteristic
65C2×C32×C5C2×D411yescharacteristic
66C2×C32×C5#4111yescharacteristic
67C32×D5—41no—
68C2×C5×D4C2×C3211yescharacteristic, complemented
69C2×C22⋊D5C2×C3211yescharacteristic, complemented
70C2×C22⋊D5C2×C3211yescharacteristic, complemented
71C22×Dic5C2×C3211yescharacteristic, complemented
72C22⋊Dic5C2×C3211yescharacteristic, complemented
73#685C2×C3211yescharacteristic, complemented
74#683C2×C3211yescharacteristic, complemented
75C23×C32—51no—
76C23×C32C2×D511yescharacteristic
77C23×C32C2×D511yescharacteristic
78C32×D4—22no—
79C32×D4—102no—
80C32×D4—102no—
81C2×C32×C4—51no—
82C2×C32×C4—51no—
83C2×C32×C4—51no—
84C2×C32×C4—102no—
85C2×C32×C4C2×D511yescharacteristic
86C22×C3×C5—24no—
87C22×C3×C5—24no—
88C22×C3×C5—24no—
89C22×C3×C5—24no—
90C22×C3×C5—24no—
91C22×C3×C5C3×D418yescomplemented
92C22×C3×C5C23×C314yes—
93C2×C3×D5—24no—
94C2×C3×D5—24no—
95C2×C3×D5—24no—
96C3×C4×C5—24no—
97C3×Dic5—24no—
98C3×Dic5—24no—
99C3×Dic5C3×D418yescomplemented
100C2×C3×D4—54no—
101C2×C3×D4—54no—
102C2×C3×D4C3×D514yescomplemented
103C22×C3×C4—54no—
104C3×C4⋊C4—54no—
105C3×C22⋊C4—54no—
106C3×C22⋊C4—54no—
107C32×C5#12111yescharacteristic, complemented, Hall
108C23×C5C22×C3211yescharacteristic
109C23×C5C22×C3211yescharacteristic
110C22×D5C22×C3211yescharacteristic
111C5×D4—22no—
112C2×C4×C5C22×C3211yescharacteristic
113C22⋊D5—22no—
114C22⋊D5—22no—
115C2×Dic5—22no—
116C2×Dic5C22×C3211yescharacteristic
117C2×Dic5C22×C3211yescharacteristic
118C2×Dic5C22×C3211yescharacteristic
119C22×C32—21no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—101no—
125C22×C32—101no—
126C22×C32—101no—
127C22×C32C22⋊D512yescomplemented
128C22×C32C22×D511yescharacteristic
129C32×C4—21no—
130C32×C4—52no—
131C32×C4—101no—
132C32×C4—101no—
133#121—51noSylow
134C2×C3×C5—28no—
135C2×C3×C5—44no—
136C2×C3×C5C2×C3×D414yes—
137C2×C3×C5C2×C3×D414yes—
138C2×C3×C5C3×#4114yes—
139C3×D5—44no—
140C23×C3—54no—
141C23×C3C2×C3×D514yes—
142C23×C3C2×C3×D514yes—
143C3×D4—28no—
144C3×D4—108no—
145C3×D4—108no—
146C2×C3×C4—54no—
147C2×C3×C4—54no—
148C2×C3×C4—54no—
149C2×C3×C4—108no—
150C2×C3×C4C2×C3×D514yes—
151C22×C5—21no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5—21no—
156C22×C5C32×D412yescomplemented
157C22×C5C23×C3211yescharacteristic
158C2×D5—21no—
159C2×D5—21no—
160C2×D5—21no—
161C4×C5—21no—
162Dic5—21no—
163Dic5—21no—
164Dic5C32×D412yescomplemented
165C2×C32—22no—
166C2×C32—41no—
167C2×C32—201no—
168C2×C32D4×D511yescharacteristic
169C2×C32#71111yescharacteristic
170C2×C32C2×C22⋊D511yescharacteristic
171C2×D4—51no—
172C2×D4—51no—
173C2×D4C32×D511yescharacteristic, complemented
174C22×C4—51no—
175C4⋊C4—51no—
176C22⋊C4—51no—
177C22⋊C4—51no—
178C3×C5C3×#12114yescomplemented
