Subgroups — C₃×C₄²×C₈×C₆₄ #72201849

Order 24576.

32796 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₈×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄³×C₆₄	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₈×C₆₄	C₂	1	12	yes	maximal
4	C₄²×C₈×C₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₄²×C₈×C₁₆	C₄	1	1	yes	characteristic
6	C₃×C₄³×C₃₂	C₄	1	1	yes	characteristic
7	C₃×C₄³×C₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₈×C₃₂	C₄	1	6	yes	—
9	C₂×C₃×C₄×C₈×C₃₂	C₂²	1	6	yes	—
10	C₂×C₃×C₄²×C₆₄	C₄	1	16	yes	—
11	C₂×C₃×C₄²×C₆₄	C₂²	1	12	yes	—
12	C₂²×C₃×C₈×C₆₄	C₂²	1	16	yes	—
13	C₃×C₄×C₈×C₆₄	C₄	1	96	yes	direct product factor
14	C₄²×C₈×C₃₂	C₂×C₃	1	1	yes	characteristic
15	C₄³×C₆₄	C₂×C₃	1	2	yes	—
16	C₂×C₄×C₈×C₆₄	C₂×C₃	1	12	yes	—
17	C₃×C₄²×C₈²	C₈	1	1	yes	characteristic
18	C₃×C₄³×C₁₆	C₈	1	1	yes	characteristic
19	C₃×C₄³×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₄×C₈×C₁₆	C₈	1	6	yes	—
21	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	6	yes	—
22	C₂×C₃×C₄²×C₃₂	C₈	1	8	yes	—
23	C₂×C₃×C₄²×C₃₂	C₂×C₄	1	3	yes	—
24	C₂×C₃×C₄²×C₃₂	C₂×C₄	1	6	yes	—
25	C₂×C₃×C₄²×C₃₂	C₂×C₄	1	8	yes	—
26	C₂×C₃×C₄²×C₃₂	C₂³	1	3	yes	—
27	C₂²×C₃×C₈×C₃₂	C₂×C₄	1	12	yes	—
28	C₂²×C₃×C₈×C₃₂	C₂³	1	4	yes	—
29	C₃×C₄×C₈×C₃₂	C₈	1	48	yes	—
30	C₃×C₄×C₈×C₃₂	C₂×C₄	1	48	yes	—
31	C₂²×C₃×C₄×C₆₄	C₂×C₄	1	48	yes	—
32	C₂²×C₃×C₄×C₆₄	C₂³	1	8	yes	—
33	C₃×C₄²×C₆₄	C₈	1	128	yes	direct product factor
34	C₃×C₄²×C₆₄	C₂×C₄	1	96	yes	—
35	C₂×C₃×C₈×C₆₄	C₂×C₄	1	192	yes	—
36	C₄²×C₈×C₁₆	C₃×C₄	1	1	yes	characteristic
37	C₄³×C₃₂	C₃×C₄	1	1	yes	characteristic
38	C₄³×C₃₂	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₄×C₈×C₃₂	C₃×C₄	1	6	yes	—
40	C₂×C₄×C₈×C₃₂	C₂²×C₃	1	6	yes	—
41	C₂×C₄²×C₆₄	C₃×C₄	1	16	yes	—
42	C₂×C₄²×C₆₄	C₂²×C₃	1	12	yes	—
43	C₂²×C₈×C₆₄	C₂²×C₃	1	16	yes	—
44	C₄×C₈×C₆₄	C₃×C₄	1	96	yes	direct product factor
45	C₃×C₄³×C₈	C₁₆	1	2	yes	—
46	C₃×C₄³×C₈	C₂×C₈	1	1	yes	characteristic
47	C₂×C₃×C₄×C₈²	C₁₆	1	6	yes	—
48	C₂×C₃×C₄×C₈²	C₂×C₈	1	6	yes	—
49	C₂×C₃×C₄²×C₁₆	C₁₆	1	8	yes	—
50	C₂×C₃×C₄²×C₁₆	C₄²	1	4	yes	—
51	C₂×C₃×C₄²×C₁₆	C₂×C₈	1	3	yes	—
52	C₂×C₃×C₄²×C₁₆	C₂×C₈	1	4	yes	—
53	C₂×C₃×C₄²×C₁₆	C₂×C₈	1	6	yes	—
54	C₂×C₃×C₄²×C₁₆	C₂²×C₄	1	3	yes	—
55	C₂²×C₃×C₈×C₁₆	C₂×C₈	1	12	yes	—
56	C₂²×C₃×C₈×C₁₆	C₂²×C₄	1	4	yes	—
57	C₃×C₄×C₈×C₁₆	C₁₆	1	48	yes	—
58	C₃×C₄×C₈×C₁₆	C₄²	1	24	yes	—
59	C₃×C₄×C₈×C₁₆	C₂×C₈	1	24	yes	—
60	C₂²×C₃×C₄×C₃₂	C₄²	1	12	yes	—
61	C₂²×C₃×C₄×C₃₂	C₂×C₈	1	24	yes	—
62	C₂²×C₃×C₄×C₃₂	C₂²×C₄	1	3	yes	—
63	C₂²×C₃×C₄×C₃₂	C₂²×C₄	1	4	yes	—
64	C₂²×C₃×C₄×C₃₂	C₂²×C₄	1	12	yes	—
65	C₂²×C₃×C₄×C₃₂	C₂⁴	1	1	yes	characteristic
66	C₃×C₄²×C₃₂	C₁₆	1	64	yes	—
67	C₃×C₄²×C₃₂	C₄²	1	24	yes	—
68	C₃×C₄²×C₃₂	C₂×C₈	1	24	yes	—
69	C₃×C₄²×C₃₂	C₂×C₈	1	24	yes	—
70	C₃×C₄²×C₃₂	C₂×C₈	1	64	yes	—
71	C₃×C₄²×C₃₂	C₂²×C₄	1	24	yes	—
72	C₂×C₃×C₈×C₃₂	C₄²	1	48	yes	—
73	C₂×C₃×C₈×C₃₂	C₂×C₈	1	96	yes	—
74	C₂×C₃×C₈×C₃₂	C₂²×C₄	1	48	yes	—
75	C₂×C₃×C₄×C₆₄	C₄²	1	192	yes	—
76	C₂×C₃×C₄×C₆₄	C₂×C₈	1	384	yes	—
77	C₂×C₃×C₄×C₆₄	C₂²×C₄	1	96	yes	—
78	C₂³×C₃×C₆₄	C₂²×C₄	1	16	yes	—
79	C₃×C₈×C₆₄	C₄²	1	256	yes	direct product factor
80	C₄²×C₈²	C₃×C₈	1	1	yes	characteristic
81	C₄³×C₁₆	C₃×C₈	1	1	yes	characteristic
82	C₄³×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
83	C₂×C₄×C₈×C₁₆	C₃×C₈	1	6	yes	—
84	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	6	yes	—
85	C₂×C₄²×C₃₂	C₃×C₈	1	8	yes	—
86	C₂×C₄²×C₃₂	C₂×C₃×C₄	1	3	yes	—
87	C₂×C₄²×C₃₂	C₂×C₃×C₄	1	6	yes	—
88	C₂×C₄²×C₃₂	C₂×C₃×C₄	1	8	yes	—
89	C₂×C₄²×C₃₂	C₂³×C₃	1	3	yes	—
90	C₂²×C₈×C₃₂	C₂×C₃×C₄	1	12	yes	—
91	C₂²×C₈×C₃₂	C₂³×C₃	1	4	yes	—
92	C₄×C₈×C₃₂	C₃×C₈	1	48	yes	—
93	C₄×C₈×C₃₂	C₂×C₃×C₄	1	48	yes	—
