Subgroups — C₂×C₃×C₄×C₉×C₆₄ #72191998

Order 13824.

1620 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₉×C₆₄	C₂	1	2	yes	maximal
3	C₃×C₄×C₉×C₆₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₄×C₆₄	C₃	1	1	yes	maximal, characteristic
5	C₂×C₄×C₉×C₆₄	C₃	1	3	yes	maximal, direct product factor
6	C₂×C₃×C₄×C₉×C₁₆	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₉×C₃₂	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₉×C₃₂	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₉×C₃₂	C₄	1	2	yes	—
10	C₃×C₄×C₉×C₃₂	C₂²	1	2	yes	—
11	C₂×C₃×C₉×C₆₄	C₄	1	8	yes	direct product factor
12	C₂×C₃×C₉×C₆₄	C₂²	1	4	yes	—
13	C₂×C₃²×C₄×C₃₂	C₂×C₃	1	1	yes	characteristic
14	C₂×C₄×C₉×C₃₂	C₂×C₃	1	3	yes	—
15	C₂²×C₃²×C₆₄	C₂×C₃	1	2	yes	—
16	C₂²×C₉×C₆₄	C₂×C₃	1	6	yes	—
17	C₃²×C₄×C₆₄	C₂×C₃	1	4	yes	—
18	C₄×C₉×C₆₄	C₂×C₃	1	12	yes	direct product factor
19	C₂×C₃×C₄×C₆₄	C₉	1	3	yes	direct product factor
20	C₂×C₃×C₄×C₆₄	C₃²	1	1	yes	characteristic
21	C₂²×C₃×C₉×C₁₆	C₈	1	1	yes	characteristic
22	C₂²×C₃×C₉×C₁₆	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₄×C₈×C₉	C₈	1	1	yes	characteristic
24	C₂×C₃×C₉×C₃₂	C₈	1	4	yes	—
25	C₂×C₃×C₉×C₃₂	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₉×C₃₂	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₉×C₃₂	C₂×C₄	1	4	yes	—
28	C₂×C₃×C₉×C₃₂	C₂³	1	1	yes	characteristic
29	C₃×C₄×C₉×C₁₆	C₈	1	2	yes	—
30	C₃×C₄×C₉×C₁₆	C₂×C₄	1	2	yes	—
31	C₃×C₉×C₆₄	C₂×C₄	1	8	yes	direct product factor
32	C₂²×C₃²×C₃₂	C₃×C₄	1	1	yes	characteristic
33	C₂²×C₃²×C₃₂	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₃²×C₄×C₁₆	C₃×C₄	1	1	yes	characteristic
35	C₂×C₃²×C₆₄	C₃×C₄	1	8	yes	—
36	C₂×C₃²×C₆₄	C₂²×C₃	1	4	yes	—
37	C₃²×C₄×C₃₂	C₃×C₄	1	2	yes	—
38	C₃²×C₄×C₃₂	C₂²×C₃	1	2	yes	—
39	C₂²×C₉×C₃₂	C₃×C₄	1	3	yes	—
40	C₂²×C₉×C₃₂	C₂²×C₃	1	3	yes	—
41	C₂×C₄×C₉×C₁₆	C₃×C₄	1	3	yes	—
42	C₂×C₉×C₆₄	C₃×C₄	1	24	yes	direct product factor
43	C₂×C₉×C₆₄	C₂²×C₃	1	12	yes	—
44	C₄×C₉×C₃₂	C₃×C₄	1	6	yes	—
45	C₄×C₉×C₃₂	C₂²×C₃	1	6	yes	—
46	C₂²×C₃×C₈×C₉	C₁₆	1	1	yes	characteristic
47	C₂²×C₃×C₈×C₉	C₂×C₈	1	1	yes	characteristic
48	C₂×C₃×C₄²×C₉	C₁₆	1	1	yes	characteristic
49	C₂×C₃×C₉×C₁₆	C₁₆	1	4	yes	—
50	C₂×C₃×C₉×C₁₆	C₄²	1	2	yes	—
51	C₂×C₃×C₉×C₁₆	C₂×C₈	1	1	yes	characteristic
52	C₂×C₃×C₉×C₁₆	C₂×C₈	1	2	yes	—