179C22×C3—24no—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—104no—
185C22×C3—104no—
186C22×C3—104no—
187C22×C3C3×C22⋊D518yescomplemented
188C22×C3C22×C3×D514yes—
189C3×C4—24no—
190C3×C4—58no—
191C3×C4—104no—
192C3×C4—104no—
193C2×C5—22no—
194C2×C5—41no—
195C2×C5C2×C32×D411yescharacteristic
196C2×C5C2×C32×D411yescharacteristic
197C2×C5C32×#4111yescharacteristic
198D5—41no—
199C32#408511yescharacteristic, direct product factor, Sylow
200C23—51no—
201C23C2×C32×D511yescharacteristic
202C23C2×C32×D511yescharacteristic
203D4—22no—
204D4—102no—
205D4—102no—
206C2×C4—51no—
207C2×C4—51no—
208C2×C4—51no—
209C2×C4—102no—
210C2×C4C2×C32×D511yescharacteristic
211C2×C3—28no—
212C2×C3—44no—
213C2×C3—204no—
214C2×C3C3×D4×D514yes—
215C2×C3C3×#71114yes—
216C2×C3C2×C3×C22⋊D514yes—
217C5C32×#12111yescharacteristic, complemented, Sylow
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—101no—
224C22—101no—
225C22—101no—
226C22C32×C22⋊D512yescomplemented
227C22C22×C32×D511yescharacteristic
228C4—21no—
229C4—52no—
230C4—101no—
231C4—101no—
232C3C3×#408514yesdirect product factor
233C2—22no—
234C2—41no—
235C2—201no—
236C2C32×D4×D511yescharacteristic
237C2C32×#71111yescharacteristic
238C2C2×C32×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C32C22×D5
commutator, cosocleC22×C5C23×C32
FrattiniC22C22×C32×D5
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C32×D4D5
hypocenterC5C32×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C2×C32×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×C32×C22⋊D5C2semidirect
3. C2×C32×C22⋊D5C2semidirect
4. C22×C32×Dic5C2semidirect
5. C32×C22⋊Dic5C2semidirect
6. C32×#685C2semidirect
7. C32×#683C2semidirect
8. C3×#4085C3direct (N × H)
21. C2×C3×C5×D4C2×C3semidirect
22. C2×C3×C22⋊D5C2×C3semidirect
23. C2×C3×C22⋊D5C2×C3semidirect
24. C22×C3×Dic5C2×C3semidirect
25. C3×C22⋊Dic5C2×C3semidirect
26. C3×#685C2×C3semidirect
27. C3×#683C2×C3semidirect
33. C22×C32×C5D4semidirect
41. C32×Dic5D4semidirect
42. #4085C32direct (N × H)
45. C2×C32×D4D5semidirect
68. C2×C5×D4C2×C32semidirect
69. C2×C22⋊D5C2×C32semidirect
70. C2×C22⋊D5C2×C32semidirect
71. C22×Dic5C2×C32semidirect
72. C22⋊Dic5C2×C32semidirect
73. #685C2×C32semidirect
74. #683C2×C32semidirect
91. C22×C3×C5C3×D4semidirect
99. C3×Dic5C3×D4semidirect
102. C2×C3×D4C3×D5semidirect
107. C32×C5#121semidirect
127. C22×C32C22⋊D5semidirect
156. C22×C5C32×D4semidirect
164. Dic5C32×D4semidirect
173. C2×D4C32×D5semidirect
178. C3×C5C3×#121semidirect
187. C22×C3C3×C22⋊D5semidirect
199. C32#4085direct (N × H)
217. C5C32×#121semidirect
226. C22C32×C22⋊D5semidirect
232. C3C3×#4085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×C32×C22⋊D52
C22×C32×Dic52
C32×C22⋊Dic52
C32×#6852
C32×#6832
C3×#40853
C32×#1215