94	C₂²×C₄×C₆₄	C₂×C₃×C₄	1	48	yes	—
95	C₂²×C₄×C₆₄	C₂³×C₃	1	8	yes	—
96	C₂×C₈×C₆₄	C₂×C₃×C₄	1	192	yes	—
97	C₄²×C₆₄	C₃×C₈	1	128	yes	direct product factor
98	C₄²×C₆₄	C₂×C₃×C₄	1	96	yes	—
99	C₂³×C₃×C₃₂	C₂×C₄²	1	6	yes	—
100	C₂³×C₃×C₃₂	C₂²×C₈	1	8	yes	—
101	C₂³×C₃×C₃₂	C₂³×C₄	1	2	yes	—
102	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	12	yes	—
103	C₂²×C₃×C₄×C₁₆	C₂×C₁₆	1	24	yes	—
104	C₂²×C₃×C₄×C₁₆	C₂×C₄²	1	6	yes	—
105	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	3	yes	—
106	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	4	yes	—
107	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	6	yes	—
108	C₂²×C₃×C₄×C₁₆	C₂³×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄²×C₈	C₃₂	1	16	yes	—
110	C₂×C₃×C₄²×C₈	C₄×C₈	1	4	yes	—
111	C₂×C₃×C₄²×C₈	C₂×C₁₆	1	3	yes	—
112	C₂×C₃×C₄²×C₈	C₂×C₁₆	1	4	yes	—
113	C₂×C₃×C₄²×C₈	C₂×C₁₆	1	12	yes	—
114	C₂×C₃×C₄²×C₈	C₂²×C₈	1	3	yes	—
115	C₂²×C₃×C₈²	C₂×C₁₆	1	12	yes	—
116	C₂²×C₃×C₈²	C₂²×C₈	1	4	yes	—
117	C₃×C₄⁴	C₂×C₁₆	1	1	yes	characteristic
118	C₂²×C₃×C₆₄	C₂×C₄²	1	96	yes	—
119	C₂²×C₃×C₆₄	C₂²×C₈	1	128	yes	—
120	C₂×C₃×C₄×C₃₂	C₄×C₈	1	48	yes	—
121	C₂×C₃×C₄×C₃₂	C₄×C₈	1	96	yes	—
122	C₂×C₃×C₄×C₃₂	C₄×C₈	1	96	yes	—
123	C₂×C₃×C₄×C₃₂	C₂×C₁₆	1	192	yes	—
124	C₂×C₃×C₄×C₃₂	C₂×C₄²	1	12	yes	—
125	C₂×C₃×C₄×C₃₂	C₂×C₄²	1	24	yes	—
126	C₂×C₃×C₄×C₃₂	C₂×C₄²	1	48	yes	—
127	C₂×C₃×C₄×C₃₂	C₂²×C₈	1	24	yes	—
128	C₂×C₃×C₄×C₃₂	C₂²×C₈	1	24	yes	—
129	C₂×C₃×C₄×C₃₂	C₂²×C₈	1	96	yes	—
130	C₂×C₃×C₄×C₃₂	C₂³×C₄	1	12	yes	—
131	C₃×C₄²×C₁₆	C₃₂	1	64	yes	—
132	C₃×C₄²×C₁₆	C₄×C₈	1	24	yes	—
133	C₃×C₄²×C₁₆	C₄×C₈	1	32	yes	—
134	C₃×C₄²×C₁₆	C₂×C₁₆	1	24	yes	—
135	C₃×C₄²×C₁₆	C₂×C₁₆	1	24	yes	—
136	C₃×C₄²×C₁₆	C₂×C₁₆	1	32	yes	—
137	C₃×C₄²×C₁₆	C₂×C₄²	1	12	yes	—
138	C₃×C₄²×C₁₆	C₂²×C₈	1	12	yes	—
139	C₂×C₃×C₈×C₁₆	C₄×C₈	1	48	yes	—
140	C₂×C₃×C₈×C₁₆	C₂×C₁₆	1	96	yes	—
141	C₂×C₃×C₈×C₁₆	C₂×C₄²	1	24	yes	—
142	C₂×C₃×C₈×C₁₆	C₂²×C₈	1	24	yes	—
143	C₃×C₄×C₈²	C₃₂	1	48	yes	—
144	C₃×C₄×C₈²	C₄×C₈	1	24	yes	—
145	C₃×C₄×C₈²	C₂×C₁₆	1	24	yes	—
146	C₃×C₄×C₆₄	C₄×C₈	1	768	yes	direct product factor
147	C₃×C₄×C₆₄	C₂×C₄²	1	128	yes	—
148	C₃×C₈×C₃₂	C₄×C₈	1	192	yes	—
149	C₃×C₈×C₃₂	C₂×C₄²	1	64	yes	—
150	C₂³×C₆₄	C₂²×C₃×C₄	1	16	yes	—
151	C₂²×C₄×C₃₂	C₃×C₄²	1	12	yes	—
152	C₂²×C₄×C₃₂	C₂×C₃×C₈	1	24	yes	—
153	C₂²×C₄×C₃₂	C₂²×C₃×C₄	1	3	yes	—
154	C₂²×C₄×C₃₂	C₂²×C₃×C₄	1	4	yes	—
155	C₂²×C₄×C₃₂	C₂²×C₃×C₄	1	12	yes	—
156	C₂²×C₄×C₃₂	C₂⁴×C₃	1	1	yes	characteristic
157	C₂×C₄²×C₁₆	C₃×C₁₆	1	8	yes	—
158	C₂×C₄²×C₁₆	C₃×C₄²	1	4	yes	—
159	C₂×C₄²×C₁₆	C₂×C₃×C₈	1	3	yes	—
160	C₂×C₄²×C₁₆	C₂×C₃×C₈	1	4	yes	—
161	C₂×C₄²×C₁₆	C₂×C₃×C₈	1	6	yes	—
162	C₂×C₄²×C₁₆	C₂²×C₃×C₄	1	3	yes	—
163	C₂²×C₈×C₁₆	C₂×C₃×C₈	1	12	yes	—
164	C₂²×C₈×C₁₆	C₂²×C₃×C₄	1	4	yes	—
165	C₄³×C₈	C₃×C₁₆	1	2	yes	—
166	C₄³×C₈	C₂×C₃×C₈	1	1	yes	characteristic
167	C₂×C₄×C₈²	C₃×C₁₆	1	6	yes	—
168	C₂×C₄×C₈²	C₂×C₃×C₈	1	6	yes	—
169	C₂×C₄×C₆₄	C₃×C₄²	1	192	yes	—
170	C₂×C₄×C₆₄	C₂×C₃×C₈	1	384	yes	—
171	C₂×C₄×C₆₄	C₂²×C₃×C₄	1	96	yes	—
172	C₄²×C₃₂	C₃×C₁₆	1	64	yes	—
173	C₄²×C₃₂	C₃×C₄²	1	24	yes	—
174	C₄²×C₃₂	C₂×C₃×C₈	1	24	yes	—
175	C₄²×C₃₂	C₂×C₃×C₈	1	24	yes	—
176	C₄²×C₃₂	C₂×C₃×C₈	1	64	yes	—
177	C₄²×C₃₂	C₂²×C₃×C₄	1	24	yes	—
178	C₂×C₈×C₃₂	C₃×C₄²	1	48	yes	—
179	C₂×C₈×C₃₂	C₂×C₃×C₈	1	96	yes	—
180	C₂×C₈×C₃₂	C₂²×C₃×C₄	1	48	yes	—
181	C₄×C₈×C₁₆	C₃×C₁₆	1	48	yes	—
182	C₄×C₈×C₁₆	C₃×C₄²	1	24	yes	—
183	C₄×C₈×C₁₆	C₂×C₃×C₈	1	24	yes	—
184	C₈×C₆₄	C₃×C₄²	1	256	yes	direct product factor
185	C₂³×C₃×C₁₆	C₂×C₄×C₈	1	6	yes	—
186	C₂³×C₃×C₁₆	C₂²×C₁₆	1	8	yes	—
187	C₂³×C₃×C₁₆	C₂²×C₄²	1	1	yes	characteristic
188	C₂³×C₃×C₁₆	C₂³×C₈	1	1	yes	characteristic
189	C₂²×C₃×C₄×C₈	C₄×C₁₆	1	12	yes	—
190	C₂²×C₃×C₄×C₈	C₂×C₃₂	1	48	yes	—