53	C₂×C₃×C₉×C₁₆	C₂×C₈	1	2	yes	—
54	C₂×C₃×C₉×C₁₆	C₂²×C₄	1	1	yes	characteristic
55	C₃×C₄×C₈×C₉	C₁₆	1	2	yes	—
56	C₃×C₄×C₈×C₉	C₂×C₈	1	2	yes	—
57	C₃×C₉×C₃₂	C₄²	1	2	yes	—
58	C₃×C₉×C₃₂	C₂×C₈	1	4	yes	—
59	C₃×C₉×C₃₂	C₂²×C₄	1	2	yes	—
60	C₂²×C₃×C₆₄	C₂×C₉	1	6	yes	—
61	C₂²×C₃×C₆₄	C₂×C₃²	1	2	yes	—
62	C₂×C₃×C₄×C₃₂	C₂×C₉	1	3	yes	—
63	C₂×C₃×C₄×C₃₂	C₂×C₃²	1	1	yes	characteristic
64	C₃×C₄×C₆₄	C₂×C₉	1	12	yes	direct product factor
65	C₃×C₄×C₆₄	C₂×C₃²	1	4	yes	—
66	C₂²×C₃²×C₁₆	C₃×C₈	1	1	yes	characteristic
67	C₂²×C₃²×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
68	C₂×C₃²×C₄×C₈	C₃×C₈	1	1	yes	characteristic
69	C₂×C₃²×C₃₂	C₃×C₈	1	4	yes	—
70	C₂×C₃²×C₃₂	C₂×C₃×C₄	1	1	yes	characteristic
71	C₂×C₃²×C₃₂	C₂×C₃×C₄	1	2	yes	—
72	C₂×C₃²×C₃₂	C₂×C₃×C₄	1	4	yes	—
73	C₂×C₃²×C₃₂	C₂³×C₃	1	1	yes	characteristic
74	C₃²×C₄×C₁₆	C₃×C₈	1	2	yes	—
75	C₃²×C₄×C₁₆	C₂×C₃×C₄	1	2	yes	—
76	C₂²×C₉×C₁₆	C₃×C₈	1	3	yes	—
77	C₂²×C₉×C₁₆	C₂×C₃×C₄	1	3	yes	—
78	C₂×C₄×C₈×C₉	C₃×C₈	1	3	yes	—
79	C₃²×C₆₄	C₂×C₃×C₄	1	8	yes	—
80	C₂×C₉×C₃₂	C₃×C₈	1	12	yes	—
81	C₂×C₉×C₃₂	C₂×C₃×C₄	1	3	yes	—
82	C₂×C₉×C₃₂	C₂×C₃×C₄	1	6	yes	—
83	C₂×C₉×C₃₂	C₂×C₃×C₄	1	12	yes	—
84	C₂×C₉×C₃₂	C₂³×C₃	1	3	yes	—
85	C₄×C₉×C₁₆	C₃×C₈	1	6	yes	—
86	C₄×C₉×C₁₆	C₂×C₃×C₄	1	6	yes	—
87	C₉×C₆₄	C₂×C₃×C₄	1	24	yes	direct product factor
88	C₂×C₄×C₆₄	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²×C₃×C₄×C₉	C₃₂	1	2	yes	—
90	C₂²×C₃×C₄×C₉	C₂×C₁₆	1	1	yes	characteristic
91	C₂×C₃×C₈×C₉	C₃₂	1	4	yes	—
92	C₂×C₃×C₈×C₉	C₄×C₈	1	2	yes	—
93	C₂×C₃×C₈×C₉	C₂×C₁₆	1	1	yes	characteristic
94	C₂×C₃×C₈×C₉	C₂×C₁₆	1	2	yes	—
95	C₂×C₃×C₈×C₉	C₂×C₁₆	1	2	yes	—
96	C₂×C₃×C₈×C₉	C₂²×C₈	1	1	yes	characteristic
97	C₃×C₄²×C₉	C₃₂	1	2	yes	—
98	C₃×C₄²×C₉	C₂×C₁₆	1	2	yes	—
99	C₃×C₉×C₁₆	C₄×C₈	1	2	yes	—
100	C₃×C₉×C₁₆	C₂×C₁₆	1	4	yes	—
101	C₃×C₉×C₁₆	C₂×C₄²	1	1	yes	characteristic
102	C₃×C₉×C₁₆	C₂²×C₈	1	1	yes	characteristic
103	C₂²×C₃×C₃₂	C₄×C₉	1	3	yes	—
104	C₂²×C₃×C₃₂	C₂²×C₉	1	3	yes	—
105	C₂²×C₃×C₃₂	C₃²×C₄	1	1	yes	characteristic
106	C₂²×C₃×C₃₂	C₂²×C₃²	1	1	yes	characteristic
107	C₂×C₃×C₄×C₁₆	C₄×C₉	1	3	yes	—
108	C₂×C₃×C₄×C₁₆	C₃²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₆₄	C₄×C₉	1	24	yes	direct product factor
110	C₂×C₃×C₆₄	C₂²×C₉	1	12	yes	—
111	C₂×C₃×C₆₄	C₃²×C₄	1	8	yes	—
112	C₂×C₃×C₆₄	C₂²×C₃²	1	4	yes	—
