Subgroups — C₂²×C₄²×C₉×C₃₂ #72196199

Order 18432.

35064 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₉×C₃₂	C₂	1	6	yes	maximal
3	C₂×C₄²×C₉×C₃₂	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₃×C₄²×C₃₂	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₈×C₉	C₄	1	1	yes	characteristic
6	C₂³×C₄×C₉×C₁₆	C₄	1	3	yes	—
7	C₂³×C₄×C₉×C₁₆	C₂²	1	3	yes	—
8	C₂×C₄²×C₉×C₁₆	C₄	1	12	yes	—
9	C₂×C₄²×C₉×C₁₆	C₂²	1	12	yes	—
10	C₂⁴×C₉×C₃₂	C₂²	1	4	yes	—
11	C₂²×C₄×C₉×C₃₂	C₄	1	96	yes	direct product factor
12	C₂²×C₄×C₉×C₃₂	C₂²	1	72	yes	—
13	C₄²×C₉×C₃₂	C₂²	1	64	yes	direct product factor
14	C₂²×C₃×C₄²×C₁₆	C₂×C₃	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₃₂	C₂×C₃	1	6	yes	—
16	C₂×C₃×C₄²×C₃₂	C₂×C₃	1	24	yes	—
17	C₂²×C₄³×C₉	C₈	1	1	yes	characteristic
18	C₂³×C₄×C₈×C₉	C₈	1	3	yes	—
19	C₂³×C₄×C₈×C₉	C₂×C₄	1	3	yes	—
20	C₂×C₄²×C₈×C₉	C₈	1	12	yes	—
21	C₂×C₄²×C₈×C₉	C₂×C₄	1	12	yes	—
22	C₂⁴×C₉×C₁₆	C₂×C₄	1	3	yes	—
23	C₂⁴×C₉×C₁₆	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₉×C₁₆	C₈	1	48	yes	—
25	C₂²×C₄×C₉×C₁₆	C₂×C₄	1	18	yes	—
26	C₂²×C₄×C₉×C₁₆	C₂×C₄	1	36	yes	—
27	C₂²×C₄×C₉×C₁₆	C₂×C₄	1	48	yes	—
28	C₂²×C₄×C₉×C₁₆	C₂³	1	18	yes	—
29	C₄²×C₉×C₁₆	C₂×C₄	1	48	yes	—
30	C₄²×C₉×C₁₆	C₂³	1	16	yes	—
31	C₂³×C₉×C₃₂	C₂×C₄	1	96	yes	—
32	C₂³×C₉×C₃₂	C₂³	1	24	yes	—
33	C₂×C₄×C₉×C₃₂	C₂×C₄	1	576	yes	direct product factor
34	C₂×C₄×C₉×C₃₂	C₂³	1	96	yes	—
35	C₂²×C₄²×C₃₂	C₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₃×C₄²×C₈	C₃×C₄	1	1	yes	characteristic
37	C₂³×C₃×C₄×C₁₆	C₃×C₄	1	3	yes	—
38	C₂³×C₃×C₄×C₁₆	C₂²×C₃	1	3	yes	—
39	C₂×C₃×C₄²×C₁₆	C₃×C₄	1	12	yes	—
40	C₂×C₃×C₄²×C₁₆	C₂²×C₃	1	12	yes	—
41	C₂²×C₃×C₄×C₃₂	C₃×C₄	1	96	yes	—
42	C₂²×C₃×C₄×C₃₂	C₂²×C₃	1	72	yes	—
43	C₂⁴×C₃×C₃₂	C₂²×C₃	1	4	yes	—
44	C₃×C₄²×C₃₂	C₂²×C₃	1	64	yes	—
45	C₂²×C₄²×C₁₆	C₂×C₉	1	1	yes	characteristic
46	C₂³×C₄×C₃₂	C₂×C₉	1	6	yes	—
47	C₂×C₄²×C₃₂	C₂×C₉	1	24	yes	direct product factor
48	C₂⁴×C₈×C₉	C₂×C₈	1	3	yes	—
49	C₂⁴×C₈×C₉	C₂²×C₄	1	1	yes	characteristic
50	C₂³×C₄²×C₉	C₁₆	1	4	yes	—
51	C₂³×C₄²×C₉	C₂×C₈	1	3	yes	—
52	C₂³×C₉×C₁₆	C₄²	1	24	yes	—
53	C₂³×C₉×C₁₆	C₂×C₈	1	48	yes	—
54	C₂³×C₉×C₁₆	C₂²×C₄	1	3	yes	—
55	C₂³×C₉×C₁₆	C₂²×C₄	1	18	yes	—
56	C₂³×C₉×C₁₆	C₂²×C₄	1	24	yes	—
57	C₂³×C₉×C₁₆	C₂⁴	1	3	yes	—
58	C₂²×C₄×C₈×C₉	C₁₆	1	48	yes	—
59	C₂²×C₄×C₈×C₉	C₄²	1	24	yes	—
60	C₂²×C₄×C₈×C₉	C₂×C₈	1	18	yes	—
61	C₂²×C₄×C₈×C₉	C₂×C₈	1	24	yes	—
62	C₂²×C₄×C₈×C₉	C₂×C₈	1	36	yes	—
63	C₂²×C₄×C₈×C₉	C₂²×C₄	1	18	yes	—
64	C₂×C₄³×C₉	C₁₆	1	12	yes	—
65	C₂×C₄³×C₉	C₂×C₈	1	12	yes	—
66	C₂²×C₉×C₃₂	C₄²	1	256	yes	direct product factor
67	C₂²×C₉×C₃₂	C₂²×C₄	1	288	yes	—
68	C₂²×C₉×C₃₂	C₂⁴	1	16	yes	—
69	C₂×C₄×C₉×C₁₆	C₄²	1	144	yes	—
70	C₂×C₄×C₉×C₁₆	C₂×C₈	1	288	yes	—
71	C₂×C₄×C₉×C₁₆	C₂²×C₄	1	36	yes	—
72	C₂×C₄×C₉×C₁₆	C₂²×C₄	1	48	yes	—
73	C₂×C₄×C₉×C₁₆	C₂²×C₄	1	144	yes	—
74	C₂×C₄×C₉×C₁₆	C₂⁴	1	12	yes	—
75	C₄²×C₈×C₉	C₂×C₈	1	48	yes	—
76	C₄²×C₈×C₉	C₂²×C₄	1	16	yes	—
77	C₄×C₉×C₃₂	C₂²×C₄	1	384	yes	direct product factor
