Finite Group Databasebeta

← #13087778

Subgroups — #13087778

Order 1440.

486 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 83 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×C5×#638C211yesmaximal, characteristic, complemented
2C2×C3×#1220C212yesmaximal, complemented
3C2×#67157C211yesmaximal, characteristic, complemented
4C2×#67156C212yesmaximal, complemented
5#10623828C211yesmaximal, characteristic, complemented
6#91567—32nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C5×C3⋊D3C2211yescharacteristic
9C22×C3×D15C2212yes—
10C5×#638—22no—
11C2×C5×C3⋊Dic3C2211yescharacteristic
12C3×#1220—24no—
13C2×C3×Dic15C2212yes—
14#67157—22no—
15#67156—24no—
16#63979—51nomaximal, Hall
17C2×#1220D312yescomplemented
18C2×C5×#67—32no—
19C2×C5×#67—61no—
20C2×C3×C22⋊D5—32no—
21C2×#1203—32no—
22C2×#1202—32no—
23C2×#1201—32no—
24Dic3×Dic5—32no—
25C22×C32×C5—21no—
26C22×C32×C5—22no—
27C22×C32×C5C2311yescharacteristic
28C2×C5×C3⋊D3—21no—
29C2×C5×C3⋊D3—22no—
30C2×C3×D15—22no—
31C2×C3×D15—22no—
32C2×C3×D15—22no—
33C5×C3⋊Dic3D412yescomplemented
34C3×Dic15D414yescomplemented
35#4086—91noHall
36C2×#638D511yescharacteristic, complemented
37C2×C3×#67—52no—
38C2×#626—52no—
39C2×#625—51no—
40Dic32—51no—
41C23×C3×C5—21no—
42C23×C3×C5C2×D312yes—
43C22×D15C2×D312yes—
44C22×C5×D3—32no—
45C22×C5×D3—61no—
46C22×C3×D5—32no—
47#1220—24no—
48C2×Dic15C2×D312yes—
49C5×#67—64no—
50C5×#67—64no—
51C2×C5×Dic3—32no—
52C2×C5×Dic3—61no—
53C3×C22⋊D5—64no—
54C2×C3×Dic5—32no—
55#1203—64no—
56#1202—64no—
57#1201—64no—
58#940—152no—
59C2×C32×C5—41no—
60C2×C32×C5C2×D412yes—
61C2×C32×C5C2×D411yescharacteristic
62C5×C3⋊D3—41no—
63C3×D15—42no—
64C2×C5×D4—91no—
65C2×C22⋊D5—32no—
66C2×C22⋊D5—92no—
67C2×D20—91no—
68C4×Dic5—91no—
69C23×C32C2×D511yescharacteristic
70C22×C3⋊D3C2×D511yescharacteristic
71C22×C3×D3—52no—
72#638—22no—
73C2×C3⋊Dic3C2×D511yescharacteristic
74C3×#67—104no—
75C2×C3×Dic3—52no—
76#626—104no—
77#625—102no—
78C22×C3×C5—22no—
79C22×C3×C5—22no—
80C22×C3×C5—22no—
81C22×C3×C5—22no—
82C22×C3×C5—21no—
83C22×C3×C5—42no—
84C22×C3×C5C22×D312yes—
85C2×D15—22no—
86C2×D15—22no—
87C2×D15—22no—
88C2×C5×D3—62no—
89C2×C5×D3—62no—
90C2×C5×D3—62no—
91C2×C5×D3—62no—
92C2×C5×D3—122no—
93C2×C3×D5—62no—
94C2×C3×D5—62no—
95C2×C3×D5—62no—
96Dic15#6714yescomplemented
97C3×Dic5—34no—
98C5×Dic3—34no—
99C5×Dic3—62no—
100C2×C3×D4—152no—
101C2×#67—32no—
102C2×#67—52no—
103C2×#67—61no—
104C2×#67—152no—
105C2×#67—152no—
106C2×D12—152no—
107C4×Dic3—152no—
108C32×C5#12711yescharacteristic, complemented, Hall
109C23×C5—91no—
110C23×C5D3211yescharacteristic
111C22×D5—32no—
112C5×D4—182no—
113C2×C4×C5—91no—
114C22⋊D5—64no—
115C22⋊D5—184no—
116C2×Dic5—32no—
117D20—182no—
118C22×C32—21no—
119C22×C32—22no—
120C22×C32C22×D511yescharacteristic
121C2×C3⋊D3—21no—
122C2×C3⋊D3—22no—
123C2×C3×D3—102no—
124C2×C3×D3—102no—