113	C₃×C₄×C₃₂	C₄×C₉	1	6	yes	—
114	C₃×C₄×C₃₂	C₂²×C₉	1	6	yes	—
115	C₃×C₄×C₃₂	C₃²×C₄	1	2	yes	—
116	C₃×C₄×C₃₂	C₂²×C₃²	1	2	yes	—
117	C₂²×C₃²×C₈	C₃×C₁₆	1	1	yes	characteristic
118	C₂²×C₃²×C₈	C₂×C₃×C₈	1	1	yes	characteristic
119	C₂×C₃²×C₄²	C₃×C₁₆	1	1	yes	characteristic
120	C₂×C₃²×C₁₆	C₃×C₁₆	1	4	yes	—
121	C₂×C₃²×C₁₆	C₃×C₄²	1	2	yes	—
122	C₂×C₃²×C₁₆	C₂×C₃×C₈	1	1	yes	characteristic
123	C₂×C₃²×C₁₆	C₂×C₃×C₈	1	2	yes	—
124	C₂×C₃²×C₁₆	C₂×C₃×C₈	1	2	yes	—
125	C₂×C₃²×C₁₆	C₂²×C₃×C₄	1	1	yes	characteristic
126	C₃²×C₄×C₈	C₃×C₁₆	1	2	yes	—
127	C₃²×C₄×C₈	C₂×C₃×C₈	1	2	yes	—
128	C₂²×C₈×C₉	C₃×C₁₆	1	3	yes	—
129	C₂²×C₈×C₉	C₂×C₃×C₈	1	3	yes	—
130	C₂×C₄²×C₉	C₃×C₁₆	1	3	yes	—
131	C₃²×C₃₂	C₃×C₄²	1	2	yes	—
132	C₃²×C₃₂	C₂×C₃×C₈	1	4	yes	—
133	C₃²×C₃₂	C₂²×C₃×C₄	1	2	yes	—
134	C₂×C₉×C₁₆	C₃×C₁₆	1	12	yes	—
135	C₂×C₉×C₁₆	C₃×C₄²	1	6	yes	—
136	C₂×C₉×C₁₆	C₂×C₃×C₈	1	3	yes	—
137	C₂×C₉×C₁₆	C₂×C₃×C₈	1	6	yes	—
138	C₂×C₉×C₁₆	C₂×C₃×C₈	1	6	yes	—
139	C₂×C₉×C₁₆	C₂²×C₃×C₄	1	3	yes	—
140	C₄×C₈×C₉	C₃×C₁₆	1	6	yes	—
141	C₄×C₈×C₉	C₂×C₃×C₈	1	6	yes	—
142	C₉×C₃₂	C₃×C₄²	1	6	yes	—
143	C₉×C₃₂	C₂×C₃×C₈	1	12	yes	—
144	C₉×C₃₂	C₂²×C₃×C₄	1	6	yes	—
145	C₂²×C₆₄	C₂×C₃×C₉	1	2	yes	—
146	C₂×C₄×C₃₂	C₂×C₃×C₉	1	1	yes	characteristic
147	C₄×C₆₄	C₂×C₃×C₉	1	4	yes	direct product factor
148	C₂³×C₃×C₉	C₂×C₃₂	1	1	yes	characteristic
149	C₂×C₃×C₄×C₉	C₆₄	1	8	yes	direct product factor
150	C₂×C₃×C₄×C₉	C₄×C₁₆	1	2	yes	—
151	C₂×C₃×C₄×C₉	C₂×C₃₂	1	1	yes	characteristic
152	C₂×C₃×C₄×C₉	C₂×C₃₂	1	2	yes	—
153	C₂×C₃×C₄×C₉	C₂×C₃₂	1	4	yes	—
154	C₂×C₃×C₄×C₉	C₂²×C₁₆	1	1	yes	characteristic
155	C₃×C₈×C₉	C₄×C₁₆	1	2	yes	—
156	C₃×C₈×C₉	C₂×C₃₂	1	4	yes	—
157	C₃×C₈×C₉	C₂×C₄×C₈	1	1	yes	characteristic
158	C₃×C₈×C₉	C₂²×C₁₆	1	1	yes	characteristic
159	C₂²×C₃×C₁₆	C₈×C₉	1	3	yes	—
160	C₂²×C₃×C₁₆	C₂×C₄×C₉	1	3	yes	—
161	C₂²×C₃×C₁₆	C₃²×C₈	1	1	yes	characteristic
162	C₂²×C₃×C₁₆	C₂×C₃²×C₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₈	C₈×C₉	1	3	yes	—
164	C₂×C₃×C₄×C₈	C₃²×C₈	1	1	yes	characteristic
165	C₂×C₃×C₃₂	C₈×C₉	1	12	yes	—
166	C₂×C₃×C₃₂	C₂×C₄×C₉	1	3	yes	—
167	C₂×C₃×C₃₂	C₂×C₄×C₉	1	6	yes	—
168	C₂×C₃×C₃₂	C₂×C₄×C₉	1	12	yes	—
169	C₂×C₃×C₃₂	C₃²×C₈	1	4	yes	—
170	C₂×C₃×C₃₂	C₂³×C₉	1	3	yes	—
171	C₂×C₃×C₃₂	C₂×C₃²×C₄	1	1	yes	characteristic
172	C₂×C₃×C₃₂	C₂×C₃²×C₄	1	2	yes	—
