Finite Group Databasebeta

← #13088942

Subgroups — #13088942

Order 1440.

710 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 144 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#10624227C211yesmaximal, characteristic, complemented
2#10624194C212yesmaximal, complemented
3C5×#3797C211yesmaximal, characteristic, complemented
4C4×D5×C3⋊D3C211yesmaximal, characteristic, complemented
5C3×#6773C212yesmaximal, complemented
6#10624052C212yesmaximal, complemented
7#10624047C212yesmaximal, complemented
8#10624031C212yesmaximal, complemented
9#10624022C212yesmaximal, complemented
10D3×#713—32nomaximal
11C2×(C3⋊D3)⋊D5C2212yes—
12C2×D5×C3⋊D3C2211yescharacteristic
13C4×C3⋊D15C2211yescharacteristic, complemented
14C4×C5×C3⋊D3C2211yescharacteristic
15C3×D60C2212yescomplemented
16C3×C5×Dic6C2212yescomplemented
17C32×C4×D5C2211yescharacteristic, complemented
18#67157C2212yescomplemented
19#67151C2214yescomplemented
20Dic3×D15C2214yescomplemented
21C5×#627C2212yescomplemented
22C5×#624C2212yes—
23#67137C2211yescharacteristic, complemented
24C3⋊D3×Dic5C2211yescharacteristic
25D5×C3⋊Dic3C2211yescharacteristic, complemented
26C3×#1202C2214yescomplemented
27C3×#1200C2214yescomplemented
28#64306—51nomaximal, Hall
29#6821—32no—
30C5×D3×Q8—32no—
31C3×#713—32no—
32D3×D20—32no—
33D3×D20—34no—
34C4×D3×D5—32no—
35C4×D3×D5—34no—
36C4×D3×D5—61no—
37#6773—34no—
38#6773D312yescomplemented
39#6766—32no—
40#6766—34no—
41C2×C3⋊D15C2311yescharacteristic
42C2×C5×C3⋊D3C2311yescharacteristic
43C2×C3×D15C2314yes—
44C2×C32×D5C2311yescharacteristic
45(C3⋊D3)⋊D5—24no—
46D5×C3⋊D3—22no—
47C32×C4×C5C2311yescharacteristic
48C3⋊Dic15C2311yescharacteristic
49C5×C3⋊Dic3C2311yescharacteristic
50C3×C5×Dic3C2314yes—
51C32×Dic5C2311yescharacteristic
52C2×#713—91noHall
53C2×C4×C3⋊D3—51no—
54C3×#235—52no—
55#3811—52no—
56#3805—52no—
57#3802—51no—
58C4×D32—52no—
59#3798—52no—
60#3797D511yescharacteristic, complemented
61#3796—52no—
62C2×D3×D5—34no—
63C2×D3×D5—32no—
64C2×D3×D5—61no—
65C3×C5×Q8—32no—
66D60—34no—
67D60C2×D312yescomplemented
68C4×D15—34no—
69C4×D15—32no—
70C4×D15—61no—
71C4×C5×D3—32no—
72C4×C5×D3—34no—
73C4×C5×D3—61no—
74C5×Dic6—34no—
75C5×Dic6C2×D312yescomplemented
76C3×D20—34no—
77C3×D20—32no—
78C3×C4×D5—21no—
79C3×C4×D5—34no—
80C3×C4×D5C2×D312yescomplemented
81#1202—34no—
82#1202—34no—
83#1202C2×D314yescomplemented
84#1200—32no—
85#1200—61no—
86#1200C2×D314yescomplemented
87D3×Dic5—32no—
88D3×Dic5—61no—
89D5×Dic3—32no—
90D5×Dic3—34no—
91D5×Dic3—61no—
92D3×#41—152no—
93C2×C32×C5C2411yescharacteristic
94C3⋊D15—21no—
95C5×C3⋊D3#4112yescomplemented
96C3×D15—24no—
97C32×D5—21no—
98C2×C5×Q8—91no—
99#713—32no—
100#713—92no—
101#713—92no—
102#713—92no—
103C2×D20—92no—