78	C₂⁴×C₃×C₁₆	C₂×C₃×C₄	1	3	yes	—
79	C₂⁴×C₃×C₁₆	C₂³×C₃	1	1	yes	characteristic
80	C₂³×C₃×C₄×C₈	C₃×C₈	1	3	yes	—
81	C₂³×C₃×C₄×C₈	C₂×C₃×C₄	1	3	yes	—
82	C₂²×C₃×C₄³	C₃×C₈	1	1	yes	characteristic
83	C₂³×C₃×C₃₂	C₂×C₃×C₄	1	96	yes	—
84	C₂³×C₃×C₃₂	C₂³×C₃	1	24	yes	—
85	C₂²×C₃×C₄×C₁₆	C₃×C₈	1	48	yes	—
86	C₂²×C₃×C₄×C₁₆	C₂×C₃×C₄	1	18	yes	—
87	C₂²×C₃×C₄×C₁₆	C₂×C₃×C₄	1	36	yes	—
88	C₂²×C₃×C₄×C₁₆	C₂×C₃×C₄	1	48	yes	—
89	C₂²×C₃×C₄×C₁₆	C₂³×C₃	1	18	yes	—
90	C₂×C₃×C₄²×C₈	C₃×C₈	1	12	yes	—
91	C₂×C₃×C₄²×C₈	C₂×C₃×C₄	1	12	yes	—
92	C₂×C₃×C₄×C₃₂	C₂×C₃×C₄	1	576	yes	—
93	C₂×C₃×C₄×C₃₂	C₂³×C₃	1	96	yes	—
94	C₃×C₄²×C₁₆	C₂×C₃×C₄	1	48	yes	—
95	C₃×C₄²×C₁₆	C₂³×C₃	1	16	yes	—
96	C₂⁴×C₄×C₉	C₂×C₁₆	1	6	yes	—
97	C₂⁴×C₄×C₉	C₂²×C₈	1	1	yes	characteristic
98	C₂³×C₈×C₉	C₄×C₈	1	24	yes	—
99	C₂³×C₈×C₉	C₂×C₁₆	1	48	yes	—
100	C₂³×C₈×C₉	C₂×C₄²	1	12	yes	—
101	C₂³×C₈×C₉	C₂²×C₈	1	3	yes	—
102	C₂³×C₈×C₉	C₂²×C₈	1	12	yes	—
103	C₂³×C₈×C₉	C₂²×C₈	1	18	yes	—
104	C₂³×C₈×C₉	C₂³×C₄	1	3	yes	—
105	C₂²×C₄²×C₉	C₃₂	1	64	yes	direct product factor
106	C₂²×C₄²×C₉	C₄×C₈	1	24	yes	—
107	C₂²×C₄²×C₉	C₂×C₁₆	1	18	yes	—
108	C₂²×C₄²×C₉	C₂×C₁₆	1	24	yes	—
109	C₂²×C₄²×C₉	C₂×C₁₆	1	48	yes	—
110	C₂²×C₄²×C₉	C₂²×C₈	1	18	yes	—
111	C₂²×C₉×C₁₆	C₄×C₈	1	192	yes	—
112	C₂²×C₉×C₁₆	C₂×C₄²	1	36	yes	—
113	C₂²×C₉×C₁₆	C₂×C₄²	1	64	yes	—
114	C₂²×C₉×C₁₆	C₂×C₄²	1	72	yes	—
115	C₂²×C₉×C₁₆	C₂²×C₈	1	144	yes	—
116	C₂²×C₉×C₁₆	C₂³×C₄	1	3	yes	—
117	C₂²×C₉×C₁₆	C₂³×C₄	1	12	yes	—
118	C₂²×C₉×C₁₆	C₂³×C₄	1	36	yes	—
119	C₂²×C₉×C₁₆	C₂⁵	1	1	yes	characteristic
120	C₂×C₄×C₈×C₉	C₄×C₈	1	144	yes	—
121	C₂×C₄×C₈×C₉	C₂×C₁₆	1	288	yes	—
122	C₂×C₄×C₈×C₉	C₂×C₄²	1	72	yes	—
123	C₂×C₄×C₈×C₉	C₂²×C₈	1	36	yes	—
124	C₂×C₄×C₈×C₉	C₂²×C₈	1	48	yes	—
125	C₂×C₄×C₈×C₉	C₂²×C₈	1	72	yes	—
126	C₂×C₄×C₈×C₉	C₂³×C₄	1	12	yes	—
127	C₄³×C₉	C₂×C₁₆	1	48	yes	—
128	C₄³×C₉	C₂²×C₈	1	16	yes	—
129	C₂×C₉×C₃₂	C₂×C₄²	1	384	yes	direct product factor
130	C₂×C₉×C₃₂	C₂³×C₄	1	96	yes	—
131	C₄×C₉×C₁₆	C₂×C₄²	1	144	yes	—
132	C₄×C₉×C₁₆	C₂²×C₈	1	192	yes	—
133	C₄×C₉×C₁₆	C₂³×C₄	1	48	yes	—
134	C₂⁴×C₃₂	C₂²×C₉	1	4	yes	—
135	C₂³×C₄×C₁₆	C₄×C₉	1	3	yes	—
136	C₂³×C₄×C₁₆	C₂²×C₉	1	3	yes	—
137	C₂²×C₄²×C₈	C₄×C₉	1	1	yes	characteristic
138	C₂²×C₄×C₃₂	C₄×C₉	1	96	yes	direct product factor
139	C₂²×C₄×C₃₂	C₂²×C₉	1	72	yes	—
140	C₂×C₄²×C₁₆	C₄×C₉	1	12	yes	—
141	C₂×C₄²×C₁₆	C₂²×C₉	1	12	yes	—
142	C₄²×C₃₂	C₂²×C₉	1	64	yes	direct product factor
143	C₂⁴×C₃×C₈	C₂×C₃×C₈	1	3	yes	—
144	C₂⁴×C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
145	C₂³×C₃×C₄²	C₃×C₁₆	1	4	yes	—
146	C₂³×C₃×C₄²	C₂×C₃×C₈	1	3	yes	—
147	C₂³×C₃×C₁₆	C₃×C₄²	1	24	yes	—
148	C₂³×C₃×C₁₆	C₂×C₃×C₈	1	48	yes	—
149	C₂³×C₃×C₁₆	C₂²×C₃×C₄	1	3	yes	—
150	C₂³×C₃×C₁₆	C₂²×C₃×C₄	1	18	yes	—
151	C₂³×C₃×C₁₆	C₂²×C₃×C₄	1	24	yes	—
152	C₂³×C₃×C₁₆	C₂⁴×C₃	1	3	yes	—
153	C₂²×C₃×C₄×C₈	C₃×C₁₆	1	48	yes	—
154	C₂²×C₃×C₄×C₈	C₃×C₄²	1	24	yes	—
155	C₂²×C₃×C₄×C₈	C₂×C₃×C₈	1	18	yes	—
156	C₂²×C₃×C₄×C₈	C₂×C₃×C₈	1	24	yes	—
157	C₂²×C₃×C₄×C₈	C₂×C₃×C₈	1	36	yes	—