173	C₂×C₃×C₃₂	C₂×C₃²×C₄	1	4	yes	—
174	C₂×C₃×C₃₂	C₂³×C₃²	1	1	yes	characteristic
175	C₃×C₄×C₁₆	C₈×C₉	1	6	yes	—
176	C₃×C₄×C₁₆	C₂×C₄×C₉	1	6	yes	—
177	C₃×C₄×C₁₆	C₃²×C₈	1	2	yes	—
178	C₃×C₄×C₁₆	C₂×C₃²×C₄	1	2	yes	—
179	C₃×C₆₄	C₂×C₄×C₉	1	24	yes	direct product factor
180	C₃×C₆₄	C₂×C₃²×C₄	1	8	yes	—
181	C₂²×C₃²×C₄	C₃×C₃₂	1	2	yes	—
182	C₂²×C₃²×C₄	C₂×C₃×C₁₆	1	1	yes	characteristic
183	C₂×C₃²×C₈	C₃×C₃₂	1	4	yes	—
184	C₂×C₃²×C₈	C₃×C₄×C₈	1	2	yes	—
185	C₂×C₃²×C₈	C₂×C₃×C₁₆	1	1	yes	characteristic
186	C₂×C₃²×C₈	C₂×C₃×C₁₆	1	2	yes	—
187	C₂×C₃²×C₈	C₂×C₃×C₁₆	1	2	yes	—
188	C₂×C₃²×C₈	C₂²×C₃×C₈	1	1	yes	characteristic
189	C₃²×C₄²	C₃×C₃₂	1	2	yes	—
190	C₃²×C₄²	C₂×C₃×C₁₆	1	2	yes	—
191	C₂²×C₄×C₉	C₃×C₃₂	1	6	yes	—
192	C₂²×C₄×C₉	C₂×C₃×C₁₆	1	3	yes	—
193	C₃²×C₁₆	C₃×C₄×C₈	1	2	yes	—
194	C₃²×C₁₆	C₂×C₃×C₁₆	1	4	yes	—
195	C₃²×C₁₆	C₂×C₃×C₄²	1	1	yes	characteristic
196	C₃²×C₁₆	C₂²×C₃×C₈	1	1	yes	characteristic
197	C₂×C₈×C₉	C₃×C₃₂	1	12	yes	—
198	C₂×C₈×C₉	C₃×C₄×C₈	1	6	yes	—
199	C₂×C₈×C₉	C₂×C₃×C₁₆	1	3	yes	—
200	C₂×C₈×C₉	C₂×C₃×C₁₆	1	6	yes	—
201	C₂×C₈×C₉	C₂×C₃×C₁₆	1	6	yes	—
202	C₂×C₈×C₉	C₂²×C₃×C₈	1	3	yes	—
203	C₄²×C₉	C₃×C₃₂	1	6	yes	—
204	C₄²×C₉	C₂×C₃×C₁₆	1	6	yes	—
205	C₉×C₁₆	C₃×C₄×C₈	1	6	yes	—
206	C₉×C₁₆	C₂×C₃×C₁₆	1	12	yes	—
207	C₉×C₁₆	C₂×C₃×C₄²	1	3	yes	—
208	C₉×C₁₆	C₂²×C₃×C₈	1	3	yes	—
209	C₂²×C₃₂	C₃×C₄×C₉	1	1	yes	characteristic
210	C₂²×C₃₂	C₂²×C₃×C₉	1	1	yes	characteristic
211	C₂×C₄×C₁₆	C₃×C₄×C₉	1	1	yes	characteristic
212	C₂×C₆₄	C₃×C₄×C₉	1	8	yes	direct product factor
213	C₂×C₆₄	C₂²×C₃×C₉	1	4	yes	—
214	C₄×C₃₂	C₃×C₄×C₉	1	2	yes	—
215	C₄×C₃₂	C₂²×C₃×C₉	1	2	yes	—
216	C₂²×C₃×C₉	C₄×C₃₂	1	2	yes	—
217	C₂²×C₃×C₉	C₂×C₆₄	1	4	yes	—
218	C₂²×C₃×C₉	C₂²×C₃₂	1	1	yes	characteristic
219	C₃×C₄×C₉	C₄×C₃₂	1	2	yes	—
220	C₃×C₄×C₉	C₂×C₆₄	1	8	yes	direct product factor
221	C₃×C₄×C₉	C₂×C₄×C₁₆	1	1	yes	characteristic
222	C₃×C₄×C₉	C₂²×C₃₂	1	1	yes	characteristic
223	C₂²×C₃×C₈	C₉×C₁₆	1	3	yes	—
224	C₂²×C₃×C₈	C₂×C₈×C₉	1	3	yes	—
225	C₂²×C₃×C₈	C₃²×C₁₆	1	1	yes	characteristic
226	C₂²×C₃×C₈	C₂×C₃²×C₈	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₉×C₁₆	1	3	yes	—
228	C₂×C₃×C₄²	C₃²×C₁₆	1	1	yes	characteristic
229	C₂×C₃×C₁₆	C₉×C₁₆	1	12	yes	—
230	C₂×C₃×C₁₆	C₄²×C₉	1	6	yes	—
231	C₂×C₃×C₁₆	C₂×C₈×C₉	1	3	yes	—
232	C₂×C₃×C₁₆	C₂×C₈×C₉	1	6	yes	—
