Subgroups — C₂²×C₃×C₈²×C₃₂ #72201865

Order 24576.

119580 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈²×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×C₈×C₃₂	C₂	1	6	yes	maximal
3	C₂×C₃×C₈²×C₃₂	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₈²×C₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₈³	C₄	1	1	yes	characteristic
6	C₂²×C₃×C₄×C₈×C₁₆	C₄	1	3	yes	—
7	C₂²×C₃×C₄×C₈×C₁₆	C₂²	1	3	yes	—
8	C₂×C₃×C₈²×C₁₆	C₄	1	12	yes	—
9	C₂×C₃×C₈²×C₁₆	C₂²	1	12	yes	—
10	C₂²×C₃×C₄²×C₃₂	C₂²	1	4	yes	—
11	C₂×C₃×C₄×C₈×C₃₂	C₄	1	72	yes	—
12	C₂×C₃×C₄×C₈×C₃₂	C₂²	1	72	yes	—
13	C₂³×C₃×C₈×C₃₂	C₄	1	24	yes	—
14	C₃×C₈²×C₃₂	C₂²	1	64	yes	direct product factor
15	C₂²×C₈²×C₁₆	C₂×C₃	1	1	yes	characteristic
16	C₂²×C₄×C₈×C₃₂	C₂×C₃	1	6	yes	—
17	C₂×C₈²×C₃₂	C₂×C₃	1	24	yes	direct product factor
18	C₂²×C₃×C₄×C₈²	C₈	1	4	yes	—
19	C₂²×C₃×C₄×C₈²	C₂×C₄	1	3	yes	—
20	C₂×C₃×C₈³	C₈	1	12	yes	—
21	C₂×C₃×C₈³	C₂×C₄	1	12	yes	—
22	C₂²×C₃×C₄²×C₁₆	C₂×C₄	1	3	yes	—
23	C₂²×C₃×C₄²×C₁₆	C₂³	1	1	yes	characteristic
24	C₂×C₃×C₄×C₈×C₁₆	C₈	1	36	yes	—
25	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	18	yes	—
26	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	36	yes	—
27	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	36	yes	—
28	C₂×C₃×C₄×C₈×C₁₆	C₂³	1	18	yes	—
29	C₂³×C₃×C₈×C₁₆	C₈	1	12	yes	—
30	C₂³×C₃×C₈×C₁₆	C₂×C₄	1	12	yes	—
31	C₃×C₈²×C₁₆	C₂×C₄	1	48	yes	—
32	C₃×C₈²×C₁₆	C₂³	1	16	yes	—
33	C₂³×C₃×C₄×C₃₂	C₂×C₄	1	24	yes	—
34	C₂×C₃×C₄²×C₃₂	C₂×C₄	1	72	yes	—
35	C₂×C₃×C₄²×C₃₂	C₂³	1	24	yes	—
36	C₂²×C₃×C₈×C₃₂	C₈	1	384	yes	direct product factor
37	C₂²×C₃×C₈×C₃₂	C₂×C₄	1	288	yes	—
38	C₃×C₄×C₈×C₃₂	C₂×C₄	1	288	yes	—
39	C₃×C₄×C₈×C₃₂	C₂³	1	96	yes	—
40	C₂²×C₈³	C₃×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₈×C₁₆	C₃×C₄	1	3	yes	—
42	C₂²×C₄×C₈×C₁₆	C₂²×C₃	1	3	yes	—
43	C₂×C₈²×C₁₆	C₃×C₄	1	12	yes	—
44	C₂×C₈²×C₁₆	C₂²×C₃	1	12	yes	—
45	C₂²×C₄²×C₃₂	C₂²×C₃	1	4	yes	—
46	C₂³×C₈×C₃₂	C₃×C₄	1	24	yes	—
47	C₂×C₄×C₈×C₃₂	C₃×C₄	1	72	yes	—
48	C₂×C₄×C₈×C₃₂	C₂²×C₃	1	72	yes	—
49	C₈²×C₃₂	C₂²×C₃	1	64	yes	direct product factor
50	C₂²×C₃×C₄²×C₈	C₂×C₈	1	6	yes	—
51	C₂²×C₃×C₄²×C₈	C₂²×C₄	1	1	yes	characteristic
52	C₂³×C₃×C₈²	C₁₆	1	16	yes	—
53	C₂³×C₃×C₈²	C₄²	1	6	yes	—
54	C₂³×C₃×C₈²	C₂×C₈	1	6	yes	—
55	C₂×C₃×C₄×C₈²	C₁₆	1	48	yes	—
56	C₂×C₃×C₄×C₈²	C₄²	1	18	yes	—
57	C₂×C₃×C₄×C₈²	C₂×C₈	1	18	yes	—
58	C₂×C₃×C₄×C₈²	C₂×C₈	1	18	yes	—
59	C₂×C₃×C₄×C₈²	C₂×C₈	1	48	yes	—
60	C₂×C₃×C₄×C₈²	C₂²×C₄	1	18	yes	—
61	C₃×C₈³	C₂×C₈	1	48	yes	—
62	C₃×C₈³	C₂²×C₄	1	16	yes	—
63	C₂³×C₃×C₄×C₁₆	C₄²	1	6	yes	—
64	C₂³×C₃×C₄×C₁₆	C₂×C₈	1	12	yes	—
65	C₂³×C₃×C₄×C₁₆	C₂²×C₄	1	6	yes	—
66	C₂×C₃×C₄²×C₁₆	C₄²	1	18	yes	—
67	C₂×C₃×C₄²×C₁₆	C₂×C₈	1	36	yes	—
68	C₂×C₃×C₄²×C₁₆	C₂²×C₄	1	3	yes	—
69	C₂×C₃×C₄²×C₁₆	C₂²×C₄	1	18	yes	—
70	C₂×C₃×C₄²×C₁₆	C₂²×C₄	1	18	yes	—
71	C₂×C₃×C₄²×C₁₆	C₂⁴	1	3	yes	—
72	C₂²×C₃×C₈×C₁₆	C₁₆	1	192	yes	—
73	C₂²×C₃×C₈×C₁₆	C₄²	1	72	yes	—
74	C₂²×C₃×C₈×C₁₆	C₂×C₈	1	144	yes	—
75	C₂²×C₃×C₈×C₁₆	C₂×C₈	1	192	yes	—
76	C₂²×C₃×C₈×C₁₆	C₂²×C₄	1	72	yes	—
77	C₃×C₄×C₈×C₁₆	C₄²	1	72	yes	—
78	C₃×C₄×C₈×C₁₆	C₂×C₈	1	144	yes	—
79	C₃×C₄×C₈×C₁₆	C₂²×C₄	1	36	yes	—
80	C₃×C₄×C₈×C₁₆	C₂²×C₄	1	48	yes	—
81	C₃×C₄×C₈×C₁₆	C₂²×C₄	1	72	yes	—
82	C₃×C₄×C₈×C₁₆	C₂⁴	1	12	yes	—
83	C₂²×C₃×C₄×C₃₂	C₄²	1	144	yes	—
84	C₂²×C₃×C₄×C₃₂	C₂×C₈	1	384	yes	—
85	C₂²×C₃×C₄×C₃₂	C₂²×C₄	1	144	yes	—
86	C₂⁴×C₃×C₃₂	C₄²	1	16	yes	—
87	C₃×C₄²×C₃₂	C₄²	1	96	yes	—
88	C₃×C₄²×C₃₂	C₂²×C₄	1	144	yes	—
89	C₃×C₄²×C₃₂	C₂⁴	1	16	yes	—
90	C₂×C₃×C₈×C₃₂	C₂×C₈	1	2304	yes	direct product factor
91	C₂×C₃×C₈×C₃₂	C₂²×C₄	1	384	yes	—
92	C₂²×C₄×C₈²	C₃×C₈	1	4	yes	—
93	C₂²×C₄×C₈²	C₂×C₃×C₄	1	3	yes	—
94	C₂×C₈³	C₃×C₈	1	12	yes	—
95	C₂×C₈³	C₂×C₃×C₄	1	12	yes	—
96	C₂²×C₄²×C₁₆	C₂×C₃×C₄	1	3	yes	—
97	C₂²×C₄²×C₁₆	C₂³×C₃	1	1	yes	characteristic
98	C₂³×C₈×C₁₆	C₃×C₈	1	12	yes	—
99	C₂³×C₈×C₁₆	C₂×C₃×C₄	1	12	yes	—
100	C₂×C₄×C₈×C₁₆	C₃×C₈	1	36	yes	—
101	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	18	yes	—
102	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	36	yes	—
103	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	36	yes	—
104	C₂×C₄×C₈×C₁₆	C₂³×C₃	1	18	yes	—
105	C₈²×C₁₆	C₂×C₃×C₄	1	48	yes	—
106	C₈²×C₁₆	C₂³×C₃	1	16	yes	—
107	C₂³×C₄×C₃₂	C₂×C₃×C₄	1	24	yes	—
108	C₂×C₄²×C₃₂	C₂×C₃×C₄	1	72	yes	—
109	C₂×C₄²×C₃₂	C₂³×C₃	1	24	yes	—
110	C₂²×C₈×C₃₂	C₃×C₈	1	384	yes	direct product factor
111	C₂²×C₈×C₃₂	C₂×C₃×C₄	1	288	yes	—
112	C₄×C₈×C₃₂	C₂×C₃×C₄	1	288	yes	—
113	C₄×C₈×C₃₂	C₂³×C₃	1	96	yes	—