158	C₂²×C₃×C₄×C₈	C₂²×C₃×C₄	1	18	yes	—
159	C₂×C₃×C₄³	C₃×C₁₆	1	12	yes	—
160	C₂×C₃×C₄³	C₂×C₃×C₈	1	12	yes	—
161	C₂²×C₃×C₃₂	C₃×C₄²	1	256	yes	—
162	C₂²×C₃×C₃₂	C₂²×C₃×C₄	1	288	yes	—
163	C₂²×C₃×C₃₂	C₂⁴×C₃	1	16	yes	—
164	C₂×C₃×C₄×C₁₆	C₃×C₄²	1	144	yes	—
165	C₂×C₃×C₄×C₁₆	C₂×C₃×C₈	1	288	yes	—
166	C₂×C₃×C₄×C₁₆	C₂²×C₃×C₄	1	36	yes	—
167	C₂×C₃×C₄×C₁₆	C₂²×C₃×C₄	1	48	yes	—
168	C₂×C₃×C₄×C₁₆	C₂²×C₃×C₄	1	144	yes	—
169	C₂×C₃×C₄×C₁₆	C₂⁴×C₃	1	12	yes	—
170	C₃×C₄²×C₈	C₂×C₃×C₈	1	48	yes	—
171	C₃×C₄²×C₈	C₂²×C₃×C₄	1	16	yes	—
172	C₃×C₄×C₃₂	C₂²×C₃×C₄	1	384	yes	—
173	C₂⁵×C₉	C₂²×C₁₆	1	1	yes	characteristic
174	C₂³×C₄×C₉	C₄×C₁₆	1	48	yes	—
175	C₂³×C₄×C₉	C₂×C₃₂	1	96	yes	—
176	C₂³×C₄×C₉	C₂×C₄×C₈	1	12	yes	—
177	C₂³×C₄×C₉	C₂²×C₁₆	1	3	yes	—
178	C₂³×C₄×C₉	C₂²×C₁₆	1	12	yes	—
179	C₂³×C₄×C₉	C₂²×C₁₆	1	36	yes	—
180	C₂³×C₄×C₉	C₂³×C₈	1	3	yes	—
181	C₂²×C₈×C₉	C₄×C₁₆	1	192	yes	—
182	C₂²×C₈×C₉	C₄³	1	16	yes	—
183	C₂²×C₈×C₉	C₂×C₄×C₈	1	36	yes	—
184	C₂²×C₈×C₉	C₂×C₄×C₈	1	48	yes	—
185	C₂²×C₈×C₉	C₂×C₄×C₈	1	72	yes	—
186	C₂²×C₈×C₉	C₂²×C₁₆	1	144	yes	—
187	C₂²×C₈×C₉	C₂²×C₄²	1	18	yes	—
188	C₂²×C₈×C₉	C₂³×C₈	1	3	yes	—
189	C₂²×C₈×C₉	C₂³×C₈	1	12	yes	—
190	C₂²×C₈×C₉	C₂³×C₈	1	18	yes	—
191	C₂²×C₈×C₉	C₂⁴×C₄	1	1	yes	characteristic
192	C₂×C₄²×C₉	C₄×C₁₆	1	144	yes	—
193	C₂×C₄²×C₉	C₂×C₃₂	1	384	yes	direct product factor
194	C₂×C₄²×C₉	C₂×C₄×C₈	1	72	yes	—
195	C₂×C₄²×C₉	C₂²×C₁₆	1	36	yes	—
196	C₂×C₄²×C₉	C₂²×C₁₆	1	64	yes	—
197	C₂×C₄²×C₉	C₂²×C₁₆	1	72	yes	—
198	C₂×C₄²×C₉	C₂³×C₈	1	12	yes	—
199	C₂×C₉×C₁₆	C₄³	1	48	yes	—
200	C₂×C₉×C₁₆	C₂×C₄×C₈	1	288	yes	—
201	C₂×C₉×C₁₆	C₂²×C₄²	1	18	yes	—
202	C₂×C₉×C₁₆	C₂²×C₄²	1	24	yes	—
203	C₂×C₉×C₁₆	C₂²×C₄²	1	48	yes	—
204	C₂×C₉×C₁₆	C₂³×C₈	1	48	yes	—
205	C₂×C₉×C₁₆	C₂⁴×C₄	1	6	yes	—
206	C₄×C₈×C₉	C₂×C₄×C₈	1	144	yes	—
207	C₄×C₈×C₉	C₂²×C₁₆	1	192	yes	—
208	C₄×C₈×C₉	C₂²×C₄²	1	24	yes	—
209	C₄×C₈×C₉	C₂³×C₈	1	24	yes	—
210	C₉×C₃₂	C₂²×C₄²	1	64	yes	direct product factor
211	C₂⁴×C₁₆	C₂×C₄×C₉	1	3	yes	—
212	C₂⁴×C₁₆	C₂³×C₉	1	1	yes	characteristic
213	C₂³×C₄×C₈	C₈×C₉	1	3	yes	—
214	C₂³×C₄×C₈	C₂×C₄×C₉	1	3	yes	—
215	C₂²×C₄³	C₈×C₉	1	1	yes	characteristic
216	C₂³×C₃₂	C₂×C₄×C₉	1	96	yes	—
217	C₂³×C₃₂	C₂³×C₉	1	24	yes	—
218	C₂²×C₄×C₁₆	C₈×C₉	1	48	yes	—
219	C₂²×C₄×C₁₆	C₂×C₄×C₉	1	18	yes	—
220	C₂²×C₄×C₁₆	C₂×C₄×C₉	1	36	yes	—
221	C₂²×C₄×C₁₆	C₂×C₄×C₉	1	48	yes	—
222	C₂²×C₄×C₁₆	C₂³×C₉	1	18	yes	—
223	C₂×C₄²×C₈	C₈×C₉	1	12	yes	—
224	C₂×C₄²×C₈	C₂×C₄×C₉	1	12	yes	—
225	C₂×C₄×C₃₂	C₂×C₄×C₉	1	576	yes	direct product factor
226	C₂×C₄×C₃₂	C₂³×C₉	1	96	yes	—
227	C₄²×C₁₆	C₂×C₄×C₉	1	48	yes	—
228	C₄²×C₁₆	C₂³×C₉	1	16	yes	—
229	C₂⁴×C₃×C₄	C₂×C₃×C₁₆	1	6	yes	—
230	C₂⁴×C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
231	C₂³×C₃×C₈	C₃×C₄×C₈	1	24	yes	—
232	C₂³×C₃×C₈	C₂×C₃×C₁₆	1	48	yes	—
233	C₂³×C₃×C₈	C₂×C₃×C₄²	1	12	yes	—
234	C₂³×C₃×C₈	C₂²×C₃×C₈	1	3	yes	—
235	C₂³×C₃×C₈	C₂²×C₃×C₈	1	12	yes	—
236	C₂³×C₃×C₈	C₂²×C₃×C₈	1	18	yes	—
237	C₂³×C₃×C₈	C₂³×C₃×C₄	1	3	yes	—
