Subgroups — C₃×#10602218 #14312750

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#65390	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3944	C₂	1	1	yes	maximal, characteristic
4	C₃×#64732	C₂	1	4	yes	maximal, complemented
5	#10602218	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃×#4072	C₄	1	1	yes	characteristic
8	C₂×C₃×#681	C₄	1	1	yes	characteristic
9	C₃×C₅×M₃₂	C₄	1	2	yes	complemented
10	C₃×C₅×M₃₂	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₁₆	C₄	1	2	yes	complemented
12	C₃×#3947	C₂²	1	2	yes	—
13	C₃×C₈×Dic₅	C₄	1	2	yes	—
14	C₃×#3944	C₄	1	2	yes	complemented
15	C₃×#3944	C₂²	1	2	yes	—
16	C₂×C₃×#672	C₄	1	2	yes	complemented
17	C₃×#2110	—	5	1	no	maximal, Hall
18	C₂×C₅×M₃₂	C₂×C₃	1	1	yes	characteristic
19	#65390	C₂×C₃	1	1	yes	characteristic
20	C₂×#3944	C₂×C₃	1	1	yes	characteristic
21	#64732	C₂×C₃	1	4	yes	complemented
22	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
29	C₃×C₂²⋊Dic₅	—	2	1	no	—
30	C₃×C₄⋊Dic₅	—	2	1	no	—
31	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
32	C₃×#681	—	2	1	no	—
33	C₃×#681	—	2	1	no	—
34	C₂×C₃×#168	C₂×C₄	1	2	yes	—
35	C₃×C₅×C₁₆	C₂×C₄	1	4	yes	—
36	C₃×#672	C₂×C₄	1	4	yes	—
37	C₂×C₃×M₃₂	—	5	1	no	—
38	C₂×C₃×M₃₂	D₅	1	1	yes	characteristic
39	C₃×#405	—	5	1	no	—
40	C₃×#347	—	5	4	no	—
41	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
42	#4072	C₃×C₄	1	1	yes	characteristic
43	C₂×#681	C₃×C₄	1	1	yes	characteristic
44	C₅×M₃₂	C₃×C₄	1	2	yes	complemented
45	C₅×M₃₂	C₂²×C₃	1	2	yes	—
46	C₂×C₅×C₁₆	C₃×C₄	1	2	yes	complemented
47	#3947	C₂²×C₃	1	2	yes	—
48	C₈×Dic₅	C₃×C₄	1	2	yes	—
49	#3944	C₃×C₄	1	2	yes	complemented
50	#3944	C₂²×C₃	1	2	yes	—
51	C₂×#672	C₃×C₄	1	2	yes	complemented
52	#2110	—	5	1	no	Sylow
53	C₂³×C₃×C₅	M₁₆	1	1	yes	characteristic
54	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	M₁₆	1	1	yes	characteristic
57	C₂×C₃×C₄×C₅	M₁₆	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	M₁₆	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₃×Dic₅	—	2	2	no	—
61	C₃×C₅×C₈	C₄²	1	1	yes	characteristic
62	C₃×C₅×C₈	C₄²	1	1	yes	characteristic
63	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
64	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
65	C₃×#168	—	2	2	no	—
66	C₂×C₃×M₁₆	—	5	1	no	—
67	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
68	C₃×#117	—	5	1	no	—
69	C₃×M₃₂	—	5	2	no	—
70	C₃×M₃₂	—	5	2	no	—
71	C₃×M₃₂	Dic₅	1	2	yes	complemented
72	C₃×M₃₂	C₂×D₅	1	2	yes	—
73	C₂×C₃×C₁₆	—	5	2	no	—
74	C₂×C₃×C₁₆	Dic₅	1	2	yes	complemented
75	C₃×#97	—	5	2	no	—
76	C₃×C₄×C₈	—	5	2	no	—
77	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
78	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
79	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
80	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
81	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
82	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
83	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
84	C₂²⋊Dic₅	—	2	1	no	—
85	C₄⋊Dic₅	—	2	1	no	—
86	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
87	#681	—	2	1	no	—
88	#681	—	2	1	no	—
89	C₂×#168	C₂×C₃×C₄	1	2	yes	—
90	C₅×C₁₆	C₂×C₃×C₄	1	4	yes	—
91	#672	C₂×C₃×C₄	1	4	yes	—
92	C₂×M₃₂	—	5	1	no	—
93	C₂×M₃₂	C₃×D₅	1	1	yes	characteristic
94	#405	—	5	1	no	—