104C2×D20—91no—
105C2×C4×D5—92no—
106C2×C4×D5—91no—
107C22×C3⋊D3—51no—
108C2×D32—52no—
109C2×C32×C4—51no—
110C2×C3⋊Dic3—51no—
111C4×C3⋊D3—51no—
112C4×C3⋊D3—51no—
113C4×C3⋊D3—51no—
114C4×C3⋊D3C2×D511yescharacteristic
115C3×#67—54no—
116C3×D12—52no—
117C3×C4×D3—54no—
118C3×Dic6C2×D512yescomplemented
119#627C2×D512yescomplemented
120#626—54no—
121#625—52no—
122#624C2×D512yes—
123D3×Dic3—54no—
124C2×D15—32no—
125C2×D15—61no—
126C2×D15C22×D314yes—
127C2×C5×D3—32no—
128C2×C5×D3—61no—
129C2×C3×D5—21no—
130C2×C3×D5—34no—
131C2×C3×D5C22×D312yes—
132D3×D5—64no—
133D3×D5—68no—
134D3×D5—64no—
135C3×C4×C5—21no—
136C3×C4×C5—34no—
137C3×C4×C5C22×D312yes—
138Dic15—32no—
139Dic15—61no—
140C3×Dic5—21no—
141C3×Dic5C22×D312yes—
142C5×Dic3—32no—
143C5×Dic3—61no—
144C5×Dic3C22×D314yes—
145C3×#41—152no—
146#239—152no—
147D3×Q8—32no—
148#237—154no—
149#237—152no—
150D3×D4—152no—
151D3×D4—154no—
152#235—52no—
153#235—154no—
154C2×C4×D3—154no—
155C2×C4×D3—152no—
156C2×C4×D3—301no—
157C32×C5C2×#4111yescharacteristic, complemented, Hall
158C22×D5—92no—
159C22×D5—91no—
160C5×Q8—32no—
161C5×Q8—92no—
162C2×C4×C5—92no—
163C2×C4×C5—91no—
164C2×Dic5—91no—
165D20—34no—
166D20—32no—
167D20—94no—
168D20—92no—
169C4×D5—34no—
170C4×D5—94no—
171C4×D5—91no—
172C4×D5—91no—
173C4×D5—91no—
174C4×D5D3211yescharacteristic, complemented
175C22×C32—51no—
176C2×C3⋊D3—51no—
177C2×C3⋊D3—102no—
178C2×C3⋊D3C22×D511yescharacteristic
179C2×C3×D3—54no—
180D32—104no—
181C32×C4—51no—
182C32×C4C22×D511yescharacteristic
183C3⋊Dic3—51no—
184C3⋊Dic3C22×D511yescharacteristic
185C3×Dic3C22×D514yes—
186C2×#41—451noSylow
187C2×C3×C5—21no—
188C2×C3×C5C23×D312yes—
189D15—24no—
190D15—62no—
191D15—62no—
192C3×D5—22no—
193C3×D5—22no—
194C3×D5—64no—
195C5×D3—34no—
196C5×D3—62no—
197C22×D3—154no—
198C22×D3—152no—
199C22×D3—301no—
200C3×Q8—32no—
201C3×D4—154no—
202C3×D4—152no—
203C2×C3×C4—52no—
204C2×C3×C4—101no—
205C2×C3×C4—154no—
206#67—54no—
207#67—154no—
208#67—154no—
209C2×Dic3—152no—
210C2×Dic3—154no—
211C2×Dic3—301no—
212D12—52no—
213D12—154no—
214C4×D3—32no—
215C4×D3—34no—
216C4×D3—54no—
217C4×D3—61no—
218C4×D3—152no—
219C4×D3—154no—
220C4×D3—152no—
221C4×D3—152no—
222C4×D3—301no—
223C4×D3—301no—
224C4×D3—301no—
225Dic6—34no—
226Dic6D3×D512yescomplemented
227C22×C5—91no—
228C2×D5—34no—
229C2×D5—91no—
230C2×D5—182no—
231C2×D5—184no—
232C2×D5C2×D3211yescharacteristic
233C4×C5—34no—
234C4×C5—91no—
235C4×C5C2×D3211yescharacteristic
236Dic5—91no—
237Dic5C2×D3211yescharacteristic
238C2×C32—101no—
239C2×C32C23×D511yescharacteristic
240C3⋊D3—101no—
241C3⋊D3#71312yescomplemented
242C3×D3—104no—
243#41—152no—
244#41—452no—
245#41—452no—
246#41—452no—
247C2×Q8—91no—
248C2×D4—452no—
249C2×D4—451no—
