Finite Group Databasebeta

← #13085728

Subgroups — #13085728

Order 1440.

270 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 62 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#10624197C211yesmaximal, characteristic, complemented
2C3×#6765C211yesmaximal, characteristic, complemented
3#10623827C211yesmaximal, characteristic, complemented
4#10623804C211yesmaximal, characteristic, complemented
5C5×D3×C3⋊C8C211yesmaximal, characteristic, complemented
6#10623758C211yesmaximal, characteristic, complemented
7C3×#6657C211yesmaximal, characteristic, complemented
8#91311—31nomaximal
9#91272—31nomaximal
10C4⋊(C3⋊D15)C2211yescharacteristic
11C3×Dic30C2211yescharacteristic
12C3×Dic30C2211yescharacteristic
13C3×C4×C5×D3C2211yescharacteristic
14C32×D20C2211yescharacteristic
15#67152—21no—
16#67149—21no—
17C3×#1201—21no—
18C3×D5×Dic3—21no—
19C5×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63935—51nomaximal, Hall
22#6817—31no—
23C3×#709—31no—
24#6769—31no—
25#6765D311yescharacteristic, complemented
26#6706—31no—
27C2×C5×C3⋊C8—31no—
28C5×D3×C8—31no—
29C3×#677—31no—
30#6662—31no—
31#6662—31no—
32#6658—31no—
33#6657D311yescharacteristic, complemented
34#6653—31no—
35#6653—31no—
36#6653—61no—
37C2×C3⋊D15—21no—
38C2×C3×C5×D3D411yescharacteristic
39C2×C32×D5—21no—
40C32×C4×C5C2311yescharacteristic
41C3×Dic15—21no—
42C3×Dic15—21no—
43C3×C5×Dic3D411yescharacteristic
44#4050—91noHall
45C3×#237—51no—
46#3799—51no—
47#3753—51no—
48C3×#214—51no—
49#3718—51no—
50#3717—51no—
51D3×C3⋊C8D511yescharacteristic, complemented
52C2×C3×C4×C5—31no—
53#1220—61no—
54D60—31no—
55D60—31no—
56D60—61no—
57C4×D15—61no—
58Dic30C2×D311yescharacteristic
59Dic30C2×D311yescharacteristic
60C4×C5×D3C2×D311yescharacteristic
61C3×C22⋊D5—61no—
62C3×D20—21no—
63C3×D20C2×D311yescharacteristic
64C3×D20C2×D311yescharacteristic
65C3×C4×D5—61no—
66C3×Dic10—31no—
67C3×Dic10—31no—
68#1203—61no—
69#1201—21no—
70#1200—61no—
71D5×Dic3—21no—
72C3×C5×C8—31no—
73C5×C3⋊C8—31no—
74C5×C3⋊C8—31no—
75C5×C3⋊C8—61no—
76C5×C3⋊C8C2×D311yescharacteristic
77#950—151no—
78#916—151no—
79C2×C32×C5C2×D411yescharacteristic
80C3⋊D15—41no—
81C3×C5×D3—21no—
82C32×D5—41no—
83#709—31no—
84#709—91no—
85C2×C5×C8—91no—
86Dic20—91no—
87D40—91no—
88#677—31no—
89#677—91no—
90C32×D4—51no—
91C4⋊(C3⋊D3)—51no—
92C3×#67—101no—
93C2×C3×Dic3—101no—
94C3×C4×D3C2×D511yescharacteristic
95C3×Dic6—51no—
96C3×Dic6—51no—
97#626—101no—
98#624—101no—
99C3⋊(C3⋊C8)C2×D511yescharacteristic
100C3×C3⋊C8C2×D511yescharacteristic
101C22×C3×C5—31no—
102C2×D15—61no—
103C2×D15—61no—
104C2×D15—121no—
105C2×C5×D3#6711yescharacteristic
106C2×C3×D5—21no—
107C2×C3×D5—21no—
108C2×C3×D5—41no—
109C3×C4×C5—21no—
110C3×C4×C5—31no—
111C3×C4×C5C22×D311yescharacteristic
112C3×C4×C5C22×D311yescharacteristic
113Dic15—21no—
114Dic15—21no—
115C3×Dic5—61no—
116C3×Dic5—61no—
117C5×Dic3#6711yescharacteristic
118C3×#41—151no—
119#239—151no—
120#237—51no—
121#235—151no—
122C3×SD16—151no—
123#216—151no—
124#216—151no—
125#215—151no—
126#214—51no—
127#213—151no—
128#213—151no—
129#213—301no—
130C2×C3⋊C8—31no—
131#204—151no—
132D3×C8—31no—
133C32×C5#13511yescharacteristic, complemented, Hall
134C2×C4×C5—31no—
135C22⋊D5—61no—
136C22⋊D5—181no—
137D20—91no—
138D20D3211yescharacteristic
