Subgroups — C₂²×C₃×C₄²×C₈×C₉ #72192049

Order 13824.

65940 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄³×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×C₄×C₈×C₉	C₂	1	6	yes	maximal
3	C₂×C₃×C₄²×C₈×C₉	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₃²×C₄²×C₈	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₈×C₉	C₃	1	3	yes	maximal, direct product factor
6	C₂³×C₃×C₄²×C₉	C₄	1	4	yes	—
7	C₂³×C₃×C₄²×C₉	C₂²	1	3	yes	—
8	C₂×C₃×C₄³×C₉	C₄	1	12	yes	—
9	C₂×C₃×C₄³×C₉	C₂²	1	12	yes	—
10	C₂⁴×C₃×C₈×C₉	C₂²	1	4	yes	—
11	C₂²×C₃×C₄×C₈×C₉	C₄	1	96	yes	direct product factor
12	C₂²×C₃×C₄×C₈×C₉	C₂²	1	72	yes	—
13	C₃×C₄²×C₈×C₉	C₂²	1	64	yes	direct product factor
14	C₂²×C₄³×C₉	C₂×C₃	1	3	yes	—
15	C₂²×C₃²×C₄³	C₂×C₃	1	1	yes	characteristic
16	C₂³×C₃²×C₄×C₈	C₂×C₃	1	6	yes	—
17	C₂³×C₄×C₈×C₉	C₂×C₃	1	18	yes	—
18	C₂×C₃²×C₄²×C₈	C₂×C₃	1	24	yes	—
19	C₂×C₄²×C₈×C₉	C₂×C₃	1	72	yes	direct product factor
20	C₂²×C₃×C₄²×C₈	C₉	1	3	yes	direct product factor
21	C₂²×C₃×C₄²×C₈	C₃²	1	1	yes	characteristic
22	C₂⁴×C₃×C₄×C₉	C₂×C₄	1	6	yes	—
23	C₂⁴×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₂³×C₃×C₈×C₉	C₂×C₄	1	96	yes	—
25	C₂³×C₃×C₈×C₉	C₂³	1	24	yes	—
26	C₂²×C₃×C₄²×C₉	C₈	1	64	yes	direct product factor
27	C₂²×C₃×C₄²×C₉	C₂×C₄	1	18	yes	—
28	C₂²×C₃×C₄²×C₉	C₂×C₄	1	48	yes	—
29	C₂²×C₃×C₄²×C₉	C₂×C₄	1	48	yes	—
30	C₂²×C₃×C₄²×C₉	C₂³	1	18	yes	—
31	C₂×C₃×C₄×C₈×C₉	C₂×C₄	1	576	yes	direct product factor
32	C₂×C₃×C₄×C₈×C₉	C₂³	1	96	yes	—
33	C₃×C₄³×C₉	C₂×C₄	1	48	yes	—
34	C₃×C₄³×C₉	C₂³	1	16	yes	—
35	C₂⁴×C₃²×C₈	C₂²×C₃	1	4	yes	—
36	C₂³×C₃²×C₄²	C₃×C₄	1	4	yes	—
37	C₂³×C₃²×C₄²	C₂²×C₃	1	3	yes	—
38	C₂²×C₃²×C₄×C₈	C₃×C₄	1	96	yes	—
39	C₂²×C₃²×C₄×C₈	C₂²×C₃	1	72	yes	—
40	C₂×C₃²×C₄³	C₃×C₄	1	12	yes	—
41	C₂×C₃²×C₄³	C₂²×C₃	1	12	yes	—
42	C₃²×C₄²×C₈	C₂²×C₃	1	64	yes	—
43	C₂⁴×C₈×C₉	C₂²×C₃	1	12	yes	—
44	C₂³×C₄²×C₉	C₃×C₄	1	12	yes	—
45	C₂³×C₄²×C₉	C₂²×C₃	1	9	yes	—
46	C₂²×C₄×C₈×C₉	C₃×C₄	1	288	yes	direct product factor
47	C₂²×C₄×C₈×C₉	C₂²×C₃	1	216	yes	—
48	C₂×C₄³×C₉	C₃×C₄	1	36	yes	—
49	C₂×C₄³×C₉	C₂²×C₃	1	36	yes	—
50	C₄²×C₈×C₉	C₂²×C₃	1	192	yes	direct product factor
51	C₂⁵×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
52	C₂³×C₃×C₄×C₉	C₄²	1	48	yes	—
53	C₂³×C₃×C₄×C₉	C₂×C₈	1	96	yes	—
54	C₂³×C₃×C₄×C₉	C₂²×C₄	1	3	yes	—
55	C₂³×C₃×C₄×C₉	C₂²×C₄	1	24	yes	—
56	C₂³×C₃×C₄×C₉	C₂²×C₄	1	36	yes	—
57	C₂³×C₃×C₄×C₉	C₂⁴	1	3	yes	—
58	C₂²×C₃×C₈×C₉	C₄²	1	256	yes	direct product factor
59	C₂²×C₃×C₈×C₉	C₂²×C₄	1	288	yes	—
60	C₂²×C₃×C₈×C₉	C₂⁴	1	16	yes	—
61	C₂×C₃×C₄²×C₉	C₄²	1	144	yes	—
62	C₂×C₃×C₄²×C₉	C₂×C₈	1	384	yes	direct product factor
63	C₂×C₃×C₄²×C₉	C₂²×C₄	1	36	yes	—
64	C₂×C₃×C₄²×C₉	C₂²×C₄	1	64	yes	—
65	C₂×C₃×C₄²×C₉	C₂²×C₄	1	144	yes	—
66	C₂×C₃×C₄²×C₉	C₂⁴	1	12	yes	—
