Subgroups — C₂×D₃×D₅⋊C₈ #11756814

Order 960.

676 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6738	C₂	1	2	yes	maximal, complemented
5	C₂×D₃×#170	C₂	1	2	yes	maximal, complemented
6	D₃×D₅⋊C₈	C₂	1	8	yes	maximal, direct product factor
7	C₂²×D₅⋊C₈	—	3	1	no	maximal, Hall
8	C₂²×D₃×D₅	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₅	C₄	1	1	yes	characteristic
10	C₂×C₄×C₅×D₃	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂×#1200	C₂²	1	1	yes	characteristic
13	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic
14	C₂×D₅×Dic₃	C₄	1	1	yes	characteristic
15	C₄×D₃×D₅	C₄	1	4	yes	—
16	C₄×D₃×D₅	C₂²	1	4	yes	—
17	C₂×C₃⋊#170	C₂²	1	2	yes	complemented
18	D₅⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
19	C₂×C₃×#170	C₂²	1	2	yes	complemented
20	C₃×D₅⋊C₈	C₂²	1	4	yes	complemented
21	#6738	C₂²	1	8	yes	complemented
22	D₃×#170	C₂²	1	8	yes	complemented
23	C₂²×D₃×C₈	—	5	1	no	maximal, Hall
24	C₂²×C₄×D₅	—	3	1	no	—
25	C₂²×#170	—	3	2	no	—
26	C₂×D₅⋊C₈	—	3	1	no	—
27	C₂×D₅⋊C₈	—	3	2	no	—
28	C₂×D₅⋊C₈	—	3	8	no	—
29	C₂×D₅⋊C₈	D₃	1	1	yes	characteristic, direct product factor
30	C₂²×D₁₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×D₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×D₅	C₂×C₄	1	1	yes	characteristic
33	C₂×D₃×D₅	C₈	1	8	yes	complemented
34	C₂×D₃×D₅	C₂×C₄	1	4	yes	—
35	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂×Dic₁₅	C₂×C₄	1	1	yes	characteristic
37	C₄×D₁₅	C₂×C₄	1	4	yes	—
38	C₂×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₅×D₃	C₂×C₄	1	4	yes	—
40	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
41	C₃×C₄×D₅	C₂×C₄	1	2	yes	—
42	C₃×C₄×D₅	C₂³	1	2	yes	—
43	#1200	C₂×C₄	1	2	yes	—
44	#1200	C₂³	1	2	yes	—
45	D₃×Dic₅	C₂×C₄	1	2	yes	—
46	D₃×Dic₅	C₂³	1	2	yes	—
47	D₅×Dic₃	C₂×C₄	1	4	yes	—
48	C₃⋊#170	C₂³	1	4	yes	complemented
49	C₃×#170	C₂³	1	4	yes	complemented
50	C₂²×C₄×D₃	—	5	1	no	—
51	C₂²×C₃×C₈	—	5	1	no	—
52	C₂²×C₃⋊C₈	—	5	1	no	—
53	C₂×D₃×C₈	—	5	8	no	—
54	C₂×D₃×C₈	—	5	2	no	—
55	C₂×D₃×C₈	—	5	2	no	—
56	C₂³×D₅	—	3	1	no	—
57	C₂²×C₄×C₅	—	3	1	no	—
58	C₂²×Dic₅	—	3	1	no	—
59	C₂×C₄×D₅	—	3	1	no	—
60	C₂×C₄×D₅	—	3	1	no	—
61	C₂×C₄×D₅	—	3	1	no	—
62	C₂×C₄×D₅	—	3	4	no	—
63	C₂×C₄×D₅	—	3	4	no	—
64	C₂×C₄×D₅	C₂×D₃	1	1	yes	characteristic
65	C₂×#170	—	3	2	no	—
66	C₂×#170	—	3	8	no	—
