Finite Group Databasebeta

← #13087303

Subgroups — #13087303

Order 1440.

250 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 76 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#10623906C211yesmaximal, characteristic
2C3×C4⋊Dic15C211yesmaximal, characteristic
3C3×C5×Dic3⋊C4C211yesmaximal, characteristic
4#10623815C211yesmaximal, characteristic
5#10623815C211yesmaximal, characteristic
6#10623814C211yesmaximal, characteristic
7Dic3×Dic15C211yesmaximal, characteristic
8#91778—31nomaximal
9#91339—31nomaximal
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17#63847—51nomaximal, Hall
18C3×C5×C4⋊C4—31no—
19C4⋊Dic15D311yescharacteristic
20#6712—31no—
21#6712—31no—
22#6712—31no—
23#6712—31no—
24#6712—31no—
25#6712—61no—
26C4×Dic15—31no—
27C5×Dic3⋊C4D311yescharacteristic
28C3×C4⋊Dic5—31no—
29#6669—31no—
30#6669—31no—
31#6668—31no—
32Dic3×Dic5—31no—
33C22×C32×C5C2311yescharacteristic
34C32×C4×C5—21no—
35C3⋊Dic15—21no—
36C3⋊Dic15Q812yes—
37C3×Dic15—21no—
38C3×Dic15—21no—
39C3×C5×Dic3—21no—
40C3×C5×Dic3—21no—
41#4035—91noHall
42#3750—51no—
43C3×C4⋊Dic3—51no—
44C3×Dic3⋊C4D511yescharacteristic
45#3724—51no—
46#3724—51no—
47Dic3⋊Dic3—51no—
48Dic32—51no—
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—31no—
51C2×C3×C4×C5—31no—
52C2×C3×C4×C5C2×D311yescharacteristic
53C2×C3×C4×C5C2×D311yescharacteristic
54C2×Dic15—31no—
55C2×Dic15—31no—
56C2×Dic15—31no—
57C2×Dic15—31no—
58C2×Dic15—61no—
59C2×Dic15—61no—
60C2×Dic15C2×D311yescharacteristic
61C2×Dic15C2×D311yescharacteristic
62C2×C5×Dic3C2×D311yescharacteristic
63C2×C5×Dic3C2×D311yescharacteristic
64C2×C3×Dic5—31no—
65C2×C3×Dic5—31no—
66#889—151no—
67#889—151no—
68C2×C32×C5C2×Q811yescharacteristic
69C2×C32×C5#4111yescharacteristic
70C2×C32×C5#4111yescharacteristic
71C5×C4⋊C4—31no—
72C4⋊Dic5—31no—
73#683—91no—
74#683—91no—
75#683—91no—
76#683—91no—
77C4×Dic5—91no—
78C2×C32×C4C2×D511yescharacteristic
79C2×C3⋊Dic3—51no—
80C2×C3⋊Dic3—51no—
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—21no—
89C3×C4×C5—21no—
90C3×C4×C5—41no—
91C3×C4×C5—61no—
92C3×C4×C5—61no—
93Dic15—21no—
94Dic15—21no—
95Dic15—32no—
96Dic15—32no—
97Dic15—62no—
98Dic15—61no—
99Dic15—61no—
100Dic15—121no—
101C3×Dic5—61no—
102C3×Dic5—61no—
103C5×Dic3—21no—
104C5×Dic3—21no—
105C3×C4⋊C4—31no—
106C3×C4⋊C4—151no—
107C4⋊Dic3—51no—
108C4⋊Dic3—151no—
109Dic3⋊C4—151no—
110Dic3⋊C4—151no—
111Dic3⋊C4—151no—
112Dic3⋊C4—151no—
113Dic3⋊C4—151no—
114Dic3⋊C4—151no—
115Dic3⋊C4—151no—
116Dic3⋊C4—301no—
117Dic3⋊C4D1511yescharacteristic
118C4×Dic3—151no—
119C4×Dic3—151no—
120C32×C5#12511yescharacteristic, complemented, Hall
121C2×C4×C5—31no—
122C2×C4×C5—31no—
123C2×C4×C5D3211yescharacteristic
124C2×Dic5—31no—
125C2×Dic5—31no—
126C2×Dic5—91no—
127C2×Dic5—91no—
128C22×C32C22×D511yescharacteristic
129C32×C4—21no—
130C3⋊Dic3—52no—
131C3⋊Dic3—101no—
132C3×Dic3—21no—
133C3×Dic3—21no—
134C3×Dic3—101no—
135C3×Dic3—101no—
136#125—451noSylow
137C2×C3×C5—21no—