238	C₂²×C₃×C₄²	C₃×C₃₂	1	64	yes	—
239	C₂²×C₃×C₄²	C₃×C₄×C₈	1	24	yes	—
240	C₂²×C₃×C₄²	C₂×C₃×C₁₆	1	18	yes	—
241	C₂²×C₃×C₄²	C₂×C₃×C₁₆	1	24	yes	—
242	C₂²×C₃×C₄²	C₂×C₃×C₁₆	1	48	yes	—
243	C₂²×C₃×C₄²	C₂²×C₃×C₈	1	18	yes	—
244	C₂²×C₃×C₁₆	C₃×C₄×C₈	1	192	yes	—
245	C₂²×C₃×C₁₆	C₂×C₃×C₄²	1	36	yes	—
246	C₂²×C₃×C₁₆	C₂×C₃×C₄²	1	64	yes	—
247	C₂²×C₃×C₁₆	C₂×C₃×C₄²	1	72	yes	—
248	C₂²×C₃×C₁₆	C₂²×C₃×C₈	1	144	yes	—
249	C₂²×C₃×C₁₆	C₂³×C₃×C₄	1	3	yes	—
250	C₂²×C₃×C₁₆	C₂³×C₃×C₄	1	12	yes	—
251	C₂²×C₃×C₁₆	C₂³×C₃×C₄	1	36	yes	—
252	C₂²×C₃×C₁₆	C₂⁵×C₃	1	1	yes	characteristic
253	C₂×C₃×C₄×C₈	C₃×C₄×C₈	1	144	yes	—
254	C₂×C₃×C₄×C₈	C₂×C₃×C₁₆	1	288	yes	—
255	C₂×C₃×C₄×C₈	C₂×C₃×C₄²	1	72	yes	—
256	C₂×C₃×C₄×C₈	C₂²×C₃×C₈	1	36	yes	—
257	C₂×C₃×C₄×C₈	C₂²×C₃×C₈	1	48	yes	—
258	C₂×C₃×C₄×C₈	C₂²×C₃×C₈	1	72	yes	—
259	C₂×C₃×C₄×C₈	C₂³×C₃×C₄	1	12	yes	—
260	C₃×C₄³	C₂×C₃×C₁₆	1	48	yes	—
261	C₃×C₄³	C₂²×C₃×C₈	1	16	yes	—
262	C₂×C₃×C₃₂	C₂×C₃×C₄²	1	384	yes	—
263	C₂×C₃×C₃₂	C₂³×C₃×C₄	1	96	yes	—
264	C₃×C₄×C₁₆	C₂×C₃×C₄²	1	144	yes	—
265	C₃×C₄×C₁₆	C₂²×C₃×C₈	1	192	yes	—
266	C₃×C₄×C₁₆	C₂³×C₃×C₄	1	48	yes	—
267	C₂⁴×C₉	C₂×C₄×C₁₆	1	12	yes	—
268	C₂⁴×C₉	C₂²×C₃₂	1	16	yes	—
269	C₂⁴×C₉	C₂³×C₁₆	1	3	yes	—
270	C₂²×C₄×C₉	C₄×C₃₂	1	384	yes	direct product factor
271	C₂²×C₄×C₉	C₄²×C₈	1	16	yes	—
272	C₂²×C₄×C₉	C₂×C₄×C₁₆	1	36	yes	—
273	C₂²×C₄×C₉	C₂×C₄×C₁₆	1	48	yes	—
274	C₂²×C₄×C₉	C₂×C₄×C₁₆	1	144	yes	—
275	C₂²×C₄×C₉	C₂²×C₃₂	1	288	yes	—
276	C₂²×C₄×C₉	C₂²×C₄×C₈	1	18	yes	—
277	C₂²×C₄×C₉	C₂³×C₁₆	1	3	yes	—
278	C₂²×C₄×C₉	C₂³×C₁₆	1	18	yes	—
279	C₂²×C₄×C₉	C₂³×C₁₆	1	24	yes	—
280	C₂²×C₄×C₉	C₂⁴×C₈	1	1	yes	characteristic
281	C₂×C₈×C₉	C₄²×C₈	1	48	yes	—
282	C₂×C₈×C₉	C₂×C₄×C₁₆	1	288	yes	—
283	C₂×C₈×C₉	C₂×C₄³	1	12	yes	—
284	C₂×C₈×C₉	C₂²×C₄×C₈	1	18	yes	—
285	C₂×C₈×C₉	C₂²×C₄×C₈	1	24	yes	—
286	C₂×C₈×C₉	C₂²×C₄×C₈	1	36	yes	—
287	C₂×C₈×C₉	C₂³×C₁₆	1	48	yes	—
288	C₂×C₈×C₉	C₂³×C₄²	1	3	yes	—
289	C₂×C₈×C₉	C₂⁴×C₈	1	3	yes	—
290	C₄²×C₉	C₂×C₄×C₁₆	1	144	yes	—
291	C₄²×C₉	C₂²×C₃₂	1	256	yes	direct product factor
292	C₄²×C₉	C₂²×C₄×C₈	1	24	yes	—
293	C₄²×C₉	C₂³×C₁₆	1	24	yes	—
294	C₉×C₁₆	C₂×C₄³	1	12	yes	—
295	C₉×C₁₆	C₂²×C₄×C₈	1	48	yes	—
296	C₉×C₁₆	C₂³×C₄²	1	4	yes	—
297	C₂⁴×C₈	C₂×C₈×C₉	1	3	yes	—
298	C₂⁴×C₈	C₂²×C₄×C₉	1	1	yes	characteristic
299	C₂³×C₄²	C₉×C₁₆	1	4	yes	—
300	C₂³×C₄²	C₂×C₈×C₉	1	3	yes	—
301	C₂³×C₁₆	C₄²×C₉	1	24	yes	—
302	C₂³×C₁₆	C₂×C₈×C₉	1	48	yes	—
303	C₂³×C₁₆	C₂²×C₄×C₉	1	3	yes	—
304	C₂³×C₁₆	C₂²×C₄×C₉	1	18	yes	—
305	C₂³×C₁₆	C₂²×C₄×C₉	1	24	yes	—
306	C₂³×C₁₆	C₂⁴×C₉	1	3	yes	—
307	C₂²×C₄×C₈	C₉×C₁₆	1	48	yes	—
308	C₂²×C₄×C₈	C₄²×C₉	1	24	yes	—
309	C₂²×C₄×C₈	C₂×C₈×C₉	1	18	yes	—
310	C₂²×C₄×C₈	C₂×C₈×C₉	1	24	yes	—
311	C₂²×C₄×C₈	C₂×C₈×C₉	1	36	yes	—
312	C₂²×C₄×C₈	C₂²×C₄×C₉	1	18	yes	—
313	C₂×C₄³	C₉×C₁₆	1	12	yes	—
314	C₂×C₄³	C₂×C₈×C₉	1	12	yes	—
315	C₂²×C₃₂	C₄²×C₉	1	256	yes	direct product factor
316	C₂²×C₃₂	C₂²×C₄×C₉	1	288	yes	—
317	C₂²×C₃₂	C₂⁴×C₉	1	16	yes	—
318	C₂×C₄×C₁₆	C₄²×C₉	1	144	yes	—
319	C₂×C₄×C₁₆	C₂×C₈×C₉	1	288	yes	—
