Finite Group Databasebeta

← #13085903

Subgroups — #13085903

Order 1440.

334 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 88 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×Dic3×D15C211yesmaximal, characteristic
2#10623829C211yesmaximal, characteristic
3Dic3×Dic15C211yesmaximal, characteristic, complemented
4C5×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#6667C211yesmaximal, characteristic
8#91394—31nomaximal
9#91347—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17Dic3×D15C414yescomplemented
18#63878—51nomaximal, Hall
19C2×C4×D15—31no—
20C2×D5×Dic3—31no—
21C4×Dic15—31no—
22C5×C4⋊Dic3—31no—
23C5×Dic3⋊C4—31no—
24C3×#685—31no—
25C3×C4⋊Dic5—31no—
26Dic3⋊Dic5D311yescharacteristic, complemented
27#6667—31no—
28#6667D311yescharacteristic
29#6665—31no—
30Dic3×Dic5—31no—
31Dic3×Dic5—31no—
32Dic3×Dic5—31no—
33Dic3×Dic5—61no—
34C22×C32×C5C2311yescharacteristic
35C2×C3×D15—21no—
36C2×C3×D15—21no—
37C2×C3×D15C2×C412yes—
38C3⋊Dic15C2×C412yes—
39C5×C3⋊Dic3—21no—
40C3×Dic15—21no—
41C3×C5×Dic3—21no—
42C3×C5×Dic3C2×C412yes—
43C32×Dic5—21no—
44#4038—91noHall
45C2×D3×Dic3—51no—
46C4×C3⋊Dic3—51no—
47C3×(C2×D3)⋊C4—51no—
48C3×Dic3⋊C4—51no—
49Dic3⋊Dic3D511yescharacteristic, complemented
50(C2×D3)⋊Dic3—51no—
51Dic32—51no—
52C22×D15C2×D311yescharacteristic
53C22×C3×D5—31no—
54C2×C3×C4×C5—31no—
55C2×C3×C4×C5—31no—
56C2×Dic15—31no—
57C2×Dic15—31no—
58C2×Dic15—61no—
59C2×Dic15C2×D311yescharacteristic
60C4×D15—34no—
61C2×C5×Dic3—31no—
62C2×C5×Dic3—31no—
63C2×C5×Dic3—61no—
64C2×C5×Dic3C2×D311yescharacteristic
65C2×C5×Dic3C2×D311yescharacteristic
66C2×C3×Dic5—21no—
67C2×C3×Dic5—31no—
68C2×C3×Dic5C2×D311yescharacteristic
69C2×C3×Dic5C2×D311yescharacteristic
70D5×Dic3—34no—
71#892—151no—
72#877—151no—
73C2×C32×C5C22×C411yescharacteristic
74C2×C32×C5#4111yescharacteristic
75C2×C32×C5#4111yescharacteristic
76C3×D15—22no—
77C2×C4×D5—91no—
78C5×C4⋊C4—91no—
79#685—31no—
80#685—91no—
81C4⋊Dic5—31no—
82C4×Dic5—91no—
83C4×Dic5—91no—
84C22×C3×D3—51no—
85C2×C32×C4—51no—
86C2×C3⋊Dic3—51no—
87C2×C3⋊Dic3C2×D511yescharacteristic
88C2×C3×Dic3—51no—
89C2×C3×Dic3C2×D511yescharacteristic
90C2×C3×Dic3C2×D511yescharacteristic
91D3×Dic3—54no—
92C22×C3×C5—21no—
93C22×C3×C5C22×D311yescharacteristic
94C22×C3×C5C22×D311yescharacteristic
95C2×D15—21no—
96C2×D15—21no—
97C2×D15C4×D312yes—
98C2×C3×D5—32no—
99C2×C3×D5—61no—
100C2×C3×D5—61no—
101C3×C4×C5—32no—
102C3×C4×C5—61no—
103Dic15—21no—
104Dic15—32no—
105Dic15—32no—
106Dic15—62no—
107C3×Dic5—22no—
108C3×Dic5—21no—
109C3×Dic5—21no—
110C3×Dic5—61no—
111C5×Dic3—21no—
112C5×Dic3—62no—
113C5×Dic3—61no—
114C5×Dic3—61no—
115C5×Dic3C4×D312yes—
116C22×Dic3—151no—
117C2×C4×D3—151no—
118C3×C4⋊C4—151no—
119C3×C22⋊C4—151no—
120#217—151no—
121(C2×D3)⋊C4—51no—
122(C2×D3)⋊C4—151no—
123C4⋊Dic3—31no—
124Dic3⋊C4—31no—
125Dic3⋊C4—51no—
126C4×Dic3—151no—
127C4×Dic3—151no—
128C4×Dic3—151no—
129C4×Dic3—151no—
130C4×Dic3—301no—
131C32×C5#11711yescharacteristic, complemented, Hall
132C22×D5—31no—
133C2×C4×C5—31no—
134C2×C4×C5—31no—
135C2×C4×C5—91no—
136C2×Dic5—31no—
137C2×Dic5—91no—
138C2×Dic5D3211yescharacteristic
139C4×D5—94no—
140C22×C32C22×D511yescharacteristic
141C2×C3×D3—52no—
142C2×C3×D3—101no—
143C2×C3×D3—101no—
144C32×C4—101no—
145C3⋊Dic3—21no—
146C3⋊Dic3—52no—
147C3×Dic3—21no—
148C3×Dic3—101no—
