Finite Group Databasebeta

← #13085747

Subgroups — #13085747

Order 1440.

288 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 58 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#10624220C211yesmaximal, characteristic, complemented
2#10624152C211yesmaximal, characteristic, complemented
3#10623804C211yesmaximal, characteristic, complemented
4#10623799C211yesmaximal, characteristic, complemented
5C5×#3710C211yesmaximal, characteristic, complemented
6C3×#6662C211yesmaximal, characteristic, complemented
7C3×#6658C211yesmaximal, characteristic, complemented
8#91275—31nomaximal
9#91272—31nomaximal
10C4⋊(C3⋊D15)C2211yescharacteristic
11C4×C5×C3⋊D3C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×Dic30C2211yescharacteristic
14C32×Dic10C2211yescharacteristic
15#67156—21no—
16#67154—21no—
17#67140—21no—
18#67137—21no—
19C3×C5×C3⋊C8C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63950—51nomaximal, Hall
22#6769—31no—
23#6769—31no—
24#6769—31no—
25#6769—61no—
26#6765—31no—
27D120—31no—
28#6706—31no—
29C5×D3×C8—31no—
30C5×D3×C8—31no—
31C3×Dic20—31no—
32C3×#677—31no—
33#6662D311yescharacteristic, complemented
34#6658—31no—
35#6658D311yescharacteristic, complemented
36#6653—31no—
37C2×C3⋊D15—21no—
38C2×C5×C3⋊D3D411yescharacteristic
39C2×C3×D15—21no—
40C32×C4×C5C2311yescharacteristic
41C5×C3⋊Dic3D411yescharacteristic
42C3×Dic15—21no—
43C32×Dic5—21no—
44#4050—91noHall
45#3832—51no—
46#3796—51no—
47C3×#216—51no—
48C3×#215—51no—
49#3717—51no—
50#3714—51no—
51#3710D511yescharacteristic, complemented
52D60—31no—
53D60—31no—
54D60—61no—
55D60C2×D311yescharacteristic
56Dic30C2×D311yescharacteristic
57C4×C5×D3—31no—
58C4×C5×D3—31no—
59C4×C5×D3—61no—
60C3×D20—31no—
61C3×Dic10—21no—
62C3×Dic10—31no—
63C3×Dic10C2×D311yescharacteristic
64C3×Dic10C2×D311yescharacteristic
65#1203—61no—
66#1203—61no—
67#1203—62no—
68#1203—61no—
69#1201—61no—
70#1200—61no—
71#1200—61no—
72#1200—61no—
73#1200—62no—
74D5×Dic3—61no—
75C3×C5×C8—31no—
76C3×C5×C8—31no—
77C5×C3⋊C8C2×D311yescharacteristic
78C5×C3⋊C8C2×D311yescharacteristic
79#919—151no—
80#916—151no—
81C2×C32×C5C2×D411yescharacteristic
82C3⋊D15—41no—
83C5×C3⋊D3—21no—
84C3×D15—41no—
85#709—91no—
86#709—91no—
87C2×C5×C8—91no—
88Dic20—31no—
89D40—91no—
90#677—31no—
91#677—91no—
92C32×Q8—51no—
93C4⋊(C3⋊D3)—51no—
94C4⋊(C3⋊D3)—101no—
95C4×C3⋊D3—101no—
96C4×C3⋊D3C2×D511yescharacteristic
97C3×D12—51no—
98C3×Dic6—51no—
99#626—101no—
100D3×Dic3—101no—
101C3×C3⋊C8C2×D511yescharacteristic
102C3×C3⋊C8C2×D511yescharacteristic
103C2×D15—21no—
104C2×D15—62no—
105C2×D15—61no—
106C2×D15—61no—
107C2×C5×D3—31no—
108C2×C5×D3—31no—
109C2×C5×D3—61no—
110C2×C3×D5—61no—
111C3×C4×C5—21no—
112C3×C4×C5C22×D311yescharacteristic
113C3×C4×C5C22×D311yescharacteristic
114Dic15—21no—
115C3×Dic5—22no—
116C3×Dic5—21no—
117C3×Dic5—21no—
118C3×Dic5—61no—
119C5×Dic3—31no—
120C5×Dic3—31no—
121C5×Dic3—61no—
122#239—151no—
123#239—151no—
124#239—151no—
125#239—301no—
126#237—151no—
127C3×Q16—151no—
128C3×SD16—151no—
129#216—51no—
130#215—51no—
131#215—151no—
132#213—151no—
133D24—151no—
134#204—151no—
135D3×C8—31no—
136D3×C8—31no—
137C32×C5#13511yescharacteristic, complemented, Hall
138C2×C4×C5—91no—
139C22⋊D5—181no—
140C22⋊D5—181no—
141D20—31no—