320	C₂×C₄×C₁₆	C₂²×C₄×C₉	1	36	yes	—
321	C₂×C₄×C₁₆	C₂²×C₄×C₉	1	48	yes	—
322	C₂×C₄×C₁₆	C₂²×C₄×C₉	1	144	yes	—
323	C₂×C₄×C₁₆	C₂⁴×C₉	1	12	yes	—
324	C₄²×C₈	C₂×C₈×C₉	1	48	yes	—
325	C₄²×C₈	C₂²×C₄×C₉	1	16	yes	—
326	C₄×C₃₂	C₂²×C₄×C₉	1	384	yes	direct product factor
327	C₂⁵×C₃	C₂²×C₃×C₁₆	1	1	yes	characteristic
328	C₂³×C₃×C₄	C₃×C₄×C₁₆	1	48	yes	—
329	C₂³×C₃×C₄	C₂×C₃×C₃₂	1	96	yes	—
330	C₂³×C₃×C₄	C₂×C₃×C₄×C₈	1	12	yes	—
331	C₂³×C₃×C₄	C₂²×C₃×C₁₆	1	3	yes	—
332	C₂³×C₃×C₄	C₂²×C₃×C₁₆	1	12	yes	—
333	C₂³×C₃×C₄	C₂²×C₃×C₁₆	1	36	yes	—
334	C₂³×C₃×C₄	C₂³×C₃×C₈	1	3	yes	—
335	C₂²×C₃×C₈	C₃×C₄×C₁₆	1	192	yes	—
336	C₂²×C₃×C₈	C₃×C₄³	1	16	yes	—
337	C₂²×C₃×C₈	C₂×C₃×C₄×C₈	1	36	yes	—
338	C₂²×C₃×C₈	C₂×C₃×C₄×C₈	1	48	yes	—
339	C₂²×C₃×C₈	C₂×C₃×C₄×C₈	1	72	yes	—
340	C₂²×C₃×C₈	C₂²×C₃×C₁₆	1	144	yes	—
341	C₂²×C₃×C₈	C₂²×C₃×C₄²	1	18	yes	—
342	C₂²×C₃×C₈	C₂³×C₃×C₈	1	3	yes	—
343	C₂²×C₃×C₈	C₂³×C₃×C₈	1	12	yes	—
344	C₂²×C₃×C₈	C₂³×C₃×C₈	1	18	yes	—
345	C₂²×C₃×C₈	C₂⁴×C₃×C₄	1	1	yes	characteristic
346	C₂×C₃×C₄²	C₃×C₄×C₁₆	1	144	yes	—
347	C₂×C₃×C₄²	C₂×C₃×C₃₂	1	384	yes	—
348	C₂×C₃×C₄²	C₂×C₃×C₄×C₈	1	72	yes	—
349	C₂×C₃×C₄²	C₂²×C₃×C₁₆	1	36	yes	—
350	C₂×C₃×C₄²	C₂²×C₃×C₁₆	1	64	yes	—
351	C₂×C₃×C₄²	C₂²×C₃×C₁₆	1	72	yes	—
352	C₂×C₃×C₄²	C₂³×C₃×C₈	1	12	yes	—
353	C₂×C₃×C₁₆	C₃×C₄³	1	48	yes	—
354	C₂×C₃×C₁₆	C₂×C₃×C₄×C₈	1	288	yes	—
355	C₂×C₃×C₁₆	C₂²×C₃×C₄²	1	18	yes	—
356	C₂×C₃×C₁₆	C₂²×C₃×C₄²	1	24	yes	—
357	C₂×C₃×C₁₆	C₂²×C₃×C₄²	1	48	yes	—
358	C₂×C₃×C₁₆	C₂³×C₃×C₈	1	48	yes	—
359	C₂×C₃×C₁₆	C₂⁴×C₃×C₄	1	6	yes	—
360	C₃×C₄×C₈	C₂×C₃×C₄×C₈	1	144	yes	—
361	C₃×C₄×C₈	C₂²×C₃×C₁₆	1	192	yes	—
362	C₃×C₄×C₈	C₂²×C₃×C₄²	1	24	yes	—
363	C₃×C₄×C₈	C₂³×C₃×C₈	1	24	yes	—
364	C₃×C₃₂	C₂²×C₃×C₄²	1	64	yes	—
365	C₂³×C₉	C₄²×C₁₆	1	16	yes	—
366	C₂³×C₉	C₂×C₄×C₃₂	1	96	yes	—
367	C₂³×C₉	C₂²×C₄×C₁₆	1	18	yes	—
368	C₂³×C₉	C₂³×C₃₂	1	24	yes	—
369	C₂³×C₉	C₂⁴×C₁₆	1	1	yes	characteristic
370	C₂×C₄×C₉	C₄²×C₁₆	1	48	yes	—
371	C₂×C₄×C₉	C₂×C₄×C₃₂	1	576	yes	direct product factor
372	C₂×C₄×C₉	C₂×C₄²×C₈	1	12	yes	—
373	C₂×C₄×C₉	C₂²×C₄×C₁₆	1	18	yes	—
374	C₂×C₄×C₉	C₂²×C₄×C₁₆	1	36	yes	—
375	C₂×C₄×C₉	C₂²×C₄×C₁₆	1	48	yes	—
376	C₂×C₄×C₉	C₂³×C₃₂	1	96	yes	—
377	C₂×C₄×C₉	C₂³×C₄×C₈	1	3	yes	—
378	C₂×C₄×C₉	C₂⁴×C₁₆	1	3	yes	—
379	C₈×C₉	C₂×C₄²×C₈	1	12	yes	—
380	C₈×C₉	C₂²×C₄×C₁₆	1	48	yes	—
381	C₈×C₉	C₂²×C₄³	1	1	yes	characteristic
382	C₈×C₉	C₂³×C₄×C₈	1	3	yes	—
383	C₂⁴×C₄	C₂×C₉×C₁₆	1	6	yes	—
384	C₂⁴×C₄	C₂²×C₈×C₉	1	1	yes	characteristic
385	C₂³×C₈	C₄×C₈×C₉	1	24	yes	—
386	C₂³×C₈	C₂×C₉×C₁₆	1	48	yes	—
387	C₂³×C₈	C₂×C₄²×C₉	1	12	yes	—
388	C₂³×C₈	C₂²×C₈×C₉	1	3	yes	—
389	C₂³×C₈	C₂²×C₈×C₉	1	12	yes	—
390	C₂³×C₈	C₂²×C₈×C₉	1	18	yes	—
391	C₂³×C₈	C₂³×C₄×C₉	1	3	yes	—
392	C₂²×C₄²	C₉×C₃₂	1	64	yes	direct product factor
393	C₂²×C₄²	C₄×C₈×C₉	1	24	yes	—
394	C₂²×C₄²	C₂×C₉×C₁₆	1	18	yes	—
395	C₂²×C₄²	C₂×C₉×C₁₆	1	24	yes	—
396	C₂²×C₄²	C₂×C₉×C₁₆	1	48	yes	—
397	C₂²×C₄²	C₂²×C₈×C₉	1	18	yes	—
398	C₂²×C₁₆	C₄×C₈×C₉	1	192	yes	—
399	C₂²×C₁₆	C₂×C₄²×C₉	1	36	yes	—