114	C₂⁴×C₃×C₁₆	C₄×C₈	1	12	yes	—
115	C₂⁴×C₃×C₁₆	C₂×C₄²	1	4	yes	—
116	C₂³×C₃×C₄×C₈	C₄×C₈	1	12	yes	—
117	C₂³×C₃×C₄×C₈	C₂×C₁₆	1	24	yes	—
118	C₂³×C₃×C₄×C₈	C₂×C₄²	1	3	yes	—
119	C₂³×C₃×C₄×C₈	C₂²×C₈	1	3	yes	—
120	C₂²×C₃×C₄³	C₂²×C₈	1	1	yes	characteristic
121	C₂³×C₃×C₃₂	C₄×C₈	1	384	yes	—
122	C₂³×C₃×C₃₂	C₂×C₄²	1	96	yes	—
123	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	36	yes	—
124	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	72	yes	—
125	C₂²×C₃×C₄×C₁₆	C₄×C₈	1	96	yes	—
126	C₂²×C₃×C₄×C₁₆	C₂×C₁₆	1	192	yes	—
127	C₂²×C₃×C₄×C₁₆	C₂×C₄²	1	18	yes	—
128	C₂²×C₃×C₄×C₁₆	C₂×C₄²	1	36	yes	—
129	C₂²×C₃×C₄×C₁₆	C₂×C₄²	1	36	yes	—
130	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	72	yes	—
131	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	96	yes	—
132	C₂²×C₃×C₄×C₁₆	C₂³×C₄	1	18	yes	—
133	C₂×C₃×C₄²×C₈	C₄×C₈	1	36	yes	—
134	C₂×C₃×C₄²×C₈	C₂×C₁₆	1	72	yes	—
135	C₂×C₃×C₄²×C₈	C₂×C₄²	1	9	yes	—
136	C₂×C₃×C₄²×C₈	C₂²×C₈	1	3	yes	—
137	C₂×C₃×C₄²×C₈	C₂²×C₈	1	9	yes	—
138	C₂×C₃×C₄²×C₈	C₂²×C₈	1	36	yes	—
139	C₂×C₃×C₄²×C₈	C₂³×C₄	1	3	yes	—
140	C₂²×C₃×C₈²	C₃₂	1	256	yes	direct product factor
141	C₂²×C₃×C₈²	C₄×C₈	1	36	yes	—
142	C₂²×C₃×C₈²	C₄×C₈	1	36	yes	—
143	C₂²×C₃×C₈²	C₄×C₈	1	96	yes	—
144	C₂²×C₃×C₈²	C₂×C₁₆	1	96	yes	—
145	C₂²×C₃×C₈²	C₂×C₁₆	1	192	yes	—
146	C₂²×C₃×C₈²	C₂×C₄²	1	36	yes	—
147	C₂²×C₃×C₈²	C₂²×C₈	1	36	yes	—
148	C₂×C₃×C₄×C₃₂	C₄×C₈	1	1152	yes	—
149	C₂×C₃×C₄×C₃₂	C₂×C₄²	1	288	yes	—
150	C₂×C₃×C₄×C₃₂	C₂²×C₈	1	1152	yes	—
151	C₂×C₃×C₄×C₃₂	C₂³×C₄	1	96	yes	—
152	C₃×C₄²×C₁₆	C₄×C₈	1	72	yes	—
153	C₃×C₄²×C₁₆	C₂×C₄²	1	18	yes	—
154	C₃×C₄²×C₁₆	C₂×C₄²	1	24	yes	—
155	C₃×C₄²×C₁₆	C₂×C₄²	1	36	yes	—
156	C₃×C₄²×C₁₆	C₂²×C₈	1	72	yes	—
157	C₃×C₄²×C₁₆	C₂³×C₄	1	3	yes	—
158	C₃×C₄²×C₁₆	C₂³×C₄	1	12	yes	—
159	C₃×C₄²×C₁₆	C₂³×C₄	1	18	yes	—
160	C₃×C₄²×C₁₆	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×C₈×C₁₆	C₄×C₈	1	576	yes	—
162	C₂×C₃×C₈×C₁₆	C₂×C₁₆	1	1152	yes	—
163	C₂×C₃×C₈×C₁₆	C₂×C₄²	1	144	yes	—
164	C₂×C₃×C₈×C₁₆	C₂²×C₈	1	576	yes	—
165	C₂×C₃×C₈×C₁₆	C₂²×C₈	1	192	yes	—
166	C₂×C₃×C₈×C₁₆	C₂³×C₄	1	48	yes	—
167	C₃×C₄×C₈²	C₄×C₈	1	72	yes	—
168	C₃×C₄×C₈²	C₂×C₁₆	1	192	yes	—
169	C₃×C₄×C₈²	C₂×C₄²	1	36	yes	—
170	C₃×C₄×C₈²	C₂²×C₈	1	36	yes	—
171	C₃×C₄×C₈²	C₂²×C₈	1	36	yes	—
172	C₃×C₄×C₈²	C₂²×C₈	1	64	yes	—
173	C₃×C₄×C₈²	C₂³×C₄	1	12	yes	—
174	C₃×C₈×C₃₂	C₂²×C₈	1	1536	yes	direct product factor
175	C₂⁴×C₃₂	C₃×C₄²	1	16	yes	—
176	C₂³×C₄×C₁₆	C₃×C₄²	1	6	yes	—
177	C₂³×C₄×C₁₆	C₂×C₃×C₈	1	12	yes	—
178	C₂³×C₄×C₁₆	C₂²×C₃×C₄	1	6	yes	—
179	C₂²×C₄²×C₈	C₂×C₃×C₈	1	6	yes	—
180	C₂²×C₄²×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
181	C₂³×C₈²	C₃×C₁₆	1	16	yes	—
182	C₂³×C₈²	C₃×C₄²	1	6	yes	—
183	C₂³×C₈²	C₂×C₃×C₈	1	6	yes	—
184	C₂²×C₄×C₃₂	C₃×C₄²	1	144	yes	—
185	C₂²×C₄×C₃₂	C₂×C₃×C₈	1	384	yes	—
186	C₂²×C₄×C₃₂	C₂²×C₃×C₄	1	144	yes	—
187	C₂×C₄²×C₁₆	C₃×C₄²	1	18	yes	—
188	C₂×C₄²×C₁₆	C₂×C₃×C₈	1	36	yes	—
189	C₂×C₄²×C₁₆	C₂²×C₃×C₄	1	3	yes	—
190	C₂×C₄²×C₁₆	C₂²×C₃×C₄	1	18	yes	—
191	C₂×C₄²×C₁₆	C₂²×C₃×C₄	1	18	yes	—
192	C₂×C₄²×C₁₆	C₂⁴×C₃	1	3	yes	—
193	C₂²×C₈×C₁₆	C₃×C₁₆	1	192	yes	—
194	C₂²×C₈×C₁₆	C₃×C₄²	1	72	yes	—
195	C₂²×C₈×C₁₆	C₂×C₃×C₈	1	144	yes	—
196	C₂²×C₈×C₁₆	C₂×C₃×C₈	1	192	yes	—
197	C₂²×C₈×C₁₆	C₂²×C₃×C₄	1	72	yes	—
198	C₂×C₄×C₈²	C₃×C₁₆	1	48	yes	—
199	C₂×C₄×C₈²	C₃×C₄²	1	18	yes	—
200	C₂×C₄×C₈²	C₂×C₃×C₈	1	18	yes	—
201	C₂×C₄×C₈²	C₂×C₃×C₈	1	18	yes	—
202	C₂×C₄×C₈²	C₂×C₃×C₈	1	48	yes	—
203	C₂×C₄×C₈²	C₂²×C₃×C₄	1	18	yes	—
204	C₄²×C₃₂	C₃×C₄²	1	96	yes	—
205	C₄²×C₃₂	C₂²×C₃×C₄	1	144	yes	—
206	C₄²×C₃₂	C₂⁴×C₃	1	16	yes	—
207	C₂×C₈×C₃₂	C₂×C₃×C₈	1	2304	yes	direct product factor
208	C₂×C₈×C₃₂	C₂²×C₃×C₄	1	384	yes	—
209	C₄×C₈×C₁₆	C₃×C₄²	1	72	yes	—
210	C₄×C₈×C₁₆	C₂×C₃×C₈	1	144	yes	—
211	C₄×C₈×C₁₆	C₂²×C₃×C₄	1	36	yes	—
212	C₄×C₈×C₁₆	C₂²×C₃×C₄	1	48	yes	—
213	C₄×C₈×C₁₆	C₂²×C₃×C₄	1	72	yes	—
214	C₄×C₈×C₁₆	C₂⁴×C₃	1	12	yes	—
215	C₈³	C₂×C₃×C₈	1	48	yes	—
216	C₈³	C₂²×C₃×C₄	1	16	yes	—
217	C₂⁴×C₃×C₈	C₄×C₁₆	1	24	yes	—
218	C₂⁴×C₃×C₈	C₄³	1	1	yes	characteristic
219	C₂⁴×C₃×C₈	C₂×C₄×C₈	1	3	yes	—
220	C₂³×C₃×C₄²	C₂×C₄×C₈	1	3	yes	—
221	C₂³×C₃×C₄²	C₂²×C₁₆	1	4	yes	—
222	C₂³×C₃×C₁₆	C₈²	1	96	yes	—
223	C₂³×C₃×C₁₆	C₄×C₁₆	1	192	yes	—
224	C₂³×C₃×C₁₆	C₄³	1	12	yes	—
225	C₂³×C₃×C₁₆	C₂×C₄×C₈	1	72	yes	—
226	C₂³×C₃×C₁₆	C₂×C₄×C₈	1	96	yes	—
227	C₂³×C₃×C₁₆	C₂²×C₄²	1	12	yes	—
228	C₂²×C₃×C₄×C₈	C₈²	1	96	yes	—
229	C₂²×C₃×C₄×C₈	C₄×C₁₆	1	72	yes	—
230	C₂²×C₃×C₄×C₈	C₄×C₁₆	1	96	yes	—
231	C₂²×C₃×C₄×C₈	C₄×C₁₆	1	144	yes	—