191	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	6	yes	—
192	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	3	yes	—
193	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	6	yes	—
194	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	8	yes	—
195	C₂²×C₃×C₄×C₈	C₂³×C₈	1	1	yes	characteristic
196	C₂×C₃×C₄³	C₄×C₁₆	1	4	yes	—
197	C₂×C₃×C₄³	C₂×C₃₂	1	8	yes	—
198	C₂×C₃×C₄³	C₂²×C₁₆	1	3	yes	—
199	C₂²×C₃×C₃₂	C₄³	1	12	yes	—
200	C₂²×C₃×C₃₂	C₂×C₄×C₈	1	24	yes	—
201	C₂²×C₃×C₃₂	C₂×C₄×C₈	1	48	yes	—
202	C₂²×C₃×C₃₂	C₂×C₄×C₈	1	48	yes	—
203	C₂²×C₃×C₃₂	C₂²×C₁₆	1	64	yes	—
204	C₂²×C₃×C₃₂	C₂²×C₄²	1	12	yes	—
205	C₂²×C₃×C₃₂	C₂³×C₈	1	16	yes	—
206	C₂×C₃×C₄×C₁₆	C₈²	1	48	yes	—
207	C₂×C₃×C₄×C₁₆	C₄×C₁₆	1	48	yes	—
208	C₂×C₃×C₄×C₁₆	C₄×C₁₆	1	48	yes	—
209	C₂×C₃×C₄×C₁₆	C₄×C₁₆	1	96	yes	—
210	C₂×C₃×C₄×C₁₆	C₂×C₃₂	1	192	yes	—
211	C₂×C₃×C₄×C₁₆	C₄³	1	12	yes	—
212	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	12	yes	—
213	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	12	yes	—
214	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	24	yes	—
215	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	24	yes	—
216	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	48	yes	—
217	C₂×C₃×C₄×C₁₆	C₂²×C₁₆	1	24	yes	—
218	C₂×C₃×C₄×C₁₆	C₂²×C₁₆	1	24	yes	—
219	C₂×C₃×C₄×C₁₆	C₂²×C₁₆	1	48	yes	—
220	C₂×C₃×C₄×C₁₆	C₂²×C₄²	1	6	yes	—
221	C₂×C₃×C₄×C₁₆	C₂³×C₈	1	6	yes	—
222	C₃×C₄²×C₈	C₆₄	1	128	yes	direct product factor
223	C₃×C₄²×C₈	C₈²	1	16	yes	—
224	C₃×C₄²×C₈	C₄×C₁₆	1	16	yes	—
225	C₃×C₄²×C₈	C₄×C₁₆	1	48	yes	—
226	C₃×C₄²×C₈	C₂×C₃₂	1	24	yes	—
227	C₃×C₄²×C₈	C₂×C₃₂	1	32	yes	—
228	C₃×C₄²×C₈	C₂×C₃₂	1	48	yes	—
229	C₃×C₄²×C₈	C₂×C₄×C₈	1	12	yes	—
230	C₃×C₄²×C₈	C₂²×C₁₆	1	12	yes	—
231	C₂×C₃×C₈²	C₄×C₁₆	1	48	yes	—
232	C₂×C₃×C₈²	C₂×C₃₂	1	96	yes	—
233	C₂×C₃×C₈²	C₂×C₄×C₈	1	24	yes	—
234	C₂×C₃×C₈²	C₂²×C₁₆	1	24	yes	—
235	C₂×C₃×C₆₄	C₄³	1	64	yes	—
236	C₂×C₃×C₆₄	C₂×C₄×C₈	1	384	yes	—
237	C₃×C₄×C₃₂	C₈²	1	192	yes	—
238	C₃×C₄×C₃₂	C₄×C₁₆	1	384	yes	—
239	C₃×C₄×C₃₂	C₄³	1	16	yes	—
240	C₃×C₄×C₃₂	C₂×C₄×C₈	1	48	yes	—
241	C₃×C₄×C₃₂	C₂×C₄×C₈	1	48	yes	—
242	C₃×C₄×C₃₂	C₂×C₄×C₈	1	192	yes	—
243	C₃×C₄×C₃₂	C₂²×C₄²	1	16	yes	—
244	C₃×C₈×C₁₆	C₄×C₁₆	1	192	yes	—
245	C₃×C₈×C₁₆	C₄³	1	16	yes	—
246	C₃×C₈×C₁₆	C₂×C₄×C₈	1	48	yes	—
247	C₂³×C₃₂	C₂×C₃×C₄²	1	6	yes	—
248	C₂³×C₃₂	C₂²×C₃×C₈	1	8	yes	—
249	C₂³×C₃₂	C₂³×C₃×C₄	1	2	yes	—
250	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	12	yes	—
251	C₂²×C₄×C₁₆	C₂×C₃×C₁₆	1	24	yes	—
252	C₂²×C₄×C₁₆	C₂×C₃×C₄²	1	6	yes	—
253	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	3	yes	—
254	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	4	yes	—
255	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	6	yes	—
256	C₂²×C₄×C₁₆	C₂³×C₃×C₄	1	1	yes	characteristic
257	C₂×C₄²×C₈	C₃×C₃₂	1	16	yes	—
258	C₂×C₄²×C₈	C₃×C₄×C₈	1	4	yes	—
259	C₂×C₄²×C₈	C₂×C₃×C₁₆	1	3	yes	—
260	C₂×C₄²×C₈	C₂×C₃×C₁₆	1	4	yes	—
261	C₂×C₄²×C₈	C₂×C₃×C₁₆	1	12	yes	—
262	C₂×C₄²×C₈	C₂²×C₃×C₈	1	3	yes	—
263	C₂²×C₈²	C₂×C₃×C₁₆	1	12	yes	—
264	C₂²×C₈²	C₂²×C₃×C₈	1	4	yes	—
265	C₄⁴	C₂×C₃×C₁₆	1	1	yes	characteristic
266	C₂²×C₆₄	C₂×C₃×C₄²	1	96	yes	—
267	C₂²×C₆₄	C₂²×C₃×C₈	1	128	yes	—
268	C₂×C₄×C₃₂	C₃×C₄×C₈	1	48	yes	—
269	C₂×C₄×C₃₂	C₃×C₄×C₈	1	96	yes	—
270	C₂×C₄×C₃₂	C₃×C₄×C₈	1	96	yes	—
271	C₂×C₄×C₃₂	C₂×C₃×C₁₆	1	192	yes	—
272	C₂×C₄×C₃₂	C₂×C₃×C₄²	1	12	yes	—
273	C₂×C₄×C₃₂	C₂×C₃×C₄²	1	24	yes	—
274	C₂×C₄×C₃₂	C₂×C₃×C₄²	1	48	yes	—
275	C₂×C₄×C₃₂	C₂²×C₃×C₈	1	24	yes	—
276	C₂×C₄×C₃₂	C₂²×C₃×C₈	1	24	yes	—
277	C₂×C₄×C₃₂	C₂²×C₃×C₈	1	96	yes	—
278	C₂×C₄×C₃₂	C₂³×C₃×C₄	1	12	yes	—
279	C₄²×C₁₆	C₃×C₃₂	1	64	yes	—
280	C₄²×C₁₆	C₃×C₄×C₈	1	24	yes	—
