Subgroups — C₂×C₅×#4699 #14438802

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×Dic₁₂	C₂	1	4	yes	maximal
2	C₂×C₅×#869	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#4699	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#494	—	3	1	no	maximal, Hall
6	C₂²×C₅×Dic₆	C₂²	1	4	yes	—
7	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₅×C₄⋊Dic₃	—	2	4	no	—
10	C₂×C₅×Dic₁₂	—	2	16	no	—
11	C₂×C₅×Dic₁₂	C₂²	1	16	yes	—
12	C₅×#869	—	2	4	no	—
13	C₅×#869	C₂²	1	8	yes	—
14	C₃×C₄×C₅×C₈	C₂²	1	4	yes	—
15	C₂×#4699	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₅×Q₁₆	—	3	4	no	—
17	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
18	C₅×#494	—	3	8	no	—
19	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
21	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₅×Dic₃	—	2	4	no	—
23	C₂×C₅×Dic₆	—	2	16	no	—
24	C₂×C₅×Dic₆	—	2	4	no	—
25	C₂×C₅×Dic₆	C₂³	1	8	yes	—
26	C₂×C₃×C₅×C₈	D₄	1	8	yes	—
27	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
28	C₃×C₄²×C₅	D₄	1	2	yes	—
29	C₃×C₄²×C₅	C₂³	1	2	yes	—
30	C₅×C₄⋊Dic₃	—	2	16	no	—
31	C₅×Dic₁₂	—	2	32	no	—
32	C₂²×Dic₁₂	C₂×C₅	1	4	yes	—
33	C₂×#869	C₂×C₅	1	2	yes	—
34	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
35	#4699	C₂×C₅	1	8	yes	direct product factor
36	C₂²×C₅×Q₈	—	3	4	no	—
37	C₂×C₅×Q₁₆	—	3	16	no	—
38	C₂×C₅×Q₁₆	—	6	16	no	—
39	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
40	C₅×C₄⋊Q₈	—	3	8	no	—
41	C₅×C₄⋊Q₈	—	6	4	no	—
42	C₂×C₅×C₄⋊C₄	—	6	4	no	—
43	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
44	C₄×C₅×C₈	C₂×D₃	1	4	yes	—
45	C₂×#494	—	3	1	no	Sylow
46	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	Q₁₆	1	8	yes	complemented
48	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
50	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
51	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
52	C₂×C₅×Dic₃	—	2	8	no	—
53	C₂×C₅×Dic₃	—	4	8	no	—
54	C₅×Dic₆	—	2	16	no	—
55	C₅×Dic₆	—	4	8	no	—
56	C₃×C₅×C₈	C₂×D₄	1	8	yes	—
57	C₂²×Dic₆	C₂²×C₅	1	4	yes	—
58	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
59	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
60	C₂×C₄⋊Dic₃	—	2	4	no	—
61	C₂×Dic₁₂	—	2	16	no	—
62	C₂×Dic₁₂	C₂²×C₅	1	16	yes	—
63	#869	—	2	4	no	—
64	#869	C₂²×C₅	1	8	yes	—
65	C₃×C₄×C₈	C₂²×C₅	1	4	yes	—
66	C₂×C₅×Q₈	—	3	8	no	—
67	C₂×C₅×Q₈	—	6	4	no	—
68	C₂×C₅×Q₈	—	6	16	no	—
69	C₂²×C₄×C₅	—	6	4	no	—
70	C₂²×C₄×C₅	D₁₂	1	2	yes	—
71	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
72	C₅×Q₁₆	—	6	32	no	—
73	C₂×C₅×C₈	D₁₂	1	8	yes	—
74	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
75	C₅×C₄⋊C₄	—	6	16	no	—
76	C₄²×C₅	D₁₂	1	2	yes	—
77	C₄²×C₅	C₂²×D₃	1	2	yes	—
78	C₂²×Q₁₆	—	3	4	no	—
79	C₂×C₄⋊Q₈	—	3	2	no	—
80	#494	—	3	8	no	—
81	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic
82	C₂²×C₃×C₅	#127	1	2	yes	—
83	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	—
84	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
85	C₃×C₄×C₅	#127	1	2	yes	—
86	C₃×C₄×C₅	C₂×Q₁₆	1	8	yes	complemented
87	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
88	C₅×Dic₃	—	4	8	no	—
89	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
90	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
91	C₂²×Dic₃	—	2	4	no	—
92	C₂×Dic₆	—	2	16	no	—
93	C₂×Dic₆	—	2	4	no	—
94	C₂×Dic₆	C₂³×C₅	1	8	yes	—
95	C₂×C₃×C₈	C₅×D₄	1	8	yes	—
96	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
97	C₃×C₄²	C₅×D₄	1	2	yes	—
98	C₃×C₄²	C₂³×C₅	1	2	yes	—
99	C₄⋊Dic₃	—	2	16	no	—
100	Dic₁₂	—	2	32	no	—
101	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
102	C₅×Q₈	—	6	16	no	—
103	C₅×Q₈	—	12	8	no	—
104	C₂×C₄×C₅	—	6	8	no	—
105	C₂×C₄×C₅	—	12	8	no	—
106	C₂×C₄×C₅	Dic₁₂	1	8	yes	complemented
107	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
108	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
109	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
110	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
111	C₅×C₈	C₂×D₁₂	1	8	yes	—
