Subgroups — C₂×C₅×#4695 #14438772

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₂₄	C₂	1	4	yes	maximal, complemented
2	C₂×C₅×#874	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4695	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#493	—	3	1	no	maximal, Hall
6	C₂²×C₅×D₁₂	—	2	4	no	—
7	C₂²×C₅×D₁₂	C₂²	1	4	yes	—
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×D₂₄	—	2	16	no	—
11	C₂×C₅×D₂₄	C₂²	1	16	yes	complemented
12	C₅×#874	—	2	4	no	—
13	C₅×#874	C₂²	1	8	yes	complemented
14	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
15	C₂×#4695	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₅×D₈	—	3	4	no	—
17	C₂×C₅×#127	—	3	2	no	—
18	C₅×#493	—	3	8	no	—
19	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
20	C₂³×C₅×D₃	—	2	4	no	—
21	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
22	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂×C₅×D₁₂	—	2	16	no	—
24	C₂×C₅×D₁₂	—	2	4	no	—
25	C₂×C₅×D₁₂	—	2	16	no	—
26	C₂×C₅×D₁₂	—	4	16	no	—
27	C₂×C₅×D₁₂	C₂³	1	8	yes	—
28	C₂×C₃×C₅×C₈	D₄	1	8	yes	complemented
29	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
30	C₃×C₄²×C₅	D₄	1	2	yes	—
31	C₃×C₄²×C₅	C₂³	1	2	yes	—
32	C₅×D₂₄	—	2	32	no	—
33	C₂²×D₂₄	C₂×C₅	1	4	yes	complemented
34	C₂×#874	C₂×C₅	1	2	yes	complemented
35	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
36	#4695	C₂×C₅	1	8	yes	direct product factor
37	C₂²×C₅×D₄	—	3	4	no	—
38	C₂²×C₅×D₄	—	6	4	no	—
39	C₂×C₅×D₈	—	3	16	no	—
40	C₂×C₅×D₈	—	6	16	no	—
41	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
42	C₅×#127	—	3	8	no	—
43	C₅×#127	—	6	4	no	—
44	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
45	C₄×C₅×C₈	C₂×D₃	1	4	yes	complemented
46	C₂×#493	—	3	1	no	Sylow
47	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₅×D₃	—	2	8	no	—
49	C₂²×C₅×D₃	—	4	8	no	—
50	C₂²×C₅×D₃	—	4	16	no	—
51	C₂×C₃×C₄×C₅	D₈	1	8	yes	complemented
52	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
54	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
55	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
56	C₅×D₁₂	—	2	16	no	—
57	C₅×D₁₂	—	4	8	no	—
58	C₅×D₁₂	—	4	32	no	—
59	C₃×C₅×C₈	C₂×D₄	1	8	yes	complemented
60	C₂²×D₁₂	—	2	4	no	—
61	C₂²×D₁₂	C₂²×C₅	1	4	yes	—
62	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
63	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
64	C₂×D₂₄	—	2	16	no	—
65	C₂×D₂₄	C₂²×C₅	1	16	yes	complemented
66	#874	—	2	4	no	—
67	#874	C₂²×C₅	1	8	yes	complemented
68	C₃×C₄×C₈	C₂²×C₅	1	4	yes	complemented
69	C₂⁴×C₅	—	6	4	no	—
70	C₂×C₅×D₄	—	3	8	no	—
71	C₂×C₅×D₄	—	6	16	no	—
72	C₂×C₅×D₄	—	6	16	no	—
73	C₂×C₅×D₄	—	6	4	no	—
74	C₂×C₅×D₄	—	12	16	no	—
75	C₂²×C₄×C₅	D₁₂	1	2	yes	—
76	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
77	C₅×D₈	—	6	32	no	—
78	C₂×C₅×C₈	D₁₂	1	8	yes	complemented
79	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
80	C₄²×C₅	D₁₂	1	2	yes	—
81	C₄²×C₅	C₂²×D₃	1	2	yes	—
82	C₂²×D₈	—	3	4	no	—
83	C₂×#127	—	3	2	no	—
84	#493	—	3	8	no	—
85	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
86	C₂²×C₃×C₅	#127	1	2	yes	—
87	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
