Finite Group Databasebeta

← #13085663

Subgroups — #13085663

Order 1440.

270 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 72 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#10624199C211yesmaximal, characteristic
2#10623817C211yesmaximal, characteristic, complemented
3#10623797C211yesmaximal, characteristic, complemented
4C5×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5#10623753C211yesmaximal, characteristic, complemented
6C3×#6651C211yesmaximal, characteristic, complemented
7C3×#6650C211yesmaximal, characteristic, complemented
8#91291—31nomaximal
9#91267—31nomaximal
10C4×C3⋊D15C2211yescharacteristic
11C3×C4×D15C2211yescharacteristic
12C3×C4×C5×D3C2211yescharacteristic
13#67153C411yescharacteristic
14#67152C411yescharacteristic
15#67151C411yescharacteristic
16#67150C411yescharacteristic
17C5×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C3⋊#168C2211yescharacteristic
19C3×C5×C3⋊C8C2211yescharacteristic
20C32×#168C2211yescharacteristic
21#63805—51nomaximal, Hall
22#6817—31no—
23#6771—31no—
24#6705—31no—
25C2×C5×C3⋊C8—31no—
26C5×D3×C8—31no—
27C3×#681—31no—
28C3×#676—31no—
29#6651—31no—
30#6651D311yescharacteristic, complemented
31#6650D311yescharacteristic, complemented
32#6648—31no—
33#6648—31no—
34#6648—31no—
35#6648—61no—
36D5×C3⋊C8—31no—
37C2×C3⋊D15C2×C411yescharacteristic
38C2×C3×D15C2×C411yescharacteristic
39C2×C3×C5×D3C2×C411yescharacteristic
40C32×C4×C5C2311yescharacteristic
41C3⋊Dic15C2×C411yescharacteristic
42C3×Dic15C2×C411yescharacteristic
43C3×C5×Dic3C2×C411yescharacteristic
44#4047—91noHall
45#3798—51no—
46C8×C3⋊D3—51no—
47C3×ΓL(1,𝔽25)—51no—
48C3×ΓL(1,𝔽25)—51no—
49#3712—51no—
50D3×C3⋊C8—51no—
51D3×C3⋊C8D511yescharacteristic, complemented
52C2×C3×C4×C5—31no—
53#1220—31no—
54#1220—31no—
55D60—31no—
56C4×D15—31no—
57C4×D15—31no—
58C4×D15—61no—
59C4×D15C2×D311yescharacteristic
60Dic30—31no—
61C4×C5×D3C2×D311yescharacteristic
62C3×C4×D5—31no—
63#1204—31no—
64#1203—31no—
65#1202—31no—
66#1201—31no—
67C3×C5×C8—31no—
68C3⋊#168C2×D311yescharacteristic
69C3×#168—21no—
70C3×#168—31no—
71C3×#168C2×D311yescharacteristic
72C3×#168C2×D311yescharacteristic
73C5×C3⋊C8—31no—
74C5×C3⋊C8—31no—
75C5×C3⋊C8—61no—
76C5×C3⋊C8C2×D311yescharacteristic
77#907—151no—
78#907—151no—
79C2×C32×C5C22×C411yescharacteristic
80C3⋊D15—21no—
81C3×D15—21no—
82C3×C5×D3—21no—
83#709—91no—
84C2×C5×C8—91no—
85#681—31no—
86#676—31no—
87#676—91no—
88C8×D5—91no—
89C8×D5—91no—
90C4×C3⋊D3—51no—
91C3×C4×D3—51no—
92C3×C4×D3C2×D511yescharacteristic
93#627—51no—
94#626—51no—
95#626—51no—
96#625—51no—
97C32×C8—51no—
98C3⋊(C3⋊C8)C2×D511yescharacteristic
99C3×C3⋊C8—51no—
100C3×C3⋊C8C2×D511yescharacteristic
101C22×C3×C5—31no—
102C2×D15—31no—
103C2×D15—31no—
104C2×D15—61no—
105C2×D15C4×D311yescharacteristic
106C2×C5×D3C4×D311yescharacteristic
107C2×C3×D5—31no—
108C3×C4×C5—21no—
109C3×C4×C5—31no—
110C3×C4×C5C22×D311yescharacteristic
111C3×C4×C5C22×D311yescharacteristic
112Dic15—31no—
113Dic15—31no—
114Dic15—61no—
115Dic15C4×D311yescharacteristic
116C3×Dic5—31no—
117C5×Dic3C4×D311yescharacteristic
118#235—151no—
119#235—151no—
120C3×M16—151no—
121C3×M16—151no—
122C2×C3⋊C8—31no—
123C2×C3⋊C8—151no—
124ΓL(1,𝔽25)—51no—
125ΓL(1,𝔽25)—51no—
126ΓL(1,𝔽25)—151no—
127ΓL(1,𝔽25)—151no—
128D3×C8—31no—
129D3×C8—151no—
130D3×C8—151no—
131D3×C8—151no—
132D3×C8—301no—
133C32×C5#13111yescharacteristic, complemented, Hall