281	C₄²×C₁₆	C₃×C₄×C₈	1	32	yes	—
282	C₄²×C₁₆	C₂×C₃×C₁₆	1	24	yes	—
283	C₄²×C₁₆	C₂×C₃×C₁₆	1	24	yes	—
284	C₄²×C₁₆	C₂×C₃×C₁₆	1	32	yes	—
285	C₄²×C₁₆	C₂×C₃×C₄²	1	12	yes	—
286	C₄²×C₁₆	C₂²×C₃×C₈	1	12	yes	—
287	C₂×C₈×C₁₆	C₃×C₄×C₈	1	48	yes	—
288	C₂×C₈×C₁₆	C₂×C₃×C₁₆	1	96	yes	—
289	C₂×C₈×C₁₆	C₂×C₃×C₄²	1	24	yes	—
290	C₂×C₈×C₁₆	C₂²×C₃×C₈	1	24	yes	—
291	C₄×C₈²	C₃×C₃₂	1	48	yes	—
292	C₄×C₈²	C₃×C₄×C₈	1	24	yes	—
293	C₄×C₈²	C₂×C₃×C₁₆	1	24	yes	—
294	C₄×C₆₄	C₃×C₄×C₈	1	768	yes	direct product factor
295	C₄×C₆₄	C₂×C₃×C₄²	1	128	yes	—
296	C₈×C₃₂	C₃×C₄×C₈	1	192	yes	—
297	C₈×C₃₂	C₂×C₃×C₄²	1	64	yes	—
298	C₂³×C₃×C₈	C₂×C₄×C₁₆	1	6	yes	—
299	C₂³×C₃×C₈	C₂²×C₃₂	1	16	yes	—
300	C₂³×C₃×C₈	C₂²×C₄×C₈	1	1	yes	characteristic
301	C₂³×C₃×C₈	C₂³×C₁₆	1	1	yes	characteristic
302	C₂²×C₃×C₄²	C₄×C₃₂	1	16	yes	—
303	C₂²×C₃×C₄²	C₂×C₄×C₁₆	1	6	yes	—
304	C₂²×C₃×C₄²	C₂²×C₃₂	1	12	yes	—
305	C₂²×C₃×C₄²	C₂³×C₁₆	1	1	yes	characteristic
306	C₂²×C₃×C₁₆	C₂×C₈²	1	24	yes	—
307	C₂²×C₃×C₁₆	C₄²×C₈	1	12	yes	—
308	C₂²×C₃×C₁₆	C₂×C₄×C₁₆	1	24	yes	—
309	C₂²×C₃×C₁₆	C₂×C₄×C₁₆	1	24	yes	—
310	C₂²×C₃×C₁₆	C₂×C₄×C₁₆	1	48	yes	—
311	C₂²×C₃×C₁₆	C₂²×C₃₂	1	64	yes	—
312	C₂²×C₃×C₁₆	C₂×C₄³	1	3	yes	—
313	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	3	yes	—
314	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	6	yes	—
315	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	8	yes	—
316	C₂²×C₃×C₁₆	C₂³×C₁₆	1	8	yes	—
317	C₂×C₃×C₄×C₈	C₈×C₁₆	1	48	yes	—
318	C₂×C₃×C₄×C₈	C₄×C₃₂	1	48	yes	—
319	C₂×C₃×C₄×C₈	C₄×C₃₂	1	48	yes	—
320	C₂×C₃×C₄×C₈	C₄×C₃₂	1	192	yes	—
321	C₂×C₃×C₄×C₈	C₂×C₆₄	1	384	yes	—
322	C₂×C₃×C₄×C₈	C₂×C₈²	1	24	yes	—
323	C₂×C₃×C₄×C₈	C₄²×C₈	1	12	yes	—
324	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	12	yes	—
325	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	12	yes	—
326	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	24	yes	—
327	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	24	yes	—
328	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	48	yes	—
329	C₂×C₃×C₄×C₈	C₂²×C₃₂	1	24	yes	—
330	C₂×C₃×C₄×C₈	C₂²×C₃₂	1	48	yes	—
331	C₂×C₃×C₄×C₈	C₂²×C₃₂	1	48	yes	—
332	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	6	yes	—
333	C₂×C₃×C₄×C₈	C₂³×C₁₆	1	6	yes	—
334	C₃×C₄³	C₈×C₁₆	1	16	yes	—
335	C₃×C₄³	C₄×C₃₂	1	16	yes	—
336	C₃×C₄³	C₂×C₆₄	1	64	yes	—
337	C₃×C₄³	C₂×C₄×C₁₆	1	12	yes	—
338	C₃×C₄³	C₂²×C₃₂	1	12	yes	—
339	C₂×C₃×C₃₂	C₂×C₈²	1	96	yes	—
340	C₂×C₃×C₃₂	C₄²×C₈	1	24	yes	—
341	C₂×C₃×C₃₂	C₄²×C₈	1	32	yes	—
342	C₂×C₃×C₃₂	C₄²×C₈	1	48	yes	—
343	C₂×C₃×C₃₂	C₂×C₄×C₁₆	1	192	yes	—
344	C₂×C₃×C₃₂	C₂×C₄³	1	8	yes	—
345	C₂×C₃×C₃₂	C₂²×C₄×C₈	1	48	yes	—
346	C₃×C₄×C₁₆	C₈×C₁₆	1	192	yes	—
347	C₃×C₄×C₁₆	C₄×C₃₂	1	384	yes	—
348	C₃×C₄×C₁₆	C₂×C₈²	1	48	yes	—
349	C₃×C₄×C₁₆	C₄²×C₈	1	16	yes	—
350	C₃×C₄×C₁₆	C₄²×C₈	1	48	yes	—
351	C₃×C₄×C₁₆	C₂×C₄×C₁₆	1	48	yes	—
352	C₃×C₄×C₁₆	C₂×C₄×C₁₆	1	48	yes	—
353	C₃×C₄×C₁₆	C₂×C₄×C₁₆	1	96	yes	—
354	C₃×C₄×C₁₆	C₂×C₄³	1	4	yes	—
355	C₃×C₄×C₁₆	C₂²×C₄×C₈	1	12	yes	—
356	C₃×C₈²	C₄×C₃₂	1	192	yes	—
357	C₃×C₈²	C₄²×C₈	1	16	yes	—
358	C₃×C₈²	C₂×C₄×C₁₆	1	48	yes	—
359	C₃×C₆₄	C₄²×C₈	1	128	yes	direct product factor
360	C₂³×C₁₆	C₂×C₃×C₄×C₈	1	6	yes	—
361	C₂³×C₁₆	C₂²×C₃×C₁₆	1	8	yes	—
362	C₂³×C₁₆	C₂²×C₃×C₄²	1	1	yes	characteristic
363	C₂³×C₁₆	C₂³×C₃×C₈	1	1	yes	characteristic
364	C₂²×C₄×C₈	C₃×C₄×C₁₆	1	12	yes	—
365	C₂²×C₄×C₈	C₂×C₃×C₃₂	1	48	yes	—
366	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	6	yes	—
367	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	3	yes	—
368	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	6	yes	—
369	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	8	yes	—