232	C₂²×C₃×C₄×C₈	C₂×C₃₂	1	384	yes	—
233	C₂²×C₃×C₄×C₈	C₄³	1	9	yes	—
234	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	9	yes	—
235	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	9	yes	—
236	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	9	yes	—
237	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	18	yes	—
238	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	48	yes	—
239	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	72	yes	—
240	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	48	yes	—
241	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	144	yes	—
242	C₂²×C₃×C₄×C₈	C₂²×C₄²	1	9	yes	—
243	C₂²×C₃×C₄×C₈	C₂³×C₈	1	9	yes	—
244	C₂×C₃×C₄³	C₂×C₄×C₈	1	9	yes	—
245	C₂×C₃×C₄³	C₂²×C₁₆	1	12	yes	—
246	C₂×C₃×C₄³	C₂³×C₈	1	3	yes	—
247	C₂²×C₃×C₃₂	C₈²	1	1024	yes	direct product factor
248	C₂²×C₃×C₃₂	C₂×C₄×C₈	1	1152	yes	—
249	C₂²×C₃×C₃₂	C₂²×C₄²	1	64	yes	—
250	C₂×C₃×C₄×C₁₆	C₈²	1	288	yes	—
251	C₂×C₃×C₄×C₁₆	C₄×C₁₆	1	576	yes	—
252	C₂×C₃×C₄×C₁₆	C₄³	1	36	yes	—
253	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	288	yes	—
254	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	288	yes	—
255	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	72	yes	—
256	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	144	yes	—
257	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	144	yes	—
258	C₂×C₃×C₄×C₁₆	C₂²×C₁₆	1	576	yes	—
259	C₂×C₃×C₄×C₁₆	C₂²×C₄²	1	18	yes	—
260	C₂×C₃×C₄×C₁₆	C₂²×C₄²	1	24	yes	—
261	C₂×C₃×C₄×C₁₆	C₂²×C₄²	1	36	yes	—
262	C₂×C₃×C₄×C₁₆	C₂³×C₈	1	48	yes	—
263	C₂×C₃×C₄×C₁₆	C₂³×C₈	1	144	yes	—
264	C₂×C₃×C₄×C₁₆	C₂⁴×C₄	1	6	yes	—
265	C₃×C₄²×C₈	C₄×C₁₆	1	144	yes	—
266	C₃×C₄²×C₈	C₄³	1	6	yes	—
267	C₃×C₄²×C₈	C₂×C₄×C₈	1	18	yes	—
268	C₃×C₄²×C₈	C₂×C₄×C₈	1	18	yes	—
269	C₃×C₄²×C₈	C₂×C₄×C₈	1	72	yes	—
270	C₃×C₄²×C₈	C₂²×C₁₆	1	144	yes	—
271	C₃×C₄²×C₈	C₂²×C₄²	1	9	yes	—
272	C₃×C₄²×C₈	C₂³×C₈	1	3	yes	—
273	C₃×C₄²×C₈	C₂³×C₈	1	9	yes	—
274	C₃×C₄²×C₈	C₂³×C₈	1	24	yes	—
275	C₃×C₄²×C₈	C₂⁴×C₄	1	1	yes	characteristic
276	C₂×C₃×C₈²	C₈²	1	288	yes	—
277	C₂×C₃×C₈²	C₄×C₁₆	1	288	yes	—
278	C₂×C₃×C₈²	C₂×C₃₂	1	1536	yes	direct product factor
279	C₂×C₃×C₈²	C₂×C₄×C₈	1	288	yes	—
280	C₂×C₃×C₈²	C₂×C₄×C₈	1	72	yes	—
281	C₂×C₃×C₈²	C₂×C₄×C₈	1	72	yes	—
282	C₂×C₃×C₈²	C₂²×C₁₆	1	256	yes	—
283	C₂×C₃×C₈²	C₂²×C₁₆	1	288	yes	—
284	C₂×C₃×C₈²	C₂²×C₄²	1	24	yes	—
285	C₂×C₃×C₈²	C₂³×C₈	1	24	yes	—
286	C₃×C₄×C₃₂	C₂×C₄×C₈	1	1152	yes	—
287	C₃×C₄×C₃₂	C₂³×C₈	1	384	yes	—
288	C₃×C₈×C₁₆	C₂×C₄×C₈	1	576	yes	—
289	C₃×C₈×C₁₆	C₂²×C₁₆	1	768	yes	—
290	C₃×C₈×C₁₆	C₂³×C₈	1	192	yes	—
291	C₂⁴×C₁₆	C₃×C₄×C₈	1	12	yes	—
292	C₂⁴×C₁₆	C₂×C₃×C₄²	1	4	yes	—
293	C₂³×C₄×C₈	C₃×C₄×C₈	1	12	yes	—
294	C₂³×C₄×C₈	C₂×C₃×C₁₆	1	24	yes	—
295	C₂³×C₄×C₈	C₂×C₃×C₄²	1	3	yes	—
296	C₂³×C₄×C₈	C₂²×C₃×C₈	1	3	yes	—
297	C₂²×C₄³	C₂²×C₃×C₈	1	1	yes	characteristic
298	C₂³×C₃₂	C₃×C₄×C₈	1	384	yes	—
299	C₂³×C₃₂	C₂×C₃×C₄²	1	96	yes	—
300	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	36	yes	—
301	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	72	yes	—
302	C₂²×C₄×C₁₆	C₃×C₄×C₈	1	96	yes	—
303	C₂²×C₄×C₁₆	C₂×C₃×C₁₆	1	192	yes	—
304	C₂²×C₄×C₁₆	C₂×C₃×C₄²	1	18	yes	—
305	C₂²×C₄×C₁₆	C₂×C₃×C₄²	1	36	yes	—
306	C₂²×C₄×C₁₆	C₂×C₃×C₄²	1	36	yes	—
307	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	72	yes	—
308	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	96	yes	—
309	C₂²×C₄×C₁₆	C₂³×C₃×C₄	1	18	yes	—
310	C₂×C₄²×C₈	C₃×C₄×C₈	1	36	yes	—
311	C₂×C₄²×C₈	C₂×C₃×C₁₆	1	72	yes	—
312	C₂×C₄²×C₈	C₂×C₃×C₄²	1	9	yes	—
313	C₂×C₄²×C₈	C₂²×C₃×C₈	1	3	yes	—
314	C₂×C₄²×C₈	C₂²×C₃×C₈	1	9	yes	—
315	C₂×C₄²×C₈	C₂²×C₃×C₈	1	36	yes	—
316	C₂×C₄²×C₈	C₂³×C₃×C₄	1	3	yes	—
317	C₂²×C₈²	C₃×C₃₂	1	256	yes	direct product factor
318	C₂²×C₈²	C₃×C₄×C₈	1	36	yes	—
319	C₂²×C₈²	C₃×C₄×C₈	1	36	yes	—
320	C₂²×C₈²	C₃×C₄×C₈	1	96	yes	—
321	C₂²×C₈²	C₂×C₃×C₁₆	1	96	yes	—
322	C₂²×C₈²	C₂×C₃×C₁₆	1	192	yes	—
323	C₂²×C₈²	C₂×C₃×C₄²	1	36	yes	—
324	C₂²×C₈²	C₂²×C₃×C₈	1	36	yes	—
325	C₂×C₄×C₃₂	C₃×C₄×C₈	1	1152	yes	—
326	C₂×C₄×C₃₂	C₂×C₃×C₄²	1	288	yes	—
327	C₂×C₄×C₃₂	C₂²×C₃×C₈	1	1152	yes	—
328	C₂×C₄×C₃₂	C₂³×C₃×C₄	1	96	yes	—
329	C₄²×C₁₆	C₃×C₄×C₈	1	72	yes	—
330	C₄²×C₁₆	C₂×C₃×C₄²	1	18	yes	—
331	C₄²×C₁₆	C₂×C₃×C₄²	1	24	yes	—
332	C₄²×C₁₆	C₂×C₃×C₄²	1	36	yes	—
333	C₄²×C₁₆	C₂²×C₃×C₈	1	72	yes	—
334	C₄²×C₁₆	C₂³×C₃×C₄	1	3	yes	—
335	C₄²×C₁₆	C₂³×C₃×C₄	1	12	yes	—
336	C₄²×C₁₆	C₂³×C₃×C₄	1	18	yes	—
337	C₄²×C₁₆	C₂⁵×C₃	1	1	yes	characteristic
