Finite Group Databasebeta

← #13089415

Subgroups — #13089415

Order 1440.

710 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C5×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#6819C212yesmaximal, complemented
3#10624236C212yesmaximal, complemented
4C2×#67155C212yesmaximal, complemented
5#10624230C214yesmaximal, complemented
6C4×(C3⋊D3)⋊D5C211yesmaximal, characteristic, complemented
7#10624224C212yesmaximal, complemented
8#10624222C211yesmaximal, characteristic, complemented
9D3×#711—32nomaximal
10C22×C5×C3⋊D3C2212yes—
11C2×(C3⋊D3)⋊D5C2211yescharacteristic
12C32×C5×D4C2211yescharacteristic, complemented
13C5×#638C2212yescomplemented
14C5×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C4×C5×C3⋊D3C2211yescharacteristic
16C3×#1220C2214yescomplemented
17C2×C3×Dic15C2214yescomplemented
18C3×C4×D15C2212yescomplemented
19C3×Dic30C2212yescomplemented
20#67158C2212yescomplemented
21#67156C2214yescomplemented
22#67155C2212yes—
23#67155C2211yescharacteristic
24#67155C2214yescomplemented
25#67154C2212yescomplemented
26#64312—51nomaximal, Hall
27#6819D312yescomplemented
28C5×D3×D4—32no—
29C5×D3×D4—61no—
30C3×#711—32no—
31D3×C22⋊D5—34no—
32#6782—34no—
33C2×D3×Dic5—34no—
34#6780—34no—
35C4×D3×D5—32no—
36#6772—32no—
37#6768—32no—
38D3×Dic10—32no—
39C22×C32×C5C2312yes—
40C2×C5×C3⋊D3—24no—
41C2×C5×C3⋊D3C2312yes—
42C2×C5×C3⋊D3C2311yescharacteristic
43C2×C3×D15C2312yes—
44(C3⋊D3)⋊D5—22no—
45C32×C4×C5C2311yescharacteristic
46C5×C3⋊Dic3C2311yescharacteristic
47C3×Dic15C2312yes—
48C3×Dic15C2314yes—
49C2×#711—91noHall
50D4×C3⋊D3D511yescharacteristic, complemented
51C3×#237—52no—
52#3811—52no—
53C2×#624—52no—
54#3804—54no—
55C4×D32—51no—
56#3799—52no—
57#3797—51no—
58C22×C5×D3—34no—
59C22×C5×D3—62no—
60C2×D3×D5—32no—
61C3×C5×D4—21no—
62C3×C5×D4C2×D312yescomplemented
63#1220C2×D314yescomplemented
64C2×Dic15C2×D314yescomplemented
65C4×D15C2×D312yescomplemented
66Dic30C2×D312yescomplemented
67C5×#67—34no—
68C5×#67—62no—
69C5×D12—32no—
70C5×D12—61no—
71C4×C5×D3—32no—
72C4×C5×D3—61no—
73C3×C22⋊D5—34no—
74C2×C3×Dic5—34no—
75C3×C4×D5—32no—
76C3×Dic10—32no—
77#1204—34no—
78#1203—34no—
79#1201—34no—
80#1200—32no—
81D3×Dic5—34no—
82D3×Dic5—32no—
83D3×Dic5—34no—
84D3×Dic5—34no—
85D5×Dic3—32no—
86D3×#41—152no—
87C2×C32×C5—22no—
88C2×C32×C5C2411yescharacteristic
89C5×C3⋊D3—22no—
90C5×C3⋊D3#4112yescomplemented
91C3×D15—22no—
92C2×C5×D4—91no—
93C2×C22⋊D5—92no—
94C22×Dic5—92no—
95#711—32no—
96#711—92no—
97#711—94no—
98C2×C4×D5—91no—
99C2×Dic10—91no—
100C22×C3⋊D3C2×D512yes—
101C2×D32—51no—
102C32×D4C2×D511yescharacteristic, complemented