138C2×C3×C5—21no—
139C2×C3×C5—21no—
140C2×C3×C5#23511yescharacteristic
141C2×C3×C5#23511yescharacteristic
142C2×C3×C5#23711yescharacteristic
143C2×C3×C5#23711yescharacteristic
144C2×C3×C5D3×Q811yescharacteristic
145C2×C3×C5D3×Q811yescharacteristic
146C2×C3×C4—21no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—151no—
150C2×C3×C4—151no—
151C2×C3×C4D3×D511yescharacteristic
152C2×C3×C4C2×D1511yescharacteristic
153C2×Dic3—51no—
154C2×Dic3—51no—
155C2×Dic3—151no—
156C2×Dic3—151no—
157C2×Dic3—151no—
158C2×Dic3—151no—
159C2×Dic3—301no—
160C2×Dic3—301no—
161C2×Dic3C2×D1511yescharacteristic
162C2×Dic3C2×D1511yescharacteristic
163C22×C5C2×D3211yescharacteristic
164C4×C5—21no—
165C4×C5—61no—
166C4×C5—61no—
167Dic5—61no—
168Dic5—61no—
169Dic5—92no—
170Dic5—181no—
171C2×C32#70911yescharacteristic
172C2×C32#71111yescharacteristic
173C2×C32Q8×D511yescharacteristic
174C4⋊C4—31no—
175C4⋊C4—151no—
176C4⋊C4—451no—
177C4⋊C4—451no—
178C4⋊C4—451no—
179C4⋊C4—451no—
180C42—451no—
181C3×C5—21no—
182C3×C5#88911yescharacteristic, complemented
183C3×C5#88911yescharacteristic, complemented
184C22×C3—21no—
185C22×C3C2×D3×D511yescharacteristic
186C22×C3C22×D1511yescharacteristic
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—41no—
190C3×C4—61no—
191C3×C4—61no—
192C3×C4—301no—
193C3×C4—301no—
194Dic3—21no—
195Dic3—21no—
196Dic3—101no—
197Dic3—101no—
198Dic3—152no—
199Dic3—152no—
200Dic3—302no—
201Dic3—301no—
202Dic3—301no—
203Dic3—601no—
204C2×C5#379511yescharacteristic
205C2×C5#379711yescharacteristic
206C2×C5#380411yescharacteristic
207C32#403511yescharacteristic, complemented, Sylow
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—151no—
211C2×C4—151no—
212C2×C4—451no—
213C2×C4—451no—
214C2×C4D3×D1511yescharacteristic
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3#676511yescharacteristic
219C2×C3D15⋊Q811yescharacteristic
220C2×C3#678211yescharacteristic
221C2×C3#681711yescharacteristic
222C2×C3#681911yescharacteristic
223C2×C3Q8×D1511yescharacteristic
224C5#6384711yescharacteristic, complemented, Sylow
225C22C2×D3×D1511yescharacteristic
226C4—21no—
227C4—61no—
228C4—61no—
229C4—301no—
230C4—301no—
231C4—452no—
232C4—901no—
233C3—21no—
234C3#9133911yescharacteristic, complemented
235C3#9177811yescharacteristic, complemented
236C2#1062419311yescharacteristic
237C2#1062419811yescharacteristic
238C2#1062421011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, prime radical, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D3×D15
hypocenterC32×C5#125
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

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#889semidirect
207. C32#4035semidirect
224. C5#63847semidirect
234. C3#91339semidirect
235. C3#91778semidirect

Maximal subgroups

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

subgroupindex
#106239062
C3×C4⋊Dic152
C3×C5×Dic3⋊C42
#106238152
#106238142
Dic3×Dic152
#917783
#913393
#638475