67	C₂×#170	C₂×D₃	1	2	yes	complemented
68	D₅⋊C₈	—	3	4	no	—
69	D₅⋊C₈	—	3	8	no	—
70	D₅⋊C₈	C₂×D₃	1	4	yes	direct product factor
71	C₂³×C₈	—	15	1	no	Sylow
72	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
73	C₂×D₁₅	C₂×C₈	1	4	yes	complemented
74	C₂×D₁₅	C₂²×C₄	1	2	yes	—
75	C₂×C₅×D₃	C₂×C₈	1	4	yes	complemented
76	C₂×C₅×D₃	C₂²×C₄	1	2	yes	—
77	C₂×C₃×D₅	C₂×C₈	1	4	yes	complemented
78	C₂×C₃×D₅	C₂²×C₄	1	2	yes	—
79	D₃×D₅	C₂×C₈	1	16	yes	complemented
80	C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
81	Dic₁₅	C₂²×C₄	1	2	yes	—
82	C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
83	C₃×Dic₅	C₂⁴	1	1	yes	characteristic
84	C₅×Dic₃	C₂²×C₄	1	2	yes	—
85	C₂³×D₃	—	5	1	no	—
86	C₂²×C₃×C₄	—	5	1	no	—
87	C₂²×Dic₃	—	5	1	no	—
88	C₂×C₄×D₃	—	5	1	no	—
89	C₂×C₄×D₃	—	5	1	no	—
90	C₂×C₄×D₃	—	5	1	no	—
91	C₂×C₄×D₃	—	5	4	no	—
92	C₂×C₄×D₃	—	5	4	no	—
93	C₂×C₄×D₃	AGL(1,𝔽₅)	1	1	yes	characteristic
94	C₂×C₃×C₈	—	5	4	no	—
95	C₂×C₃×C₈	—	5	2	no	—
96	C₂×C₃⋊C₈	—	5	4	no	—
97	C₂×C₃⋊C₈	—	5	2	no	—
98	D₃×C₈	—	5	8	no	—
99	D₃×C₈	—	5	8	no	—
100	C₂³×C₅	—	3	1	no	—
101	C₂²×D₅	—	3	1	no	—
102	C₂²×D₅	—	3	8	no	—
103	C₂²×D₅	—	3	4	no	—
104	C₂²×D₅	C₄×D₃	1	1	yes	characteristic
105	C₂×C₄×C₅	—	3	1	no	—
106	C₂×C₄×C₅	—	3	4	no	—
107	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
108	C₂×Dic₅	—	3	1	no	—
109	C₂×Dic₅	—	3	2	no	—
110	C₂×Dic₅	—	3	2	no	—
111	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
112	C₄×D₅	—	3	4	no	—
113	C₄×D₅	—	3	4	no	—
114	C₄×D₅	—	3	2	no	—
115	C₄×D₅	—	3	2	no	—
116	C₄×D₅	C₄×D₃	1	2	yes	—
117	C₄×D₅	C₂²×D₃	1	2	yes	—
118	#170	—	3	4	no	—
119	#170	C₂²×D₃	1	4	yes	complemented
120	C₂³×C₄	—	15	1	no	—
121	C₂²×C₈	—	5	1	no	—
122	C₂²×C₈	—	15	8	no	—
123	C₂²×C₈	—	15	2	no	—
124	C₂²×C₈	—	15	2	no	—
125	C₂²×C₈	—	15	1	no	—
126	C₂×C₃×C₅	C₂²×C₈	1	2	yes	complemented
127	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
128	D₁₅	C₂²×C₈	1	4	yes	complemented
129	C₃×D₅	C₂²×C₈	1	4	yes	complemented
130	C₅×D₃	C₂²×C₈	1	4	yes	complemented
131	C₂³×C₃	—	5	1	no	—
132	C₂²×D₃	—	5	1	no	—
133	C₂²×D₃	—	5	8	no	—
134	C₂²×D₃	—	5	4	no	—
135	C₂²×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
136	C₂×C₃×C₄	—	5	1	no	—
137	C₂×C₃×C₄	—	5	2	no	—
138	C₂×C₃×C₄	—	5	2	no	—
139	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
140	C₂×Dic₃	—	5	1	no	—