67	C₃×C₄×C₈×C₉	C₂²×C₄	1	384	yes	direct product factor
68	C₂³×C₃×C₄×C₈	C₂×C₉	1	18	yes	—
69	C₂³×C₃×C₄×C₈	C₂×C₃²	1	6	yes	—
70	C₂²×C₃×C₄³	C₂×C₉	1	3	yes	—
71	C₂²×C₃×C₄³	C₂×C₃²	1	1	yes	characteristic
72	C₂×C₃×C₄²×C₈	C₂×C₉	1	72	yes	direct product factor
73	C₂×C₃×C₄²×C₈	C₂×C₃²	1	24	yes	—
74	C₂⁴×C₃²×C₄	C₂×C₃×C₄	1	6	yes	—
75	C₂⁴×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
76	C₂³×C₃²×C₈	C₂×C₃×C₄	1	96	yes	—
77	C₂³×C₃²×C₈	C₂³×C₃	1	24	yes	—
78	C₂²×C₃²×C₄²	C₃×C₈	1	64	yes	—
79	C₂²×C₃²×C₄²	C₂×C₃×C₄	1	18	yes	—
80	C₂²×C₃²×C₄²	C₂×C₃×C₄	1	48	yes	—
81	C₂²×C₃²×C₄²	C₂×C₃×C₄	1	48	yes	—
82	C₂²×C₃²×C₄²	C₂³×C₃	1	18	yes	—
83	C₂⁴×C₄×C₉	C₂×C₃×C₄	1	18	yes	—
84	C₂⁴×C₄×C₉	C₂³×C₃	1	3	yes	—
85	C₂×C₃²×C₄×C₈	C₂×C₃×C₄	1	576	yes	—
86	C₂×C₃²×C₄×C₈	C₂³×C₃	1	96	yes	—
87	C₃²×C₄³	C₂×C₃×C₄	1	48	yes	—
88	C₃²×C₄³	C₂³×C₃	1	16	yes	—
89	C₂³×C₈×C₉	C₂×C₃×C₄	1	288	yes	—
90	C₂³×C₈×C₉	C₂³×C₃	1	72	yes	—
91	C₂²×C₄²×C₉	C₃×C₈	1	192	yes	direct product factor
92	C₂²×C₄²×C₉	C₂×C₃×C₄	1	54	yes	—
93	C₂²×C₄²×C₉	C₂×C₃×C₄	1	144	yes	—
94	C₂²×C₄²×C₉	C₂×C₃×C₄	1	144	yes	—
95	C₂²×C₄²×C₉	C₂³×C₃	1	54	yes	—
96	C₂×C₄×C₈×C₉	C₂×C₃×C₄	1	1728	yes	direct product factor
97	C₂×C₄×C₈×C₉	C₂³×C₃	1	288	yes	—
98	C₄³×C₉	C₂×C₃×C₄	1	144	yes	—
99	C₄³×C₉	C₂³×C₃	1	48	yes	—
100	C₂²×C₄²×C₈	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
101	C₂⁴×C₃×C₉	C₂×C₄²	1	12	yes	—
102	C₂⁴×C₃×C₉	C₂²×C₈	1	16	yes	—
103	C₂⁴×C₃×C₉	C₂³×C₄	1	3	yes	—
104	C₂²×C₃×C₄×C₉	C₄×C₈	1	384	yes	direct product factor
105	C₂²×C₃×C₄×C₉	C₂×C₄²	1	36	yes	—
106	C₂²×C₃×C₄×C₉	C₂×C₄²	1	64	yes	—
107	C₂²×C₃×C₄×C₉	C₂×C₄²	1	144	yes	—
108	C₂²×C₃×C₄×C₉	C₂²×C₈	1	288	yes	—
109	C₂²×C₃×C₄×C₉	C₂³×C₄	1	3	yes	—
110	C₂²×C₃×C₄×C₉	C₂³×C₄	1	24	yes	—
111	C₂²×C₃×C₄×C₉	C₂³×C₄	1	36	yes	—
112	C₂²×C₃×C₄×C₉	C₂⁵	1	1	yes	characteristic
113	C₂×C₃×C₈×C₉	C₂×C₄²	1	384	yes	direct product factor
114	C₂×C₃×C₈×C₉	C₂³×C₄	1	96	yes	—
115	C₃×C₄²×C₉	C₂×C₄²	1	144	yes	—
116	C₃×C₄²×C₉	C₂²×C₈	1	256	yes	direct product factor
117	C₃×C₄²×C₉	C₂³×C₄	1	48	yes	—
118	C₂⁴×C₃×C₈	C₂²×C₉	1	12	yes	—
119	C₂⁴×C₃×C₈	C₂²×C₃²	1	4	yes	—
120	C₂³×C₃×C₄²	C₄×C₉	1	12	yes	—
121	C₂³×C₃×C₄²	C₂²×C₉	1	9	yes	—
122	C₂³×C₃×C₄²	C₃²×C₄	1	4	yes	—
123	C₂³×C₃×C₄²	C₂²×C₃²	1	3	yes	—
124	C₂²×C₃×C₄×C₈	C₄×C₉	1	288	yes	direct product factor
125	C₂²×C₃×C₄×C₈	C₂²×C₉	1	216	yes	—
126	C₂²×C₃×C₄×C₈	C₃²×C₄	1	96	yes	—
127	C₂²×C₃×C₄×C₈	C₂²×C₃²	1	72	yes	—
128	C₂×C₃×C₄³	C₄×C₉	1	36	yes	—
129	C₂×C₃×C₄³	C₂²×C₉	1	36	yes	—
130	C₂×C₃×C₄³	C₃²×C₄	1	12	yes	—
131	C₂×C₃×C₄³	C₂²×C₃²	1	12	yes	—
132	C₃×C₄²×C₈	C₂²×C₉	1	192	yes	direct product factor
133	C₃×C₄²×C₈	C₂²×C₃²	1	64	yes	—
134	C₂⁵×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
135	C₂³×C₃²×C₄	C₃×C₄²	1	48	yes	—
