Subgroups — C₂×C₅×(C₂×D₃)⋊C₈ #11750607

Order 960.

404 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×(C₂×D₃)⋊C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₅×C₂²⋊C₈	—	3	1	no	maximal, Hall
6	C₂³×C₅×D₃	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×Dic₃	C₄	1	1	yes	characteristic
9	C₂×C₄×C₅×D₃	—	2	2	no	—
10	C₂×C₄×C₅×D₃	—	2	2	no	—
11	C₂×C₄×C₅×D₃	C₄	1	2	yes	—
12	C₂×C₄×C₅×D₃	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₈	—	2	2	no	—
14	C₂×C₃×C₅×C₈	C₂²	1	2	yes	complemented
15	C₂×C₅×C₃⋊C₈	—	2	2	no	—
16	C₂×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
17	C₂×(C₂×D₃)⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂³×C₄×C₅	—	3	1	no	—
19	C₂²×C₅×C₈	—	3	1	no	—
20	C₂²×C₅×C₈	D₃	1	1	yes	characteristic, complemented
21	C₅×C₂²⋊C₈	—	3	4	no	—
22	C₂³×C₃×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅×D₃	—	2	2	no	—
24	C₂²×C₅×D₃	—	2	2	no	—
25	C₂²×C₅×D₃	C₈	1	4	yes	complemented
26	C₂²×C₅×D₃	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
29	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂×C₅×Dic₃	—	2	2	no	—
32	C₂×C₅×Dic₃	C₂×C₄	1	2	yes	—
33	C₄×C₅×D₃	—	2	4	no	—
34	C₄×C₅×D₃	—	2	2	no	—
35	C₄×C₅×D₃	—	2	2	no	—
36	C₃×C₅×C₈	—	2	2	no	—
37	C₅×C₃⋊C₈	—	2	2	no	—
38	C₂²×C₄×D₃	C₂×C₅	1	1	yes	characteristic
39	C₂²×C₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
40	C₂²×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
41	(C₂×D₃)⋊C₈	C₂×C₅	1	4	yes	direct product factor
42	C₂⁴×C₅	—	3	1	no	—
43	C₂²×C₄×C₅	—	3	1	no	—
44	C₂²×C₄×C₅	—	3	2	no	—
45	C₂²×C₄×C₅	—	3	2	no	—
46	C₂²×C₄×C₅	—	6	2	no	—
47	C₂²×C₄×C₅	—	6	2	no	—
48	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	3	2	no	—
51	C₂×C₅×C₈	—	6	2	no	—
52	C₂×C₅×C₈	C₂×D₃	1	2	yes	complemented
53	C₂×C₂²⋊C₈	—	3	1	no	Sylow
54	C₂²×C₃×C₅	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₃×C₅	C₂×C₈	1	2	yes	—
56	C₂²×C₃×C₅	M₁₆	1	2	yes	—
57	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₅×D₃	—	2	8	no	—
59	C₂×C₅×D₃	—	2	2	no	—
60	C₂×C₅×D₃	—	2	2	no	—
61	C₂×C₅×D₃	C₂×C₈	1	4	yes	complemented
62	C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
63	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
64	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
65	C₅×Dic₃	—	2	2	no	—
66	C₂³×D₃	C₄×C₅	1	1	yes	characteristic
67	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
68	C₂²×Dic₃	C₄×C₅	1	1	yes	characteristic
69	C₂×C₄×D₃	—	2	2	no	—
70	C₂×C₄×D₃	—	2	2	no	—
71	C₂×C₄×D₃	C₄×C₅	1	2	yes	—
72	C₂×C₄×D₃	C₂²×C₅	1	2	yes	—
73	C₂×C₃×C₈	—	2	2	no	—
74	C₂×C₃×C₈	C₂²×C₅	1	2	yes	complemented
75	C₂×C₃⋊C₈	—	2	2	no	—
76	C₂×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
77	C₂³×C₅	—	3	4	no	—
78	C₂³×C₅	—	3	2	no	—
79	C₂³×C₅	—	6	2	no	—
