Finite Group Databasebeta

← #13087555

Subgroups — #13087555

Order 1440.

274 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 74 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#10623913C211yesmaximal, characteristic
2C3×#6719C211yesmaximal, characteristic
3C3×C5×#217C211yesmaximal, characteristic
4Dic3⋊Dic15C211yesmaximal, characteristic, complemented
5#10623815C211yesmaximal, characteristic, complemented
6#10623814C211yesmaximal, characteristic, complemented
7Dic3×Dic15C211yesmaximal, characteristic, complemented
8#91768—31nomaximal
9#91531—31nomaximal
10C23×C32×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17#63956—51nomaximal, Hall
18C3×C5×C22⋊C4—31no—
19#6719—31no—
20#6719—31no—
21#6719—61no—
22#6719D311yescharacteristic
23C4⋊Dic15—31no—
24#6712—31no—
25#6712—31no—
26C4×Dic15—31no—
27C5×#217D311yescharacteristic
28C3×C22⋊Dic5—31no—
29Dic3⋊Dic5—31no—
30#6669—31no—
31#6668—31no—
32Dic3×Dic5—31no—
33C22×C32×C5—21no—
34C22×C32×C5—21no—
35C22×C32×C5—21no—
36C22×C32×C5C2311yescharacteristic
37C3⋊Dic15—21no—
38C3⋊Dic15—21no—
39C3×Dic15—21no—
40C3×Dic15—21no—
41C3×C5×Dic3—21no—
42C3×C5×Dic3—21no—
43#4025—91noHall
44#3757—51no—
45C3×#217—51no—
46C3×#217D511yescharacteristic
47#3724—51no—
48Dic3⋊Dic3—51no—
49Dic3⋊Dic3—51no—
50Dic32—51no—
51C23×C3×C5—21no—
52C23×C3×C5C2×D311yescharacteristic
53C23×C3×C5C2×D311yescharacteristic
54C2×C3×C4×C5—31no—
55C2×C3×C4×C5—31no—
56C2×Dic15—31no—
57C2×Dic15—31no—
58C2×Dic15—31no—
59C2×Dic15—31no—
60C2×Dic15—61no—
61C2×Dic15—61no—
62C2×Dic15C2×D311yescharacteristic
63C2×Dic15C2×D311yescharacteristic
64C2×C5×Dic3C2×D311yescharacteristic
65C2×C5×Dic3C2×D311yescharacteristic
66C2×C3×Dic5—31no—
67C2×C3×Dic5—31no—
68#879—151no—
69#879—151no—
70C2×C32×C5—41no—
71C2×C32×C5#4111yescharacteristic
72C2×C32×C5#4111yescharacteristic
73C2×C32×C5#4111yescharacteristic
74C5×C22⋊C4—31no—
75C22⋊Dic5—31no—
76C22⋊Dic5—91no—
77C4⋊Dic5—91no—
78#683—91no—
79#683—91no—
80C4×Dic5—91no—
81C23×C32C2×D511yescharacteristic
82C2×C3⋊Dic3—51no—
83C2×C3⋊Dic3—51no—
84C2×C3×Dic3—51no—
85C2×C3×Dic3—51no—
86C2×C3×Dic3C2×D511yescharacteristic
87C2×C3×Dic3C2×D511yescharacteristic
88C22×C3×C5—22no—
89C22×C3×C5—21no—
90C22×C3×C5—21no—
91C22×C3×C5—21no—
92C22×C3×C5—21no—
93C22×C3×C5—21no—
94C22×C3×C5—21no—
95C22×C3×C5—21no—
96C22×C3×C5—41no—
97C22×C3×C5—41no—
98C22×C3×C5C22×D311yescharacteristic
99C22×C3×C5C22×D311yescharacteristic
100C3×C4×C5—61no—
101C3×C4×C5—61no—
102Dic15—21no—
103Dic15—21no—
104Dic15—61no—
105Dic15—61no—
106Dic15—61no—
107Dic15—61no—
108Dic15—121no—
109Dic15—121no—
110C3×Dic5—61no—
111C3×Dic5—61no—
112C5×Dic3—21no—
113C5×Dic3—21no—
114C3×C22⋊C4—31no—
115C3×C22⋊C4—151no—
116#217—51no—
117#217—151no—
118#217—151no—
119#217—301no—
120#217D1511yescharacteristic
121C4⋊Dic3—151no—
122C4⋊Dic3—151no—
123Dic3⋊C4—151no—
124Dic3⋊C4—151no—
125Dic3⋊C4—151no—
126Dic3⋊C4—151no—
127C4×Dic3—151no—
128C4×Dic3—151no—
129C32×C5#12611yescharacteristic, complemented, Hall
130C23×C5D3211yescharacteristic
131C2×C4×C5—31no—
132C2×C4×C5—31no—
133C2×Dic5—31no—
134C2×Dic5—31no—
135C2×Dic5—91no—
136C2×Dic5—91no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C22×D511yescharacteristic
141C3⋊Dic3—101no—
142C3⋊Dic3—101no—
143C3×Dic3—21no—
144C3×Dic3—21no—
145C3×Dic3—101no—