95	#347	—	5	4	no	—
96	C₂²×C₃×C₅	—	4	1	no	—
97	C₂²×C₃×C₅	#97	1	1	yes	characteristic
98	C₂²×C₃×C₅	#97	1	1	yes	characteristic
99	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
100	C₃×C₄×C₅	#97	1	1	yes	characteristic
101	C₃×C₄×C₅	#97	1	1	yes	characteristic
102	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
103	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
104	C₃×Dic₅	—	4	2	no	—
105	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
106	C₃×M₁₆	—	10	1	no	—
107	C₃×M₁₆	—	10	1	no	—
108	C₂×C₃×C₈	—	5	2	no	—
109	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
110	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
111	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
112	C₂×C₃×C₈	C₂×Dic₅	1	1	yes	characteristic
113	C₂×C₃×C₈	C₂×Dic₅	1	1	yes	characteristic
114	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
115	C₃×C₄⋊C₄	—	10	1	no	—
116	C₃×C₂²⋊C₄	—	10	1	no	—
117	C₃×C₄²	—	5	2	no	—
118	C₃×C₁₆	—	5	4	no	—
119	C₃×C₁₆	C₂×Dic₅	1	4	yes	—
120	C₂³×C₅	C₃×M₁₆	1	1	yes	characteristic
121	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
122	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
123	C₂×C₄×C₅	C₃×M₁₆	1	1	yes	characteristic
124	C₂×C₄×C₅	C₃×M₁₆	1	1	yes	characteristic
125	C₂×C₄×C₅	C₃×M₁₆	1	1	yes	characteristic
126	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
127	C₂×Dic₅	—	2	2	no	—
128	C₅×C₈	C₃×C₄²	1	1	yes	characteristic
129	C₅×C₈	C₃×C₄²	1	1	yes	characteristic
130	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
131	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
132	#168	—	2	2	no	—
133	C₂×M₁₆	—	5	1	no	—
134	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
135	#117	—	5	1	no	—
136	M₃₂	—	5	2	no	—
137	M₃₂	—	5	2	no	—
138	M₃₂	C₃×Dic₅	1	2	yes	complemented
139	M₃₂	C₂×C₃×D₅	1	2	yes	—
140	C₂×C₁₆	—	5	2	no	—
141	C₂×C₁₆	C₃×Dic₅	1	2	yes	complemented
142	#97	—	5	2	no	—
143	C₄×C₈	—	5	2	no	—
144	C₂×C₃×C₅	—	2	1	no	—
145	C₂×C₃×C₅	—	2	1	no	—
146	C₂×C₃×C₅	—	2	1	no	—
147	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
148	C₂³×C₃	#676	1	1	yes	characteristic
149	C₂×C₃×C₄	—	10	2	no	—
150	C₂×C₃×C₄	#676	1	1	yes	characteristic
151	C₂×C₃×C₄	#676	1	1	yes	characteristic
152	C₂×C₃×C₄	#676	1	1	yes	characteristic
153	C₂×C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
154	C₂×C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
155	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
156	C₃×C₈	—	10	2	no	—
157	C₃×C₈	C₄×Dic₅	1	1	yes	characteristic
158	C₃×C₈	C₄×Dic₅	1	1	yes	characteristic
159	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
160	C₃×C₈	C₂²×Dic₅	1	1	yes	characteristic
161	C₂²×C₅	—	4	1	no	—
162	C₂²×C₅	C₃×#97	1	1	yes	characteristic
163	C₂²×C₅	C₃×#97	1	1	yes	characteristic
164	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
165	C₄×C₅	C₃×#97	1	1	yes	characteristic
166	C₄×C₅	C₃×#97	1	1	yes	characteristic
167	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
168	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
169	Dic₅	—	4	2	no	—
170	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
171	M₁₆	—	10	1	no	—
172	M₁₆	—	10	1	no	—
173	C₂×C₈	—	5	2	no	—
174	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
175	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