233	C₂×C₃×C₁₆	C₂×C₈×C₉	1	6	yes	—
234	C₂×C₃×C₁₆	C₃²×C₁₆	1	4	yes	—
235	C₂×C₃×C₁₆	C₂²×C₄×C₉	1	3	yes	—
236	C₂×C₃×C₁₆	C₃²×C₄²	1	2	yes	—
237	C₂×C₃×C₁₆	C₂×C₃²×C₈	1	1	yes	characteristic
238	C₂×C₃×C₁₆	C₂×C₃²×C₈	1	2	yes	—
239	C₂×C₃×C₁₆	C₂×C₃²×C₈	1	2	yes	—
240	C₂×C₃×C₁₆	C₂²×C₃²×C₄	1	1	yes	characteristic
241	C₃×C₄×C₈	C₉×C₁₆	1	6	yes	—
242	C₃×C₄×C₈	C₂×C₈×C₉	1	6	yes	—
243	C₃×C₄×C₈	C₃²×C₁₆	1	2	yes	—
244	C₃×C₄×C₈	C₂×C₃²×C₈	1	2	yes	—
245	C₃×C₃₂	C₄²×C₉	1	6	yes	—
246	C₃×C₃₂	C₂×C₈×C₉	1	12	yes	—
247	C₃×C₃₂	C₂²×C₄×C₉	1	6	yes	—
248	C₃×C₃₂	C₃²×C₄²	1	2	yes	—
249	C₃×C₃₂	C₂×C₃²×C₈	1	4	yes	—
250	C₃×C₃₂	C₂²×C₃²×C₄	1	2	yes	—
251	C₂³×C₃²	C₂×C₃×C₃₂	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₃×C₆₄	1	8	yes	—
253	C₂×C₃²×C₄	C₃×C₄×C₁₆	1	2	yes	—
254	C₂×C₃²×C₄	C₂×C₃×C₃₂	1	1	yes	characteristic
255	C₂×C₃²×C₄	C₂×C₃×C₃₂	1	2	yes	—
256	C₂×C₃²×C₄	C₂×C₃×C₃₂	1	4	yes	—
257	C₂×C₃²×C₄	C₂²×C₃×C₁₆	1	1	yes	characteristic
258	C₂³×C₉	C₂×C₃×C₃₂	1	3	yes	—
259	C₃²×C₈	C₃×C₄×C₁₆	1	2	yes	—
260	C₃²×C₈	C₂×C₃×C₃₂	1	4	yes	—
261	C₃²×C₈	C₂×C₃×C₄×C₈	1	1	yes	characteristic
262	C₃²×C₈	C₂²×C₃×C₁₆	1	1	yes	characteristic
263	C₂×C₄×C₉	C₃×C₆₄	1	24	yes	direct product factor
264	C₂×C₄×C₉	C₃×C₄×C₁₆	1	6	yes	—
265	C₂×C₄×C₉	C₂×C₃×C₃₂	1	3	yes	—
266	C₂×C₄×C₉	C₂×C₃×C₃₂	1	6	yes	—
267	C₂×C₄×C₉	C₂×C₃×C₃₂	1	12	yes	—
268	C₂×C₄×C₉	C₂²×C₃×C₁₆	1	3	yes	—
269	C₈×C₉	C₃×C₄×C₁₆	1	6	yes	—
270	C₈×C₉	C₂×C₃×C₃₂	1	12	yes	—
271	C₈×C₉	C₂×C₃×C₄×C₈	1	3	yes	—
272	C₈×C₉	C₂²×C₃×C₁₆	1	3	yes	—
273	C₂²×C₁₆	C₃×C₈×C₉	1	1	yes	characteristic
274	C₂²×C₁₆	C₂×C₃×C₄×C₉	1	1	yes	characteristic
275	C₂×C₄×C₈	C₃×C₈×C₉	1	1	yes	characteristic
276	C₂×C₃₂	C₃×C₈×C₉	1	4	yes	—
277	C₂×C₃₂	C₂×C₃×C₄×C₉	1	1	yes	characteristic
278	C₂×C₃₂	C₂×C₃×C₄×C₉	1	2	yes	—
279	C₂×C₃₂	C₂×C₃×C₄×C₉	1	4	yes	—
280	C₂×C₃₂	C₂³×C₃×C₉	1	1	yes	characteristic
281	C₄×C₁₆	C₃×C₈×C₉	1	2	yes	—
282	C₄×C₁₆	C₂×C₃×C₄×C₉	1	2	yes	—
283	C₆₄	C₂×C₃×C₄×C₉	1	8	yes	direct product factor
284	C₂×C₃×C₉	C₄×C₆₄	1	4	yes	direct product factor
285	C₂×C₃×C₉	C₂×C₄×C₃₂	1	1	yes	characteristic
286	C₂×C₃×C₉	C₂²×C₆₄	1	2	yes	—
287	C₂²×C₃×C₄	C₉×C₃₂	1	6	yes	—
288	C₂²×C₃×C₄	C₂×C₉×C₁₆	1	3	yes	—
289	C₂²×C₃×C₄	C₃²×C₃₂	1	2	yes	—
290	C₂²×C₃×C₄	C₂×C₃²×C₁₆	1	1	yes	characteristic
291	C₂×C₃×C₈	C₉×C₃₂	1	12	yes	—
292	C₂×C₃×C₈	C₄×C₈×C₉	1	6	yes	—