141	C₂×Dic₃	—	5	4	no	—
142	C₂×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
143	C₄×D₃	—	5	2	no	—
144	C₄×D₃	—	5	2	no	—
145	C₄×D₃	—	5	4	no	—
146	C₄×D₃	—	5	2	no	—
147	C₄×D₃	—	5	2	no	—
148	C₄×D₃	C₂×AGL(1,𝔽₅)	1	4	yes	—
149	C₃×C₈	—	5	4	no	—
150	C₃⋊C₈	—	5	4	no	—
151	C₂²×C₅	—	3	4	no	—
152	C₂²×C₅	—	3	2	no	—
153	C₂²×C₅	C₂×C₄×D₃	1	1	yes	characteristic
154	C₂×D₅	—	3	4	no	—
155	C₂×D₅	—	3	2	no	—
156	C₂×D₅	—	3	16	no	—
157	C₂×D₅	D₃×C₈	1	4	yes	complemented
158	C₂×D₅	C₂×C₄×D₃	1	2	yes	—
159	C₄×C₅	—	3	2	no	—
160	C₄×C₅	C₂×C₄×D₃	1	2	yes	—
161	Dic₅	—	3	2	no	—
162	Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
163	Dic₅	C₂³×D₃	1	1	yes	characteristic
164	C₂⁴	—	15	1	no	—
165	C₂²×C₄	—	3	1	no	—
166	C₂²×C₄	—	5	1	no	—
167	C₂²×C₄	—	15	1	no	—
168	C₂²×C₄	—	15	4	no	—
169	C₂²×C₄	—	15	4	no	—
170	C₂²×C₄	—	15	1	no	—
171	C₂²×C₄	—	15	1	no	—
172	C₂²×C₄	—	15	1	no	—
173	C₂×C₈	—	5	4	no	—
174	C₂×C₈	—	5	2	no	—
175	C₂×C₈	—	15	8	no	—
176	C₂×C₈	—	15	8	no	—
177	C₂×C₈	—	15	4	no	—
178	C₂×C₈	—	15	2	no	—
179	C₃×C₅	C₂³×C₈	1	1	yes	characteristic, complemented, Hall
180	C₂²×C₃	—	5	4	no	—
181	C₂²×C₃	—	5	2	no	—
182	C₂²×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
183	C₂×D₃	—	5	4	no	—
184	C₂×D₃	—	5	2	no	—
185	C₂×D₃	—	5	16	no	—
186	C₂×D₃	D₅⋊C₈	1	4	yes	direct product factor
187	C₂×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
188	C₃×C₄	—	5	1	no	—
189	C₃×C₄	—	5	1	no	—
190	C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
191	Dic₃	—	5	2	no	—
192	Dic₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
193	C₂×C₅	—	3	4	no	—
194	C₂×C₅	C₂×D₃×C₈	1	2	yes	complemented
195	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
196	D₅	—	3	4	no	—
197	D₅	C₂×D₃×C₈	1	4	yes	complemented
198	C₂³	—	3	1	no	—
199	C₂³	—	5	1	no	—
200	C₂³	—	15	4	no	—
201	C₂³	—	15	8	no	—
202	C₂³	—	15	1	no	—
203	C₂×C₄	—	3	1	no	—
204	C₂×C₄	—	3	4	no	—
205	C₂×C₄	—	5	1	no	—
206	C₂×C₄	—	5	2	no	—
207	C₂×C₄	—	5	2	no	—
208	C₂×C₄	—	15	2	no	—
209	C₂×C₄	—	15	2	no	—
210	C₂×C₄	—	15	4	no	—
211	C₂×C₄	—	15	2	no	—
212	C₂×C₄	—	15	2	no	—
213	C₂×C₄	—	15	1	no	—
214	C₂×C₄	—	15	4	no	—
215	C₂×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₈	—	5	4	no	—
217	C₈	—	15	4	no	—
218	C₂×C₃	—	5	4	no	—
219	C₂×C₃	C₂×D₅⋊C₈	1	2	yes	complemented