125C2×C3×D3—102no—
126C3⋊Dic3C22⋊D512yescomplemented
127C3×Dic3—54no—
128#127—451noSylow
129C2×C3×C5—22no—
130C2×C3×C5—21no—
131C2×C3×C5—42no—
132C2×C3×C5—42no—
133C2×C3×C5D3×D412yes—
134C2×C3×C5D3×D412yes—
135C2×C3×C5C2×#6712yes—
136D15—42no—
137C3×D5—122no—
138C5×D3—122no—
139C5×D3—122no—
140C23×C3—21no—
141C23×C3—152no—
142C23×C3D3×D512yes—
143C22×D3—32no—
144C22×D3—52no—
145C22×D3—61no—
146C3×D4—304no—
147C2×C3×C4—152no—
148#67—64no—
149#67—64no—
150#67—104no—
151#67—304no—
152#67—304no—
153C2×Dic3—32no—
154C2×Dic3—52no—
155C2×Dic3—61no—
156D12—304no—
157C22×C5—22no—
158C22×C5—21no—
159C22×C5—182no—
160C22×C5—181no—
161C22×C5C2×D3211yescharacteristic
162C2×D5—62no—
163C2×D5—62no—
164C2×D5—62no—
165C4×C5—92no—
166Dic5—34no—
167C2×C32—41no—
168C2×C32D4×D512yes—
169C2×C32C2×C22⋊D511yescharacteristic
170C3⋊D3—41no—
171C3×D3—202no—
172C2×D4—91no—
173C2×D4—152no—
174C2×D4—451no—
175C2×D4—452no—
176C42—451no—
177C3×C5—21no—
178C3×C5#94012yescomplemented
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—22no—
183C22×C3—21no—
184C22×C3—42no—
185C22×C3—302no—
186C22×C3—302no—
187C22×C3—302no—
188C22×C3C2×D3×D512yes—
189C2×D3—62no—
190C2×D3—62no—
191C2×D3—62no—
192C2×D3—62no—
193C2×D3—102no—
194C2×D3—102no—
195C2×D3—102no—
196C2×D3—122no—
197C3×C4—154no—
198Dic3—34no—
199Dic3—54no—
200Dic3—62no—
201C2×C5—41no—
202C2×C5—361no—
203C2×C5D3×#6712yes—
204C2×C5#381111yescharacteristic
205D5—122no—
206C32#408611yescharacteristic, complemented, Sylow
207C23—91no—
208C23—152no—
209C23(C3⋊D3)⋊D511yescharacteristic
210D4—182no—
211D4—304no—
212D4—902no—
213D4—904no—
214C2×C4—91no—
215C2×C4—152no—
216C2×C3—22no—
217C2×C3—21no—
218C2×C3—42no—
219C2×C3—42no—
220C2×C3—602no—
221C2×C3D5×#6712yes—
222C2×C3D3×C22⋊D512yes—
223C2×C3#679012yes—
224D3—122no—
225D3—122no—
226D3—202no—
227C5#6397911yescharacteristic, complemented, Sylow
228C22—22no—
229C22—21no—
230C22—182no—
231C22—181no—
232C22—302no—
233C22—302no—
234C22—302no—
235C22C2×(C3⋊D3)⋊D511yescharacteristic
236C4—92no—
237C4—154no—
238C3—21no—
239C3#9156712yescomplemented
240C2—41no—
241C2—361no—
242C2—602no—
243C2#1062423512yes—
244C2#1062423611yescharacteristic
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23(C3⋊D3)⋊D5
hypocenterC32×C5#127
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C5×#638C2semidirect
2. C2×C3×#1220C2semidirect
3. C2×#67157C2semidirect
4. C2×#67156C2semidirect
5. #10623828C2semidirect
17. C2×#1220D3semidirect
33. C5×C3⋊Dic3D4semidirect
34. C3×Dic15D4semidirect
36. C2×#638D5semidirect
96. Dic15#67semidirect
108. C32×C5#127semidirect
126. C3⋊Dic3C22⋊D5semidirect
178. C3×C5#940semidirect
206. C32#4086semidirect
227. C5#63979semidirect
239. C3#91567semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6382
C2×C3×#12202
C2×#671572
C2×#671562
#106238282
#915673
#639795