Subgroups — C₃×#10600543 #14294865

Order 1920.

592 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic
4	C₃×#64770	C₂	1	4	yes	maximal
5	#10600543	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
9	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
10	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
11	C₂²×C₃×#168	C₂²	1	2	yes	—
12	C₃×C₄×C₅×C₈	C₄	1	4	yes	complemented
13	C₃×C₄×#168	C₄	1	4	yes	complemented
14	C₃×#1744	—	5	1	no	maximal, Hall
15	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
16	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic
18	#64770	C₂×C₃	1	4	yes	—
19	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
23	C₂×C₃×C₅×C₈	—	2	4	no	—
24	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
25	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
26	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
27	C₃×C₄×Dic₅	—	2	4	no	—
28	C₃×C₄×Dic₅	—	2	4	no	—
29	C₃×C₄×Dic₅	C₈	1	8	yes	complemented
30	C₂×C₃×#168	—	2	4	no	—
31	C₂×C₃×#168	C₂×C₄	1	4	yes	—
32	C₂×C₃×C₄×C₈	—	5	1	no	—
33	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic
34	C₃×C₄³	—	5	1	no	—
35	C₃×#336	—	5	4	no	—
36	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
37	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
38	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
39	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
40	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
41	C₂²×#168	C₂²×C₃	1	2	yes	—
42	C₄×C₅×C₈	C₃×C₄	1	4	yes	complemented
43	C₄×#168	C₃×C₄	1	4	yes	complemented
44	#1744	—	5	1	no	Sylow
45	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
47	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
48	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	—
49	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	—
50	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×C₅	#41	1	4	yes	—
53	C₂×C₃×Dic₅	—	2	4	no	—
54	C₂×C₃×Dic₅	—	2	4	no	—
55	C₂×C₃×Dic₅	C₂×C₈	1	8	yes	—
56	C₃×C₅×C₈	—	2	4	no	—
57	C₃×#168	—	2	4	no	—
58	C₂²×C₃×C₈	—	5	2	no	—
59	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
60	C₂×C₃×C₄²	—	5	2	no	—
61	C₂×C₃×C₄²	—	5	2	no	—
62	C₂×C₃×C₄²	—	5	2	no	—
63	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
64	C₃×C₄×C₈	—	5	4	no	—
65	C₃×C₄×C₈	Dic₅	1	4	yes	complemented
66	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
69	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
70	C₂×C₅×C₈	—	2	4	no	—
71	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
72	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
73	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
74	C₄×Dic₅	—	2	4	no	—
75	C₄×Dic₅	—	2	4	no	—
76	C₄×Dic₅	C₃×C₈	1	8	yes	complemented
77	C₂×#168	—	2	4	no	—
78	C₂×#168	C₂×C₃×C₄	1	4	yes	—
79	C₂×C₄×C₈	—	5	1	no	—
80	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic
81	C₄³	—	5	1	no	—
82	#336	—	5	4	no	—
83	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
84	C₂²×C₃×C₅	#117	1	2	yes	—
85	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
86	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
87	C₃×C₄×C₅	C₄×C₈	1	4	yes	—
88	C₃×C₄×C₅	#97	1	4	yes	—
89	C₃×C₄×C₅	#117	1	2	yes	—
90	C₃×C₄×C₅	#117	1	2	yes	—
91	C₃×Dic₅	—	2	8	no	—
92	C₂²×C₃×C₄	—	5	4	no	—
93	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
94	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
95	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
96	C₂×C₃×C₈	—	2	4	no	—
97	C₂×C₃×C₈	—	5	4	no	—
98	C₂×C₃×C₈	—	10	4	no	—
99	C₂×C₃×C₈	C₂×Dic₅	1	4	yes	—
100	C₃×C₄²	—	5	8	no	—
101	C₃×C₄²	—	10	4	no	—
102	C₃×C₄²	—	10	4	no	—
103	C₃×C₄²	C₄×D₅	1	2	yes	—
104	C₃×C₄²	C₂×Dic₅	1	2	yes	—
105	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
106	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
107	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
108	C₂×C₄×C₅	C₂×C₃×C₈	1	4	yes	—
109	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	—
110	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
111	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
112	C₂×C₄×C₅	C₃×#41	1	4	yes	—
113	C₂×Dic₅	—	2	4	no	—
114	C₂×Dic₅	—	2	4	no	—
115	C₂×Dic₅	C₂×C₃×C₈	1	8	yes	—