338	C₂×C₈×C₁₆	C₃×C₄×C₈	1	576	yes	—
339	C₂×C₈×C₁₆	C₂×C₃×C₁₆	1	1152	yes	—
340	C₂×C₈×C₁₆	C₂×C₃×C₄²	1	144	yes	—
341	C₂×C₈×C₁₆	C₂²×C₃×C₈	1	576	yes	—
342	C₂×C₈×C₁₆	C₂²×C₃×C₈	1	192	yes	—
343	C₂×C₈×C₁₆	C₂³×C₃×C₄	1	48	yes	—
344	C₄×C₈²	C₃×C₄×C₈	1	72	yes	—
345	C₄×C₈²	C₂×C₃×C₁₆	1	192	yes	—
346	C₄×C₈²	C₂×C₃×C₄²	1	36	yes	—
347	C₄×C₈²	C₂²×C₃×C₈	1	36	yes	—
348	C₄×C₈²	C₂²×C₃×C₈	1	36	yes	—
349	C₄×C₈²	C₂²×C₃×C₈	1	64	yes	—
350	C₄×C₈²	C₂³×C₃×C₄	1	12	yes	—
351	C₈×C₃₂	C₂²×C₃×C₈	1	1536	yes	direct product factor
352	C₂⁴×C₃×C₄	C₄²×C₈	1	1	yes	characteristic
353	C₂⁴×C₃×C₄	C₂×C₄×C₁₆	1	6	yes	—
354	C₂³×C₃×C₈	C₈×C₁₆	1	192	yes	—
355	C₂³×C₃×C₈	C₄×C₃₂	1	384	yes	—
356	C₂³×C₃×C₈	C₂×C₈²	1	24	yes	—
357	C₂³×C₃×C₈	C₄²×C₈	1	3	yes	—
358	C₂³×C₃×C₈	C₄²×C₈	1	9	yes	—
359	C₂³×C₃×C₈	C₄²×C₈	1	24	yes	—
360	C₂³×C₃×C₈	C₂×C₄×C₁₆	1	48	yes	—
361	C₂³×C₃×C₈	C₂×C₄×C₁₆	1	144	yes	—
362	C₂³×C₃×C₈	C₂×C₄³	1	3	yes	—
363	C₂³×C₃×C₈	C₂²×C₄×C₈	1	9	yes	—
364	C₂²×C₃×C₄²	C₂×C₈²	1	24	yes	—
365	C₂²×C₃×C₄²	C₄²×C₈	1	9	yes	—
366	C₂²×C₃×C₄²	C₂×C₄×C₁₆	1	18	yes	—
367	C₂²×C₃×C₄²	C₂×C₄×C₁₆	1	24	yes	—
368	C₂²×C₃×C₄²	C₂×C₄×C₁₆	1	36	yes	—
369	C₂²×C₃×C₄²	C₂²×C₃₂	1	64	yes	—
370	C₂²×C₃×C₄²	C₂²×C₄×C₈	1	9	yes	—
371	C₂²×C₃×C₄²	C₂³×C₁₆	1	12	yes	—
372	C₂²×C₃×C₁₆	C₈×C₁₆	1	768	yes	—
373	C₂²×C₃×C₁₆	C₂×C₈²	1	256	yes	—
374	C₂²×C₃×C₁₆	C₂×C₈²	1	288	yes	—
375	C₂²×C₃×C₁₆	C₄²×C₈	1	144	yes	—
376	C₂²×C₃×C₁₆	C₂×C₄×C₁₆	1	576	yes	—
377	C₂²×C₃×C₁₆	C₂×C₄³	1	12	yes	—
378	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	48	yes	—
379	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	144	yes	—
380	C₂²×C₃×C₁₆	C₂³×C₄²	1	4	yes	—
381	C₂×C₃×C₄×C₈	C₈×C₁₆	1	576	yes	—
382	C₂×C₃×C₄×C₈	C₄×C₃₂	1	1152	yes	—
383	C₂×C₃×C₄×C₈	C₂×C₈²	1	288	yes	—
384	C₂×C₃×C₄×C₈	C₂×C₈²	1	72	yes	—
385	C₂×C₃×C₄×C₈	C₂×C₈²	1	72	yes	—
386	C₂×C₃×C₄×C₈	C₄²×C₈	1	18	yes	—
387	C₂×C₃×C₄×C₈	C₄²×C₈	1	18	yes	—
388	C₂×C₃×C₄×C₈	C₄²×C₈	1	72	yes	—
389	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	288	yes	—
390	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	288	yes	—
391	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	72	yes	—
392	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	144	yes	—
393	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	144	yes	—
394	C₂×C₃×C₄×C₈	C₂²×C₃₂	1	1152	yes	—
395	C₂×C₃×C₄×C₈	C₂×C₄³	1	9	yes	—
396	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	9	yes	—
397	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	9	yes	—
398	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	9	yes	—
399	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	18	yes	—
400	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	48	yes	—
401	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	72	yes	—
402	C₂×C₃×C₄×C₈	C₂³×C₁₆	1	72	yes	—
403	C₂×C₃×C₄×C₈	C₂³×C₁₆	1	96	yes	—
404	C₂×C₃×C₄×C₈	C₂³×C₄²	1	3	yes	—
405	C₂×C₃×C₄×C₈	C₂⁴×C₈	1	3	yes	—
406	C₃×C₄³	C₄²×C₈	1	6	yes	—
407	C₃×C₄³	C₂×C₄×C₁₆	1	36	yes	—
408	C₃×C₄³	C₂²×C₄×C₈	1	9	yes	—
409	C₃×C₄³	C₂³×C₁₆	1	12	yes	—
410	C₃×C₄³	C₂⁴×C₈	1	1	yes	characteristic
411	C₂×C₃×C₃₂	C₂×C₈²	1	1536	yes	direct product factor
412	C₂×C₃×C₃₂	C₂²×C₄×C₈	1	384	yes	—
413	C₃×C₄×C₁₆	C₂×C₈²	1	288	yes	—
414	C₃×C₄×C₁₆	C₄²×C₈	1	144	yes	—
415	C₃×C₄×C₁₆	C₂×C₄×C₁₆	1	576	yes	—
416	C₃×C₄×C₁₆	C₂²×C₄×C₈	1	72	yes	—
417	C₃×C₄×C₁₆	C₂²×C₄×C₈	1	96	yes	—
418	C₃×C₄×C₁₆	C₂²×C₄×C₈	1	144	yes	—
419	C₃×C₄×C₁₆	C₂³×C₁₆	1	192	yes	—
420	C₃×C₄×C₁₆	C₂⁴×C₈	1	24	yes	—
421	C₃×C₈²	C₂×C₈²	1	288	yes	—
422	C₃×C₈²	C₂×C₄×C₁₆	1	288	yes	—
423	C₃×C₈²	C₂²×C₃₂	1	1024	yes	direct product factor
424	C₃×C₈²	C₂²×C₄×C₈	1	96	yes	—
425	C₃×C₈²	C₂³×C₁₆	1	96	yes	—
426	C₂⁴×C₈	C₃×C₄×C₁₆	1	24	yes	—
427	C₂⁴×C₈	C₃×C₄³	1	1	yes	characteristic
428	C₂⁴×C₈	C₂×C₃×C₄×C₈	1	3	yes	—
429	C₂³×C₄²	C₂×C₃×C₄×C₈	1	3	yes	—
430	C₂³×C₄²	C₂²×C₃×C₁₆	1	4	yes	—
431	C₂³×C₁₆	C₃×C₈²	1	96	yes	—
432	C₂³×C₁₆	C₃×C₄×C₁₆	1	192	yes	—
433	C₂³×C₁₆	C₃×C₄³	1	12	yes	—
434	C₂³×C₁₆	C₂×C₃×C₄×C₈	1	72	yes	—
435	C₂³×C₁₆	C₂×C₃×C₄×C₈	1	96	yes	—
436	C₂³×C₁₆	C₂²×C₃×C₄²	1	12	yes	—
437	C₂²×C₄×C₈	C₃×C₈²	1	96	yes	—
438	C₂²×C₄×C₈	C₃×C₄×C₁₆	1	72	yes	—
439	C₂²×C₄×C₈	C₃×C₄×C₁₆	1	96	yes	—
440	C₂²×C₄×C₈	C₃×C₄×C₁₆	1	144	yes	—
441	C₂²×C₄×C₈	C₂×C₃×C₃₂	1	384	yes	—
442	C₂²×C₄×C₈	C₃×C₄³	1	9	yes	—
443	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	9	yes	—
444	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	9	yes	—
445	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	9	yes	—