112	C₂²×Q₈	—	3	4	no	—
113	C₂×Q₁₆	—	3	16	no	—
114	C₂×Q₁₆	—	6	16	no	—
115	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
116	C₄⋊Q₈	—	3	8	no	—
117	C₄⋊Q₈	—	6	4	no	—
118	C₂×C₄⋊C₄	—	6	4	no	—
119	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
120	C₄×C₈	C₂×C₅×D₃	1	4	yes	—
121	C₂×C₃×C₅	#494	1	4	yes	complemented
122	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
123	C₂×C₃×C₅	C₂²×Q₁₆	1	2	yes	—
124	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄	C₅×Q₁₆	1	8	yes	complemented
126	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
128	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
129	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
130	C₂×Dic₃	—	2	8	no	—
131	C₂×Dic₃	—	4	8	no	—
132	Dic₆	—	2	16	no	—
133	Dic₆	—	4	8	no	—
134	C₃×C₈	C₂×C₅×D₄	1	8	yes	—
135	C₂²×C₅	#874	1	2	yes	—
136	C₂²×C₅	C₂×Dic₁₂	1	4	yes	—
137	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
138	C₄×C₅	—	12	8	no	—
139	C₄×C₅	#874	1	2	yes	—
140	C₄×C₅	C₂×Dic₁₂	1	8	yes	complemented
141	C₄×C₅	C₂²×D₁₂	1	2	yes	—
142	C₂×Q₈	—	3	8	no	—
143	C₂×Q₈	—	6	4	no	—
144	C₂×Q₈	—	6	16	no	—
145	C₂²×C₄	—	6	4	no	—
146	C₂²×C₄	C₅×D₁₂	1	2	yes	—
147	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
148	Q₁₆	—	6	32	no	—
149	C₂×C₈	C₅×D₁₂	1	8	yes	—
150	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
151	C₄⋊C₄	—	6	16	no	—
152	C₄²	C₅×D₁₂	1	2	yes	—
153	C₄²	C₂²×C₅×D₃	1	2	yes	—
154	C₃×C₅	C₂×#494	1	1	yes	characteristic, complemented, Hall
155	C₂²×C₃	C₅×#127	1	2	yes	—
156	C₂²×C₃	C₂×C₅×Q₁₆	1	4	yes	—
157	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
158	C₃×C₄	C₅×#127	1	2	yes	—
159	C₃×C₄	C₂×C₅×Q₁₆	1	8	yes	complemented
160	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
161	Dic₃	—	4	8	no	—
162	C₂×C₅	#4699	1	4	yes	direct product factor
163	C₂×C₅	C₂×#874	1	1	yes	characteristic
164	C₂×C₅	C₂²×Dic₁₂	1	2	yes	—
165	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
166	Q₈	—	6	16	no	—
167	Q₈	—	12	8	no	—
168	C₂×C₄	—	6	8	no	—
169	C₂×C₄	—	12	8	no	—
170	C₂×C₄	C₅×Dic₁₂	1	8	yes	complemented
171	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
172	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
173	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
174	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
175	C₈	C₂×C₅×D₁₂	1	8	yes	—
176	C₂×C₃	C₅×#494	1	4	yes	complemented
177	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
178	C₂×C₃	C₂²×C₅×Q₁₆	1	2	yes	—
179	C₅	C₂×#4699	1	1	yes	characteristic, direct product factor, Sylow
180	C₂²	C₅×#874	1	2	yes	—
181	C₂²	C₂×C₅×Dic₁₂	1	4	yes	—
182	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
183	C₄	—	12	8	no	—
184	C₄	C₅×#874	1	2	yes	—
185	C₄	C₂×C₅×Dic₁₂	1	8	yes	complemented
186	C₄	C₂²×C₅×D₁₂	1	2	yes	—
187	C₃	C₂×C₅×#494	1	1	yes	characteristic, complemented, Sylow
188	C₂	C₅×#4699	1	4	yes	direct product factor
189	C₂	C₂×C₅×#874	1	1	yes	characteristic
190	C₂	C₂²×C₅×Dic₁₂	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, prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×#494
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
4. C₅×#4699	C₂	direct (N × H)
15. C₂×#4699	C₅	direct (N × H)
35. #4699	C₂×C₅	direct (N × H)
47. C₂×C₃×C₄×C₅	Q₁₆	semidirect
86. C₃×C₄×C₅	C₂×Q₁₆	semidirect
106. C₂×C₄×C₅	Dic₁₂	semidirect
121. C₂×C₃×C₅	#494	semidirect
125. C₂×C₃×C₄	C₅×Q₁₆	semidirect
140. C₄×C₅	C₂×Dic₁₂	semidirect
154. C₃×C₅	C₂×#494	semidirect
159. C₃×C₄	C₂×C₅×Q₁₆	semidirect
162. C₂×C₅	#4699	direct (N × H)
170. C₂×C₄	C₅×Dic₁₂	semidirect
176. C₂×C₃	C₅×#494	semidirect
179. C₅	C₂×#4699	direct (N × H)
185. C₄	C₂×C₅×Dic₁₂	semidirect
187. C₃	C₂×C₅×#494	semidirect
188. C₂	C₅×#4699	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×Dic₁₂	2
C₂×C₅×#869	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#4699	2
C₂×C₅×#494	3
C₂×#4699	5

Subgroups — C2×C5×#4699 #14438802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4699 #14438802