250C22×C4—451no—
251C22×C4—452no—
252C3×C5—21no—
253C3×C5D3×#4112yescomplemented
254C22×C3—52no—
255C22×C3—101no—
256C22×C3—154no—
257C2×D3—32no—
258C2×D3—54no—
259C2×D3—61no—
260C2×D3—152no—
261C2×D3—301no—
262C2×D3—308no—
263C2×D3—304no—
264C2×D3—304no—
265C3×C4—21no—
266C3×C4—34no—
267C3×C4—52no—
268C3×C4—101no—
269C3×C4C2×D3×D512yes—
270Dic3—32no—
271Dic3—61no—
272Dic3—152no—
273Dic3—301no—
274Dic3C2×D3×D514yes—
275C2×C5—92no—
276C2×C5C22×D3211yescharacteristic
277D5—21no—
278D5—64no—
279D5—181no—
280C32C2×#71311yescharacteristic, complemented, Sylow
281C23—451no—
282C23—452no—
283Q8—32no—
284Q8—92no—
285D4—154no—
286D4—152no—
287D4—454no—
288D4—452no—
289C2×C4—51no—
290C2×C4—92no—
291C2×C4—91no—
292C2×C4—154no—
293C2×C4—454no—
294C2×C4—451no—
295C2×C4—451no—
296C2×C4—451no—
297C2×C4—451no—
298C2×C3—21no—
299C2×C3—102no—
300C2×C3—102no—
301C2×C3—304no—
302C2×C3C22×D3×D512yes—
303D3—34no—
304D3—62no—
305D3—104no—
306D3—302no—
307D3—302no—
308C5#6430611yescharacteristic, complemented, Sylow
309C22—51no—
310C22—91no—
311C22—154no—
312C22—451no—
313C22—902no—
314C22—904no—
315C4—34no—
316C4—51no—
317C4—91no—
318C4—451no—
319C4D32×D511yescharacteristic
320C3—21no—
321C3D3×#71312yescomplemented
322C2—92no—
323C2—101no—
324C2—304no—
325C2—901no—
326C2C2×D32×D511yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×D5
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C4×C5C23
hypercenterC4D32×D5
hypocenterC32×C5C2×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #10624227C2semidirect
2. #10624194C2semidirect
3. C5×#3797C2semidirect
4. C4×D5×C3⋊D3C2semidirect
5. C3×#6773C2semidirect
6. #10624052C2semidirect
7. #10624047C2semidirect
8. #10624031C2semidirect
9. #10624022C2semidirect
13. C4×C3⋊D15C22semidirect
15. C3×D60C22semidirect
16. C3×C5×Dic6C22semidirect
17. C32×C4×D5C22semidirect
18. #67157C22semidirect
19. #67151C22semidirect
20. Dic3×D15C22semidirect
21. C5×#627C22semidirect
23. #67137C22semidirect
25. D5×C3⋊Dic3C22semidirect
26. C3×#1202C22semidirect
27. C3×#1200C22semidirect
38. #6773D3semidirect
60. #3797D5semidirect
67. D60C2×D3semidirect
75. C5×Dic6C2×D3semidirect
80. C3×C4×D5C2×D3semidirect
83. #1202C2×D3semidirect
86. #1200C2×D3semidirect
95. C5×C3⋊D3#41semidirect
118. C3×Dic6C2×D5semidirect
119. #627C2×D5semidirect
157. C32×C5C2×#41semidirect
174. C4×D5D32semidirect
226. Dic6D3×D5semidirect
241. C3⋊D3#713semidirect
253. C3×C5D3×#41semidirect
280. C32C2×#713semidirect
308. C5#64306semidirect
321. C3D3×#713semidirect

Maximal subgroups

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

subgroupindex
#106242272
#106241942
C5×#37972
C4×D5×C3⋊D32
C3×#67732
#106240522
#106240472
#106240312
#106240222
D3×#7133
#643065