134C2×C4×C5—31no—
135C22⋊D5—91no—
136C22⋊D5—91no—
137D20—91no—
138C4×D5—31no—
139C4×D5—91no—
140Dic10—91no—
141C5×C8—31no—
142C5×C8—91no—
143#168—31no—
144#168D3211yescharacteristic
145C2×C3⋊D3—51no—
146C2×C3×D3—51no—
147C2×C3×D3C4×D511yescharacteristic
148C32×C4C22×D511yescharacteristic
149C3⋊Dic3—51no—
150C3×Dic3—51no—
151C3×Dic3C4×D511yescharacteristic
152#131—451noSylow
153C2×C3×C5—21no—
154C2×C3×C5—61no—
155C2×C3×C5C2×C4×D311yescharacteristic
156C2×C3×C5C2×C4×D311yescharacteristic
157D15—21no—
158D15—62no—
159D15—61no—
160D15—61no—
161C3×D5—61no—
162C5×D3—21no—
163C2×C3×C4—31no—
164C2×C3×C4—151no—
165#67—151no—
166#67—151no—
167#67—151no—
168#67—151no—
169D12—151no—
170D12—151no—
171C4×D3—51no—
172C4×D3—151no—
173C4×D3—151no—
174C4×D3—301no—
175C4×D3D3×D511yescharacteristic
176Dic6—151no—
177Dic6—151no—
178C3×C8—31no—
179C3×C8—51no—
180C3×C8—51no—
181C3×C8—101no—
182C3×C8—151no—
183C3⋊C8—31no—
184C3⋊C8—31no—
185C3⋊C8—51no—
186C3⋊C8—61no—
187C3⋊C8D3×D511yescharacteristic
188C22×C5—31no—
189C2×D5—31no—
190C2×D5—91no—
191C4×C5—31no—
192C4×C5C2×D3211yescharacteristic
193Dic5—31no—
194Dic5—91no—
195C2×C32C2×C4×D511yescharacteristic
196C3⋊D3—101no—
197C3×D3—21no—
198C3×D3—101no—
199#41—451no—
200M16—151no—
201M16—151no—
202M16—451no—
203C2×C8—91no—
204C2×C8—451no—
205C2×C8—451no—
206C3×C5—21no—
207C3×C5#90711yescharacteristic, complemented
208C3×C5#90711yescharacteristic, complemented
209C22×C3—31no—
210C22×C3—151no—
211C2×D3—51no—
212C2×D3—151no—
213C2×D3—151no—
214C2×D3—301no—
215C2×D3#120011yescharacteristic
216C3×C4—21no—
217C3×C4—31no—
218C3×C4—151no—
219C3×C4C2×D3×D511yescharacteristic
220C3×C4C2×D3×D511yescharacteristic
221Dic3—51no—
222Dic3—151no—
223Dic3—151no—
224Dic3—301no—
225Dic3#120011yescharacteristic
226C2×C5—61no—
227C2×C5C4×D3211yescharacteristic
228D5—61no—
229D5—181no—
230C32#404711yescharacteristic, complemented, Sylow
231Q8—451no—
232D4—451no—
233D4—451no—
234D4—451no—
235C2×C4—31no—
236C2×C4—151no—
237C2×C4—451no—
238C8—31no—
239C8—51no—
240C8—91no—
241C8—151no—
242C2×C3—21no—
243C2×C3—61no—
244C2×C3—301no—
245C2×C3C4×D3×D511yescharacteristic
246C2×C3C2×#120011yescharacteristic
247D3—21no—
248D3—101no—
249D3—302no—
250D3—301no—
251D3—301no—
252C5#6380511yescharacteristic, complemented, Sylow
253C22—31no—
254C22—151no—
255C22—451no—
256C4—31no—
257C4—151no—
258C4—451no—
259C4D32×D511yescharacteristic
260C3—21no—
261C3#9126711yescharacteristic, complemented
262C3#9129111yescharacteristic, complemented
263C2—61no—
264C2—301no—
265C2—901no—
266C2D3×#120011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4D32×D5
commutator, socleC2×C32×C5C22×C4
Fitting, cosocleC32×C4×C5C23
prime radical#10624199C2
hypocenterC32×C5#131
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #10623817C2semidirect
3. #10623797C2semidirect
4. C5×D3×C3⋊C8C2semidirect
5. #10623753C2semidirect
6. C3×#6651C2semidirect
7. C3×#6650C2semidirect
30. #6651D3semidirect
31. #6650D3semidirect
51. D3×C3⋊C8D5semidirect
133. C32×C5#131semidirect
207. C3×C5#907semidirect
208. C3×C5#907semidirect
230. C32#4047semidirect
252. C5#63805semidirect
261. C3#91267semidirect
262. C3#91291semidirect

Maximal subgroups

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

subgroupindex
#106241992
#106238172
#106237972
C5×D3×C3⋊C82
#106237532
C3×#66512
C3×#66502
#912913
#912673
#638055