293	C₂×C₃×C₈	C₂×C₉×C₁₆	1	3	yes	—
294	C₂×C₃×C₈	C₂×C₉×C₁₆	1	6	yes	—
295	C₂×C₃×C₈	C₂×C₉×C₁₆	1	6	yes	—
296	C₂×C₃×C₈	C₃²×C₃₂	1	4	yes	—
297	C₂×C₃×C₈	C₂²×C₈×C₉	1	3	yes	—
298	C₂×C₃×C₈	C₃²×C₄×C₈	1	2	yes	—
299	C₂×C₃×C₈	C₂×C₃²×C₁₆	1	1	yes	characteristic
300	C₂×C₃×C₈	C₂×C₃²×C₁₆	1	2	yes	—
301	C₂×C₃×C₈	C₂×C₃²×C₁₆	1	2	yes	—
302	C₂×C₃×C₈	C₂²×C₃²×C₈	1	1	yes	characteristic
303	C₃×C₄²	C₉×C₃₂	1	6	yes	—
304	C₃×C₄²	C₂×C₉×C₁₆	1	6	yes	—
305	C₃×C₄²	C₃²×C₃₂	1	2	yes	—
306	C₃×C₄²	C₂×C₃²×C₁₆	1	2	yes	—
307	C₃×C₁₆	C₄×C₈×C₉	1	6	yes	—
308	C₃×C₁₆	C₂×C₉×C₁₆	1	12	yes	—
309	C₃×C₁₆	C₂×C₄²×C₉	1	3	yes	—
310	C₃×C₁₆	C₂²×C₈×C₉	1	3	yes	—
311	C₃×C₁₆	C₃²×C₄×C₈	1	2	yes	—
312	C₃×C₁₆	C₂×C₃²×C₁₆	1	4	yes	—
313	C₃×C₁₆	C₂×C₃²×C₄²	1	1	yes	characteristic
314	C₃×C₁₆	C₂²×C₃²×C₈	1	1	yes	characteristic
315	C₂²×C₃²	C₃×C₄×C₃₂	1	2	yes	—
316	C₂²×C₃²	C₂×C₃×C₆₄	1	4	yes	—
317	C₂²×C₃²	C₂²×C₃×C₃₂	1	1	yes	characteristic
318	C₃²×C₄	C₃×C₄×C₃₂	1	2	yes	—
319	C₃²×C₄	C₂×C₃×C₆₄	1	8	yes	—
320	C₃²×C₄	C₂×C₃×C₄×C₁₆	1	1	yes	characteristic
321	C₃²×C₄	C₂²×C₃×C₃₂	1	1	yes	characteristic
322	C₂²×C₉	C₃×C₄×C₃₂	1	6	yes	—
323	C₂²×C₉	C₂×C₃×C₆₄	1	12	yes	—
324	C₂²×C₉	C₂²×C₃×C₃₂	1	3	yes	—
325	C₄×C₉	C₃×C₄×C₃₂	1	6	yes	—
326	C₄×C₉	C₂×C₃×C₆₄	1	24	yes	direct product factor
327	C₄×C₉	C₂×C₃×C₄×C₁₆	1	3	yes	—
328	C₄×C₉	C₂²×C₃×C₃₂	1	3	yes	—
329	C₂²×C₈	C₃×C₉×C₁₆	1	1	yes	characteristic
330	C₂²×C₈	C₂×C₃×C₈×C₉	1	1	yes	characteristic
331	C₂×C₄²	C₃×C₉×C₁₆	1	1	yes	characteristic
332	C₂×C₁₆	C₃×C₉×C₁₆	1	4	yes	—
333	C₂×C₁₆	C₃×C₄²×C₉	1	2	yes	—
334	C₂×C₁₆	C₂×C₃×C₈×C₉	1	1	yes	characteristic
335	C₂×C₁₆	C₂×C₃×C₈×C₉	1	2	yes	—
336	C₂×C₁₆	C₂×C₃×C₈×C₉	1	2	yes	—
337	C₂×C₁₆	C₂²×C₃×C₄×C₉	1	1	yes	characteristic
338	C₄×C₈	C₃×C₉×C₁₆	1	2	yes	—
339	C₄×C₈	C₂×C₃×C₈×C₉	1	2	yes	—
340	C₃₂	C₃×C₄²×C₉	1	2	yes	—
341	C₃₂	C₂×C₃×C₈×C₉	1	4	yes	—
342	C₃₂	C₂²×C₃×C₄×C₉	1	2	yes	—
343	C₃×C₉	C₂×C₄×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³×C₃	C₂×C₉×C₃₂	1	3	yes	—
345	C₂³×C₃	C₂×C₃²×C₃₂	1	1	yes	characteristic
346	C₂×C₃×C₄	C₉×C₆₄	1	24	yes	direct product factor
347	C₂×C₃×C₄	C₄×C₉×C₁₆	1	6	yes	—
348	C₂×C₃×C₄	C₂×C₉×C₃₂	1	3	yes	—
349	C₂×C₃×C₄	C₂×C₉×C₃₂	1	6	yes	—
350	C₂×C₃×C₄	C₂×C₉×C₃₂	1	12	yes	—
351	C₂×C₃×C₄	C₃²×C₆₄	1	8	yes	—
352	C₂×C₃×C₄	C₂²×C₉×C₁₆	1	3	yes	—
353	C₂×C₃×C₄	C₃²×C₄×C₁₆	1	2	yes	—