136	C₂³×C₃²×C₄	C₂×C₃×C₈	1	96	yes	—
137	C₂³×C₃²×C₄	C₂²×C₃×C₄	1	3	yes	—
138	C₂³×C₃²×C₄	C₂²×C₃×C₄	1	24	yes	—
139	C₂³×C₃²×C₄	C₂²×C₃×C₄	1	36	yes	—
140	C₂³×C₃²×C₄	C₂⁴×C₃	1	3	yes	—
141	C₂⁵×C₉	C₂²×C₃×C₄	1	3	yes	—
142	C₂²×C₃²×C₈	C₃×C₄²	1	256	yes	—
143	C₂²×C₃²×C₈	C₂²×C₃×C₄	1	288	yes	—
144	C₂²×C₃²×C₈	C₂⁴×C₃	1	16	yes	—
145	C₂×C₃²×C₄²	C₃×C₄²	1	144	yes	—
146	C₂×C₃²×C₄²	C₂×C₃×C₈	1	384	yes	—
147	C₂×C₃²×C₄²	C₂²×C₃×C₄	1	36	yes	—
148	C₂×C₃²×C₄²	C₂²×C₃×C₄	1	64	yes	—
149	C₂×C₃²×C₄²	C₂²×C₃×C₄	1	144	yes	—
150	C₂×C₃²×C₄²	C₂⁴×C₃	1	12	yes	—
151	C₂³×C₄×C₉	C₃×C₄²	1	144	yes	—
152	C₂³×C₄×C₉	C₂×C₃×C₈	1	288	yes	—
153	C₂³×C₄×C₉	C₂²×C₃×C₄	1	9	yes	—
154	C₂³×C₄×C₉	C₂²×C₃×C₄	1	72	yes	—
155	C₂³×C₄×C₉	C₂²×C₃×C₄	1	108	yes	—
156	C₂³×C₄×C₉	C₂⁴×C₃	1	9	yes	—
157	C₃²×C₄×C₈	C₂²×C₃×C₄	1	384	yes	—
158	C₂²×C₈×C₉	C₃×C₄²	1	768	yes	direct product factor
159	C₂²×C₈×C₉	C₂²×C₃×C₄	1	864	yes	—
160	C₂²×C₈×C₉	C₂⁴×C₃	1	48	yes	—
161	C₂×C₄²×C₉	C₃×C₄²	1	432	yes	—
162	C₂×C₄²×C₉	C₂×C₃×C₈	1	1152	yes	direct product factor
163	C₂×C₄²×C₉	C₂²×C₃×C₄	1	108	yes	—
164	C₂×C₄²×C₉	C₂²×C₃×C₄	1	432	yes	—
165	C₂×C₄²×C₉	C₂²×C₃×C₄	1	192	yes	—
166	C₂×C₄²×C₉	C₂⁴×C₃	1	36	yes	—
167	C₄×C₈×C₉	C₂²×C₃×C₄	1	1152	yes	direct product factor
168	C₂³×C₄×C₈	C₂×C₃×C₉	1	6	yes	—
169	C₂²×C₄³	C₂×C₃×C₉	1	1	yes	characteristic
170	C₂×C₄²×C₈	C₂×C₃×C₉	1	24	yes	direct product factor
171	C₂³×C₃×C₉	C₄³	1	16	yes	—
172	C₂³×C₃×C₉	C₂×C₄×C₈	1	96	yes	—
173	C₂³×C₃×C₉	C₂²×C₄²	1	18	yes	—
174	C₂³×C₃×C₉	C₂³×C₈	1	24	yes	—
175	C₂³×C₃×C₉	C₂⁴×C₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₉	C₄³	1	48	yes	—
177	C₂×C₃×C₄×C₉	C₂×C₄×C₈	1	576	yes	direct product factor
178	C₂×C₃×C₄×C₉	C₂²×C₄²	1	18	yes	—
179	C₂×C₃×C₄×C₉	C₂²×C₄²	1	48	yes	—
180	C₂×C₃×C₄×C₉	C₂²×C₄²	1	48	yes	—
181	C₂×C₃×C₄×C₉	C₂³×C₈	1	96	yes	—
182	C₂×C₃×C₄×C₉	C₂⁴×C₄	1	6	yes	—
183	C₃×C₈×C₉	C₂²×C₄²	1	64	yes	direct product factor
184	C₂⁴×C₃×C₄	C₂×C₄×C₉	1	18	yes	—
185	C₂⁴×C₃×C₄	C₂³×C₉	1	3	yes	—
186	C₂⁴×C₃×C₄	C₂×C₃²×C₄	1	6	yes	—
187	C₂⁴×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
188	C₂³×C₃×C₈	C₂×C₄×C₉	1	288	yes	—
189	C₂³×C₃×C₈	C₂³×C₉	1	72	yes	—
190	C₂³×C₃×C₈	C₂×C₃²×C₄	1	96	yes	—
191	C₂³×C₃×C₈	C₂³×C₃²	1	24	yes	—
192	C₂²×C₃×C₄²	C₈×C₉	1	192	yes	direct product factor
193	C₂²×C₃×C₄²	C₂×C₄×C₉	1	54	yes	—
194	C₂²×C₃×C₄²	C₂×C₄×C₉	1	144	yes	—
195	C₂²×C₃×C₄²	C₂×C₄×C₉	1	144	yes	—
196	C₂²×C₃×C₄²	C₃²×C₈	1	64	yes	—
197	C₂²×C₃×C₄²	C₂³×C₉	1	54	yes	—
198	C₂²×C₃×C₄²	C₂×C₃²×C₄	1	18	yes	—
199	C₂²×C₃×C₄²	C₂×C₃²×C₄	1	48	yes	—
200	C₂²×C₃×C₄²	C₂×C₃²×C₄	1	48	yes	—
201	C₂²×C₃×C₄²	C₂³×C₃²	1	18	yes	—
202	C₂×C₃×C₄×C₈	C₂×C₄×C₉	1	1728	yes	direct product factor
203	C₂×C₃×C₄×C₈	C₂³×C₉	1	288	yes	—
204	C₂×C₃×C₄×C₈	C₂×C₃²×C₄	1	576	yes	—