370	C₂²×C₄×C₈	C₂³×C₃×C₈	1	1	yes	characteristic
371	C₂×C₄³	C₃×C₄×C₁₆	1	4	yes	—
372	C₂×C₄³	C₂×C₃×C₃₂	1	8	yes	—
373	C₂×C₄³	C₂²×C₃×C₁₆	1	3	yes	—
374	C₂²×C₃₂	C₃×C₄³	1	12	yes	—
375	C₂²×C₃₂	C₂×C₃×C₄×C₈	1	24	yes	—
376	C₂²×C₃₂	C₂×C₃×C₄×C₈	1	48	yes	—
377	C₂²×C₃₂	C₂×C₃×C₄×C₈	1	48	yes	—
378	C₂²×C₃₂	C₂²×C₃×C₁₆	1	64	yes	—
379	C₂²×C₃₂	C₂²×C₃×C₄²	1	12	yes	—
380	C₂²×C₃₂	C₂³×C₃×C₈	1	16	yes	—
381	C₂×C₄×C₁₆	C₃×C₈²	1	48	yes	—
382	C₂×C₄×C₁₆	C₃×C₄×C₁₆	1	48	yes	—
383	C₂×C₄×C₁₆	C₃×C₄×C₁₆	1	48	yes	—
384	C₂×C₄×C₁₆	C₃×C₄×C₁₆	1	96	yes	—
385	C₂×C₄×C₁₆	C₂×C₃×C₃₂	1	192	yes	—
386	C₂×C₄×C₁₆	C₃×C₄³	1	12	yes	—
387	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	12	yes	—
388	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	12	yes	—
389	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	24	yes	—
390	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	24	yes	—
391	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	48	yes	—
392	C₂×C₄×C₁₆	C₂²×C₃×C₁₆	1	24	yes	—
393	C₂×C₄×C₁₆	C₂²×C₃×C₁₆	1	24	yes	—
394	C₂×C₄×C₁₆	C₂²×C₃×C₁₆	1	48	yes	—
395	C₂×C₄×C₁₆	C₂²×C₃×C₄²	1	6	yes	—
396	C₂×C₄×C₁₆	C₂³×C₃×C₈	1	6	yes	—
397	C₄²×C₈	C₃×C₆₄	1	128	yes	direct product factor
398	C₄²×C₈	C₃×C₈²	1	16	yes	—
399	C₄²×C₈	C₃×C₄×C₁₆	1	16	yes	—
400	C₄²×C₈	C₃×C₄×C₁₆	1	48	yes	—
401	C₄²×C₈	C₂×C₃×C₃₂	1	24	yes	—
402	C₄²×C₈	C₂×C₃×C₃₂	1	32	yes	—
403	C₄²×C₈	C₂×C₃×C₃₂	1	48	yes	—
404	C₄²×C₈	C₂×C₃×C₄×C₈	1	12	yes	—
405	C₄²×C₈	C₂²×C₃×C₁₆	1	12	yes	—
406	C₂×C₈²	C₃×C₄×C₁₆	1	48	yes	—
407	C₂×C₈²	C₂×C₃×C₃₂	1	96	yes	—
408	C₂×C₈²	C₂×C₃×C₄×C₈	1	24	yes	—
409	C₂×C₈²	C₂²×C₃×C₁₆	1	24	yes	—
410	C₂×C₆₄	C₃×C₄³	1	64	yes	—
411	C₂×C₆₄	C₂×C₃×C₄×C₈	1	384	yes	—
412	C₄×C₃₂	C₃×C₈²	1	192	yes	—
413	C₄×C₃₂	C₃×C₄×C₁₆	1	384	yes	—
414	C₄×C₃₂	C₃×C₄³	1	16	yes	—
415	C₄×C₃₂	C₂×C₃×C₄×C₈	1	48	yes	—
416	C₄×C₃₂	C₂×C₃×C₄×C₈	1	48	yes	—
417	C₄×C₃₂	C₂×C₃×C₄×C₈	1	192	yes	—
418	C₄×C₃₂	C₂²×C₃×C₄²	1	16	yes	—
419	C₈×C₁₆	C₃×C₄×C₁₆	1	192	yes	—
420	C₈×C₁₆	C₃×C₄³	1	16	yes	—
421	C₈×C₁₆	C₂×C₃×C₄×C₈	1	48	yes	—
422	C₂³×C₃×C₄	C₂×C₄×C₃₂	1	12	yes	—
423	C₂³×C₃×C₄	C₂²×C₄×C₁₆	1	1	yes	characteristic
424	C₂³×C₃×C₄	C₂³×C₃₂	1	2	yes	—
425	C₂²×C₃×C₈	C₂×C₈×C₁₆	1	24	yes	—
426	C₂²×C₃×C₈	C₄²×C₁₆	1	12	yes	—
427	C₂²×C₃×C₈	C₂×C₄×C₃₂	1	24	yes	—
428	C₂²×C₃×C₈	C₂×C₄×C₃₂	1	24	yes	—
429	C₂²×C₃×C₈	C₂×C₄×C₃₂	1	96	yes	—
430	C₂²×C₃×C₈	C₂²×C₆₄	1	128	yes	—
431	C₂²×C₃×C₈	C₂²×C₈²	1	4	yes	—
432	C₂²×C₃×C₈	C₂×C₄²×C₈	1	3	yes	—
433	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	3	yes	—
434	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	4	yes	—
435	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	6	yes	—
436	C₂²×C₃×C₈	C₂³×C₃₂	1	8	yes	—
437	C₂×C₃×C₄²	C₈×C₃₂	1	64	yes	—
438	C₂×C₃×C₄²	C₄×C₆₄	1	128	yes	—
439	C₂×C₃×C₄²	C₂×C₈×C₁₆	1	24	yes	—
440	C₂×C₃×C₄²	C₄²×C₁₆	1	12	yes	—
441	C₂×C₃×C₄²	C₂×C₄×C₃₂	1	12	yes	—
442	C₂×C₃×C₄²	C₂×C₄×C₃₂	1	24	yes	—
443	C₂×C₃×C₄²	C₂×C₄×C₃₂	1	48	yes	—
444	C₂×C₃×C₄²	C₂²×C₆₄	1	96	yes	—
445	C₂×C₃×C₄²	C₂²×C₄×C₁₆	1	6	yes	—
446	C₂×C₃×C₄²	C₂³×C₃₂	1	6	yes	—
447	C₂×C₃×C₁₆	C₄×C₈²	1	24	yes	—
448	C₂×C₃×C₁₆	C₂×C₈×C₁₆	1	96	yes	—
449	C₂×C₃×C₁₆	C₄²×C₁₆	1	24	yes	—
450	C₂×C₃×C₁₆	C₄²×C₁₆	1	24	yes	—
451	C₂×C₃×C₁₆	C₄²×C₁₆	1	32	yes	—
452	C₂×C₃×C₁₆	C₂×C₄×C₃₂	1	192	yes	—
453	C₂×C₃×C₁₆	C₄⁴	1	1	yes	characteristic
454	C₂×C₃×C₁₆	C₂²×C₈²	1	12	yes	—
455	C₂×C₃×C₁₆	C₂×C₄²×C₈	1	3	yes	—
456	C₂×C₃×C₁₆	C₂×C₄²×C₈	1	4	yes	—
457	C₂×C₃×C₁₆	C₂×C₄²×C₈	1	12	yes	—
458	C₂×C₃×C₁₆	C₂²×C₄×C₁₆	1	24	yes	—
459	C₃×C₄×C₈	C₈×C₃₂	1	192	yes	—
460	C₃×C₄×C₈	C₄×C₆₄	1	768	yes	direct product factor
461	C₃×C₄×C₈	C₄×C₈²	1	24	yes	—
462	C₃×C₄×C₈	C₂×C₈×C₁₆	1	48	yes	—
463	C₃×C₄×C₈	C₄²×C₁₆	1	24	yes	—
464	C₃×C₄×C₈	C₄²×C₁₆	1	32	yes	—