220	C₂×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
221	D₃	—	5	4	no	—
222	D₃	C₂×D₅⋊C₈	1	4	yes	direct product factor
223	C₅	C₂²×D₃×C₈	1	1	yes	characteristic, complemented, Sylow
224	C₂²	—	3	4	no	—
225	C₂²	—	3	2	no	—
226	C₂²	—	5	4	no	—
227	C₂²	—	5	2	no	—
228	C₂²	—	15	16	no	—
229	C₂²	—	15	4	no	—
230	C₂²	—	15	2	no	—
231	C₂²	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
232	C₄	—	3	2	no	—
233	C₄	—	5	1	no	—
234	C₄	—	5	1	no	—
235	C₄	—	15	2	no	—
236	C₄	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	—
237	C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic, complemented, Sylow
238	C₂	—	3	4	no	—
239	C₂	—	5	4	no	—
240	C₂	—	15	4	no	—
241	C₂	D₃×D₅⋊C₈	1	2	yes	direct product factor
242	C₂	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₂³×C₈
Frattini	C₂	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄×C₅	C₂×C₄
socle	C₂²×C₃×C₅	C₂²×C₄
prime radical	C₂²×D₃×D₅	C₄
cosocle	C₃×Dic₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×D₅⋊(C₃⋊C₈)	C₂	semidirect
3. C₂×C₃×D₅⋊C₈	C₂	semidirect
4. C₂×#6738	C₂	semidirect
5. C₂×D₃×#170	C₂	semidirect
6. D₃×D₅⋊C₈	C₂	direct (N × H)
17. C₂×C₃⋊#170	C₂²	semidirect
18. D₅⋊(C₃⋊C₈)	C₂²	semidirect
19. C₂×C₃×#170	C₂²	semidirect
20. C₃×D₅⋊C₈	C₂²	semidirect
21. #6738	C₂²	semidirect
22. D₃×#170	C₂²	semidirect
29. C₂×D₅⋊C₈	D₃	direct (N × H)
33. C₂×D₃×D₅	C₈	semidirect
48. C₃⋊#170	C₂³	semidirect
49. C₃×#170	C₂³	semidirect
67. C₂×#170	C₂×D₃	semidirect
70. D₅⋊C₈	C₂×D₃	direct (N × H)
73. C₂×D₁₅	C₂×C₈	semidirect
75. C₂×C₅×D₃	C₂×C₈	semidirect
77. C₂×C₃×D₅	C₂×C₈	semidirect
79. D₃×D₅	C₂×C₈	semidirect
119. #170	C₂²×D₃	semidirect
126. C₂×C₃×C₅	C₂²×C₈	semidirect
128. D₁₅	C₂²×C₈	semidirect
129. C₃×D₅	C₂²×C₈	semidirect
130. C₅×D₃	C₂²×C₈	semidirect
157. C₂×D₅	D₃×C₈	semidirect
179. C₃×C₅	C₂³×C₈	semidirect
186. C₂×D₃	D₅⋊C₈	direct (N × H)
194. C₂×C₅	C₂×D₃×C₈	semidirect
197. D₅	C₂×D₃×C₈	semidirect
219. C₂×C₃	C₂×D₅⋊C₈	semidirect
222. D₃	C₂×D₅⋊C₈	direct (N × H)
223. C₅	C₂²×D₃×C₈	semidirect
237. C₃	C₂²×D₅⋊C₈	semidirect
241. C₂	D₃×D₅⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×D₅	2
C₂×D₅⋊(C₃⋊C₈)	2
C₂×C₃×D₅⋊C₈	2
C₂×#6738	2
C₂×D₃×#170	2
D₃×D₅⋊C₈	2
C₂²×D₅⋊C₈	3
C₂²×D₃×C₈	5

Subgroups — C2×D3×D5⋊C8 #11756814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×D₅⋊C₈ #11756814