446	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	18	yes	—
447	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	48	yes	—
448	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	72	yes	—
449	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	48	yes	—
450	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	144	yes	—
451	C₂²×C₄×C₈	C₂²×C₃×C₄²	1	9	yes	—
452	C₂²×C₄×C₈	C₂³×C₃×C₈	1	9	yes	—
453	C₂×C₄³	C₂×C₃×C₄×C₈	1	9	yes	—
454	C₂×C₄³	C₂²×C₃×C₁₆	1	12	yes	—
455	C₂×C₄³	C₂³×C₃×C₈	1	3	yes	—
456	C₂²×C₃₂	C₃×C₈²	1	1024	yes	direct product factor
457	C₂²×C₃₂	C₂×C₃×C₄×C₈	1	1152	yes	—
458	C₂²×C₃₂	C₂²×C₃×C₄²	1	64	yes	—
459	C₂×C₄×C₁₆	C₃×C₈²	1	288	yes	—
460	C₂×C₄×C₁₆	C₃×C₄×C₁₆	1	576	yes	—
461	C₂×C₄×C₁₆	C₃×C₄³	1	36	yes	—
462	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	288	yes	—
463	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	288	yes	—
464	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	72	yes	—
465	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	144	yes	—
466	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	144	yes	—
467	C₂×C₄×C₁₆	C₂²×C₃×C₁₆	1	576	yes	—
468	C₂×C₄×C₁₆	C₂²×C₃×C₄²	1	18	yes	—
469	C₂×C₄×C₁₆	C₂²×C₃×C₄²	1	24	yes	—
470	C₂×C₄×C₁₆	C₂²×C₃×C₄²	1	36	yes	—
471	C₂×C₄×C₁₆	C₂³×C₃×C₈	1	48	yes	—
472	C₂×C₄×C₁₆	C₂³×C₃×C₈	1	144	yes	—
473	C₂×C₄×C₁₆	C₂⁴×C₃×C₄	1	6	yes	—
474	C₄²×C₈	C₃×C₄×C₁₆	1	144	yes	—
475	C₄²×C₈	C₃×C₄³	1	6	yes	—
476	C₄²×C₈	C₂×C₃×C₄×C₈	1	18	yes	—
477	C₄²×C₈	C₂×C₃×C₄×C₈	1	18	yes	—
478	C₄²×C₈	C₂×C₃×C₄×C₈	1	72	yes	—
479	C₄²×C₈	C₂²×C₃×C₁₆	1	144	yes	—
480	C₄²×C₈	C₂²×C₃×C₄²	1	9	yes	—
481	C₄²×C₈	C₂³×C₃×C₈	1	3	yes	—
482	C₄²×C₈	C₂³×C₃×C₈	1	9	yes	—
483	C₄²×C₈	C₂³×C₃×C₈	1	24	yes	—
484	C₄²×C₈	C₂⁴×C₃×C₄	1	1	yes	characteristic
485	C₂×C₈²	C₃×C₈²	1	288	yes	—
486	C₂×C₈²	C₃×C₄×C₁₆	1	288	yes	—
487	C₂×C₈²	C₂×C₃×C₃₂	1	1536	yes	direct product factor
488	C₂×C₈²	C₂×C₃×C₄×C₈	1	288	yes	—
489	C₂×C₈²	C₂×C₃×C₄×C₈	1	72	yes	—
490	C₂×C₈²	C₂×C₃×C₄×C₈	1	72	yes	—
491	C₂×C₈²	C₂²×C₃×C₁₆	1	256	yes	—
492	C₂×C₈²	C₂²×C₃×C₁₆	1	288	yes	—
493	C₂×C₈²	C₂²×C₃×C₄²	1	24	yes	—
494	C₂×C₈²	C₂³×C₃×C₈	1	24	yes	—
495	C₄×C₃₂	C₂×C₃×C₄×C₈	1	1152	yes	—
496	C₄×C₃₂	C₂³×C₃×C₈	1	384	yes	—
497	C₈×C₁₆	C₂×C₃×C₄×C₈	1	576	yes	—
498	C₈×C₁₆	C₂²×C₃×C₁₆	1	768	yes	—
499	C₈×C₁₆	C₂³×C₃×C₈	1	192	yes	—
500	C₂⁵×C₃	C₄²×C₁₆	1	1	yes	characteristic
501	C₂³×C₃×C₄	C₄×C₈²	1	12	yes	—
502	C₂³×C₃×C₄	C₂×C₈×C₁₆	1	48	yes	—
503	C₂³×C₃×C₄	C₄²×C₁₆	1	3	yes	—
504	C₂³×C₃×C₄	C₄²×C₁₆	1	12	yes	—
505	C₂³×C₃×C₄	C₄²×C₁₆	1	18	yes	—
506	C₂³×C₃×C₄	C₂×C₄×C₃₂	1	96	yes	—
507	C₂³×C₃×C₄	C₂×C₄²×C₈	1	3	yes	—
508	C₂³×C₃×C₄	C₂²×C₄×C₁₆	1	18	yes	—
509	C₂²×C₃×C₈	C₈×C₃₂	1	1536	yes	direct product factor
510	C₂²×C₃×C₈	C₄×C₈²	1	36	yes	—
511	C₂²×C₃×C₈	C₄×C₈²	1	36	yes	—
512	C₂²×C₃×C₈	C₄×C₈²	1	64	yes	—
513	C₂²×C₃×C₈	C₂×C₈×C₁₆	1	576	yes	—
514	C₂²×C₃×C₈	C₂×C₈×C₁₆	1	192	yes	—
515	C₂²×C₃×C₈	C₄²×C₁₆	1	72	yes	—
516	C₂²×C₃×C₈	C₂×C₄×C₃₂	1	1152	yes	—
517	C₂²×C₃×C₈	C₂²×C₈²	1	36	yes	—
518	C₂²×C₃×C₈	C₂×C₄²×C₈	1	3	yes	—
519	C₂²×C₃×C₈	C₂×C₄²×C₈	1	9	yes	—
520	C₂²×C₃×C₈	C₂×C₄²×C₈	1	36	yes	—
521	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	72	yes	—
522	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	96	yes	—
523	C₂²×C₃×C₈	C₂²×C₄³	1	1	yes	characteristic
524	C₂²×C₃×C₈	C₂³×C₄×C₈	1	3	yes	—
525	C₂×C₃×C₄²	C₄×C₈²	1	36	yes	—
526	C₂×C₃×C₄²	C₂×C₈×C₁₆	1	144	yes	—
527	C₂×C₃×C₄²	C₄²×C₁₆	1	18	yes	—
528	C₂×C₃×C₄²	C₄²×C₁₆	1	24	yes	—
529	C₂×C₃×C₄²	C₄²×C₁₆	1	36	yes	—
530	C₂×C₃×C₄²	C₂×C₄×C₃₂	1	288	yes	—
531	C₂×C₃×C₄²	C₂²×C₈²	1	36	yes	—
532	C₂×C₃×C₄²	C₂×C₄²×C₈	1	9	yes	—
533	C₂×C₃×C₄²	C₂²×C₄×C₁₆	1	18	yes	—
534	C₂×C₃×C₄²	C₂²×C₄×C₁₆	1	36	yes	—
535	C₂×C₃×C₄²	C₂²×C₄×C₁₆	1	36	yes	—
536	C₂×C₃×C₄²	C₂³×C₃₂	1	96	yes	—
537	C₂×C₃×C₄²	C₂³×C₄×C₈	1	3	yes	—
538	C₂×C₃×C₄²	C₂⁴×C₁₆	1	4	yes	—
539	C₂×C₃×C₁₆	C₄×C₈²	1	192	yes	—
540	C₂×C₃×C₁₆	C₂×C₈×C₁₆	1	1152	yes	—
541	C₂×C₃×C₁₆	C₂²×C₈²	1	96	yes	—
542	C₂×C₃×C₁₆	C₂²×C₈²	1	192	yes	—
543	C₂×C₃×C₁₆	C₂×C₄²×C₈	1	72	yes	—
544	C₂×C₃×C₁₆	C₂²×C₄×C₁₆	1	192	yes	—
545	C₂×C₃×C₁₆	C₂³×C₄×C₈	1	24	yes	—
546	C₃×C₄×C₈	C₄×C₈²	1	72	yes	—
547	C₃×C₄×C₈	C₂×C₈×C₁₆	1	576	yes	—
548	C₃×C₄×C₈	C₄²×C₁₆	1	72	yes	—
549	C₃×C₄×C₈	C₂×C₄×C₃₂	1	1152	yes	—
550	C₃×C₄×C₈	C₂²×C₈²	1	36	yes	—
551	C₃×C₄×C₈	C₂²×C₈²	1	36	yes	—
552	C₃×C₄×C₈	C₂²×C₈²	1	96	yes	—
553	C₃×C₄×C₈	C₂×C₄²×C₈	1	36	yes	—
554	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	36	yes	—