465	C₃×C₄×C₈	C₂×C₄×C₃₂	1	48	yes	—
466	C₃×C₄×C₈	C₂×C₄×C₃₂	1	96	yes	—
467	C₃×C₄×C₈	C₂×C₄×C₃₂	1	96	yes	—
468	C₃×C₄×C₈	C₂×C₄²×C₈	1	4	yes	—
469	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	12	yes	—
470	C₃×C₃₂	C₄×C₈²	1	48	yes	—
471	C₃×C₃₂	C₄²×C₁₆	1	64	yes	—
472	C₃×C₃₂	C₂×C₄²×C₈	1	16	yes	—
473	C₂³×C₈	C₂×C₃×C₄×C₁₆	1	6	yes	—
474	C₂³×C₈	C₂²×C₃×C₃₂	1	16	yes	—
475	C₂³×C₈	C₂²×C₃×C₄×C₈	1	1	yes	characteristic
476	C₂³×C₈	C₂³×C₃×C₁₆	1	1	yes	characteristic
477	C₂²×C₄²	C₃×C₄×C₃₂	1	16	yes	—
478	C₂²×C₄²	C₂×C₃×C₄×C₁₆	1	6	yes	—
479	C₂²×C₄²	C₂²×C₃×C₃₂	1	12	yes	—
480	C₂²×C₄²	C₂³×C₃×C₁₆	1	1	yes	characteristic
481	C₂²×C₁₆	C₂×C₃×C₈²	1	24	yes	—
482	C₂²×C₁₆	C₃×C₄²×C₈	1	12	yes	—
483	C₂²×C₁₆	C₂×C₃×C₄×C₁₆	1	24	yes	—
484	C₂²×C₁₆	C₂×C₃×C₄×C₁₆	1	24	yes	—
485	C₂²×C₁₆	C₂×C₃×C₄×C₁₆	1	48	yes	—
486	C₂²×C₁₆	C₂²×C₃×C₃₂	1	64	yes	—
487	C₂²×C₁₆	C₂×C₃×C₄³	1	3	yes	—
488	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	3	yes	—
489	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	6	yes	—
490	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	8	yes	—
491	C₂²×C₁₆	C₂³×C₃×C₁₆	1	8	yes	—
492	C₂×C₄×C₈	C₃×C₈×C₁₆	1	48	yes	—
493	C₂×C₄×C₈	C₃×C₄×C₃₂	1	48	yes	—
494	C₂×C₄×C₈	C₃×C₄×C₃₂	1	48	yes	—
495	C₂×C₄×C₈	C₃×C₄×C₃₂	1	192	yes	—
496	C₂×C₄×C₈	C₂×C₃×C₆₄	1	384	yes	—
497	C₂×C₄×C₈	C₂×C₃×C₈²	1	24	yes	—
498	C₂×C₄×C₈	C₃×C₄²×C₈	1	12	yes	—
499	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	12	yes	—
500	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	12	yes	—
501	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	24	yes	—
502	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	24	yes	—
503	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	48	yes	—
504	C₂×C₄×C₈	C₂²×C₃×C₃₂	1	24	yes	—
505	C₂×C₄×C₈	C₂²×C₃×C₃₂	1	48	yes	—
506	C₂×C₄×C₈	C₂²×C₃×C₃₂	1	48	yes	—
507	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	6	yes	—
508	C₂×C₄×C₈	C₂³×C₃×C₁₆	1	6	yes	—
509	C₄³	C₃×C₈×C₁₆	1	16	yes	—
510	C₄³	C₃×C₄×C₃₂	1	16	yes	—
511	C₄³	C₂×C₃×C₆₄	1	64	yes	—
512	C₄³	C₂×C₃×C₄×C₁₆	1	12	yes	—
513	C₄³	C₂²×C₃×C₃₂	1	12	yes	—
514	C₂×C₃₂	C₂×C₃×C₈²	1	96	yes	—
515	C₂×C₃₂	C₃×C₄²×C₈	1	24	yes	—
516	C₂×C₃₂	C₃×C₄²×C₈	1	32	yes	—
517	C₂×C₃₂	C₃×C₄²×C₈	1	48	yes	—
518	C₂×C₃₂	C₂×C₃×C₄×C₁₆	1	192	yes	—
519	C₂×C₃₂	C₂×C₃×C₄³	1	8	yes	—
520	C₂×C₃₂	C₂²×C₃×C₄×C₈	1	48	yes	—
521	C₄×C₁₆	C₃×C₈×C₁₆	1	192	yes	—
522	C₄×C₁₆	C₃×C₄×C₃₂	1	384	yes	—
523	C₄×C₁₆	C₂×C₃×C₈²	1	48	yes	—
524	C₄×C₁₆	C₃×C₄²×C₈	1	16	yes	—
525	C₄×C₁₆	C₃×C₄²×C₈	1	48	yes	—
526	C₄×C₁₆	C₂×C₃×C₄×C₁₆	1	48	yes	—
527	C₄×C₁₆	C₂×C₃×C₄×C₁₆	1	48	yes	—
528	C₄×C₁₆	C₂×C₃×C₄×C₁₆	1	96	yes	—
529	C₄×C₁₆	C₂×C₃×C₄³	1	4	yes	—
530	C₄×C₁₆	C₂²×C₃×C₄×C₈	1	12	yes	—
531	C₈²	C₃×C₄×C₃₂	1	192	yes	—
532	C₈²	C₃×C₄²×C₈	1	16	yes	—
533	C₈²	C₂×C₃×C₄×C₁₆	1	48	yes	—
534	C₆₄	C₃×C₄²×C₈	1	128	yes	direct product factor
535	C₂⁴×C₃	C₂²×C₄×C₃₂	1	1	yes	characteristic
536	C₂²×C₃×C₄	C₂×C₈×C₃₂	1	48	yes	—
537	C₂²×C₃×C₄	C₄²×C₃₂	1	24	yes	—
538	C₂²×C₃×C₄	C₂×C₄×C₆₄	1	96	yes	—
539	C₂²×C₃×C₄	C₂²×C₈×C₁₆	1	4	yes	—
540	C₂²×C₃×C₄	C₂×C₄²×C₁₆	1	3	yes	—
541	C₂²×C₃×C₄	C₂²×C₄×C₃₂	1	3	yes	—
542	C₂²×C₃×C₄	C₂²×C₄×C₃₂	1	4	yes	—
543	C₂²×C₃×C₄	C₂²×C₄×C₃₂	1	12	yes	—
544	C₂²×C₃×C₄	C₂³×C₆₄	1	16	yes	—
545	C₂×C₃×C₈	C₄×C₈×C₁₆	1	24	yes	—
546	C₂×C₃×C₈	C₂×C₈×C₃₂	1	96	yes	—
547	C₂×C₃×C₈	C₄²×C₃₂	1	24	yes	—
548	C₂×C₃×C₈	C₄²×C₃₂	1	24	yes	—
549	C₂×C₃×C₈	C₄²×C₃₂	1	64	yes	—
550	C₂×C₃×C₈	C₂×C₄×C₆₄	1	384	yes	—
551	C₂×C₃×C₈	C₂×C₄×C₈²	1	6	yes	—
552	C₂×C₃×C₈	C₄³×C₈	1	1	yes	characteristic
553	C₂×C₃×C₈	C₂²×C₈×C₁₆	1	12	yes	—
554	C₂×C₃×C₈	C₂×C₄²×C₁₆	1	3	yes	—
555	C₂×C₃×C₈	C₂×C₄²×C₁₆	1	4	yes	—
556	C₂×C₃×C₈	C₂×C₄²×C₁₆	1	6	yes	—