139C4×D5—61no—
140C4×D5—181no—
141Dic10—31no—
142Dic10—31no—
143C5×C8—31no—
144C5×C8—91no—
145C22×C32—101no—
146C2×C3⋊D3—101no—
147C2×C3×D3D2011yescharacteristic
148C32×C4C22×D511yescharacteristic
149C3×Dic3—101no—
150C3×Dic3—101no—
151C3×Dic3D2011yescharacteristic
152#135—451noSylow
153C2×C3×C5—21no—
154C2×C3×C5—61no—
155C2×C3×C5D3×D411yescharacteristic
156C2×C3×C5C2×#6711yescharacteristic
157D15—121no—
158D15—121no—
159D15—241no—
160C3×D5—41no—
161C3×D5—41no—
162C3×D5—81no—
163C5×D3—21no—
164C3×Q8—151no—
165C3×Q8—151no—
166C3×D4—51no—
167C3×D4—51no—
168C3×D4—101no—
169C3×D4—301no—
170C2×C3×C4—31no—
171C2×C3×C4—301no—
172#67—101no—
173#67—301no—
174C2×Dic3—101no—
175D12—151no—
176D12—151no—
177D12—301no—
178D12—301no—
179C4×D3—301no—
180C4×D3—301no—
181C4×D3D3×D511yescharacteristic
182Dic6—51no—
183Dic6—51no—
184C3×C8—31no—
185C3⋊C8—31no—
186C3⋊C8—31no—
187C3⋊C8—61no—
188C3⋊C8D3×D511yescharacteristic
189C22×C5—31no—
190C2×D5—21no—
191C2×D5—181no—
192C4×C5—31no—
193C4×C5C2×D3211yescharacteristic
194Dic5—61no—
195Dic5—61no—
196C2×C32—201no—
197C2×C32C2×D2011yescharacteristic
198C3⋊D3—201no—
199C3×D3—21no—
200#41—151no—
201#41—451no—
202Q16—451no—
203SD16—151no—
204SD16—451no—
205D8—451no—
206C2×C8—91no—
207C3×C5—21no—
208C3×C5#91611yescharacteristic, complemented
209C3×C5#95011yescharacteristic, complemented
210C22×C3—31no—
211C22×C3—101no—
212C22×C3—101no—
213C22×C3—201no—
214C2×D3—301no—
215C2×D3—301no—
216C2×D3—601no—
217C2×D3#120211yescharacteristic
218C3×C4—21no—
219C3×C4—31no—
220C3×C4—301no—
221C3×C4—301no—
222C3×C4C2×D3×D511yescharacteristic
223C3×C4C2×D3×D511yescharacteristic
224Dic3—101no—
225Dic3—101no—
226Dic3#120211yescharacteristic
227C2×C5—61no—
228C2×C5D3×#6711yescharacteristic
229D5—41no—
230D5—361no—
231C32#405011yescharacteristic, complemented, Sylow
232Q8—151no—
233Q8—151no—
234D4—51no—
235D4—301no—
236D4—451no—
237D4—901no—
238C2×C4—31no—
239C2×C4—301no—
240C2×C4—901no—
241C8—31no—
242C8—91no—
243C2×C3—21no—
244C2×C3—61no—
245C2×C3—201no—
246C2×C3—201no—
247C2×C3—401no—
248C2×C3D3×D2011yescharacteristic
249C2×C3C2×#120211yescharacteristic
250D3—21no—
251D3—601no—
252D3—601no—
253D3—1201no—
254C5#6393511yescharacteristic, complemented, Sylow
255C22—31no—
256C22—101no—
257C22—901no—
258C4—31no—
259C4—301no—
260C4—301no—
261C4D32×D511yescharacteristic
262C3—21no—
263C3#9127211yescharacteristic, complemented
264C3#9131111yescharacteristic, complemented
265C2—61no—
266C2—201no—
267C2—1801no—
268C2D3×#120211yescharacteristic
subgroupG/H
centerC2D3×#1202
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5#135
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #10624197C2semidirect
2. C3×#6765C2semidirect
3. #10623827C2semidirect
4. #10623804C2semidirect
5. C5×D3×C3⋊C8C2semidirect
6. #10623758C2semidirect
7. C3×#6657C2semidirect
25. #6765D3semidirect
33. #6657D3semidirect
51. D3×C3⋊C8D5semidirect
133. C32×C5#135semidirect
208. C3×C5#916semidirect
209. C3×C5#950semidirect
231. C32#4050semidirect
254. C5#63935semidirect
263. C3#91272semidirect
264. C3#91311semidirect

Maximal subgroups

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

subgroupindex
#106241972
C3×#67652
#106238272
#106238042
C5×D3×C3⋊C82
#106237582
C3×#66572
#913113
#912723
#639355