205	C₂×C₃×C₄×C₈	C₂³×C₃²	1	96	yes	—
206	C₃×C₄³	C₂×C₄×C₉	1	144	yes	—
207	C₃×C₄³	C₂³×C₉	1	48	yes	—
208	C₃×C₄³	C₂×C₃²×C₄	1	48	yes	—
209	C₃×C₄³	C₂³×C₃²	1	16	yes	—
210	C₂⁴×C₃²	C₂×C₃×C₄²	1	12	yes	—
211	C₂⁴×C₃²	C₂²×C₃×C₈	1	16	yes	—
212	C₂⁴×C₃²	C₂³×C₃×C₄	1	3	yes	—
213	C₂²×C₃²×C₄	C₃×C₄×C₈	1	384	yes	—
214	C₂²×C₃²×C₄	C₂×C₃×C₄²	1	36	yes	—
215	C₂²×C₃²×C₄	C₂×C₃×C₄²	1	64	yes	—
216	C₂²×C₃²×C₄	C₂×C₃×C₄²	1	144	yes	—
217	C₂²×C₃²×C₄	C₂²×C₃×C₈	1	288	yes	—
218	C₂²×C₃²×C₄	C₂³×C₃×C₄	1	3	yes	—
219	C₂²×C₃²×C₄	C₂³×C₃×C₄	1	24	yes	—
220	C₂²×C₃²×C₄	C₂³×C₃×C₄	1	36	yes	—
221	C₂²×C₃²×C₄	C₂⁵×C₃	1	1	yes	characteristic
222	C₂⁴×C₉	C₂×C₃×C₄²	1	36	yes	—
223	C₂⁴×C₉	C₂²×C₃×C₈	1	48	yes	—
224	C₂⁴×C₉	C₂³×C₃×C₄	1	9	yes	—
225	C₂×C₃²×C₈	C₂×C₃×C₄²	1	384	yes	—
226	C₂×C₃²×C₈	C₂³×C₃×C₄	1	96	yes	—
227	C₃²×C₄²	C₂×C₃×C₄²	1	144	yes	—
228	C₃²×C₄²	C₂²×C₃×C₈	1	256	yes	—
229	C₃²×C₄²	C₂³×C₃×C₄	1	48	yes	—
230	C₂²×C₄×C₉	C₃×C₄×C₈	1	1152	yes	direct product factor
231	C₂²×C₄×C₉	C₂×C₃×C₄²	1	108	yes	—
232	C₂²×C₄×C₉	C₂×C₃×C₄²	1	432	yes	—
233	C₂²×C₄×C₉	C₂×C₃×C₄²	1	192	yes	—
234	C₂²×C₄×C₉	C₂²×C₃×C₈	1	864	yes	—
235	C₂²×C₄×C₉	C₂³×C₃×C₄	1	9	yes	—
236	C₂²×C₄×C₉	C₂³×C₃×C₄	1	72	yes	—
237	C₂²×C₄×C₉	C₂³×C₃×C₄	1	108	yes	—
238	C₂²×C₄×C₉	C₂⁵×C₃	1	3	yes	—
239	C₂×C₈×C₉	C₂×C₃×C₄²	1	1152	yes	direct product factor
240	C₂×C₈×C₉	C₂³×C₃×C₄	1	288	yes	—
241	C₄²×C₉	C₂×C₃×C₄²	1	432	yes	—
242	C₄²×C₉	C₂²×C₃×C₈	1	768	yes	direct product factor
243	C₄²×C₉	C₂³×C₃×C₄	1	144	yes	—
244	C₂⁴×C₈	C₂²×C₃×C₉	1	4	yes	—
245	C₂³×C₄²	C₃×C₄×C₉	1	4	yes	—
246	C₂³×C₄²	C₂²×C₃×C₉	1	3	yes	—
247	C₂²×C₄×C₈	C₃×C₄×C₉	1	96	yes	direct product factor
248	C₂²×C₄×C₈	C₂²×C₃×C₉	1	72	yes	—
249	C₂×C₄³	C₃×C₄×C₉	1	12	yes	—
250	C₂×C₄³	C₂²×C₃×C₉	1	12	yes	—
251	C₄²×C₈	C₂²×C₃×C₉	1	64	yes	direct product factor
252	C₂²×C₃×C₉	C₄²×C₈	1	64	yes	direct product factor
253	C₂²×C₃×C₉	C₂×C₄³	1	12	yes	—
254	C₂²×C₃×C₉	C₂²×C₄×C₈	1	72	yes	—
255	C₂²×C₃×C₉	C₂³×C₄²	1	3	yes	—
256	C₂²×C₃×C₉	C₂⁴×C₈	1	4	yes	—
257	C₃×C₄×C₉	C₂×C₄³	1	12	yes	—
258	C₃×C₄×C₉	C₂²×C₄×C₈	1	96	yes	direct product factor
259	C₃×C₄×C₉	C₂³×C₄²	1	4	yes	—
260	C₂⁵×C₃	C₂²×C₄×C₉	1	3	yes	—
261	C₂⁵×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
262	C₂³×C₃×C₄	C₄²×C₉	1	144	yes	—
263	C₂³×C₃×C₄	C₂×C₈×C₉	1	288	yes	—
264	C₂³×C₃×C₄	C₂²×C₄×C₉	1	9	yes	—
265	C₂³×C₃×C₄	C₂²×C₄×C₉	1	72	yes	—
266	C₂³×C₃×C₄	C₂²×C₄×C₉	1	108	yes	—
267	C₂³×C₃×C₄	C₃²×C₄²	1	48	yes	—
268	C₂³×C₃×C₄	C₂×C₃²×C₈	1	96	yes	—
269	C₂³×C₃×C₄	C₂⁴×C₉	1	9	yes	—
270	C₂³×C₃×C₄	C₂²×C₃²×C₄	1	3	yes	—
271	C₂³×C₃×C₄	C₂²×C₃²×C₄	1	24	yes	—
272	C₂³×C₃×C₄	C₂²×C₃²×C₄	1	36	yes	—
273	C₂³×C₃×C₄	C₂⁴×C₃²	1	3	yes	—
274	C₂²×C₃×C₈	C₄²×C₉	1	768	yes	direct product factor
275	C₂²×C₃×C₈	C₂²×C₄×C₉	1	864	yes	—
276	C₂²×C₃×C₈	C₃²×C₄²	1	256	yes	—