80	C₂³×C₅	—	6	2	no	—
81	C₂³×C₅	C₄×D₃	1	1	yes	characteristic
82	C₂×C₄×C₅	—	3	2	no	—
83	C₂×C₄×C₅	—	6	2	no	—
84	C₂×C₄×C₅	—	6	4	no	—
85	C₂×C₄×C₅	—	6	2	no	—
86	C₂×C₄×C₅	—	6	2	no	—
87	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
88	C₂×C₄×C₅	D₁₂	1	2	yes	—
89	C₂×C₄×C₅	#67	1	2	yes	—
90	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
91	C₅×C₈	—	2	2	no	—
92	C₅×C₈	—	6	2	no	—
93	C₂³×C₄	—	3	1	no	—
94	C₂²×C₈	—	3	1	no	—
95	C₂²×C₈	C₅×D₃	1	1	yes	characteristic, complemented
96	C₂²⋊C₈	—	3	4	no	—
97	C₂×C₃×C₅	C₂²⋊C₈	1	4	yes	complemented
98	C₂×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
101	C₅×D₃	—	2	4	no	—
102	C₂³×C₃	C₂×C₄×C₅	1	1	yes	characteristic
103	C₂²×D₃	—	2	2	no	—
104	C₂²×D₃	—	2	2	no	—
105	C₂²×D₃	C₅×C₈	1	4	yes	complemented
106	C₂²×D₃	C₂×C₄×C₅	1	2	yes	—
107	C₂×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄	C₅×D₄	1	2	yes	—
109	C₂×C₃×C₄	C₅×D₄	1	2	yes	—
110	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
111	C₂×Dic₃	—	2	2	no	—
112	C₂×Dic₃	C₂×C₄×C₅	1	2	yes	—
113	C₄×D₃	—	2	4	no	—
114	C₄×D₃	—	2	2	no	—
115	C₄×D₃	—	2	2	no	—
116	C₃×C₈	—	2	2	no	—
117	C₃⋊C₈	—	2	2	no	—
118	C₂²×C₅	—	3	4	no	—
119	C₂²×C₅	—	6	8	no	—
120	C₂²×C₅	—	6	2	no	—
121	C₂²×C₅	—	6	2	no	—
122	C₂²×C₅	D₃×C₈	1	2	yes	—
123	C₂²×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
124	C₂²×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
125	C₂²×C₅	C₂×C₄×D₃	1	1	yes	characteristic
126	C₄×C₅	—	6	2	no	—
127	C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
128	C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
129	C₄×C₅	C₂×#67	1	1	yes	characteristic
130	C₂⁴	—	3	1	no	—
131	C₂²×C₄	—	3	1	no	—
132	C₂²×C₄	—	3	2	no	—
133	C₂²×C₄	—	3	2	no	—
134	C₂²×C₄	—	6	2	no	—
135	C₂²×C₄	—	6	2	no	—
136	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	3	2	no	—
139	C₂×C₈	—	6	2	no	—
140	C₂×C₈	C₂×C₅×D₃	1	2	yes	complemented
141	C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
142	C₂²×C₃	C₅×C₂²⋊C₄	1	2	yes	—
143	C₂²×C₃	C₂×C₅×C₈	1	2	yes	—
144	C₂²×C₃	C₅×M₁₆	1	2	yes	—
145	C₂²×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
146	C₂×D₃	—	2	2	no	—
147	C₂×D₃	—	2	2	no	—
148	C₂×D₃	—	2	8	no	—
149	C₂×D₃	C₂×C₅×C₈	1	4	yes	complemented
150	C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
151	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
152	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
153	Dic₃	—	2	2	no	—
154	C₂×C₅	—	6	4	no	—
155	C₂×C₅	(C₂×D₃)⋊C₈	1	4	yes	direct product factor
156	C₂×C₅	C₂×D₃×C₈	1	1	yes	characteristic
157	C₂×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
158	C₂×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
159	C₂³	—	3	4	no	—
160	C₂³	—	3	2	no	—
161	C₂³	—	6	2	no	—