149C3×Dic3C4×D512yes—
150#117—451noSylow
151C2×C3×C5—21no—
152C2×C3×C5—21no—
153C2×C3×C5—21no—
154C2×C3×C5C2×C4×D311yescharacteristic
155C2×C3×C5C2×C4×D311yescharacteristic
156C2×C3×C5#23711yescharacteristic
157C2×C3×C5#23711yescharacteristic
158C2×C3×C5#23711yescharacteristic
159C2×C3×C5#23911yescharacteristic
160D15—22no—
161C3×D5—62no—
162C23×C3—151no—
163C22×D3—51no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—51no—
167C2×C3×C4—51no—
168C2×C3×C4—101no—
169C2×C3×C4—151no—
170C2×Dic3—31no—
171C2×Dic3—31no—
172C2×Dic3—51no—
173C2×Dic3—61no—
174C2×Dic3—151no—
175C2×Dic3—151no—
176C2×Dic3—154no—
177C2×Dic3—301no—
178C2×Dic3D3×D511yescharacteristic
179C2×Dic3D3×D511yescharacteristic
180C4×D3—154no—
181C22×C5C2×D3211yescharacteristic
182C2×D5—32no—
183C2×D5—61no—
184C2×D5—61no—
185C4×C5—32no—
186C4×C5—61no—
187C4×C5—181no—
188Dic5—21no—
189Dic5—61no—
190Dic5—92no—
191C2×C32C2×C4×D511yescharacteristic
192C2×C32#71111yescharacteristic
193C2×C32#71311yescharacteristic
194C3×D3—102no—
195C22×C4—451no—
196C4⋊C4—91no—
197C4⋊C4—151no—
198C22⋊C4—151no—
199C22⋊C4—451no—
200C42—451no—
201C42—451no—
202C3×C5—21no—
203C3×C5#87711yescharacteristic, complemented
204C3×C5#89211yescharacteristic, complemented
205C22×C3—21no—
206C22×C3—152no—
207C22×C3—301no—
208C22×C3—301no—
209C22×C3C2×D3×D511yescharacteristic
210C22×C3C2×D3×D511yescharacteristic
211C2×D3—52no—
212C2×D3—101no—
213C2×D3—101no—
214C3×C4—32no—
215C3×C4—61no—
216C3×C4—102no—
217C3×C4—101no—
218C3×C4—101no—
219C3×C4—301no—
220Dic3—21no—
221Dic3—62no—
222Dic3—61no—
223Dic3—61no—
224Dic3—101no—
225Dic3—152no—
226Dic3—152no—
227Dic3—302no—
228Dic3#120012yes—
229C2×C5#379611yescharacteristic
230C2×C5C4×D3211yescharacteristic
231C2×C5#380511yescharacteristic
232D5—62no—
233C32#403811yescharacteristic, complemented, Sylow
234C23—151no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—51no—
238C2×C4—91no—
239C2×C4—151no—
240C2×C4—454no—
241C2×C4—451no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—302no—
246C2×C3#676611yescharacteristic
247C2×C3#676611yescharacteristic
248C2×C3#676811yescharacteristic
249C2×C3C4×D3×D511yescharacteristic
250C2×C3#678011yescharacteristic
251C2×C3C2×#120011yescharacteristic
252D3—102no—
253C5#6387811yescharacteristic, complemented, Sylow
254C22—152no—
255C22—301no—
256C22—301no—
257C22D32×D511yescharacteristic
258C4—32no—
259C4—61no—
260C4—101no—
261C4—181no—
262C4—301no—
263C4—452no—
264C3—21no—
265C3#9134711yescharacteristic, complemented
266C3#9139411yescharacteristic, complemented
267C2—302no—
268C2D3×#120011yescharacteristic
269C2#1062404711yescharacteristic
270C2#1062405611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC22×C3×D15C22
hypocenterC32×C5#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
3. Dic3×Dic15C2semidirect
4. C5×Dic3⋊Dic3C2semidirect
5. Dic5×C3⋊Dic3C2semidirect
6. C3×Dic3⋊Dic5C2semidirect
17. Dic3×D15C4semidirect
26. Dic3⋊Dic5D3semidirect
49. Dic3⋊Dic3D5semidirect
131. C32×C5#117semidirect
203. C3×C5#877semidirect
204. C3×C5#892semidirect
233. C32#4038semidirect
253. C5#63878semidirect
265. C3#91347semidirect
266. C3#91394semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D152
#106238292
Dic3×Dic152
C5×Dic3⋊Dic32
Dic5×C3⋊Dic32
C3×Dic3⋊Dic52
C3×#66672
#913943
#913473
#638785