277	C₂²×C₃×C₈	C₂⁴×C₉	1	48	yes	—
278	C₂²×C₃×C₈	C₂²×C₃²×C₄	1	288	yes	—
279	C₂²×C₃×C₈	C₂⁴×C₃²	1	16	yes	—
280	C₂×C₃×C₄²	C₄²×C₉	1	432	yes	—
281	C₂×C₃×C₄²	C₂×C₈×C₉	1	1152	yes	direct product factor
282	C₂×C₃×C₄²	C₂²×C₄×C₉	1	108	yes	—
283	C₂×C₃×C₄²	C₂²×C₄×C₉	1	432	yes	—
284	C₂×C₃×C₄²	C₂²×C₄×C₉	1	192	yes	—
285	C₂×C₃×C₄²	C₃²×C₄²	1	144	yes	—
286	C₂×C₃×C₄²	C₂×C₃²×C₈	1	384	yes	—
287	C₂×C₃×C₄²	C₂⁴×C₉	1	36	yes	—
288	C₂×C₃×C₄²	C₂²×C₃²×C₄	1	36	yes	—
289	C₂×C₃×C₄²	C₂²×C₃²×C₄	1	64	yes	—
290	C₂×C₃×C₄²	C₂²×C₃²×C₄	1	144	yes	—
291	C₂×C₃×C₄²	C₂⁴×C₃²	1	12	yes	—
292	C₃×C₄×C₈	C₂²×C₄×C₉	1	1152	yes	direct product factor
293	C₃×C₄×C₈	C₂²×C₃²×C₄	1	384	yes	—
294	C₂³×C₃²	C₃×C₄³	1	16	yes	—
295	C₂³×C₃²	C₂×C₃×C₄×C₈	1	96	yes	—
296	C₂³×C₃²	C₂²×C₃×C₄²	1	18	yes	—
297	C₂³×C₃²	C₂³×C₃×C₈	1	24	yes	—
298	C₂³×C₃²	C₂⁴×C₃×C₄	1	1	yes	characteristic
299	C₂×C₃²×C₄	C₃×C₄³	1	48	yes	—
300	C₂×C₃²×C₄	C₂×C₃×C₄×C₈	1	576	yes	—
301	C₂×C₃²×C₄	C₂²×C₃×C₄²	1	18	yes	—
302	C₂×C₃²×C₄	C₂²×C₃×C₄²	1	48	yes	—
303	C₂×C₃²×C₄	C₂²×C₃×C₄²	1	48	yes	—
304	C₂×C₃²×C₄	C₂³×C₃×C₈	1	96	yes	—
305	C₂×C₃²×C₄	C₂⁴×C₃×C₄	1	6	yes	—
306	C₂³×C₉	C₃×C₄³	1	48	yes	—
307	C₂³×C₉	C₂×C₃×C₄×C₈	1	288	yes	—
308	C₂³×C₉	C₂²×C₃×C₄²	1	54	yes	—
309	C₂³×C₉	C₂³×C₃×C₈	1	72	yes	—
310	C₂³×C₉	C₂⁴×C₃×C₄	1	3	yes	—
311	C₃²×C₈	C₂²×C₃×C₄²	1	64	yes	—
312	C₂×C₄×C₉	C₃×C₄³	1	144	yes	—
313	C₂×C₄×C₉	C₂×C₃×C₄×C₈	1	1728	yes	direct product factor
314	C₂×C₄×C₉	C₂²×C₃×C₄²	1	54	yes	—
315	C₂×C₄×C₉	C₂²×C₃×C₄²	1	144	yes	—
316	C₂×C₄×C₉	C₂²×C₃×C₄²	1	144	yes	—
317	C₂×C₄×C₉	C₂³×C₃×C₈	1	288	yes	—
318	C₂×C₄×C₉	C₂⁴×C₃×C₄	1	18	yes	—
319	C₈×C₉	C₂²×C₃×C₄²	1	192	yes	direct product factor
320	C₂⁴×C₄	C₂×C₃×C₄×C₉	1	6	yes	—
321	C₂⁴×C₄	C₂³×C₃×C₉	1	1	yes	characteristic
322	C₂³×C₈	C₂×C₃×C₄×C₉	1	96	yes	—
323	C₂³×C₈	C₂³×C₃×C₉	1	24	yes	—
324	C₂²×C₄²	C₃×C₈×C₉	1	64	yes	direct product factor
325	C₂²×C₄²	C₂×C₃×C₄×C₉	1	18	yes	—
326	C₂²×C₄²	C₂×C₃×C₄×C₉	1	48	yes	—
327	C₂²×C₄²	C₂×C₃×C₄×C₉	1	48	yes	—
328	C₂²×C₄²	C₂³×C₃×C₉	1	18	yes	—
329	C₂×C₄×C₈	C₂×C₃×C₄×C₉	1	576	yes	direct product factor
330	C₂×C₄×C₈	C₂³×C₃×C₉	1	96	yes	—
331	C₄³	C₂×C₃×C₄×C₉	1	48	yes	—
332	C₄³	C₂³×C₃×C₉	1	16	yes	—
333	C₂×C₃×C₉	C₂×C₄²×C₈	1	24	yes	direct product factor
334	C₂×C₃×C₉	C₂²×C₄³	1	1	yes	characteristic
335	C₂×C₃×C₉	C₂³×C₄×C₈	1	6	yes	—
336	C₂⁴×C₃	C₂×C₄²×C₉	1	36	yes	—
337	C₂⁴×C₃	C₂²×C₈×C₉	1	48	yes	—
338	C₂⁴×C₃	C₂³×C₄×C₉	1	9	yes	—
339	C₂⁴×C₃	C₂×C₃²×C₄²	1	12	yes	—
340	C₂⁴×C₃	C₂²×C₃²×C₈	1	16	yes	—
341	C₂⁴×C₃	C₂³×C₃²×C₄	1	3	yes	—
342	C₂²×C₃×C₄	C₄×C₈×C₉	1	1152	yes	direct product factor
343	C₂²×C₃×C₄	C₂×C₄²×C₉	1	108	yes	—
344	C₂²×C₃×C₄	C₂×C₄²×C₉	1	432	yes	—
345	C₂²×C₃×C₄	C₂×C₄²×C₉	1	192	yes	—
346	C₂²×C₃×C₄	C₂²×C₈×C₉	1	864	yes	—
347	C₂²×C₃×C₄	C₃²×C₄×C₈	1	384	yes	—