116	C₅×C₈	—	2	4	no	—
117	#168	—	2	4	no	—
118	C₂²×C₈	—	5	2	no	—
119	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
120	C₂×C₄²	—	5	2	no	—
121	C₂×C₄²	—	5	2	no	—
122	C₂×C₄²	—	5	2	no	—
123	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
124	C₄×C₈	—	5	4	no	—
125	C₄×C₈	C₃×Dic₅	1	4	yes	complemented
126	C₂×C₃×C₅	#376	1	1	yes	characteristic
127	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
128	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
129	C₂×C₃×C₅	#431	1	4	yes	—
130	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
131	C₂×C₃×C₄	—	5	8	no	—
132	C₂×C₃×C₄	—	10	4	no	—
133	C₂×C₃×C₄	—	10	4	no	—
134	C₂×C₃×C₄	C₈×D₅	1	4	yes	—
135	C₂×C₃×C₄	#676	1	4	yes	—
136	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
137	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
138	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
139	C₂×C₃×C₄	#709	1	4	yes	—
140	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
141	C₃×C₈	—	2	4	no	—
142	C₃×C₈	—	10	4	no	—
143	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
144	C₂²×C₅	C₃×#117	1	2	yes	—
145	C₂²×C₅	C₂²×C₃×C₈	1	2	yes	—
146	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
147	C₄×C₅	C₃×C₄×C₈	1	4	yes	—
148	C₄×C₅	C₃×#97	1	4	yes	—
149	C₄×C₅	C₃×#117	1	2	yes	—
150	C₄×C₅	C₃×#117	1	2	yes	—
151	Dic₅	—	2	8	no	—
152	C₂²×C₄	—	5	4	no	—
153	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
154	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
155	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	5	4	no	—
158	C₂×C₈	—	10	4	no	—
159	C₂×C₈	C₂×C₃×Dic₅	1	4	yes	—
160	C₄²	—	5	8	no	—
161	C₄²	—	10	4	no	—
162	C₄²	—	10	4	no	—
163	C₄²	C₃×C₄×D₅	1	2	yes	—
164	C₄²	C₂×C₃×Dic₅	1	2	yes	—
165	C₃×C₅	#1744	1	1	yes	characteristic, complemented, Hall
166	C₂²×C₃	#4018	1	2	yes	—
167	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
168	C₂²×C₃	C₂×#676	1	2	yes	—
169	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
170	C₃×C₄	—	10	8	no	—
171	C₃×C₄	C₈×Dic₅	1	4	yes	—
172	C₃×C₄	#3947	1	4	yes	—
173	C₃×C₄	#4018	1	2	yes	—
174	C₃×C₄	#4072	1	2	yes	—
175	C₂×C₅	C₃×#376	1	1	yes	characteristic
176	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
177	C₂×C₅	C₂×C₃×#97	1	1	yes	characteristic
178	C₂×C₅	C₃×#431	1	4	yes	—
179	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
180	C₂×C₄	—	5	8	no	—
181	C₂×C₄	—	10	4	no	—
182	C₂×C₄	—	10	4	no	—
183	C₂×C₄	C₃×C₈×D₅	1	4	yes	—
184	C₂×C₄	C₃×#676	1	4	yes	—
185	C₂×C₄	C₃×C₄×Dic₅	1	2	yes	—
186	C₂×C₄	C₃×C₄×Dic₅	1	2	yes	—
187	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
188	C₂×C₄	C₃×#709	1	4	yes	—
189	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
190	C₈	—	2	4	no	—
191	C₈	—	10	4	no	—
192	C₂×C₃	#64974	1	4	yes	—
193	C₂×C₃	#65221	1	1	yes	characteristic
194	C₂×C₃	C₂×C₈×Dic₅	1	1	yes	characteristic
195	C₂×C₃	C₂×#3947	1	1	yes	characteristic
196	C₅	C₃×#1744	1	1	yes	characteristic, complemented, Sylow
197	C₂²	C₃×#4018	1	2	yes	—
198	C₂²	C₂×C₃×C₈×D₅	1	2	yes	—
199	C₂²	C₂×C₃×#676	1	2	yes	—
200	C₂²	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
201	C₄	—	10	8	no	—
202	C₄	C₃×C₈×Dic₅	1	4	yes	—
203	C₄	C₃×#3947	1	4	yes	—
204	C₄	C₃×#4018	1	2	yes	—
205	C₄	C₃×#4072	1	2	yes	—
206	C₃	#10600543	1	1	yes	characteristic, direct product factor, Sylow
207	C₂	C₃×#64974	1	4	yes	—
208	C₂	C₃×#65221	1	1	yes	characteristic
209	C₂	C₂×C₃×C₈×Dic₅	1	1	yes	characteristic
210	C₂	C₂×C₃×#3947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄²	C₂×D₅
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×#1744
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #10600543	C₃	direct (N × H)
12. C₃×C₄×C₅×C₈	C₄	semidirect
13. C₃×C₄×#168	C₄	semidirect
29. C₃×C₄×Dic₅	C₈	semidirect
42. C₄×C₅×C₈	C₃×C₄	semidirect
43. C₄×#168	C₃×C₄	semidirect
65. C₃×C₄×C₈	Dic₅	semidirect
76. C₄×Dic₅	C₃×C₈	semidirect
125. C₄×C₈	C₃×Dic₅	semidirect
165. C₃×C₅	#1744	semidirect
196. C₅	C₃×#1744	semidirect
206. C₃	#10600543	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×C₃×C₄×C₅×C₈	2
C₃×C₄²×Dic₅	2
C₂×C₃×C₄×#168	2
C₃×#64770	2
#10600543	3
C₃×#1744	5

Subgroups — C3×#10600543 #14294865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600543 #14294865