354	C₂×C₃×C₄	C₂×C₃²×C₃₂	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂×C₃²×C₃₂	1	2	yes	—
356	C₂×C₃×C₄	C₂×C₃²×C₃₂	1	4	yes	—
357	C₂×C₃×C₄	C₂²×C₃²×C₁₆	1	1	yes	characteristic
358	C₃×C₈	C₄×C₉×C₁₆	1	6	yes	—
359	C₃×C₈	C₂×C₉×C₃₂	1	12	yes	—
360	C₃×C₈	C₂×C₄×C₈×C₉	1	3	yes	—
361	C₃×C₈	C₂²×C₉×C₁₆	1	3	yes	—
362	C₃×C₈	C₃²×C₄×C₁₆	1	2	yes	—
363	C₃×C₈	C₂×C₃²×C₃₂	1	4	yes	—
364	C₃×C₈	C₂×C₃²×C₄×C₈	1	1	yes	characteristic
365	C₃×C₈	C₂²×C₃²×C₁₆	1	1	yes	characteristic
366	C₂×C₃²	C₃×C₄×C₆₄	1	4	yes	—
367	C₂×C₃²	C₂×C₃×C₄×C₃₂	1	1	yes	characteristic
368	C₂×C₃²	C₂²×C₃×C₆₄	1	2	yes	—
369	C₂×C₉	C₃×C₄×C₆₄	1	12	yes	direct product factor
370	C₂×C₉	C₂×C₃×C₄×C₃₂	1	3	yes	—
371	C₂×C₉	C₂²×C₃×C₆₄	1	6	yes	—
372	C₂²×C₄	C₃×C₉×C₃₂	1	2	yes	—
373	C₂²×C₄	C₂×C₃×C₉×C₁₆	1	1	yes	characteristic
374	C₂×C₈	C₃×C₉×C₃₂	1	4	yes	—
375	C₂×C₈	C₃×C₄×C₈×C₉	1	2	yes	—
376	C₂×C₈	C₂×C₃×C₉×C₁₆	1	1	yes	characteristic
377	C₂×C₈	C₂×C₃×C₉×C₁₆	1	2	yes	—
378	C₂×C₈	C₂×C₃×C₉×C₁₆	1	2	yes	—
379	C₂×C₈	C₂²×C₃×C₈×C₉	1	1	yes	characteristic
380	C₄²	C₃×C₉×C₃₂	1	2	yes	—
381	C₄²	C₂×C₃×C₉×C₁₆	1	2	yes	—
382	C₁₆	C₃×C₄×C₈×C₉	1	2	yes	—
383	C₁₆	C₂×C₃×C₉×C₁₆	1	4	yes	—
384	C₁₆	C₂×C₃×C₄²×C₉	1	1	yes	characteristic
385	C₁₆	C₂²×C₃×C₈×C₉	1	1	yes	characteristic
386	C₂²×C₃	C₄×C₉×C₃₂	1	6	yes	—
387	C₂²×C₃	C₂×C₉×C₆₄	1	12	yes	—
388	C₂²×C₃	C₂²×C₉×C₃₂	1	3	yes	—
389	C₂²×C₃	C₃²×C₄×C₃₂	1	2	yes	—
390	C₂²×C₃	C₂×C₃²×C₆₄	1	4	yes	—
391	C₂²×C₃	C₂²×C₃²×C₃₂	1	1	yes	characteristic
392	C₃×C₄	C₄×C₉×C₃₂	1	6	yes	—
393	C₃×C₄	C₂×C₉×C₆₄	1	24	yes	direct product factor
394	C₃×C₄	C₂×C₄×C₉×C₁₆	1	3	yes	—
395	C₃×C₄	C₂²×C₉×C₃₂	1	3	yes	—
396	C₃×C₄	C₃²×C₄×C₃₂	1	2	yes	—
397	C₃×C₄	C₂×C₃²×C₆₄	1	8	yes	—
398	C₃×C₄	C₂×C₃²×C₄×C₁₆	1	1	yes	characteristic
399	C₃×C₄	C₂²×C₃²×C₃₂	1	1	yes	characteristic
400	C₃²	C₂×C₃×C₄×C₆₄	1	1	yes	characteristic
401	C₉	C₂×C₃×C₄×C₆₄	1	3	yes	direct product factor
402	C₂³	C₂×C₃×C₉×C₃₂	1	1	yes	characteristic
403	C₂×C₄	C₃×C₉×C₆₄	1	8	yes	direct product factor
404	C₂×C₄	C₃×C₄×C₉×C₁₆	1	2	yes	—
405	C₂×C₄	C₂×C₃×C₉×C₃₂	1	1	yes	characteristic
406	C₂×C₄	C₂×C₃×C₉×C₃₂	1	2	yes	—
407	C₂×C₄	C₂×C₃×C₉×C₃₂	1	4	yes	—
408	C₂×C₄	C₂²×C₃×C₉×C₁₆	1	1	yes	characteristic
409	C₈	C₃×C₄×C₉×C₁₆	1	2	yes	—
410	C₈	C₂×C₃×C₉×C₃₂	1	4	yes	—
411	C₈	C₂×C₃×C₄×C₈×C₉	1	1	yes	characteristic
