Finite Group Databasebeta

← #13085745

Subgroups — #13085745

Order 1440.

288 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 56 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#10624194C211yesmaximal, characteristic, complemented
2#10624151C211yesmaximal, characteristic, complemented
3#10623821C211yesmaximal, characteristic, complemented
4#10623794C211yesmaximal, characteristic, complemented
5C5×#3717C211yesmaximal, characteristic, complemented
6C3×#6661C211yesmaximal, characteristic, complemented
7C3×#6658C211yesmaximal, characteristic, complemented
8#91523—31nomaximal
9#91276—31nomaximal
10C4×C3⋊D15C2211yescharacteristic
11C5×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×C5×Dic6C2211yescharacteristic
14C32×Dic10C2211yescharacteristic
15#67151—21no—
16Dic3×D15—21no—
17#67140—21no—
18C3⋊D3×Dic5—21no—
19C3×C3⋊#168C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63950—51nomaximal, Hall
22#6821—31no—
23#6768—31no—
24#6768—31no—
25#6768—61no—
26#6766—31no—
27C8×D15—31no—
28C5×#215—31no—
29C5×#204—31no—
30C3×#689—31no—
31C3×#677—31no—
32#6661D311yescharacteristic, complemented
33#6658D311yescharacteristic, complemented
34#6654—31no—
35#6652—31no—
36#6648—31no—
37C2×C3⋊D15D411yescharacteristic
38C2×C5×C3⋊D3—21no—
39C2×C3×D15—21no—
40C32×C4×C5C2311yescharacteristic
41C3⋊Dic15D411yescharacteristic
42C3×C5×Dic3—21no—
43C32×Dic5—21no—
44#4062—91noHall
45#3832—51no—
46#3796—51no—
47C3×#216—51no—
48C3×#215—51no—
49#3717D511yescharacteristic, complemented
50#3714—51no—
51#3710—51no—
52C3×C5×Q8—31no—
53D60—61no—
54D60C2×D311yescharacteristic
55C4×D15—31no—
56C4×D15—31no—
57C4×D15—61no—
58C4×D15—61no—
59C5×D12—31no—
60C5×D12—31no—
61C5×D12—61no—
62C5×Dic6C2×D311yescharacteristic
63C3×D20—31no—
64C3×Dic10—21no—
65C3×Dic10C2×D311yescharacteristic
66C3×Dic10C2×D311yescharacteristic
67#1203—61no—
68#1203—61no—
69#1203—62no—
70#1202—61no—
71D3×Dic5—61no—
72D3×Dic5—61no—
73D3×Dic5—62no—
74D5×Dic3—61no—
75C3×C5×C8—31no—
76C3⋊#168C2×D311yescharacteristic
77C3×#168—31no—
78C5×C3⋊C8C2×D311yescharacteristic
79#919—151no—
80#916—151no—
81C2×C32×C5C2×D411yescharacteristic
82C3⋊D15—21no—
83C5×C3⋊D3—41no—
84C3×D15—41no—
85#713—91no—
86#711—91no—
87C5×SD16—91no—
88#689—31no—
89#686—91no—
90#677—31no—
91C8×D5—91no—
92C32×Q8—51no—
93C4⋊(C3⋊D3)—101no—
94C4⋊(C3⋊D3)C2×D511yescharacteristic
95C4×C3⋊D3—51no—
96C4×C3⋊D3—101no—
97C3×D12—51no—
98C3×Dic6C2×D511yescharacteristic
99#626—101no—
100D3×Dic3—101no—
101C3×C3⋊C8—51no—
102C3×C3⋊C8C2×D511yescharacteristic
103C2×D15—21no—
104C2×D15—31no—
105C2×D15—31no—
106C2×D15—61no—
107C2×C5×D3—62no—
108C2×C5×D3—61no—
109C2×C5×D3—61no—
110C2×C3×D5—61no—
111C3×C4×C5—21no—
112C3×C4×C5—61no—
113C3×C4×C5C22×D311yescharacteristic
114C3×C4×C5C22×D311yescharacteristic
115Dic15—31no—
116Dic15—31no—
117Dic15—61no—
118C3×Dic5—22no—
119C3×Dic5—21no—
120C3×Dic5—21no—
121C5×Dic3—21no—
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—31no—
131#215—51no—
132#213—151no—
133D24—151no—
134#204—31no—
135D3×C8—151no—
136D3×C8—151no—
137C32×C5#13511yescharacteristic, complemented, Hall
138C5×Q8—31no—
139C5×D4—91no—
140C22⋊D5—181no—
141C2×Dic5—181no—
142D20—31no—