555	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	72	yes	—
556	C₃×C₄×C₈	C₂²×C₄×C₁₆	1	96	yes	—
557	C₃×C₄×C₈	C₂³×C₃₂	1	384	yes	—
558	C₃×C₄×C₈	C₂³×C₄×C₈	1	12	yes	—
559	C₃×C₄×C₈	C₂⁴×C₁₆	1	12	yes	—
560	C₃×C₃₂	C₂²×C₈²	1	256	yes	direct product factor
561	C₂⁴×C₄	C₃×C₄²×C₈	1	1	yes	characteristic
562	C₂⁴×C₄	C₂×C₃×C₄×C₁₆	1	6	yes	—
563	C₂³×C₈	C₃×C₈×C₁₆	1	192	yes	—
564	C₂³×C₈	C₃×C₄×C₃₂	1	384	yes	—
565	C₂³×C₈	C₂×C₃×C₈²	1	24	yes	—
566	C₂³×C₈	C₃×C₄²×C₈	1	3	yes	—
567	C₂³×C₈	C₃×C₄²×C₈	1	9	yes	—
568	C₂³×C₈	C₃×C₄²×C₈	1	24	yes	—
569	C₂³×C₈	C₂×C₃×C₄×C₁₆	1	48	yes	—
570	C₂³×C₈	C₂×C₃×C₄×C₁₆	1	144	yes	—
571	C₂³×C₈	C₂×C₃×C₄³	1	3	yes	—
572	C₂³×C₈	C₂²×C₃×C₄×C₈	1	9	yes	—
573	C₂²×C₄²	C₂×C₃×C₈²	1	24	yes	—
574	C₂²×C₄²	C₃×C₄²×C₈	1	9	yes	—
575	C₂²×C₄²	C₂×C₃×C₄×C₁₆	1	18	yes	—
576	C₂²×C₄²	C₂×C₃×C₄×C₁₆	1	24	yes	—
577	C₂²×C₄²	C₂×C₃×C₄×C₁₆	1	36	yes	—
578	C₂²×C₄²	C₂²×C₃×C₃₂	1	64	yes	—
579	C₂²×C₄²	C₂²×C₃×C₄×C₈	1	9	yes	—
580	C₂²×C₄²	C₂³×C₃×C₁₆	1	12	yes	—
581	C₂²×C₁₆	C₃×C₈×C₁₆	1	768	yes	—
582	C₂²×C₁₆	C₂×C₃×C₈²	1	256	yes	—
583	C₂²×C₁₆	C₂×C₃×C₈²	1	288	yes	—
584	C₂²×C₁₆	C₃×C₄²×C₈	1	144	yes	—
585	C₂²×C₁₆	C₂×C₃×C₄×C₁₆	1	576	yes	—
586	C₂²×C₁₆	C₂×C₃×C₄³	1	12	yes	—
587	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	48	yes	—
588	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	144	yes	—
589	C₂²×C₁₆	C₂³×C₃×C₄²	1	4	yes	—
590	C₂×C₄×C₈	C₃×C₈×C₁₆	1	576	yes	—
591	C₂×C₄×C₈	C₃×C₄×C₃₂	1	1152	yes	—
592	C₂×C₄×C₈	C₂×C₃×C₈²	1	288	yes	—
593	C₂×C₄×C₈	C₂×C₃×C₈²	1	72	yes	—
594	C₂×C₄×C₈	C₂×C₃×C₈²	1	72	yes	—
595	C₂×C₄×C₈	C₃×C₄²×C₈	1	18	yes	—
596	C₂×C₄×C₈	C₃×C₄²×C₈	1	18	yes	—
597	C₂×C₄×C₈	C₃×C₄²×C₈	1	72	yes	—
598	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	288	yes	—
599	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	288	yes	—
600	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	72	yes	—
601	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	144	yes	—
602	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	144	yes	—
603	C₂×C₄×C₈	C₂²×C₃×C₃₂	1	1152	yes	—
604	C₂×C₄×C₈	C₂×C₃×C₄³	1	9	yes	—
605	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	9	yes	—
606	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	9	yes	—
607	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	9	yes	—
608	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	18	yes	—
609	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	48	yes	—
610	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	72	yes	—
611	C₂×C₄×C₈	C₂³×C₃×C₁₆	1	72	yes	—
612	C₂×C₄×C₈	C₂³×C₃×C₁₆	1	96	yes	—
613	C₂×C₄×C₈	C₂³×C₃×C₄²	1	3	yes	—
614	C₂×C₄×C₈	C₂⁴×C₃×C₈	1	3	yes	—
615	C₄³	C₃×C₄²×C₈	1	6	yes	—
616	C₄³	C₂×C₃×C₄×C₁₆	1	36	yes	—
617	C₄³	C₂²×C₃×C₄×C₈	1	9	yes	—
618	C₄³	C₂³×C₃×C₁₆	1	12	yes	—
619	C₄³	C₂⁴×C₃×C₈	1	1	yes	characteristic
620	C₂×C₃₂	C₂×C₃×C₈²	1	1536	yes	direct product factor
621	C₂×C₃₂	C₂²×C₃×C₄×C₈	1	384	yes	—
622	C₄×C₁₆	C₂×C₃×C₈²	1	288	yes	—
623	C₄×C₁₆	C₃×C₄²×C₈	1	144	yes	—
624	C₄×C₁₆	C₂×C₃×C₄×C₁₆	1	576	yes	—
625	C₄×C₁₆	C₂²×C₃×C₄×C₈	1	72	yes	—
626	C₄×C₁₆	C₂²×C₃×C₄×C₈	1	96	yes	—
627	C₄×C₁₆	C₂²×C₃×C₄×C₈	1	144	yes	—
628	C₄×C₁₆	C₂³×C₃×C₁₆	1	192	yes	—
629	C₄×C₁₆	C₂⁴×C₃×C₈	1	24	yes	—
630	C₈²	C₂×C₃×C₈²	1	288	yes	—
631	C₈²	C₂×C₃×C₄×C₁₆	1	288	yes	—
632	C₈²	C₂²×C₃×C₃₂	1	1024	yes	direct product factor
633	C₈²	C₂²×C₃×C₄×C₈	1	96	yes	—
634	C₈²	C₂³×C₃×C₁₆	1	96	yes	—
635	C₂⁴×C₃	C₄×C₈×C₁₆	1	12	yes	—
636	C₂⁴×C₃	C₄²×C₃₂	1	16	yes	—
637	C₂⁴×C₃	C₂×C₄²×C₁₆	1	3	yes	—
638	C₂²×C₃×C₄	C₈³	1	16	yes	—
639	C₂²×C₃×C₄	C₄×C₈×C₁₆	1	36	yes	—
640	C₂²×C₃×C₄	C₄×C₈×C₁₆	1	48	yes	—
641	C₂²×C₃×C₄	C₄×C₈×C₁₆	1	72	yes	—
642	C₂²×C₃×C₄	C₂×C₈×C₃₂	1	384	yes	—
643	C₂²×C₃×C₄	C₄²×C₃₂	1	144	yes	—
644	C₂²×C₃×C₄	C₂×C₄×C₈²	1	18	yes	—
645	C₂²×C₃×C₄	C₂²×C₈×C₁₆	1	72	yes	—
646	C₂²×C₃×C₄	C₂×C₄²×C₁₆	1	3	yes	—
647	C₂²×C₃×C₄	C₂×C₄²×C₁₆	1	18	yes	—
648	C₂²×C₃×C₄	C₂×C₄²×C₁₆	1	18	yes	—
649	C₂²×C₃×C₄	C₂²×C₄×C₃₂	1	144	yes	—
650	C₂²×C₃×C₄	C₂²×C₄²×C₈	1	1	yes	characteristic
651	C₂²×C₃×C₄	C₂³×C₄×C₁₆	1	6	yes	—
652	C₂×C₃×C₈	C₈³	1	48	yes	—
653	C₂×C₃×C₈	C₄×C₈×C₁₆	1	144	yes	—
654	C₂×C₃×C₈	C₂×C₈×C₃₂	1	2304	yes	direct product factor
655	C₂×C₃×C₈	C₂×C₄×C₈²	1	18	yes	—
656	C₂×C₃×C₈	C₂×C₄×C₈²	1	18	yes	—
657	C₂×C₃×C₈	C₂×C₄×C₈²	1	48	yes	—
658	C₂×C₃×C₈	C₂²×C₈×C₁₆	1	144	yes	—
659	C₂×C₃×C₈	C₂²×C₈×C₁₆	1	192	yes	—
660	C₂×C₃×C₈	C₂×C₄²×C₁₆	1	36	yes	—
661	C₂×C₃×C₈	C₂²×C₄×C₃₂	1	384	yes	—
662	C₂×C₃×C₈	C₂³×C₈²	1	6	yes	—
663	C₂×C₃×C₈	C₂²×C₄²×C₈	1	6	yes	—