146C3×Dic3—101no—
147#126—451noSylow
148C2×C3×C5—21no—
149C2×C3×C5—21no—
150C2×C3×C5—21no—
151C2×C3×C5—42no—
152C2×C3×C5—41no—
153C2×C3×C5—41no—
154C2×C3×C5#23511yescharacteristic
155C2×C3×C5#23511yescharacteristic
156C2×C3×C5#23711yescharacteristic
157C2×C3×C5#23711yescharacteristic
158C2×C3×C5#23711yescharacteristic
159C2×C3×C5#23711yescharacteristic
160C23×C3—21no—
161C23×C3D3×D511yescharacteristic
162C23×C3C2×D1511yescharacteristic
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—151no—
166C2×C3×C4—151no—
167C2×Dic3—51no—
168C2×Dic3—51no—
169C2×Dic3—151no—
170C2×Dic3—151no—
171C2×Dic3—151no—
172C2×Dic3—151no—
173C2×Dic3—301no—
174C2×Dic3—301no—
175C2×Dic3C2×D1511yescharacteristic
176C2×Dic3C2×D1511yescharacteristic
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5C2×D3211yescharacteristic
181C4×C5—61no—
182C4×C5—61no—
183Dic5—61no—
184Dic5—61no—
185Dic5—181no—
186Dic5—181no—
187C2×C32—41no—
188C2×C32#70911yescharacteristic
189C2×C32#71111yescharacteristic
190C2×C32#71111yescharacteristic
191C4⋊C4—451no—
192C4⋊C4—451no—
193C4⋊C4—451no—
194C22⋊C4—31no—
195C22⋊C4—151no—
196C22⋊C4—451no—
197C42—451no—
198C3×C5—21no—
199C3×C5#87911yescharacteristic, complemented
200C3×C5#87911yescharacteristic, complemented
201C22×C3—22no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—41no—
210C22×C3—41no—
211C22×C3C2×D3×D511yescharacteristic
212C22×C3C22×D1511yescharacteristic
213C3×C4—61no—
214C3×C4—61no—
215C3×C4—301no—
216C3×C4—301no—
217Dic3—21no—
218Dic3—21no—
219Dic3—101no—
220Dic3—101no—
221Dic3—301no—
222Dic3—301no—
223Dic3—301no—
224Dic3—301no—
225Dic3—601no—
226Dic3—601no—
227C2×C5—41no—
228C2×C5#380411yescharacteristic
229C2×C5#380411yescharacteristic
230C2×C5#380511yescharacteristic
231C32#402511yescharacteristic, complemented, Sylow
232C23D3×D1511yescharacteristic
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—151no—
236C2×C4—151no—
237C2×C4—451no—
238C2×C4—451no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—42no—
243C2×C3—41no—
244C2×C3—41no—
245C2×C3#677911yescharacteristic
246C2×C3#678011yescharacteristic
247C2×C3#678211yescharacteristic
248C2×C3#681711yescharacteristic
249C2×C3#681911yescharacteristic
250C2×C3#681911yescharacteristic
251C5#6395611yescharacteristic, complemented, Sylow
252C22—21no—
253C22—21no—
254C22—21no—
255C22C2×D3×D1511yescharacteristic
256C4—61no—
257C4—61no—
258C4—301no—
259C4—301no—
260C4—901no—
261C4—901no—
262C3—21no—
263C3#9153111yescharacteristic, complemented
264C3#9176811yescharacteristic, complemented
265C2—41no—
266C2#1062420711yescharacteristic
267C2#1062420811yescharacteristic
268C2#1062421011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
Fitting, prime radicalC23×C32×C5C22
hypercenterC23D3×D15
hypocenterC32×C5#126
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
4. Dic3⋊Dic15C2semidirect
5. #10623815C2semidirect
6. #10623814C2semidirect
7. Dic3×Dic15C2semidirect
129. C32×C5#126semidirect
199. C3×C5#879semidirect
200. C3×C5#879semidirect
231. C32#4025semidirect
251. C5#63956semidirect
263. C3#91531semidirect
264. C3#91768semidirect

Maximal subgroups

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

subgroupindex
#106239132
C3×#67192
C3×C5×#2172
Dic3⋊Dic152
#106238152
#106238142
Dic3×Dic152
#917683
#915313
#639565