142D20—91no—
143C4×D5—181no—
144C4×D5—181no—
145Dic10—31no—
146Dic10D3211yescharacteristic
147C5×C8—31no—
148C5×C8—31no—
149C2×C3⋊D3—101no—
150C2×C3⋊D3D2011yescharacteristic
151C2×C3×D3—101no—
152C32×C4—101no—
153C32×C4C22×D511yescharacteristic
154C3⋊Dic3D2011yescharacteristic
155C3×Dic3—101no—
156#135—451noSylow
157C2×C3×C5—21no—
158C2×C3×C5D3×D411yescharacteristic
159C2×C3×C5D3×D411yescharacteristic
160D15—41no—
161D15—122no—
162D15—121no—
163D15—121no—
164C3×D5—121no—
165C5×D3—61no—
166C5×D3—61no—
167C5×D3—121no—
168C3×Q8—51no—
169C3×Q8—51no—
170C3×Q8—101no—
171C3×Q8—151no—
172C3×D4—151no—
173#67—301no—
174C2×Dic3—301no—
175D12—51no—
176D12—151no—
177D12—151no—
178D12—301no—
179D12—301no—
180D12—301no—
181D12—302no—
182D12—301no—
183C4×D3—31no—
184C4×D3—31no—
185C4×D3—61no—
186C4×D3—301no—
187C4×D3—301no—
188C4×D3—301no—
189C4×D3—302no—
190Dic6—51no—
191C3×C8—31no—
192C3×C8—31no—
193C3⋊C8D3×D511yescharacteristic
194C3⋊C8D3×D511yescharacteristic
195C22×C5—91no—
196C2×D5—61no—
197C2×D5—181no—
198C4×C5—91no—
199C4×C5C2×D3211yescharacteristic
200Dic5—21no—
201Dic5—61no—
202C2×C32C2×D2011yescharacteristic
203C3⋊D3—21no—
204C3⋊D3—201no—
205C3×D3—201no—
206#41—451no—
207#41—451no—
208Q16—151no—
209SD16—151no—
210SD16—451no—
211D8—451no—
212C2×C8—91no—
213C3×C5—21no—
214C3×C5#91611yescharacteristic, complemented
215C3×C5#91911yescharacteristic, complemented
216C22×C3—301no—
217C2×D3—31no—
218C2×D3—31no—
219C2×D3—61no—
220C2×D3—101no—
221C2×D3—302no—
222C2×D3—301no—
223C2×D3—301no—
224C3×C4—21no—
225C3×C4—102no—
226C3×C4—101no—
227C3×C4—101no—
228C3×C4—301no—
229C3×C4C2×D3×D511yescharacteristic
230C3×C4C2×D3×D511yescharacteristic
231Dic3—31no—
232Dic3—31no—
233Dic3—61no—
234Dic3—101no—
235C2×C5—181no—
236C2×C5#381111yescharacteristic
237D5—121no—
238D5—361no—
239C32#405011yescharacteristic, complemented, Sylow
240Q8—51no—
241Q8—151no—
242D4—151no—
243D4—451no—
244D4—901no—
245D4—901no—
246C2×C4—91no—
247C2×C4—901no—
248C2×C4—901no—
249C8—31no—
250C8—31no—
251C2×C3—21no—
252C2×C3—601no—
253C2×C3D3×D2011yescharacteristic
254C2×C3D3×D2011yescharacteristic
255D3—61no—
256D3—61no—
257D3—121no—
258D3—201no—
259D3—602no—
260D3—601no—
261D3—601no—
262C5#6395011yescharacteristic, complemented, Sylow
263C22—91no—
264C22—301no—
265C22—901no—
266C4—91no—
267C4—101no—
268C4—301no—
269C4D32×D511yescharacteristic
270C3—21no—
271C3#9127211yescharacteristic, complemented
272C3#9127511yescharacteristic, complemented
273C2—181no—
274C2—601no—
275C2—1801no—
276C2#1062403111yescharacteristic
subgroupG/H
centerC2#10624031
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. #10624220C2semidirect
2. #10624152C2semidirect
3. #10623804C2semidirect
4. #10623799C2semidirect
5. C5×#3710C2semidirect
6. C3×#6662C2semidirect
7. C3×#6658C2semidirect
33. #6662D3semidirect
35. #6658D3semidirect
51. #3710D5semidirect
137. C32×C5#135semidirect
214. C3×C5#916semidirect
215. C3×C5#919semidirect
239. C32#4050semidirect
262. C5#63950semidirect
271. C3#91272semidirect
272. C3#91275semidirect

Maximal subgroups

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

subgroupindex
#106242202
#106241522
#106238042
#106237992
C5×#37102
C3×#66622
C3×#66582
#912753
#912723
#639505