664	C₂×C₃×C₈	C₂³×C₄×C₁₆	1	12	yes	—
665	C₃×C₄²	C₄×C₈×C₁₆	1	72	yes	—
666	C₃×C₄²	C₄²×C₃₂	1	96	yes	—
667	C₃×C₄²	C₂×C₄×C₈²	1	18	yes	—
668	C₃×C₄²	C₂²×C₈×C₁₆	1	72	yes	—
669	C₃×C₄²	C₂×C₄²×C₁₆	1	18	yes	—
670	C₃×C₄²	C₂²×C₄×C₃₂	1	144	yes	—
671	C₃×C₄²	C₂³×C₈²	1	6	yes	—
672	C₃×C₄²	C₂³×C₄×C₁₆	1	6	yes	—
673	C₃×C₄²	C₂⁴×C₃₂	1	16	yes	—
674	C₃×C₁₆	C₂×C₄×C₈²	1	48	yes	—
675	C₃×C₁₆	C₂²×C₈×C₁₆	1	192	yes	—
676	C₃×C₁₆	C₂³×C₈²	1	16	yes	—
677	C₂⁵	C₃×C₄²×C₁₆	1	1	yes	characteristic
678	C₂³×C₄	C₃×C₄×C₈²	1	12	yes	—
679	C₂³×C₄	C₂×C₃×C₈×C₁₆	1	48	yes	—
680	C₂³×C₄	C₃×C₄²×C₁₆	1	3	yes	—
681	C₂³×C₄	C₃×C₄²×C₁₆	1	12	yes	—
682	C₂³×C₄	C₃×C₄²×C₁₆	1	18	yes	—
683	C₂³×C₄	C₂×C₃×C₄×C₃₂	1	96	yes	—
684	C₂³×C₄	C₂×C₃×C₄²×C₈	1	3	yes	—
685	C₂³×C₄	C₂²×C₃×C₄×C₁₆	1	18	yes	—
686	C₂²×C₈	C₃×C₈×C₃₂	1	1536	yes	direct product factor
687	C₂²×C₈	C₃×C₄×C₈²	1	36	yes	—
688	C₂²×C₈	C₃×C₄×C₈²	1	36	yes	—
689	C₂²×C₈	C₃×C₄×C₈²	1	64	yes	—
690	C₂²×C₈	C₂×C₃×C₈×C₁₆	1	576	yes	—
691	C₂²×C₈	C₂×C₃×C₈×C₁₆	1	192	yes	—
692	C₂²×C₈	C₃×C₄²×C₁₆	1	72	yes	—
693	C₂²×C₈	C₂×C₃×C₄×C₃₂	1	1152	yes	—
694	C₂²×C₈	C₂²×C₃×C₈²	1	36	yes	—
695	C₂²×C₈	C₂×C₃×C₄²×C₈	1	3	yes	—
696	C₂²×C₈	C₂×C₃×C₄²×C₈	1	9	yes	—
697	C₂²×C₈	C₂×C₃×C₄²×C₈	1	36	yes	—
698	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	72	yes	—
699	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	96	yes	—
700	C₂²×C₈	C₂²×C₃×C₄³	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₃×C₄×C₈	1	3	yes	—
702	C₂×C₄²	C₃×C₄×C₈²	1	36	yes	—
703	C₂×C₄²	C₂×C₃×C₈×C₁₆	1	144	yes	—
704	C₂×C₄²	C₃×C₄²×C₁₆	1	18	yes	—
705	C₂×C₄²	C₃×C₄²×C₁₆	1	24	yes	—
706	C₂×C₄²	C₃×C₄²×C₁₆	1	36	yes	—
707	C₂×C₄²	C₂×C₃×C₄×C₃₂	1	288	yes	—
708	C₂×C₄²	C₂²×C₃×C₈²	1	36	yes	—
709	C₂×C₄²	C₂×C₃×C₄²×C₈	1	9	yes	—
710	C₂×C₄²	C₂²×C₃×C₄×C₁₆	1	18	yes	—
711	C₂×C₄²	C₂²×C₃×C₄×C₁₆	1	36	yes	—
712	C₂×C₄²	C₂²×C₃×C₄×C₁₆	1	36	yes	—
713	C₂×C₄²	C₂³×C₃×C₃₂	1	96	yes	—
714	C₂×C₄²	C₂³×C₃×C₄×C₈	1	3	yes	—
715	C₂×C₄²	C₂⁴×C₃×C₁₆	1	4	yes	—
716	C₂×C₁₆	C₃×C₄×C₈²	1	192	yes	—
717	C₂×C₁₆	C₂×C₃×C₈×C₁₆	1	1152	yes	—
718	C₂×C₁₆	C₂²×C₃×C₈²	1	96	yes	—
719	C₂×C₁₆	C₂²×C₃×C₈²	1	192	yes	—
720	C₂×C₁₆	C₂×C₃×C₄²×C₈	1	72	yes	—
721	C₂×C₁₆	C₂²×C₃×C₄×C₁₆	1	192	yes	—
722	C₂×C₁₆	C₂³×C₃×C₄×C₈	1	24	yes	—
723	C₄×C₈	C₃×C₄×C₈²	1	72	yes	—
724	C₄×C₈	C₂×C₃×C₈×C₁₆	1	576	yes	—
725	C₄×C₈	C₃×C₄²×C₁₆	1	72	yes	—
726	C₄×C₈	C₂×C₃×C₄×C₃₂	1	1152	yes	—
727	C₄×C₈	C₂²×C₃×C₈²	1	36	yes	—
728	C₄×C₈	C₂²×C₃×C₈²	1	36	yes	—
729	C₄×C₈	C₂²×C₃×C₈²	1	96	yes	—
730	C₄×C₈	C₂×C₃×C₄²×C₈	1	36	yes	—
731	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	36	yes	—
732	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	72	yes	—
733	C₄×C₈	C₂²×C₃×C₄×C₁₆	1	96	yes	—
734	C₄×C₈	C₂³×C₃×C₃₂	1	384	yes	—
735	C₄×C₈	C₂³×C₃×C₄×C₈	1	12	yes	—
736	C₄×C₈	C₂⁴×C₃×C₁₆	1	12	yes	—
737	C₃₂	C₂²×C₃×C₈²	1	256	yes	direct product factor
738	C₂³×C₃	C₄×C₈×C₃₂	1	96	yes	—
739	C₂³×C₃	C₂×C₄²×C₃₂	1	24	yes	—
740	C₂³×C₃	C₈²×C₁₆	1	16	yes	—
741	C₂³×C₃	C₂×C₄×C₈×C₁₆	1	18	yes	—
742	C₂³×C₃	C₂²×C₄²×C₁₆	1	1	yes	characteristic
743	C₂×C₃×C₄	C₄×C₈×C₃₂	1	288	yes	—
744	C₂×C₃×C₄	C₂²×C₈×C₃₂	1	288	yes	—
745	C₂×C₃×C₄	C₂×C₄²×C₃₂	1	72	yes	—
746	C₂×C₃×C₄	C₂³×C₄×C₃₂	1	24	yes	—
747	C₂×C₃×C₄	C₈²×C₁₆	1	48	yes	—
748	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	18	yes	—
749	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	36	yes	—
750	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	36	yes	—
751	C₂×C₃×C₄	C₂³×C₈×C₁₆	1	12	yes	—
752	C₂×C₃×C₄	C₂²×C₄²×C₁₆	1	3	yes	—
753	C₂×C₃×C₄	C₂×C₈³	1	12	yes	—
754	C₂×C₃×C₄	C₂²×C₄×C₈²	1	3	yes	—
755	C₃×C₈	C₂²×C₈×C₃₂	1	384	yes	direct product factor
756	C₃×C₈	C₂×C₄×C₈×C₁₆	1	36	yes	—
757	C₃×C₈	C₂³×C₈×C₁₆	1	12	yes	—
758	C₃×C₈	C₂×C₈³	1	12	yes	—
759	C₃×C₈	C₂²×C₄×C₈²	1	4	yes	—
760	C₂⁴	C₃×C₄²×C₃₂	1	16	yes	—
761	C₂⁴	C₃×C₄×C₈×C₁₆	1	12	yes	—
762	C₂⁴	C₂×C₃×C₄²×C₁₆	1	3	yes	—
763	C₂²×C₄	C₂×C₃×C₈×C₃₂	1	384	yes	—
764	C₂²×C₄	C₃×C₄²×C₃₂	1	144	yes	—
765	C₂²×C₄	C₂²×C₃×C₄×C₃₂	1	144	yes	—
766	C₂²×C₄	C₃×C₄×C₈×C₁₆	1	36	yes	—
767	C₂²×C₄	C₃×C₄×C₈×C₁₆	1	48	yes	—
768	C₂²×C₄	C₃×C₄×C₈×C₁₆	1	72	yes	—
769	C₂²×C₄	C₂²×C₃×C₈×C₁₆	1	72	yes	—
770	C₂²×C₄	C₂×C₃×C₄²×C₁₆	1	3	yes	—
771	C₂²×C₄	C₂×C₃×C₄²×C₁₆	1	18	yes	—
772	C₂²×C₄	C₂×C₃×C₄²×C₁₆	1	18	yes	—
773	C₂²×C₄	C₂³×C₃×C₄×C₁₆	1	6	yes	—
774	C₂²×C₄	C₃×C₈³	1	16	yes	—
775	C₂²×C₄	C₂×C₃×C₄×C₈²	1	18	yes	—
776	C₂²×C₄	C₂²×C₃×C₄²×C₈	1	1	yes	characteristic
777	C₂×C₈	C₂×C₃×C₈×C₃₂	1	2304	yes	direct product factor
778	C₂×C₈	C₂²×C₃×C₄×C₃₂	1	384	yes	—