162	C₂³	—	6	2	no	—
163	C₂³	C₄×C₅×D₃	1	1	yes	characteristic
164	C₂×C₄	—	3	2	no	—
165	C₂×C₄	—	6	2	no	—
166	C₂×C₄	—	6	4	no	—
167	C₂×C₄	—	6	2	no	—
168	C₂×C₄	—	6	2	no	—
169	C₂×C₄	C₄×C₅×D₃	1	1	yes	characteristic
170	C₂×C₄	C₅×D₁₂	1	2	yes	—
171	C₂×C₄	C₅×#67	1	2	yes	—
172	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	6	2	no	—
175	C₂×C₃	C₅×C₂²⋊C₈	1	4	yes	complemented
176	C₂×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
178	C₂×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
179	D₃	—	2	4	no	—
180	C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
181	C₂²	—	3	4	no	—
182	C₂²	—	6	2	no	—
183	C₂²	—	6	2	no	—
184	C₂²	—	6	8	no	—
185	C₂²	C₅×D₃×C₈	1	2	yes	—
186	C₂²	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
187	C₂²	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
188	C₂²	C₂×C₄×C₅×D₃	1	1	yes	characteristic
189	C₄	—	6	2	no	—
190	C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
191	C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
192	C₄	C₂×C₅×#67	1	1	yes	characteristic
193	C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
194	C₂	—	6	4	no	—
195	C₂	C₅×(C₂×D₃)⋊C₈	1	4	yes	direct product factor
196	C₂	C₂×C₅×D₃×C₈	1	1	yes	characteristic
197	C₂	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
198	C₂	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₃
commutator	C₂×C₃	C₂²×C₅×C₈
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×C₄
prime radical	C₂³×C₅×D₃	C₄
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×C₂²⋊C₈
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×C₈	C₂	semidirect
3. C₂²×C₅×C₃⋊C₈	C₂	semidirect
4. C₅×(C₂×D₃)⋊C₈	C₂	direct (N × H)
14. C₂×C₃×C₅×C₈	C₂²	semidirect
16. C₂×C₅×C₃⋊C₈	C₂²	semidirect
17. C₂×(C₂×D₃)⋊C₈	C₅	direct (N × H)
20. C₂²×C₅×C₈	D₃	semidirect
25. C₂²×C₅×D₃	C₈	semidirect
39. C₂²×C₃×C₈	C₂×C₅	semidirect
40. C₂²×C₃⋊C₈	C₂×C₅	semidirect
41. (C₂×D₃)⋊C₈	C₂×C₅	direct (N × H)
52. C₂×C₅×C₈	C₂×D₃	semidirect
61. C₂×C₅×D₃	C₂×C₈	semidirect
74. C₂×C₃×C₈	C₂²×C₅	semidirect
76. C₂×C₃⋊C₈	C₂²×C₅	semidirect
95. C₂²×C₈	C₅×D₃	semidirect
97. C₂×C₃×C₅	C₂²⋊C₈	semidirect
105. C₂²×D₃	C₅×C₈	semidirect
140. C₂×C₈	C₂×C₅×D₃	semidirect
141. C₃×C₅	C₂×C₂²⋊C₈	semidirect
149. C₂×D₃	C₂×C₅×C₈	semidirect
155. C₂×C₅	(C₂×D₃)⋊C₈	direct (N × H)
175. C₂×C₃	C₅×C₂²⋊C₈	semidirect
180. C₅	C₂×(C₂×D₃)⋊C₈	direct (N × H)
193. C₃	C₂×C₅×C₂²⋊C₈	semidirect
195. C₂	C₅×(C₂×D₃)⋊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
C₂²×C₄×C₅×D₃	2
C₂²×C₃×C₅×C₈	2
C₂²×C₅×C₃⋊C₈	2
C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×C₂²⋊C₈	3
C₂×(C₂×D₃)⋊C₈	5

Subgroups — C2×C5×(C2×D3)⋊C8 #11750607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×(C₂×D₃)⋊C₈ #11750607