143D20—181no—
144C4×D5—91no—
145C4×D5—181no—
146Dic10D3211yescharacteristic
147C5×C8—31no—
148#168—31no—
149C2×C3⋊D3—21no—
150C2×C3⋊D3—51no—
151C2×C3×D3—101no—
152C32×C4—101no—
153C32×C4C22×D511yescharacteristic
154C3⋊Dic3—51no—
155C3×Dic3—21no—
156#135—451noSylow
157C2×C3×C5—21no—
158C2×C3×C5D3×D411yescharacteristic
159C2×C3×C5D3×D411yescharacteristic
160D15—41no—
161D15—61no—
162D15—61no—
163D15—121no—
164C3×D5—121no—
165C5×D3—122no—
166C5×D3—121no—
167C5×D3—121no—
168C3×Q8—31no—
169C3×Q8—51no—
170C3×Q8—51no—
171C3×Q8—101no—
172C3×D4—151no—
173#67—301no—
174C2×Dic3—301no—
175D12—31no—
176D12—31no—
177D12—51no—
178D12—61no—
179D12—301no—
180D12—301no—
181D12—301no—
182D12—302no—
183C4×D3—151no—
184C4×D3—151no—
185C4×D3—301no—
186C4×D3—301no—
187C4×D3—301no—
188C4×D3—301no—
189C4×D3—302no—
190Dic6D3×D511yescharacteristic
191C3×C8—31no—
192C3×C8—151no—
193C3⋊C8—51no—
194C3⋊C8D3×D511yescharacteristic
195C22×C5—181no—
196C2×D5—61no—
197C2×D5—91no—
198C4×C5—61no—
199C4×C5C2×D3211yescharacteristic
200Dic5—21no—
201Dic5—91no—
202C2×C32D4×D511yescharacteristic
203C3⋊D3—41no—
204C3⋊D3—101no—
205C3×D3—201no—
206#41—451no—
207#41—451no—
208Q16—151no—
209SD16—91no—
210SD16—151no—
211D8—451no—
212C2×C8—451no—
213C3×C5—21no—
214C3×C5#91611yescharacteristic, complemented
215C3×C5#91911yescharacteristic, complemented
216C22×C3—301no—
217C2×D3—62no—
218C2×D3—61no—
219C2×D3—61no—
220C2×D3—101no—
221C2×D3—151no—
222C2×D3—151no—
223C2×D3—301no—
224C3×C4—21no—
225C3×C4—61no—
226C3×C4—102no—
227C3×C4—101no—
228C3×C4—101no—
229C3×C4C2×D3×D511yescharacteristic
230C3×C4C2×D3×D511yescharacteristic
231Dic3—21no—
232Dic3—151no—
233Dic3—151no—
234Dic3—301no—
235C2×C5—361no—
236C2×C5#381111yescharacteristic
237D5—121no—
238D5—181no—
239C32#406211yescharacteristic, complemented, Sylow
240Q8—31no—
241Q8—51no—
242D4—91no—
243D4—151no—
244D4—901no—
245D4—901no—
246C2×C4—451no—
247C2×C4—901no—
248C2×C4—901no—
249C8—31no—
250C8—151no—
251C2×C3—21no—
252C2×C3—601no—
253C2×C3#677711yescharacteristic
254C2×C3#679011yescharacteristic
255D3—122no—
256D3—121no—
257D3—121no—
258D3—201no—
259D3—301no—
260D3—301no—
261D3—601no—
262C5#6395011yescharacteristic, complemented, Sylow
263C22—181no—
264C22—301no—
265C22—451no—
266C4—61no—
267C4—101no—
268C4—451no—
269C4D32×D511yescharacteristic
270C3—21no—
271C3#9127611yescharacteristic, complemented
272C3#9152311yescharacteristic, complemented
273C2—361no—
274C2—601no—
275C2—901no—
276C2#1062403011yescharacteristic
subgroupG/H
centerC2#10624030
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. #10624194C2semidirect
2. #10624151C2semidirect
3. #10623821C2semidirect
4. #10623794C2semidirect
5. C5×#3717C2semidirect
6. C3×#6661C2semidirect
7. C3×#6658C2semidirect
32. #6661D3semidirect
33. #6658D3semidirect
49. #3717D5semidirect
137. C32×C5#135semidirect
214. C3×C5#916semidirect
215. C3×C5#919semidirect
239. C32#4062semidirect
262. C5#63950semidirect
271. C3#91276semidirect
272. C3#91523semidirect

Maximal subgroups

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

subgroupindex
#106241942
#106241512
#106238212
#106237942
C5×#37172
C3×#66612
C3×#66582
#915233
#912763
#639505