400	C₂²×C₁₆	C₂×C₄²×C₉	1	64	yes	—
401	C₂²×C₁₆	C₂×C₄²×C₉	1	72	yes	—
402	C₂²×C₁₆	C₂²×C₈×C₉	1	144	yes	—
403	C₂²×C₁₆	C₂³×C₄×C₉	1	3	yes	—
404	C₂²×C₁₆	C₂³×C₄×C₉	1	12	yes	—
405	C₂²×C₁₆	C₂³×C₄×C₉	1	36	yes	—
406	C₂²×C₁₆	C₂⁵×C₉	1	1	yes	characteristic
407	C₂×C₄×C₈	C₄×C₈×C₉	1	144	yes	—
408	C₂×C₄×C₈	C₂×C₉×C₁₆	1	288	yes	—
409	C₂×C₄×C₈	C₂×C₄²×C₉	1	72	yes	—
410	C₂×C₄×C₈	C₂²×C₈×C₉	1	36	yes	—
411	C₂×C₄×C₈	C₂²×C₈×C₉	1	48	yes	—
412	C₂×C₄×C₈	C₂²×C₈×C₉	1	72	yes	—
413	C₂×C₄×C₈	C₂³×C₄×C₉	1	12	yes	—
414	C₄³	C₂×C₉×C₁₆	1	48	yes	—
415	C₄³	C₂²×C₈×C₉	1	16	yes	—
416	C₂×C₃₂	C₂×C₄²×C₉	1	384	yes	direct product factor
417	C₂×C₃₂	C₂³×C₄×C₉	1	96	yes	—
418	C₄×C₁₆	C₂×C₄²×C₉	1	144	yes	—
419	C₄×C₁₆	C₂²×C₈×C₉	1	192	yes	—
420	C₄×C₁₆	C₂³×C₄×C₉	1	48	yes	—
421	C₂⁴×C₃	C₂×C₃×C₄×C₁₆	1	12	yes	—
422	C₂⁴×C₃	C₂²×C₃×C₃₂	1	16	yes	—
423	C₂⁴×C₃	C₂³×C₃×C₁₆	1	3	yes	—
424	C₂²×C₃×C₄	C₃×C₄×C₃₂	1	384	yes	—
425	C₂²×C₃×C₄	C₃×C₄²×C₈	1	16	yes	—
426	C₂²×C₃×C₄	C₂×C₃×C₄×C₁₆	1	36	yes	—
427	C₂²×C₃×C₄	C₂×C₃×C₄×C₁₆	1	48	yes	—
428	C₂²×C₃×C₄	C₂×C₃×C₄×C₁₆	1	144	yes	—
429	C₂²×C₃×C₄	C₂²×C₃×C₃₂	1	288	yes	—
430	C₂²×C₃×C₄	C₂²×C₃×C₄×C₈	1	18	yes	—
431	C₂²×C₃×C₄	C₂³×C₃×C₁₆	1	3	yes	—
432	C₂²×C₃×C₄	C₂³×C₃×C₁₆	1	18	yes	—
433	C₂²×C₃×C₄	C₂³×C₃×C₁₆	1	24	yes	—
434	C₂²×C₃×C₄	C₂⁴×C₃×C₈	1	1	yes	characteristic
435	C₂×C₃×C₈	C₃×C₄²×C₈	1	48	yes	—
436	C₂×C₃×C₈	C₂×C₃×C₄×C₁₆	1	288	yes	—
437	C₂×C₃×C₈	C₂×C₃×C₄³	1	12	yes	—
438	C₂×C₃×C₈	C₂²×C₃×C₄×C₈	1	18	yes	—
439	C₂×C₃×C₈	C₂²×C₃×C₄×C₈	1	24	yes	—
440	C₂×C₃×C₈	C₂²×C₃×C₄×C₈	1	36	yes	—
441	C₂×C₃×C₈	C₂³×C₃×C₁₆	1	48	yes	—
442	C₂×C₃×C₈	C₂³×C₃×C₄²	1	3	yes	—
443	C₂×C₃×C₈	C₂⁴×C₃×C₈	1	3	yes	—
444	C₃×C₄²	C₂×C₃×C₄×C₁₆	1	144	yes	—
445	C₃×C₄²	C₂²×C₃×C₃₂	1	256	yes	—
446	C₃×C₄²	C₂²×C₃×C₄×C₈	1	24	yes	—
447	C₃×C₄²	C₂³×C₃×C₁₆	1	24	yes	—
448	C₃×C₁₆	C₂×C₃×C₄³	1	12	yes	—
449	C₃×C₁₆	C₂²×C₃×C₄×C₈	1	48	yes	—
450	C₃×C₁₆	C₂³×C₃×C₄²	1	4	yes	—
451	C₂²×C₉	C₄²×C₃₂	1	64	yes	direct product factor
452	C₂²×C₉	C₂×C₄²×C₁₆	1	12	yes	—
453	C₂²×C₉	C₂²×C₄×C₃₂	1	72	yes	—
454	C₂²×C₉	C₂³×C₄×C₁₆	1	3	yes	—
455	C₂²×C₉	C₂⁴×C₃₂	1	4	yes	—
456	C₄×C₉	C₂×C₄²×C₁₆	1	12	yes	—
457	C₄×C₉	C₂²×C₄×C₃₂	1	96	yes	direct product factor
458	C₄×C₉	C₂²×C₄²×C₈	1	1	yes	characteristic
459	C₄×C₉	C₂³×C₄×C₁₆	1	3	yes	—
460	C₂⁵	C₂²×C₉×C₁₆	1	1	yes	characteristic
461	C₂³×C₄	C₄×C₉×C₁₆	1	48	yes	—
462	C₂³×C₄	C₂×C₉×C₃₂	1	96	yes	—
463	C₂³×C₄	C₂×C₄×C₈×C₉	1	12	yes	—
464	C₂³×C₄	C₂²×C₉×C₁₆	1	3	yes	—
465	C₂³×C₄	C₂²×C₉×C₁₆	1	12	yes	—
466	C₂³×C₄	C₂²×C₉×C₁₆	1	36	yes	—
467	C₂³×C₄	C₂³×C₈×C₉	1	3	yes	—
468	C₂²×C₈	C₄×C₉×C₁₆	1	192	yes	—
469	C₂²×C₈	C₄³×C₉	1	16	yes	—
470	C₂²×C₈	C₂×C₄×C₈×C₉	1	36	yes	—
471	C₂²×C₈	C₂×C₄×C₈×C₉	1	48	yes	—
472	C₂²×C₈	C₂×C₄×C₈×C₉	1	72	yes	—
473	C₂²×C₈	C₂²×C₉×C₁₆	1	144	yes	—
474	C₂²×C₈	C₂²×C₄²×C₉	1	18	yes	—
475	C₂²×C₈	C₂³×C₈×C₉	1	3	yes	—
476	C₂²×C₈	C₂³×C₈×C₉	1	12	yes	—
477	C₂²×C₈	C₂³×C₈×C₉	1	18	yes	—
478	C₂²×C₈	C₂⁴×C₄×C₉	1	1	yes	characteristic
479	C₂×C₄²	C₄×C₉×C₁₆	1	144	yes	—