412	C₈	C₂²×C₃×C₉×C₁₆	1	1	yes	characteristic
413	C₂×C₃	C₄×C₉×C₆₄	1	12	yes	direct product factor
414	C₂×C₃	C₃²×C₄×C₆₄	1	4	yes	—
415	C₂×C₃	C₂²×C₉×C₆₄	1	6	yes	—
416	C₂×C₃	C₂²×C₃²×C₆₄	1	2	yes	—
417	C₂×C₃	C₂×C₄×C₉×C₃₂	1	3	yes	—
418	C₂×C₃	C₂×C₃²×C₄×C₃₂	1	1	yes	characteristic
419	C₂²	C₂×C₃×C₉×C₆₄	1	4	yes	—
420	C₂²	C₃×C₄×C₉×C₃₂	1	2	yes	—
421	C₂²	C₂²×C₃×C₉×C₃₂	1	1	yes	characteristic
422	C₄	C₂×C₃×C₉×C₆₄	1	8	yes	direct product factor
423	C₄	C₃×C₄×C₉×C₃₂	1	2	yes	—
424	C₄	C₂²×C₃×C₉×C₃₂	1	1	yes	characteristic
425	C₄	C₂×C₃×C₄×C₉×C₁₆	1	1	yes	characteristic
426	C₃	C₂×C₄×C₉×C₆₄	1	3	yes	direct product factor
427	C₃	C₂×C₃²×C₄×C₆₄	1	1	yes	characteristic
428	C₂	C₃×C₄×C₉×C₆₄	1	4	yes	direct product factor
429	C₂	C₂²×C₃×C₉×C₆₄	1	2	yes	—
430	C₂	C₂×C₃×C₄×C₉×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₃₂	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂×C₃×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₉×C₆₄	C₂	direct (N × H)
5. C₂×C₄×C₉×C₆₄	C₃	direct (N × H)
11. C₂×C₃×C₉×C₆₄	C₄	direct (N × H)
18. C₄×C₉×C₆₄	C₂×C₃	direct (N × H)
19. C₂×C₃×C₄×C₆₄	C₉	direct (N × H)
31. C₃×C₉×C₆₄	C₂×C₄	direct (N × H)
42. C₂×C₉×C₆₄	C₃×C₄	direct (N × H)
64. C₃×C₄×C₆₄	C₂×C₉	direct (N × H)
87. C₉×C₆₄	C₂×C₃×C₄	direct (N × H)
88. C₂×C₄×C₆₄	C₃×C₉	direct (N × H)
109. C₂×C₃×C₆₄	C₄×C₉	direct (N × H)
147. C₄×C₆₄	C₂×C₃×C₉	direct (N × H)
149. C₂×C₃×C₄×C₉	C₆₄	direct (N × H)
179. C₃×C₆₄	C₂×C₄×C₉	direct (N × H)
212. C₂×C₆₄	C₃×C₄×C₉	direct (N × H)
220. C₃×C₄×C₉	C₂×C₆₄	direct (N × H)
263. C₂×C₄×C₉	C₃×C₆₄	direct (N × H)
283. C₆₄	C₂×C₃×C₄×C₉	direct (N × H)
284. C₂×C₃×C₉	C₄×C₆₄	direct (N × H)
326. C₄×C₉	C₂×C₃×C₆₄	direct (N × H)
343. C₃×C₉	C₂×C₄×C₆₄	direct (N × H)
346. C₂×C₃×C₄	C₉×C₆₄	direct (N × H)
369. C₂×C₉	C₃×C₄×C₆₄	direct (N × H)
393. C₃×C₄	C₂×C₉×C₆₄	direct (N × H)
401. C₉	C₂×C₃×C₄×C₆₄	direct (N × H)
403. C₂×C₄	C₃×C₉×C₆₄	direct (N × H)
413. C₂×C₃	C₄×C₉×C₆₄	direct (N × H)
422. C₄	C₂×C₃×C₉×C₆₄	direct (N × H)
426. C₃	C₂×C₄×C₉×C₆₄	direct (N × H)
428. C₂	C₃×C₄×C₉×C₆₄	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×C₉×C₃₂	2
C₂²×C₃×C₉×C₆₄	2
C₃×C₄×C₉×C₆₄	2
C₂×C₃²×C₄×C₆₄	3
C₂×C₄×C₉×C₆₄	3

Subgroups — C2×C3×C4×C9×C64 #72191998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₉×C₆₄ #72191998