Finite Group Databasebeta

← #13086157

Subgroups — #13086157

Order 1440.

250 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#10623832C211yesmaximal, characteristic
2#10623814C211yesmaximal, characteristic
3Dic3×Dic15C211yesmaximal, characteristic
4C5×Dic3⋊Dic3C211yesmaximal, characteristic
5#10623773C211yesmaximal, characteristic
6C3×Dic3⋊Dic5C211yesmaximal, characteristic
7C3×Dic3⋊Dic5C211yesmaximal, characteristic
8#91384—31nomaximal
9#91346—31nomaximal
10C2×C3⋊Dic15C2211yescharacteristic
11C2×C5×C3⋊Dic3C2211yescharacteristic
12C2×C3×Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#63845—51nomaximal, Hall
18#6712—31no—
19C4×Dic15—31no—
20C5×C4⋊Dic3—31no—
21C5×Dic3⋊C4—31no—
22C3×C4⋊Dic5—31no—
23C3×C4⋊Dic5—31no—
24Dic3⋊Dic5—31no—
25Dic3⋊Dic5—31no—
26Dic3⋊Dic5D311yescharacteristic
27Dic3⋊Dic5D311yescharacteristic
28#6668—31no—
29#6668—31no—
30#6668—31no—
31#6668—61no—
32Dic3×Dic5—31no—
33C22×C32×C5C2311yescharacteristic
34C3⋊Dic15—21no—
35C5×C3⋊Dic3—21no—
36C3×Dic15—21no—
37C3×Dic15—21no—
38C3×C5×Dic3—21no—
39C3×C5×Dic3Q812yes—
40C32×Dic5—21no—
41#4036—91noHall
42C4⋊(C3⋊Dic3)—51no—
43C3×Dic3⋊C4—51no—
44C3×Dic3⋊C4—51no—
45#3724—51no—
46Dic3⋊Dic3—51no—
47Dic3⋊Dic3D511yescharacteristic
48Dic32—51no—
49C2×C3×C4×C5—31no—
50C2×C3×C4×C5—31no—
51C2×Dic15—31no—
52C2×Dic15—31no—
53C2×Dic15—61no—
54C2×Dic15C2×D311yescharacteristic
55C2×Dic15C2×D311yescharacteristic
56C2×C5×Dic3—31no—
57C2×C5×Dic3—31no—
58C2×C5×Dic3—61no—
59C2×C5×Dic3C2×D311yescharacteristic
60C2×C5×Dic3C2×D311yescharacteristic
61C2×C3×Dic5—21no—
62C2×C3×Dic5—31no—
63C2×C3×Dic5—31no—
64C2×C3×Dic5C2×D311yescharacteristic
65C2×C3×Dic5C2×D311yescharacteristic
66#890—151no—
67#889—151no—
68C2×C32×C5C2×Q811yescharacteristic
69C2×C32×C5#4111yescharacteristic
70C2×C32×C5#4111yescharacteristic
71C5×C4⋊C4—91no—
72C4⋊Dic5—31no—
73C4⋊Dic5—31no—
74C4⋊Dic5—91no—
75#683—91no—
76#683—91no—
77C4×Dic5—91no—
78C2×C32×C4—51no—
79C2×C3⋊Dic3—51no—
80C2×C3⋊Dic3C2×D511yescharacteristic
81C2×C3×Dic3—51no—
82C2×C3×Dic3—51no—
83C2×C3×Dic3C2×D511yescharacteristic
84C2×C3×Dic3C2×D511yescharacteristic
85C22×C3×C5—21no—
86C22×C3×C5C22×D311yescharacteristic
87C22×C3×C5C22×D311yescharacteristic
88C3×C4×C5—32no—
89C3×C4×C5—61no—
90Dic15—21no—
91Dic15—21no—
92Dic15—61no—
93Dic15—61no—
94Dic15—121no—
95C3×Dic5—22no—
96C3×Dic5—21no—
97C3×Dic5—21no—
98C3×Dic5—61no—
99C3×Dic5—61no—
100C5×Dic3—21no—
101C5×Dic3—61no—
102C5×Dic3—61no—
103C5×Dic3—121no—
104C5×Dic3Dic612yes—
105C3×C4⋊C4—151no—
106C3×C4⋊C4—151no—
107C4⋊Dic3—31no—
108C4⋊Dic3—151no—
109C4⋊Dic3—151no—
110C4⋊Dic3—151no—
111C4⋊Dic3—301no—
112Dic3⋊C4—31no—
113Dic3⋊C4—51no—
114Dic3⋊C4—51no—
115Dic3⋊C4—151no—
116Dic3⋊C4—151no—
117Dic3⋊C4—151no—
118C4×Dic3—151no—
119C4×Dic3—151no—
120C32×C5#12511yescharacteristic, complemented, Hall
121C2×C4×C5—31no—
122C2×C4×C5—31no—
123C2×C4×C5—91no—
124C2×Dic5—31no—
125C2×Dic5—31no—
126C2×Dic5—91no—
127C2×Dic5D3211yescharacteristic
128C22×C32C22×D511yescharacteristic
129C32×C4—101no—