348	C₂²×C₃×C₄	C₂³×C₄×C₉	1	9	yes	—
349	C₂²×C₃×C₄	C₂³×C₄×C₉	1	72	yes	—
350	C₂²×C₃×C₄	C₂³×C₄×C₉	1	108	yes	—
351	C₂²×C₃×C₄	C₂×C₃²×C₄²	1	36	yes	—
352	C₂²×C₃×C₄	C₂×C₃²×C₄²	1	64	yes	—
353	C₂²×C₃×C₄	C₂×C₃²×C₄²	1	144	yes	—
354	C₂²×C₃×C₄	C₂²×C₃²×C₈	1	288	yes	—
355	C₂²×C₃×C₄	C₂⁵×C₉	1	3	yes	—
356	C₂²×C₃×C₄	C₂³×C₃²×C₄	1	3	yes	—
357	C₂²×C₃×C₄	C₂³×C₃²×C₄	1	24	yes	—
358	C₂²×C₃×C₄	C₂³×C₃²×C₄	1	36	yes	—
359	C₂²×C₃×C₄	C₂⁵×C₃²	1	1	yes	characteristic
360	C₂×C₃×C₈	C₂×C₄²×C₉	1	1152	yes	direct product factor
361	C₂×C₃×C₈	C₂³×C₄×C₉	1	288	yes	—
362	C₂×C₃×C₈	C₂×C₃²×C₄²	1	384	yes	—
363	C₂×C₃×C₈	C₂³×C₃²×C₄	1	96	yes	—
364	C₃×C₄²	C₂×C₄²×C₉	1	432	yes	—
365	C₃×C₄²	C₂²×C₈×C₉	1	768	yes	direct product factor
366	C₃×C₄²	C₂³×C₄×C₉	1	144	yes	—
367	C₃×C₄²	C₂×C₃²×C₄²	1	144	yes	—
368	C₃×C₄²	C₂²×C₃²×C₈	1	256	yes	—
369	C₃×C₄²	C₂³×C₃²×C₄	1	48	yes	—
370	C₂²×C₃²	C₃×C₄²×C₈	1	64	yes	—
371	C₂²×C₃²	C₂×C₃×C₄³	1	12	yes	—
372	C₂²×C₃²	C₂²×C₃×C₄×C₈	1	72	yes	—
373	C₂²×C₃²	C₂³×C₃×C₄²	1	3	yes	—
374	C₂²×C₃²	C₂⁴×C₃×C₈	1	4	yes	—
375	C₃²×C₄	C₂×C₃×C₄³	1	12	yes	—
376	C₃²×C₄	C₂²×C₃×C₄×C₈	1	96	yes	—
377	C₃²×C₄	C₂³×C₃×C₄²	1	4	yes	—
378	C₂²×C₉	C₃×C₄²×C₈	1	192	yes	direct product factor
379	C₂²×C₉	C₂×C₃×C₄³	1	36	yes	—
380	C₂²×C₉	C₂²×C₃×C₄×C₈	1	216	yes	—
381	C₂²×C₉	C₂³×C₃×C₄²	1	9	yes	—
382	C₂²×C₉	C₂⁴×C₃×C₈	1	12	yes	—
383	C₄×C₉	C₂×C₃×C₄³	1	36	yes	—
384	C₄×C₉	C₂²×C₃×C₄×C₈	1	288	yes	direct product factor
385	C₄×C₉	C₂³×C₃×C₄²	1	12	yes	—
386	C₂⁵	C₂²×C₃×C₄×C₉	1	1	yes	characteristic
387	C₂³×C₄	C₃×C₄²×C₉	1	48	yes	—
388	C₂³×C₄	C₂×C₃×C₈×C₉	1	96	yes	—
389	C₂³×C₄	C₂²×C₃×C₄×C₉	1	3	yes	—
390	C₂³×C₄	C₂²×C₃×C₄×C₉	1	24	yes	—
391	C₂³×C₄	C₂²×C₃×C₄×C₉	1	36	yes	—
392	C₂³×C₄	C₂⁴×C₃×C₉	1	3	yes	—
393	C₂²×C₈	C₃×C₄²×C₉	1	256	yes	direct product factor
394	C₂²×C₈	C₂²×C₃×C₄×C₉	1	288	yes	—
395	C₂²×C₈	C₂⁴×C₃×C₉	1	16	yes	—
396	C₂×C₄²	C₃×C₄²×C₉	1	144	yes	—
397	C₂×C₄²	C₂×C₃×C₈×C₉	1	384	yes	direct product factor
398	C₂×C₄²	C₂²×C₃×C₄×C₉	1	36	yes	—
399	C₂×C₄²	C₂²×C₃×C₄×C₉	1	64	yes	—
400	C₂×C₄²	C₂²×C₃×C₄×C₉	1	144	yes	—
401	C₂×C₄²	C₂⁴×C₃×C₉	1	12	yes	—
402	C₄×C₈	C₂²×C₃×C₄×C₉	1	384	yes	direct product factor
403	C₃×C₉	C₂²×C₄²×C₈	1	1	yes	characteristic, direct product factor, Sylow
404	C₂³×C₃	C₄³×C₉	1	48	yes	—
405	C₂³×C₃	C₂×C₄×C₈×C₉	1	288	yes	—
406	C₂³×C₃	C₂²×C₄²×C₉	1	54	yes	—
407	C₂³×C₃	C₂³×C₈×C₉	1	72	yes	—
408	C₂³×C₃	C₃²×C₄³	1	16	yes	—
409	C₂³×C₃	C₂×C₃²×C₄×C₈	1	96	yes	—
410	C₂³×C₃	C₂⁴×C₄×C₉	1	3	yes	—
411	C₂³×C₃	C₂²×C₃²×C₄²	1	18	yes	—
412	C₂³×C₃	C₂³×C₃²×C₈	1	24	yes	—
413	C₂³×C₃	C₂⁴×C₃²×C₄	1	1	yes	characteristic
414	C₂×C₃×C₄	C₄³×C₉	1	144	yes	—
415	C₂×C₃×C₄	C₂×C₄×C₈×C₉	1	1728	yes	direct product factor
416	C₂×C₃×C₄	C₂²×C₄²×C₉	1	54	yes	—
417	C₂×C₃×C₄	C₂²×C₄²×C₉	1	144	yes	—