779	C₂×C₈	C₃×C₄×C₈×C₁₆	1	144	yes	—
780	C₂×C₈	C₂²×C₃×C₈×C₁₆	1	144	yes	—
781	C₂×C₈	C₂²×C₃×C₈×C₁₆	1	192	yes	—
782	C₂×C₈	C₂×C₃×C₄²×C₁₆	1	36	yes	—
783	C₂×C₈	C₂³×C₃×C₄×C₁₆	1	12	yes	—
784	C₂×C₈	C₃×C₈³	1	48	yes	—
785	C₂×C₈	C₂×C₃×C₄×C₈²	1	18	yes	—
786	C₂×C₈	C₂×C₃×C₄×C₈²	1	18	yes	—
787	C₂×C₈	C₂×C₃×C₄×C₈²	1	48	yes	—
788	C₂×C₈	C₂³×C₃×C₈²	1	6	yes	—
789	C₂×C₈	C₂²×C₃×C₄²×C₈	1	6	yes	—
790	C₄²	C₃×C₄²×C₃₂	1	96	yes	—
791	C₄²	C₂⁴×C₃×C₃₂	1	16	yes	—
792	C₄²	C₂²×C₃×C₄×C₃₂	1	144	yes	—
793	C₄²	C₃×C₄×C₈×C₁₆	1	72	yes	—
794	C₄²	C₂²×C₃×C₈×C₁₆	1	72	yes	—
795	C₄²	C₂×C₃×C₄²×C₁₆	1	18	yes	—
796	C₄²	C₂³×C₃×C₄×C₁₆	1	6	yes	—
797	C₄²	C₂×C₃×C₄×C₈²	1	18	yes	—
798	C₄²	C₂³×C₃×C₈²	1	6	yes	—
799	C₁₆	C₂²×C₃×C₈×C₁₆	1	192	yes	—
800	C₁₆	C₂×C₃×C₄×C₈²	1	48	yes	—
801	C₁₆	C₂³×C₃×C₈²	1	16	yes	—
802	C₂²×C₃	C₈²×C₃₂	1	64	yes	direct product factor
803	C₂²×C₃	C₂×C₄×C₈×C₃₂	1	72	yes	—
804	C₂²×C₃	C₂²×C₄²×C₃₂	1	4	yes	—
805	C₂²×C₃	C₂×C₈²×C₁₆	1	12	yes	—
806	C₂²×C₃	C₂²×C₄×C₈×C₁₆	1	3	yes	—
807	C₃×C₄	C₂×C₄×C₈×C₃₂	1	72	yes	—
808	C₃×C₄	C₂³×C₈×C₃₂	1	24	yes	—
809	C₃×C₄	C₂×C₈²×C₁₆	1	12	yes	—
810	C₃×C₄	C₂²×C₄×C₈×C₁₆	1	3	yes	—
811	C₃×C₄	C₂²×C₈³	1	1	yes	characteristic
812	C₂³	C₃×C₄×C₈×C₃₂	1	96	yes	—
813	C₂³	C₂×C₃×C₄²×C₃₂	1	24	yes	—
814	C₂³	C₃×C₈²×C₁₆	1	16	yes	—
815	C₂³	C₂×C₃×C₄×C₈×C₁₆	1	18	yes	—
816	C₂³	C₂²×C₃×C₄²×C₁₆	1	1	yes	characteristic
817	C₂×C₄	C₃×C₄×C₈×C₃₂	1	288	yes	—
818	C₂×C₄	C₂²×C₃×C₈×C₃₂	1	288	yes	—
819	C₂×C₄	C₂×C₃×C₄²×C₃₂	1	72	yes	—
820	C₂×C₄	C₂³×C₃×C₄×C₃₂	1	24	yes	—
821	C₂×C₄	C₃×C₈²×C₁₆	1	48	yes	—
822	C₂×C₄	C₂³×C₃×C₈×C₁₆	1	12	yes	—
823	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	18	yes	—
824	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	36	yes	—
825	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	36	yes	—
826	C₂×C₄	C₂²×C₃×C₄²×C₁₆	1	3	yes	—
827	C₂×C₄	C₂×C₃×C₈³	1	12	yes	—
828	C₂×C₄	C₂²×C₃×C₄×C₈²	1	3	yes	—
829	C₈	C₂²×C₃×C₈×C₃₂	1	384	yes	direct product factor
830	C₈	C₂³×C₃×C₈×C₁₆	1	12	yes	—
831	C₈	C₂×C₃×C₄×C₈×C₁₆	1	36	yes	—
832	C₈	C₂×C₃×C₈³	1	12	yes	—
833	C₈	C₂²×C₃×C₄×C₈²	1	4	yes	—
834	C₂×C₃	C₂×C₈²×C₃₂	1	24	yes	direct product factor
835	C₂×C₃	C₂²×C₄×C₈×C₃₂	1	6	yes	—
836	C₂×C₃	C₂²×C₈²×C₁₆	1	1	yes	characteristic
837	C₂²	C₃×C₈²×C₃₂	1	64	yes	direct product factor
838	C₂²	C₂×C₃×C₄×C₈×C₃₂	1	72	yes	—
839	C₂²	C₂²×C₃×C₄²×C₃₂	1	4	yes	—
840	C₂²	C₂×C₃×C₈²×C₁₆	1	12	yes	—
841	C₂²	C₂²×C₃×C₄×C₈×C₁₆	1	3	yes	—
842	C₄	C₂³×C₃×C₈×C₃₂	1	24	yes	—
843	C₄	C₂×C₃×C₄×C₈×C₃₂	1	72	yes	—
844	C₄	C₂×C₃×C₈²×C₁₆	1	12	yes	—
845	C₄	C₂²×C₃×C₄×C₈×C₁₆	1	3	yes	—
846	C₄	C₂²×C₃×C₈³	1	1	yes	characteristic
847	C₃	C₂²×C₈²×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
848	C₂	C₂×C₃×C₈²×C₃₂	1	24	yes	direct product factor
849	C₂	C₂²×C₃×C₄×C₈×C₃₂	1	6	yes	—
850	C₂	C₂²×C₃×C₈²×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²×C₁₆	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₄²×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₈²×C₃₂	C₂	direct (N × H)
4. C₂²×C₈²×C₃₂	C₃	direct (N × H)
14. C₃×C₈²×C₃₂	C₂²	direct (N × H)
17. C₂×C₈²×C₃₂	C₂×C₃	direct (N × H)
36. C₂²×C₃×C₈×C₃₂	C₈	direct (N × H)
49. C₈²×C₃₂	C₂²×C₃	direct (N × H)
90. C₂×C₃×C₈×C₃₂	C₂×C₈	direct (N × H)
110. C₂²×C₈×C₃₂	C₃×C₈	direct (N × H)
140. C₂²×C₃×C₈²	C₃₂	direct (N × H)
174. C₃×C₈×C₃₂	C₂²×C₈	direct (N × H)
207. C₂×C₈×C₃₂	C₂×C₃×C₈	direct (N × H)
247. C₂²×C₃×C₃₂	C₈²	direct (N × H)
278. C₂×C₃×C₈²	C₂×C₃₂	direct (N × H)
317. C₂²×C₈²	C₃×C₃₂	direct (N × H)
351. C₈×C₃₂	C₂²×C₃×C₈	direct (N × H)
411. C₂×C₃×C₃₂	C₂×C₈²	direct (N × H)
423. C₃×C₈²	C₂²×C₃₂	direct (N × H)
456. C₂²×C₃₂	C₃×C₈²	direct (N × H)
487. C₂×C₈²	C₂×C₃×C₃₂	direct (N × H)
509. C₂²×C₃×C₈	C₈×C₃₂	direct (N × H)
560. C₃×C₃₂	C₂²×C₈²	direct (N × H)
620. C₂×C₃₂	C₂×C₃×C₈²	direct (N × H)
632. C₈²	C₂²×C₃×C₃₂	direct (N × H)
654. C₂×C₃×C₈	C₂×C₈×C₃₂	direct (N × H)
686. C₂²×C₈	C₃×C₈×C₃₂	direct (N × H)
737. C₃₂	C₂²×C₃×C₈²	direct (N × H)
755. C₃×C₈	C₂²×C₈×C₃₂	direct (N × H)
777. C₂×C₈	C₂×C₃×C₈×C₃₂	direct (N × H)
802. C₂²×C₃	C₈²×C₃₂	direct (N × H)
829. C₈	C₂²×C₃×C₈×C₃₂	direct (N × H)
834. C₂×C₃	C₂×C₈²×C₃₂	direct (N × H)
837. C₂²	C₃×C₈²×C₃₂	direct (N × H)
847. C₃	C₂²×C₈²×C₃₂	direct (N × H)
848. C₂	C₂×C₃×C₈²×C₃₂	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×C₃×C₈²×C₁₆	2
C₂²×C₃×C₄×C₈×C₃₂	2
C₂×C₃×C₈²×C₃₂	2
C₂²×C₈²×C₃₂	3

Subgroups — C22×C3×C82×C32 #72201865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₈²×C₃₂ #72201865