176	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
177	C₂×C₈	C₂×C₃×Dic₅	1	1	yes	characteristic
178	C₂×C₈	C₂×C₃×Dic₅	1	1	yes	characteristic
179	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
180	C₄⋊C₄	—	10	1	no	—
181	C₂²⋊C₄	—	10	1	no	—
182	C₄²	—	5	2	no	—
183	C₁₆	—	5	4	no	—
184	C₁₆	C₂×C₃×Dic₅	1	4	yes	—
185	C₃×C₅	#2110	1	1	yes	characteristic, complemented, Hall
186	C₂²×C₃	—	4	1	no	—
187	C₂²×C₃	#3947	1	1	yes	characteristic
188	C₂²×C₃	#3947	1	1	yes	characteristic
189	C₂²×C₃	C₂×#676	1	1	yes	characteristic
190	C₃×C₄	—	20	2	no	—
191	C₃×C₄	#3947	1	1	yes	characteristic
192	C₃×C₄	#3947	1	1	yes	characteristic
193	C₃×C₄	C₂×#676	1	1	yes	characteristic
194	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
195	C₂×C₅	—	2	1	no	—
196	C₂×C₅	—	2	1	no	—
197	C₂×C₅	—	2	1	no	—
198	C₂×C₅	C₂×C₃×#97	1	1	yes	characteristic
199	C₂³	C₃×#676	1	1	yes	characteristic
200	C₂×C₄	—	10	2	no	—
201	C₂×C₄	C₃×#676	1	1	yes	characteristic
202	C₂×C₄	C₃×#676	1	1	yes	characteristic
203	C₂×C₄	C₃×#676	1	1	yes	characteristic
204	C₂×C₄	C₃×C₄×Dic₅	1	1	yes	characteristic
205	C₂×C₄	C₃×C₄×Dic₅	1	1	yes	characteristic
206	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
207	C₈	—	10	2	no	—
208	C₈	C₃×C₄×Dic₅	1	1	yes	characteristic
209	C₈	C₃×C₄×Dic₅	1	1	yes	characteristic
210	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
211	C₈	C₂²×C₃×Dic₅	1	1	yes	characteristic
212	C₂×C₃	—	2	1	no	—
213	C₂×C₃	—	2	1	no	—
214	C₂×C₃	—	2	1	no	—
215	C₂×C₃	C₂×#3947	1	1	yes	characteristic
216	C₅	C₃×#2110	1	1	yes	characteristic, complemented, Sylow
217	C₂²	—	4	1	no	—
218	C₂²	C₃×#3947	1	1	yes	characteristic
219	C₂²	C₃×#3947	1	1	yes	characteristic
220	C₂²	C₂×C₃×#676	1	1	yes	characteristic
221	C₄	—	20	2	no	—
222	C₄	C₃×#3947	1	1	yes	characteristic
223	C₄	C₃×#3947	1	1	yes	characteristic
224	C₄	C₂×C₃×#676	1	1	yes	characteristic
225	C₄	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
226	C₃	#10602218	1	1	yes	characteristic, direct product factor, Sylow
227	C₂	—	2	1	no	—
228	C₂	—	2	1	no	—
229	C₂	—	2	1	no	—
230	C₂	C₂×C₃×#3947	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₄×Dic₅
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂×C₈	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂×C₃×C₅	C₂×#97
prime radical	C₂³×C₃×C₅	M₁₆
cosocle	C₂×C₅×C₈	C₂³×C₃
hypercenter	C₂×C₃×M₃₂	D₅
hypocenter	C₅	C₃×#2110
LCS	G ▷ C₄×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×M₃₂

Complements

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

N	H ≅ G/N	type
4. C₃×#64732	C₂	semidirect
5. #10602218	C₃	direct (N × H)
9. C₃×C₅×M₃₂	C₄	semidirect
11. C₂×C₃×C₅×C₁₆	C₄	semidirect
14. C₃×#3944	C₄	semidirect
16. C₂×C₃×#672	C₄	semidirect
21. #64732	C₂×C₃	semidirect
44. C₅×M₃₂	C₃×C₄	semidirect
46. C₂×C₅×C₁₆	C₃×C₄	semidirect
49. #3944	C₃×C₄	semidirect
51. C₂×#672	C₃×C₄	semidirect
71. C₃×M₃₂	Dic₅	semidirect
74. C₂×C₃×C₁₆	Dic₅	semidirect
138. M₃₂	C₃×Dic₅	semidirect
141. C₂×C₁₆	C₃×Dic₅	semidirect
185. C₃×C₅	#2110	semidirect
216. C₅	C₃×#2110	semidirect
226. C₃	#10602218	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×C₅×M₃₂	2
C₃×#65390	2
C₂×C₃×#3944	2
C₃×#64732	2
#10602218	3
C₃×#2110	5

Subgroups — C3×#10602218 #14312750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602218 #14312750