418	C₂×C₃×C₄	C₂²×C₄²×C₉	1	144	yes	—
419	C₂×C₃×C₄	C₂³×C₈×C₉	1	288	yes	—
420	C₂×C₃×C₄	C₃²×C₄³	1	48	yes	—
421	C₂×C₃×C₄	C₂×C₃²×C₄×C₈	1	576	yes	—
422	C₂×C₃×C₄	C₂⁴×C₄×C₉	1	18	yes	—
423	C₂×C₃×C₄	C₂²×C₃²×C₄²	1	18	yes	—
424	C₂×C₃×C₄	C₂²×C₃²×C₄²	1	48	yes	—
425	C₂×C₃×C₄	C₂²×C₃²×C₄²	1	48	yes	—
426	C₂×C₃×C₄	C₂³×C₃²×C₈	1	96	yes	—
427	C₂×C₃×C₄	C₂⁴×C₃²×C₄	1	6	yes	—
428	C₃×C₈	C₂²×C₄²×C₉	1	192	yes	direct product factor
429	C₃×C₈	C₂²×C₃²×C₄²	1	64	yes	—
430	C₂×C₃²	C₂×C₃×C₄²×C₈	1	24	yes	—
431	C₂×C₃²	C₂²×C₃×C₄³	1	1	yes	characteristic
432	C₂×C₃²	C₂³×C₃×C₄×C₈	1	6	yes	—
433	C₂×C₉	C₂×C₃×C₄²×C₈	1	72	yes	direct product factor
434	C₂×C₉	C₂²×C₃×C₄³	1	3	yes	—
435	C₂×C₉	C₂³×C₃×C₄×C₈	1	18	yes	—
436	C₂⁴	C₂×C₃×C₄²×C₉	1	12	yes	—
437	C₂⁴	C₂²×C₃×C₈×C₉	1	16	yes	—
438	C₂⁴	C₂³×C₃×C₄×C₉	1	3	yes	—
439	C₂²×C₄	C₃×C₄×C₈×C₉	1	384	yes	direct product factor
440	C₂²×C₄	C₂×C₃×C₄²×C₉	1	36	yes	—
441	C₂²×C₄	C₂×C₃×C₄²×C₉	1	64	yes	—
442	C₂²×C₄	C₂×C₃×C₄²×C₉	1	144	yes	—
443	C₂²×C₄	C₂²×C₃×C₈×C₉	1	288	yes	—
444	C₂²×C₄	C₂³×C₃×C₄×C₉	1	3	yes	—
445	C₂²×C₄	C₂³×C₃×C₄×C₉	1	24	yes	—
446	C₂²×C₄	C₂³×C₃×C₄×C₉	1	36	yes	—
447	C₂²×C₄	C₂⁵×C₃×C₉	1	1	yes	characteristic
448	C₂×C₈	C₂×C₃×C₄²×C₉	1	384	yes	direct product factor
449	C₂×C₈	C₂³×C₃×C₄×C₉	1	96	yes	—
450	C₄²	C₂×C₃×C₄²×C₉	1	144	yes	—
451	C₄²	C₂²×C₃×C₈×C₉	1	256	yes	direct product factor
452	C₄²	C₂³×C₃×C₄×C₉	1	48	yes	—
453	C₂²×C₃	C₄²×C₈×C₉	1	192	yes	direct product factor
454	C₂²×C₃	C₂×C₄³×C₉	1	36	yes	—
455	C₂²×C₃	C₂²×C₄×C₈×C₉	1	216	yes	—
456	C₂²×C₃	C₂³×C₄²×C₉	1	9	yes	—
457	C₂²×C₃	C₂⁴×C₈×C₉	1	12	yes	—
458	C₂²×C₃	C₃²×C₄²×C₈	1	64	yes	—
459	C₂²×C₃	C₂×C₃²×C₄³	1	12	yes	—
460	C₂²×C₃	C₂²×C₃²×C₄×C₈	1	72	yes	—
461	C₂²×C₃	C₂³×C₃²×C₄²	1	3	yes	—
462	C₂²×C₃	C₂⁴×C₃²×C₈	1	4	yes	—
463	C₃×C₄	C₂×C₄³×C₉	1	36	yes	—
464	C₃×C₄	C₂²×C₄×C₈×C₉	1	288	yes	direct product factor
465	C₃×C₄	C₂³×C₄²×C₉	1	12	yes	—
466	C₃×C₄	C₂×C₃²×C₄³	1	12	yes	—
467	C₃×C₄	C₂²×C₃²×C₄×C₈	1	96	yes	—
468	C₃×C₄	C₂³×C₃²×C₄²	1	4	yes	—
469	C₃²	C₂²×C₃×C₄²×C₈	1	1	yes	characteristic
470	C₉	C₂²×C₃×C₄²×C₈	1	3	yes	direct product factor
471	C₂³	C₃×C₄³×C₉	1	16	yes	—
472	C₂³	C₂×C₃×C₄×C₈×C₉	1	96	yes	—
473	C₂³	C₂²×C₃×C₄²×C₉	1	18	yes	—
474	C₂³	C₂³×C₃×C₈×C₉	1	24	yes	—
475	C₂³	C₂⁴×C₃×C₄×C₉	1	1	yes	characteristic
476	C₂×C₄	C₃×C₄³×C₉	1	48	yes	—
477	C₂×C₄	C₂×C₃×C₄×C₈×C₉	1	576	yes	direct product factor
478	C₂×C₄	C₂²×C₃×C₄²×C₉	1	18	yes	—
479	C₂×C₄	C₂²×C₃×C₄²×C₉	1	48	yes	—
480	C₂×C₄	C₂²×C₃×C₄²×C₉	1	48	yes	—
481	C₂×C₄	C₂³×C₃×C₈×C₉	1	96	yes	—
482	C₂×C₄	C₂⁴×C₃×C₄×C₉	1	6	yes	—
483	C₈	C₂²×C₃×C₄²×C₉	1	64	yes	direct product factor
484	C₂×C₃	C₂×C₄²×C₈×C₉	1	72	yes	direct product factor
485	C₂×C₃	C₂×C₃²×C₄²×C₈	1	24	yes	—
486	C₂×C₃	C₂³×C₄×C₈×C₉	1	18	yes	—