88	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
89	C₂×C₅×D₃	—	4	8	no	—
90	C₂×C₅×D₃	—	4	16	no	—
91	C₂×C₅×D₃	—	8	16	no	—
92	C₃×C₄×C₅	#127	1	2	yes	—
93	C₃×C₄×C₅	C₂×D₈	1	8	yes	complemented
94	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
95	C₂³×D₃	—	2	4	no	—
96	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
97	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
98	C₂×D₁₂	—	2	16	no	—
99	C₂×D₁₂	—	2	4	no	—
100	C₂×D₁₂	—	2	16	no	—
101	C₂×D₁₂	—	4	16	no	—
102	C₂×D₁₂	C₂³×C₅	1	8	yes	—
103	C₂×C₃×C₈	C₅×D₄	1	8	yes	complemented
104	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
105	C₃×C₄²	C₅×D₄	1	2	yes	—
106	C₃×C₄²	C₂³×C₅	1	2	yes	—
107	D₂₄	—	2	32	no	—
108	C₂³×C₅	—	6	8	no	—
109	C₂³×C₅	—	12	8	no	—
110	C₂³×C₅	—	12	16	no	—
111	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
112	C₅×D₄	—	6	16	no	—
113	C₅×D₄	—	12	8	no	—
114	C₅×D₄	—	12	32	no	—
115	C₂×C₄×C₅	D₂₄	1	8	yes	complemented
116	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
117	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
118	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
119	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
120	C₅×C₈	C₂×D₁₂	1	8	yes	complemented
121	C₂²×D₄	—	3	4	no	—
122	C₂²×D₄	—	6	4	no	—
123	C₂×D₈	—	3	16	no	—
124	C₂×D₈	—	6	16	no	—
125	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
126	#127	—	3	8	no	—
127	#127	—	6	4	no	—
128	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
129	C₄×C₈	C₂×C₅×D₃	1	4	yes	complemented
130	C₂×C₃×C₅	#493	1	4	yes	complemented
131	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
132	C₂×C₃×C₅	C₂²×D₈	1	2	yes	—
133	C₅×D₃	—	8	8	no	—
134	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
135	C₂²×D₃	—	2	8	no	—
136	C₂²×D₃	—	4	8	no	—
137	C₂²×D₃	—	4	16	no	—
138	C₂×C₃×C₄	C₅×D₈	1	8	yes	complemented
139	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
141	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
142	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
143	D₁₂	—	2	16	no	—
144	D₁₂	—	4	8	no	—
145	D₁₂	—	4	32	no	—
146	C₃×C₈	C₂×C₅×D₄	1	8	yes	complemented
147	C₂²×C₅	—	12	8	no	—
148	C₂²×C₅	—	12	16	no	—
149	C₂²×C₅	—	24	16	no	—
150	C₂²×C₅	#874	1	2	yes	—
151	C₂²×C₅	C₂×D₂₄	1	4	yes	—
152	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
153	C₄×C₅	#874	1	2	yes	—
154	C₄×C₅	C₂×D₂₄	1	8	yes	complemented
155	C₄×C₅	C₂²×D₁₂	1	2	yes	—
156	C₂⁴	—	6	4	no	—
157	C₂×D₄	—	3	8	no	—
158	C₂×D₄	—	6	16	no	—
159	C₂×D₄	—	6	16	no	—
160	C₂×D₄	—	6	4	no	—
161	C₂×D₄	—	12	16	no	—
162	C₂²×C₄	C₅×D₁₂	1	2	yes	—
163	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
164	D₈	—	6	32	no	—
165	C₂×C₈	C₅×D₁₂	1	8	yes	complemented
166	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
167	C₄²	C₅×D₁₂	1	2	yes	—
168	C₄²	C₂²×C₅×D₃	1	2	yes	—
169	C₃×C₅	C₂×#493	1	1	yes	characteristic, complemented, Hall
170	C₂²×C₃	C₅×#127	1	2	yes	—
171	C₂²×C₃	C₂×C₅×D₈	1	4	yes	—
172	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
173	C₂×D₃	—	4	8	no	—
174	C₂×D₃	—	4	16	no	—
175	C₂×D₃	—	8	16	no	—
176	C₃×C₄	C₅×#127	1	2	yes	—
177	C₃×C₄	C₂×C₅×D₈	1	8	yes	complemented