557	C₂×C₃×C₈	C₂²×C₄×C₃₂	1	24	yes	—
558	C₃×C₄²	C₈×C₆₄	1	256	yes	direct product factor
559	C₃×C₄²	C₄×C₈×C₁₆	1	24	yes	—
560	C₃×C₄²	C₂×C₈×C₃₂	1	48	yes	—
561	C₃×C₄²	C₄²×C₃₂	1	24	yes	—
562	C₃×C₄²	C₂×C₄×C₆₄	1	192	yes	—
563	C₃×C₄²	C₂×C₄²×C₁₆	1	4	yes	—
564	C₃×C₄²	C₂²×C₄×C₃₂	1	12	yes	—
565	C₃×C₁₆	C₄×C₈×C₁₆	1	48	yes	—
566	C₃×C₁₆	C₄²×C₃₂	1	64	yes	—
567	C₃×C₁₆	C₂×C₄×C₈²	1	6	yes	—
568	C₃×C₁₆	C₄³×C₈	1	2	yes	—
569	C₃×C₁₆	C₂×C₄²×C₁₆	1	8	yes	—
570	C₂³×C₄	C₂×C₃×C₄×C₃₂	1	12	yes	—
571	C₂³×C₄	C₂²×C₃×C₄×C₁₆	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₃×C₃₂	1	2	yes	—
573	C₂²×C₈	C₂×C₃×C₈×C₁₆	1	24	yes	—
574	C₂²×C₈	C₃×C₄²×C₁₆	1	12	yes	—
575	C₂²×C₈	C₂×C₃×C₄×C₃₂	1	24	yes	—
576	C₂²×C₈	C₂×C₃×C₄×C₃₂	1	24	yes	—
577	C₂²×C₈	C₂×C₃×C₄×C₃₂	1	96	yes	—
578	C₂²×C₈	C₂²×C₃×C₆₄	1	128	yes	—
579	C₂²×C₈	C₂²×C₃×C₈²	1	4	yes	—
580	C₂²×C₈	C₂×C₃×C₄²×C₈	1	3	yes	—
581	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	3	yes	—
582	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	4	yes	—
583	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	6	yes	—
584	C₂²×C₈	C₂³×C₃×C₃₂	1	8	yes	—
585	C₂×C₄²	C₃×C₈×C₃₂	1	64	yes	—
586	C₂×C₄²	C₃×C₄×C₆₄	1	128	yes	—
587	C₂×C₄²	C₂×C₃×C₈×C₁₆	1	24	yes	—
588	C₂×C₄²	C₃×C₄²×C₁₆	1	12	yes	—
589	C₂×C₄²	C₂×C₃×C₄×C₃₂	1	12	yes	—
590	C₂×C₄²	C₂×C₃×C₄×C₃₂	1	24	yes	—
591	C₂×C₄²	C₂×C₃×C₄×C₃₂	1	48	yes	—
592	C₂×C₄²	C₂²×C₃×C₆₄	1	96	yes	—
593	C₂×C₄²	C₂²×C₃×C₄×C₁₆	1	6	yes	—
594	C₂×C₄²	C₂³×C₃×C₃₂	1	6	yes	—
595	C₂×C₁₆	C₃×C₄×C₈²	1	24	yes	—
596	C₂×C₁₆	C₂×C₃×C₈×C₁₆	1	96	yes	—
597	C₂×C₁₆	C₃×C₄²×C₁₆	1	24	yes	—
598	C₂×C₁₆	C₃×C₄²×C₁₆	1	24	yes	—
599	C₂×C₁₆	C₃×C₄²×C₁₆	1	32	yes	—
600	C₂×C₁₆	C₂×C₃×C₄×C₃₂	1	192	yes	—
601	C₂×C₁₆	C₃×C₄⁴	1	1	yes	characteristic
602	C₂×C₁₆	C₂²×C₃×C₈²	1	12	yes	—
603	C₂×C₁₆	C₂×C₃×C₄²×C₈	1	3	yes	—
604	C₂×C₁₆	C₂×C₃×C₄²×C₈	1	4	yes	—
605	C₂×C₁₆	C₂×C₃×C₄²×C₈	1	12	yes	—
606	C₂×C₁₆	C₂²×C₃×C₄×C₁₆	1	24	yes	—
607	C₄×C₈	C₃×C₈×C₃₂	1	192	yes	—
608	C₄×C₈	C₃×C₄×C₆₄	1	768	yes	direct product factor
609	C₄×C₈	C₃×C₄×C₈²	1	24	yes	—
610	C₄×C₈	C₂×C₃×C₈×C₁₆	1	48	yes	—
611	C₄×C₈	C₃×C₄²×C₁₆	1	24	yes	—
612	C₄×C₈	C₃×C₄²×C₁₆	1	32	yes	—
613	C₄×C₈	C₂×C₃×C₄×C₃₂	1	48	yes	—
614	C₄×C₈	C₂×C₃×C₄×C₃₂	1	96	yes	—
615	C₄×C₈	C₂×C₃×C₄×C₃₂	1	96	yes	—
616	C₄×C₈	C₂×C₃×C₄²×C₈	1	4	yes	—
617	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	12	yes	—
618	C₃₂	C₃×C₄×C₈²	1	48	yes	—
619	C₃₂	C₃×C₄²×C₁₆	1	64	yes	—
620	C₃₂	C₂×C₃×C₄²×C₈	1	16	yes	—
621	C₂³×C₃	C₂²×C₄×C₆₄	1	8	yes	—
622	C₂³×C₃	C₂²×C₈×C₃₂	1	4	yes	—
623	C₂³×C₃	C₂×C₄²×C₃₂	1	3	yes	—
624	C₂×C₃×C₄	C₄²×C₆₄	1	96	yes	—
625	C₂×C₃×C₄	C₂×C₈×C₆₄	1	192	yes	—
626	C₂×C₃×C₄	C₂²×C₄×C₆₄	1	48	yes	—
627	C₂×C₃×C₄	C₄×C₈×C₃₂	1	48	yes	—
628	C₂×C₃×C₄	C₂²×C₈×C₃₂	1	12	yes	—
629	C₂×C₃×C₄	C₂×C₄²×C₃₂	1	3	yes	—
630	C₂×C₃×C₄	C₂×C₄²×C₃₂	1	6	yes	—
631	C₂×C₃×C₄	C₂×C₄²×C₃₂	1	8	yes	—
632	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	6	yes	—
633	C₂×C₃×C₄	C₄³×C₁₆	1	1	yes	characteristic
634	C₃×C₈	C₄²×C₆₄	1	128	yes	direct product factor
635	C₃×C₈	C₄×C₈×C₃₂	1	48	yes	—
636	C₃×C₈	C₂×C₄²×C₃₂	1	8	yes	—
637	C₃×C₈	C₂×C₄×C₈×C₁₆	1	6	yes	—
638	C₃×C₈	C₄³×C₁₆	1	1	yes	characteristic
639	C₃×C₈	C₄²×C₈²	1	1	yes	characteristic
640	C₂⁴	C₂²×C₃×C₄×C₃₂	1	1	yes	characteristic
641	C₂²×C₄	C₂³×C₃×C₆₄	1	16	yes	—
642	C₂²×C₄	C₂×C₃×C₄×C₆₄	1	96	yes	—
643	C₂²×C₄	C₂×C₃×C₈×C₃₂	1	48	yes	—
644	C₂²×C₄	C₃×C₄²×C₃₂	1	24	yes	—
645	C₂²×C₄	C₂²×C₃×C₄×C₃₂	1	3	yes	—
646	C₂²×C₄	C₂²×C₃×C₄×C₃₂	1	4	yes	—
647	C₂²×C₄	C₂²×C₃×C₄×C₃₂	1	12	yes	—
648	C₂²×C₄	C₂²×C₃×C₈×C₁₆	1	4	yes	—
649	C₂²×C₄	C₂×C₃×C₄²×C₁₆	1	3	yes	—
650	C₂×C₈	C₂×C₃×C₄×C₆₄	1	384	yes	—
651	C₂×C₈	C₂×C₃×C₈×C₃₂	1	96	yes	—
652	C₂×C₈	C₃×C₄²×C₃₂	1	24	yes	—
653	C₂×C₈	C₃×C₄²×C₃₂	1	24	yes	—