480	C₂×C₄²	C₂×C₉×C₃₂	1	384	yes	direct product factor
481	C₂×C₄²	C₂×C₄×C₈×C₉	1	72	yes	—
482	C₂×C₄²	C₂²×C₉×C₁₆	1	36	yes	—
483	C₂×C₄²	C₂²×C₉×C₁₆	1	64	yes	—
484	C₂×C₄²	C₂²×C₉×C₁₆	1	72	yes	—
485	C₂×C₄²	C₂³×C₈×C₉	1	12	yes	—
486	C₂×C₁₆	C₄³×C₉	1	48	yes	—
487	C₂×C₁₆	C₂×C₄×C₈×C₉	1	288	yes	—
488	C₂×C₁₆	C₂²×C₄²×C₉	1	18	yes	—
489	C₂×C₁₆	C₂²×C₄²×C₉	1	24	yes	—
490	C₂×C₁₆	C₂²×C₄²×C₉	1	48	yes	—
491	C₂×C₁₆	C₂³×C₈×C₉	1	48	yes	—
492	C₂×C₁₆	C₂⁴×C₄×C₉	1	6	yes	—
493	C₄×C₈	C₂×C₄×C₈×C₉	1	144	yes	—
494	C₄×C₈	C₂²×C₉×C₁₆	1	192	yes	—
495	C₄×C₈	C₂²×C₄²×C₉	1	24	yes	—
496	C₄×C₈	C₂³×C₈×C₉	1	24	yes	—
497	C₃₂	C₂²×C₄²×C₉	1	64	yes	direct product factor
498	C₂³×C₃	C₃×C₄²×C₁₆	1	16	yes	—
499	C₂³×C₃	C₂×C₃×C₄×C₃₂	1	96	yes	—
500	C₂³×C₃	C₂²×C₃×C₄×C₁₆	1	18	yes	—
501	C₂³×C₃	C₂³×C₃×C₃₂	1	24	yes	—
502	C₂³×C₃	C₂⁴×C₃×C₁₆	1	1	yes	characteristic
503	C₂×C₃×C₄	C₃×C₄²×C₁₆	1	48	yes	—
504	C₂×C₃×C₄	C₂×C₃×C₄×C₃₂	1	576	yes	—
505	C₂×C₃×C₄	C₂×C₃×C₄²×C₈	1	12	yes	—
506	C₂×C₃×C₄	C₂²×C₃×C₄×C₁₆	1	18	yes	—
507	C₂×C₃×C₄	C₂²×C₃×C₄×C₁₆	1	36	yes	—
508	C₂×C₃×C₄	C₂²×C₃×C₄×C₁₆	1	48	yes	—
509	C₂×C₃×C₄	C₂³×C₃×C₃₂	1	96	yes	—
510	C₂×C₃×C₄	C₂³×C₃×C₄×C₈	1	3	yes	—
511	C₂×C₃×C₄	C₂⁴×C₃×C₁₆	1	3	yes	—
512	C₃×C₈	C₂×C₃×C₄²×C₈	1	12	yes	—
513	C₃×C₈	C₂²×C₃×C₄×C₁₆	1	48	yes	—
514	C₃×C₈	C₂²×C₃×C₄³	1	1	yes	characteristic
515	C₃×C₈	C₂³×C₃×C₄×C₈	1	3	yes	—
516	C₂×C₉	C₂×C₄²×C₃₂	1	24	yes	direct product factor
517	C₂×C₉	C₂³×C₄×C₃₂	1	6	yes	—
518	C₂×C₉	C₂²×C₄²×C₁₆	1	1	yes	characteristic
519	C₂⁴	C₂×C₄×C₉×C₁₆	1	12	yes	—
520	C₂⁴	C₂²×C₉×C₃₂	1	16	yes	—
521	C₂⁴	C₂³×C₉×C₁₆	1	3	yes	—
522	C₂²×C₄	C₄×C₉×C₃₂	1	384	yes	direct product factor
523	C₂²×C₄	C₄²×C₈×C₉	1	16	yes	—
524	C₂²×C₄	C₂×C₄×C₉×C₁₆	1	36	yes	—
525	C₂²×C₄	C₂×C₄×C₉×C₁₆	1	48	yes	—
526	C₂²×C₄	C₂×C₄×C₉×C₁₆	1	144	yes	—
527	C₂²×C₄	C₂²×C₉×C₃₂	1	288	yes	—
528	C₂²×C₄	C₂²×C₄×C₈×C₉	1	18	yes	—
529	C₂²×C₄	C₂³×C₉×C₁₆	1	3	yes	—
530	C₂²×C₄	C₂³×C₉×C₁₆	1	18	yes	—
531	C₂²×C₄	C₂³×C₉×C₁₆	1	24	yes	—
532	C₂²×C₄	C₂⁴×C₈×C₉	1	1	yes	characteristic
533	C₂×C₈	C₄²×C₈×C₉	1	48	yes	—
534	C₂×C₈	C₂×C₄×C₉×C₁₆	1	288	yes	—
535	C₂×C₈	C₂×C₄³×C₉	1	12	yes	—
536	C₂×C₈	C₂²×C₄×C₈×C₉	1	18	yes	—
537	C₂×C₈	C₂²×C₄×C₈×C₉	1	24	yes	—
538	C₂×C₈	C₂²×C₄×C₈×C₉	1	36	yes	—
539	C₂×C₈	C₂³×C₉×C₁₆	1	48	yes	—
540	C₂×C₈	C₂³×C₄²×C₉	1	3	yes	—
541	C₂×C₈	C₂⁴×C₈×C₉	1	3	yes	—
542	C₄²	C₂×C₄×C₉×C₁₆	1	144	yes	—
543	C₄²	C₂²×C₉×C₃₂	1	256	yes	direct product factor
544	C₄²	C₂²×C₄×C₈×C₉	1	24	yes	—
545	C₄²	C₂³×C₉×C₁₆	1	24	yes	—
546	C₁₆	C₂×C₄³×C₉	1	12	yes	—
547	C₁₆	C₂²×C₄×C₈×C₉	1	48	yes	—
548	C₁₆	C₂³×C₄²×C₉	1	4	yes	—
549	C₂²×C₃	C₃×C₄²×C₃₂	1	64	yes	—
550	C₂²×C₃	C₂⁴×C₃×C₃₂	1	4	yes	—
551	C₂²×C₃	C₂²×C₃×C₄×C₃₂	1	72	yes	—
552	C₂²×C₃	C₂×C₃×C₄²×C₁₆	1	12	yes	—
553	C₂²×C₃	C₂³×C₃×C₄×C₁₆	1	3	yes	—
554	C₃×C₄	C₂²×C₃×C₄×C₃₂	1	96	yes	—
555	C₃×C₄	C₂×C₃×C₄²×C₁₆	1	12	yes	—
556	C₃×C₄	C₂³×C₃×C₄×C₁₆	1	3	yes	—
557	C₃×C₄	C₂²×C₃×C₄²×C₈	1	1	yes	characteristic
558	C₉	C₂²×C₄²×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