178	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
179	C₂×C₅	—	24	8	no	—
180	C₂×C₅	#4695	1	4	yes	direct product factor
181	C₂×C₅	C₂×#874	1	1	yes	characteristic
182	C₂×C₅	C₂²×D₂₄	1	2	yes	—
183	C₂³	—	6	8	no	—
184	C₂³	—	12	8	no	—
185	C₂³	—	12	16	no	—
186	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
187	D₄	—	6	16	no	—
188	D₄	—	12	8	no	—
189	D₄	—	12	32	no	—
190	C₂×C₄	C₅×D₂₄	1	8	yes	complemented
191	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
192	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
193	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
194	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
195	C₈	C₂×C₅×D₁₂	1	8	yes	complemented
196	C₂×C₃	C₅×#493	1	4	yes	complemented
197	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
198	C₂×C₃	C₂²×C₅×D₈	1	2	yes	—
199	D₃	—	8	8	no	—
200	C₅	C₂×#4695	1	1	yes	characteristic, direct product factor, Sylow
201	C₂²	—	12	8	no	—
202	C₂²	—	12	16	no	—
203	C₂²	—	24	16	no	—
204	C₂²	C₅×#874	1	2	yes	—
205	C₂²	C₂×C₅×D₂₄	1	4	yes	—
206	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
207	C₄	C₅×#874	1	2	yes	—
208	C₄	C₂×C₅×D₂₄	1	8	yes	complemented
209	C₄	C₂²×C₅×D₁₂	1	2	yes	—
210	C₃	C₂×C₅×#493	1	1	yes	characteristic, complemented, Sylow
211	C₂	—	24	8	no	—
212	C₂	C₅×#4695	1	4	yes	direct product factor
213	C₂	C₂×C₅×#874	1	1	yes	characteristic
214	C₂	C₂²×C₅×D₂₄	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×#493
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₂₄	C₂	semidirect
2. C₂×C₅×#874	C₂	semidirect
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₅×#4695	C₂	direct (N × H)
11. C₂×C₅×D₂₄	C₂²	semidirect
13. C₅×#874	C₂²	semidirect
14. C₃×C₄×C₅×C₈	C₂²	semidirect
15. C₂×#4695	C₅	direct (N × H)
19. C₂×C₄×C₅×C₈	D₃	semidirect
28. C₂×C₃×C₅×C₈	D₄	semidirect
33. C₂²×D₂₄	C₂×C₅	semidirect
34. C₂×#874	C₂×C₅	semidirect
35. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
36. #4695	C₂×C₅	direct (N × H)
45. C₄×C₅×C₈	C₂×D₃	semidirect
51. C₂×C₃×C₄×C₅	D₈	semidirect
59. C₃×C₅×C₈	C₂×D₄	semidirect
65. C₂×D₂₄	C₂²×C₅	semidirect
67. #874	C₂²×C₅	semidirect
68. C₃×C₄×C₈	C₂²×C₅	semidirect
78. C₂×C₅×C₈	D₁₂	semidirect
85. C₂×C₄×C₈	C₅×D₃	semidirect
93. C₃×C₄×C₅	C₂×D₈	semidirect
103. C₂×C₃×C₈	C₅×D₄	semidirect
115. C₂×C₄×C₅	D₂₄	semidirect
120. C₅×C₈	C₂×D₁₂	semidirect
129. C₄×C₈	C₂×C₅×D₃	semidirect
130. C₂×C₃×C₅	#493	semidirect
138. C₂×C₃×C₄	C₅×D₈	semidirect
146. C₃×C₈	C₂×C₅×D₄	semidirect
154. C₄×C₅	C₂×D₂₄	semidirect
165. C₂×C₈	C₅×D₁₂	semidirect
169. C₃×C₅	C₂×#493	semidirect
177. C₃×C₄	C₂×C₅×D₈	semidirect
180. C₂×C₅	#4695	direct (N × H)
190. C₂×C₄	C₅×D₂₄	semidirect
195. C₈	C₂×C₅×D₁₂	semidirect
196. C₂×C₃	C₅×#493	semidirect
200. C₅	C₂×#4695	direct (N × H)
208. C₄	C₂×C₅×D₂₄	semidirect
210. C₃	C₂×C₅×#493	semidirect
212. C₂	C₅×#4695	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×C₅×D₂₄	2
C₂×C₅×#874	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#4695	2
C₂×C₅×#493	3
C₂×#4695	5

Subgroups — C2×C5×#4695 #14438772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4695 #14438772