654	C₂×C₈	C₃×C₄²×C₃₂	1	64	yes	—
655	C₂×C₈	C₂²×C₃×C₄×C₃₂	1	24	yes	—
656	C₂×C₈	C₃×C₄×C₈×C₁₆	1	24	yes	—
657	C₂×C₈	C₂²×C₃×C₈×C₁₆	1	12	yes	—
658	C₂×C₈	C₂×C₃×C₄²×C₁₆	1	3	yes	—
659	C₂×C₈	C₂×C₃×C₄²×C₁₆	1	4	yes	—
660	C₂×C₈	C₂×C₃×C₄²×C₁₆	1	6	yes	—
661	C₂×C₈	C₂×C₃×C₄×C₈²	1	6	yes	—
662	C₂×C₈	C₃×C₄³×C₈	1	1	yes	characteristic
663	C₄²	C₃×C₈×C₆₄	1	256	yes	direct product factor
664	C₄²	C₂×C₃×C₄×C₆₄	1	192	yes	—
665	C₄²	C₂×C₃×C₈×C₃₂	1	48	yes	—
666	C₄²	C₃×C₄²×C₃₂	1	24	yes	—
667	C₄²	C₂²×C₃×C₄×C₃₂	1	12	yes	—
668	C₄²	C₃×C₄×C₈×C₁₆	1	24	yes	—
669	C₄²	C₂×C₃×C₄²×C₁₆	1	4	yes	—
670	C₁₆	C₃×C₄²×C₃₂	1	64	yes	—
671	C₁₆	C₃×C₄×C₈×C₁₆	1	48	yes	—
672	C₁₆	C₂×C₃×C₄²×C₁₆	1	8	yes	—
673	C₁₆	C₂×C₃×C₄×C₈²	1	6	yes	—
674	C₁₆	C₃×C₄³×C₈	1	2	yes	—
675	C₂²×C₃	C₂²×C₈×C₆₄	1	16	yes	—
676	C₂²×C₃	C₂×C₄²×C₆₄	1	12	yes	—
677	C₂²×C₃	C₂×C₄×C₈×C₃₂	1	6	yes	—
678	C₂²×C₃	C₄³×C₃₂	1	1	yes	characteristic
679	C₃×C₄	C₄×C₈×C₆₄	1	96	yes	direct product factor
680	C₃×C₄	C₂×C₄²×C₆₄	1	16	yes	—
681	C₃×C₄	C₂×C₄×C₈×C₃₂	1	6	yes	—
682	C₃×C₄	C₄³×C₃₂	1	1	yes	characteristic
683	C₃×C₄	C₄²×C₈×C₁₆	1	1	yes	characteristic
684	C₂³	C₂²×C₃×C₄×C₆₄	1	8	yes	—
685	C₂³	C₂²×C₃×C₈×C₃₂	1	4	yes	—
686	C₂³	C₂×C₃×C₄²×C₃₂	1	3	yes	—
687	C₂×C₄	C₂×C₃×C₈×C₆₄	1	192	yes	—
688	C₂×C₄	C₃×C₄²×C₆₄	1	96	yes	—
689	C₂×C₄	C₂²×C₃×C₄×C₆₄	1	48	yes	—
690	C₂×C₄	C₃×C₄×C₈×C₃₂	1	48	yes	—
691	C₂×C₄	C₂²×C₃×C₈×C₃₂	1	12	yes	—
692	C₂×C₄	C₂×C₃×C₄²×C₃₂	1	3	yes	—
693	C₂×C₄	C₂×C₃×C₄²×C₃₂	1	6	yes	—
694	C₂×C₄	C₂×C₃×C₄²×C₃₂	1	8	yes	—
695	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	6	yes	—
696	C₂×C₄	C₃×C₄³×C₁₆	1	1	yes	characteristic
697	C₈	C₃×C₄²×C₆₄	1	128	yes	direct product factor
698	C₈	C₃×C₄×C₈×C₃₂	1	48	yes	—
699	C₈	C₂×C₃×C₄²×C₃₂	1	8	yes	—
700	C₈	C₂×C₃×C₄×C₈×C₁₆	1	6	yes	—
701	C₈	C₃×C₄³×C₁₆	1	1	yes	characteristic
702	C₈	C₃×C₄²×C₈²	1	1	yes	characteristic
703	C₂×C₃	C₂×C₄×C₈×C₆₄	1	12	yes	—
704	C₂×C₃	C₄³×C₆₄	1	2	yes	—
705	C₂×C₃	C₄²×C₈×C₃₂	1	1	yes	characteristic
706	C₂²	C₂²×C₃×C₈×C₆₄	1	16	yes	—
707	C₂²	C₂×C₃×C₄²×C₆₄	1	12	yes	—
708	C₂²	C₂×C₃×C₄×C₈×C₃₂	1	6	yes	—
709	C₂²	C₃×C₄³×C₃₂	1	1	yes	characteristic
710	C₄	C₃×C₄×C₈×C₆₄	1	96	yes	direct product factor
711	C₄	C₂×C₃×C₄²×C₆₄	1	16	yes	—
712	C₄	C₂×C₃×C₄×C₈×C₃₂	1	6	yes	—
713	C₄	C₃×C₄³×C₃₂	1	1	yes	characteristic
714	C₄	C₃×C₄²×C₈×C₁₆	1	1	yes	characteristic
715	C₃	C₄²×C₈×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
716	C₂	C₂×C₃×C₄×C₈×C₆₄	1	12	yes	—
717	C₂	C₃×C₄³×C₆₄	1	2	yes	—
718	C₂	C₃×C₄²×C₈×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄×C₃₂	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂²×C₄×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄²×C₈×C₆₄	C₃	direct (N × H)
13. C₃×C₄×C₈×C₆₄	C₄	direct (N × H)
33. C₃×C₄²×C₆₄	C₈	direct (N × H)
44. C₄×C₈×C₆₄	C₃×C₄	direct (N × H)
79. C₃×C₈×C₆₄	C₄²	direct (N × H)
97. C₄²×C₆₄	C₃×C₈	direct (N × H)
146. C₃×C₄×C₆₄	C₄×C₈	direct (N × H)
184. C₈×C₆₄	C₃×C₄²	direct (N × H)
222. C₃×C₄²×C₈	C₆₄	direct (N × H)
294. C₄×C₆₄	C₃×C₄×C₈	direct (N × H)
359. C₃×C₆₄	C₄²×C₈	direct (N × H)
397. C₄²×C₈	C₃×C₆₄	direct (N × H)
460. C₃×C₄×C₈	C₄×C₆₄	direct (N × H)
534. C₆₄	C₃×C₄²×C₈	direct (N × H)
558. C₃×C₄²	C₈×C₆₄	direct (N × H)
608. C₄×C₈	C₃×C₄×C₆₄	direct (N × H)
634. C₃×C₈	C₄²×C₆₄	direct (N × H)
663. C₄²	C₃×C₈×C₆₄	direct (N × H)
679. C₃×C₄	C₄×C₈×C₆₄	direct (N × H)
697. C₈	C₃×C₄²×C₆₄	direct (N × H)
710. C₄	C₃×C₄×C₈×C₆₄	direct (N × H)
715. C₃	C₄²×C₈×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
C₃×C₄²×C₈×C₃₂	2
C₃×C₄³×C₆₄	2
C₂×C₃×C₄×C₈×C₆₄	2
C₄²×C₈×C₆₄	3

Subgroups — C3×C42×C8×C64 #72201849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄²×C₈×C₆₄ #72201849