103#638C2×D512yescomplemented
104C4⋊(C3⋊D3)C2×D511yescharacteristic, complemented
105C4×C3⋊D3C2×D511yescharacteristic
106C3×#67—54no—
107C2×C3×Dic3—54no—
108C3×C4×D3—52no—
109C3×Dic6—52no—
110#627—52no—
111#626—54no—
112#624—52no—
113#624—51no—
114#624—54no—
115D3×Dic3—52no—
116C22×C3×C5—22no—
117C22×C3×C5C22×D314yes—
118C2×D15C22×D312yes—
119C2×C5×D3—32no—
120C2×C5×D3—34no—
121C2×C5×D3—61no—
122C2×C5×D3—62no—
123C2×C5×D3—68no—
124C2×C5×D3—124no—
125C2×C3×D5—32no—
126D3×D5—64no—
127C3×C4×C5—21no—
128C3×C4×C5C22×D312yes—
129Dic15C22×D312yes—
130Dic15C22×D314yes—
131C3×Dic5—32no—
132C3×Dic5—34no—
133C5×Dic3—32no—
134C5×Dic3—61no—
135C3×#41—152no—
136#239—152no—
137D3×Q8—152no—
138#237—52no—
139#237—154no—
140D3×D4—32no—
141D3×D4—61no—
142D3×D4—154no—
143#235—152no—
144#235—154no—
145C2×C4×D3—152no—
146C2×C4×D3—154no—
147C32×C5C2×#4111yescharacteristic, complemented, Hall
148C23×C5—92no—
149C22×D5—91no—
150C5×D4—92no—
151C5×D4—91no—
152C5×D4D3211yescharacteristic, complemented
153C2×C4×C5—91no—
154C22⋊D5—34no—
155C22⋊D5—94no—
156C2×Dic5—34no—
157C2×Dic5—92no—
158C2×Dic5—91no—
159C2×Dic5—94no—
160C4×D5—32no—
161C4×D5—92no—
162Dic10—32no—
163Dic10—92no—
164C22×C32C22×D512yes—
165C2×C3⋊D3—24no—
166C2×C3⋊D3C22×D512yes—
167C2×C3⋊D3C22×D511yescharacteristic
168C2×C3×D3—52no—
169D32—102no—
170C32×C4C22×D511yescharacteristic
171C3⋊Dic3C22×D511yescharacteristic
172C3×Dic3—52no—
173C3×Dic3—54no—
174C2×#41—451noSylow
175C2×C3×C5—24no—
176C2×C3×C5—21no—
177C2×C3×C5—42no—
178C2×C3×C5C23×D312yes—
179D15—22no—
180C3×D5—62no—
181C5×D3—34no—
182C5×D3—62no—
183C5×D3—64no—
184C5×D3—122no—
185C22×D3—34no—
186C22×D3—62no—
187C22×D3—152no—
188C3×Q8—152no—
189C3×D4—21no—
190C3×D4—154no—
191C3×D4D3×D512yescomplemented
192C2×C3×C4—154no—
193C2×C3×C4—152no—
194#67—34no—
195#67—54no—
196#67—62no—
197#67—154no—
198C2×Dic3—54no—
199C2×Dic3—152no—
200D12—32no—
201D12—61no—
202D12—154no—
203C4×D3—32no—
204C4×D3—52no—
205C4×D3—61no—
206C4×D3—152no—
207C4×D3—152no—
208C4×D3—154no—
209C4×D3—154no—
210C4×D3—154no—
211Dic6—52no—
212Dic6—154no—
213C22×C5—91no—
214C22×C5—92no—
215C22×C5—184no—
216C22×C5C2×D3212yes—
217C2×D5—32no—
218C2×D5—182no—
219C4×C5—91no—
220C4×C5C2×D3211yescharacteristic
221Dic5—34no—
222Dic5—32no—
223C2×C32—22no—
224C2×C32C23×D511yescharacteristic
225C3⋊D3—22no—
226C3⋊D3#71112yescomplemented
227C3×D3—102no—
228#41—152no—
229#41—454no—
230#41—452no—
231C2×Q8—451no—
232C2×D4—91no—
233C2×D4—452no—
234C22×C4—451no—
235C22×C4—452no—
236C3×C5—21no—
237C3×C5D3×#4112yescomplemented
238C22×C3—22no—
239C22×C3—152no—
240C22×C3C2×D3×D514yes—