559	C₂³	C₂×C₄×C₉×C₃₂	1	96	yes	—
560	C₂³	C₂³×C₉×C₃₂	1	24	yes	—
561	C₂³	C₄²×C₉×C₁₆	1	16	yes	—
562	C₂³	C₂²×C₄×C₉×C₁₆	1	18	yes	—
563	C₂³	C₂⁴×C₉×C₁₆	1	1	yes	characteristic
564	C₂×C₄	C₂×C₄×C₉×C₃₂	1	576	yes	direct product factor
565	C₂×C₄	C₂³×C₉×C₃₂	1	96	yes	—
566	C₂×C₄	C₄²×C₉×C₁₆	1	48	yes	—
567	C₂×C₄	C₂²×C₄×C₉×C₁₆	1	18	yes	—
568	C₂×C₄	C₂²×C₄×C₉×C₁₆	1	36	yes	—
569	C₂×C₄	C₂²×C₄×C₉×C₁₆	1	48	yes	—
570	C₂×C₄	C₂⁴×C₉×C₁₆	1	3	yes	—
571	C₂×C₄	C₂×C₄²×C₈×C₉	1	12	yes	—
572	C₂×C₄	C₂³×C₄×C₈×C₉	1	3	yes	—
573	C₈	C₂²×C₄×C₉×C₁₆	1	48	yes	—
574	C₈	C₂×C₄²×C₈×C₉	1	12	yes	—
575	C₈	C₂³×C₄×C₈×C₉	1	3	yes	—
576	C₈	C₂²×C₄³×C₉	1	1	yes	characteristic
577	C₂×C₃	C₂×C₃×C₄²×C₃₂	1	24	yes	—
578	C₂×C₃	C₂³×C₃×C₄×C₃₂	1	6	yes	—
579	C₂×C₃	C₂²×C₃×C₄²×C₁₆	1	1	yes	characteristic
580	C₂²	C₄²×C₉×C₃₂	1	64	yes	direct product factor
581	C₂²	C₂²×C₄×C₉×C₃₂	1	72	yes	—
582	C₂²	C₂⁴×C₉×C₃₂	1	4	yes	—
583	C₂²	C₂×C₄²×C₉×C₁₆	1	12	yes	—
584	C₂²	C₂³×C₄×C₉×C₁₆	1	3	yes	—
585	C₄	C₂²×C₄×C₉×C₃₂	1	96	yes	direct product factor
586	C₄	C₂×C₄²×C₉×C₁₆	1	12	yes	—
587	C₄	C₂³×C₄×C₉×C₁₆	1	3	yes	—
588	C₄	C₂²×C₄²×C₈×C₉	1	1	yes	characteristic
589	C₃	C₂²×C₃×C₄²×C₃₂	1	1	yes	characteristic
590	C₂	C₂×C₄²×C₉×C₃₂	1	24	yes	direct product factor
591	C₂	C₂³×C₄×C₉×C₃₂	1	6	yes	—
592	C₂	C₂²×C₄²×C₉×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₁₆	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₂²×C₃×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×C₄²×C₉×C₃₂	C₂	direct (N × H)
11. C₂²×C₄×C₉×C₃₂	C₄	direct (N × H)
13. C₄²×C₉×C₃₂	C₂²	direct (N × H)
33. C₂×C₄×C₉×C₃₂	C₂×C₄	direct (N × H)
35. C₂²×C₄²×C₃₂	C₉	direct (N × H)
47. C₂×C₄²×C₃₂	C₂×C₉	direct (N × H)
66. C₂²×C₉×C₃₂	C₄²	direct (N × H)
77. C₄×C₉×C₃₂	C₂²×C₄	direct (N × H)
105. C₂²×C₄²×C₉	C₃₂	direct (N × H)
129. C₂×C₉×C₃₂	C₂×C₄²	direct (N × H)
138. C₂²×C₄×C₃₂	C₄×C₉	direct (N × H)
142. C₄²×C₃₂	C₂²×C₉	direct (N × H)
193. C₂×C₄²×C₉	C₂×C₃₂	direct (N × H)
210. C₉×C₃₂	C₂²×C₄²	direct (N × H)
225. C₂×C₄×C₃₂	C₂×C₄×C₉	direct (N × H)
270. C₂²×C₄×C₉	C₄×C₃₂	direct (N × H)
291. C₄²×C₉	C₂²×C₃₂	direct (N × H)
315. C₂²×C₃₂	C₄²×C₉	direct (N × H)
326. C₄×C₃₂	C₂²×C₄×C₉	direct (N × H)
371. C₂×C₄×C₉	C₂×C₄×C₃₂	direct (N × H)
392. C₂²×C₄²	C₉×C₃₂	direct (N × H)
416. C₂×C₃₂	C₂×C₄²×C₉	direct (N × H)
451. C₂²×C₉	C₄²×C₃₂	direct (N × H)
457. C₄×C₉	C₂²×C₄×C₃₂	direct (N × H)
480. C₂×C₄²	C₂×C₉×C₃₂	direct (N × H)
497. C₃₂	C₂²×C₄²×C₉	direct (N × H)
516. C₂×C₉	C₂×C₄²×C₃₂	direct (N × H)
522. C₂²×C₄	C₄×C₉×C₃₂	direct (N × H)
543. C₄²	C₂²×C₉×C₃₂	direct (N × H)
558. C₉	C₂²×C₄²×C₃₂	direct (N × H)
564. C₂×C₄	C₂×C₄×C₉×C₃₂	direct (N × H)
580. C₂²	C₄²×C₉×C₃₂	direct (N × H)
585. C₄	C₂²×C₄×C₉×C₃₂	direct (N × H)
590. C₂	C₂×C₄²×C₉×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×C₄²×C₉×C₁₆	2
C₂³×C₄×C₉×C₃₂	2
C₂×C₄²×C₉×C₃₂	2
C₂²×C₃×C₄²×C₃₂	3

Subgroups — C22×C42×C9×C32 #72196199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄²×C₉×C₃₂ #72196199