130C3⋊Dic3—21no—
131C3⋊Dic3—101no—
132C3×Dic3—21no—
133C3×Dic3—101no—
134C3×Dic3—101no—
135C3×Dic3Dic1012yes—
136#125—451noSylow
137C2×C3×C5—21no—
138C2×C3×C5—21no—
139C2×C3×C5—21no—
140C2×C3×C5C2×Dic611yescharacteristic
141C2×C3×C5#23511yescharacteristic
142C2×C3×C5#23711yescharacteristic
143C2×C3×C5#23711yescharacteristic
144C2×C3×C5D3×Q811yescharacteristic
145C2×C3×C5#23911yescharacteristic
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—51no—
149C2×C3×C4—51no—
150C2×C3×C4—101no—
151C2×C3×C4—151no—
152C2×C3×C4—151no—
153C2×Dic3—31no—
154C2×Dic3—31no—
155C2×Dic3—51no—
156C2×Dic3—51no—
157C2×Dic3—61no—
158C2×Dic3—151no—
159C2×Dic3—151no—
160C2×Dic3—301no—
161C2×Dic3D3×D511yescharacteristic
162C2×Dic3D3×D511yescharacteristic
163C22×C5C2×D3211yescharacteristic
164C4×C5—32no—
165C4×C5—61no—
166C4×C5—181no—
167Dic5—21no—
168Dic5—61no—
169Dic5—61no—
170Dic5—181no—
171C2×C32C2×Dic1011yescharacteristic
172C2×C32#71111yescharacteristic
173C2×C32#71311yescharacteristic
174C4⋊C4—91no—
175C4⋊C4—151no—
176C4⋊C4—151no—
177C4⋊C4—451no—
178C4⋊C4—451no—
179C4⋊C4—451no—
180C42—451no—
181C3×C5—21no—
182C3×C5#88911yescharacteristic, complemented
183C3×C5#89011yescharacteristic, complemented
184C22×C3—21no—
185C22×C3C2×D3×D511yescharacteristic
186C22×C3C2×D3×D511yescharacteristic
187C3×C4—32no—
188C3×C4—61no—
189C3×C4—102no—
190C3×C4—101no—
191C3×C4—101no—
192C3×C4—301no—
193C3×C4—301no—
194Dic3—21no—
195Dic3—61no—
196Dic3—61no—
197Dic3—101no—
198Dic3—101no—
199Dic3—121no—
200Dic3—301no—
201Dic3—301no—
202Dic3—601no—
203Dic3#120412yes—
204C2×C5D3×Dic611yescharacteristic
205C2×C5#379911yescharacteristic
206C2×C5#380511yescharacteristic
207C32#403611yescharacteristic, complemented, Sylow
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—51no—
211C2×C4—91no—
212C2×C4—151no—
213C2×C4—151no—
214C2×C4—451no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3#676611yescharacteristic
219C2×C3#676611yescharacteristic
220C2×C3D3×Dic1011yescharacteristic
221C2×C3#676811yescharacteristic
222C2×C3#678211yescharacteristic
223C2×C3C2×#120411yescharacteristic
224C5#6384511yescharacteristic, complemented, Sylow
225C22D32×D511yescharacteristic
226C4—32no—
227C4—61no—
228C4—101no—
229C4—181no—
230C4—301no—
231C4—301no—
232C4—901no—
233C3—21no—
234C3#9134611yescharacteristic, complemented
235C3#9138411yescharacteristic, complemented
236C2D3×#120411yescharacteristic
237C2#1062404711yescharacteristic
238C2#1062405111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, prime radical, cosocleC22×C32×C5C23
hypocenterC32×C5#125
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
120. C32×C5#125semidirect
182. C3×C5#889semidirect
183. C3×C5#890semidirect
207. C32#4036semidirect
224. C5#63845semidirect
234. C3#91346semidirect
235. C3#91384semidirect

Maximal subgroups

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

subgroupindex
#106238322
#106238142
Dic3×Dic152
C5×Dic3⋊Dic32
#106237732
C3×Dic3⋊Dic52
#913843
#913463
#638455