241C2×D3—32no—
242C2×D3—34no—
243C2×D3—52no—
244C2×D3—61no—
245C2×D3—62no—
246C2×D3—68no—
247C2×D3—124no—
248C2×D3—304no—
249C3×C4—21no—
250C3×C4—154no—
251C3×C4—152no—
252C3×C4C2×D3×D512yes—
253Dic3—32no—
254Dic3—54no—
255Dic3—52no—
256Dic3—61no—
257C2×C5—22no—
258C2×C5—92no—
259C2×C5—182no—
260C2×C5C22×D3211yescharacteristic
261D5—62no—
262C32C2×#71111yescharacteristic, complemented, Sylow
263C23—92no—
264C23—451no—
265Q8—152no—
266Q8—452no—
267D4—92no—
268D4—91no—
269D4—154no—
270D4—454no—
271D4(C3⋊D3)⋊D511yescharacteristic, complemented
272C2×C4—91no—
273C2×C4—154no—
274C2×C4—152no—
275C2×C4—452no—
276C2×C4—451no—
277C2×C4—452no—
278C2×C4—454no—
279C2×C3—24no—
280C2×C3—21no—
281C2×C3—42no—
282C2×C3—302no—
283C2×C3C22×D3×D512yes—
284D3—34no—
285D3—62no—
286D3—64no—
287D3—102no—
288D3—122no—
289C5#6431211yescharacteristic, complemented, Sylow
290C22—91no—
291C22—92no—
292C22—152no—
293C22—184no—
294C22—902no—
295C22C2×(C3⋊D3)⋊D512yes—
296C4—91no—
297C4—152no—
298C4—154no—
299C4C2×(C3⋊D3)⋊D511yescharacteristic
300C3—21no—
301C3D3×#71112yescomplemented
302C2—22no—
303C2—92no—
304C2—182no—
305C2—302no—
306C2C22×(C3⋊D3)⋊D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×(C3⋊D3)⋊D5
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C5×D4C22
hypercenterD4(C3⋊D3)⋊D5
hypocenterC32×C5C2×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C5×D4×C3⋊D3C2semidirect
2. C3×#6819C2semidirect
3. #10624236C2semidirect
4. C2×#67155C2semidirect
5. #10624230C2semidirect
6. C4×(C3⋊D3)⋊D5C2semidirect
7. #10624224C2semidirect
8. #10624222C2semidirect
12. C32×C5×D4C22semidirect
13. C5×#638C22semidirect
14. C5×C4⋊(C3⋊D3)C22semidirect
16. C3×#1220C22semidirect
17. C2×C3×Dic15C22semidirect
18. C3×C4×D15C22semidirect
19. C3×Dic30C22semidirect
20. #67158C22semidirect
21. #67156C22semidirect
24. #67155C22semidirect
25. #67154C22semidirect
27. #6819D3semidirect
50. D4×C3⋊D3D5semidirect
62. C3×C5×D4C2×D3semidirect
63. #1220C2×D3semidirect
64. C2×Dic15C2×D3semidirect
65. C4×D15C2×D3semidirect
66. Dic30C2×D3semidirect
90. C5×C3⋊D3#41semidirect
102. C32×D4C2×D5semidirect
103. #638C2×D5semidirect
104. C4⋊(C3⋊D3)C2×D5semidirect
147. C32×C5C2×#41semidirect
152. C5×D4D32semidirect
191. C3×D4D3×D5semidirect
226. C3⋊D3#711semidirect
237. C3×C5D3×#41semidirect
262. C32C2×#711semidirect
271. D4(C3⋊D3)⋊D5semidirect
289. C5#64312semidirect
301. C3D3×#711semidirect

Maximal subgroups

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

subgroupindex
C5×D4×C3⋊D32
C3×#68192
#106242362
C2×#671552
#106242302
C4×(C3⋊D3)⋊D52
#106242242
#106242222
D3×#7113
#643125