487	C₂×C₃	C₂³×C₃²×C₄×C₈	1	6	yes	—
488	C₂×C₃	C₂²×C₃²×C₄³	1	1	yes	characteristic
489	C₂×C₃	C₂²×C₄³×C₉	1	3	yes	—
490	C₂²	C₃×C₄²×C₈×C₉	1	64	yes	direct product factor
491	C₂²	C₂²×C₃×C₄×C₈×C₉	1	72	yes	—
492	C₂²	C₂⁴×C₃×C₈×C₉	1	4	yes	—
493	C₂²	C₂×C₃×C₄³×C₉	1	12	yes	—
494	C₂²	C₂³×C₃×C₄²×C₉	1	3	yes	—
495	C₄	C₂²×C₃×C₄×C₈×C₉	1	96	yes	direct product factor
496	C₄	C₂×C₃×C₄³×C₉	1	12	yes	—
497	C₄	C₂³×C₃×C₄²×C₉	1	4	yes	—
498	C₃	C₂²×C₄²×C₈×C₉	1	3	yes	direct product factor
499	C₃	C₂²×C₃²×C₄²×C₈	1	1	yes	characteristic
500	C₂	C₂×C₃×C₄²×C₈×C₉	1	24	yes	direct product factor
501	C₂	C₂³×C₃×C₄×C₈×C₉	1	6	yes	—
502	C₂	C₂²×C₃×C₄³×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₄	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₂²×C₃×C₄
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×C₄²×C₈×C₉	C₂	direct (N × H)
5. C₂²×C₄²×C₈×C₉	C₃	direct (N × H)
11. C₂²×C₃×C₄×C₈×C₉	C₄	direct (N × H)
13. C₃×C₄²×C₈×C₉	C₂²	direct (N × H)
19. C₂×C₄²×C₈×C₉	C₂×C₃	direct (N × H)
20. C₂²×C₃×C₄²×C₈	C₉	direct (N × H)
26. C₂²×C₃×C₄²×C₉	C₈	direct (N × H)
31. C₂×C₃×C₄×C₈×C₉	C₂×C₄	direct (N × H)
46. C₂²×C₄×C₈×C₉	C₃×C₄	direct (N × H)
50. C₄²×C₈×C₉	C₂²×C₃	direct (N × H)
58. C₂²×C₃×C₈×C₉	C₄²	direct (N × H)
62. C₂×C₃×C₄²×C₉	C₂×C₈	direct (N × H)
67. C₃×C₄×C₈×C₉	C₂²×C₄	direct (N × H)
72. C₂×C₃×C₄²×C₈	C₂×C₉	direct (N × H)
91. C₂²×C₄²×C₉	C₃×C₈	direct (N × H)
96. C₂×C₄×C₈×C₉	C₂×C₃×C₄	direct (N × H)
100. C₂²×C₄²×C₈	C₃×C₉	direct (N × H)
104. C₂²×C₃×C₄×C₉	C₄×C₈	direct (N × H)
113. C₂×C₃×C₈×C₉	C₂×C₄²	direct (N × H)
116. C₃×C₄²×C₉	C₂²×C₈	direct (N × H)
124. C₂²×C₃×C₄×C₈	C₄×C₉	direct (N × H)
132. C₃×C₄²×C₈	C₂²×C₉	direct (N × H)
158. C₂²×C₈×C₉	C₃×C₄²	direct (N × H)
162. C₂×C₄²×C₉	C₂×C₃×C₈	direct (N × H)
167. C₄×C₈×C₉	C₂²×C₃×C₄	direct (N × H)
170. C₂×C₄²×C₈	C₂×C₃×C₉	direct (N × H)
177. C₂×C₃×C₄×C₉	C₂×C₄×C₈	direct (N × H)
183. C₃×C₈×C₉	C₂²×C₄²	direct (N × H)
192. C₂²×C₃×C₄²	C₈×C₉	direct (N × H)
202. C₂×C₃×C₄×C₈	C₂×C₄×C₉	direct (N × H)
230. C₂²×C₄×C₉	C₃×C₄×C₈	direct (N × H)
239. C₂×C₈×C₉	C₂×C₃×C₄²	direct (N × H)
242. C₄²×C₉	C₂²×C₃×C₈	direct (N × H)
247. C₂²×C₄×C₈	C₃×C₄×C₉	direct (N × H)
251. C₄²×C₈	C₂²×C₃×C₉	direct (N × H)
252. C₂²×C₃×C₉	C₄²×C₈	direct (N × H)
258. C₃×C₄×C₉	C₂²×C₄×C₈	direct (N × H)
274. C₂²×C₃×C₈	C₄²×C₉	direct (N × H)
281. C₂×C₃×C₄²	C₂×C₈×C₉	direct (N × H)
292. C₃×C₄×C₈	C₂²×C₄×C₉	direct (N × H)
313. C₂×C₄×C₉	C₂×C₃×C₄×C₈	direct (N × H)
319. C₈×C₉	C₂²×C₃×C₄²	direct (N × H)
324. C₂²×C₄²	C₃×C₈×C₉	direct (N × H)
329. C₂×C₄×C₈	C₂×C₃×C₄×C₉	direct (N × H)
333. C₂×C₃×C₉	C₂×C₄²×C₈	direct (N × H)
342. C₂²×C₃×C₄	C₄×C₈×C₉	direct (N × H)
360. C₂×C₃×C₈	C₂×C₄²×C₉	direct (N × H)
365. C₃×C₄²	C₂²×C₈×C₉	direct (N × H)
378. C₂²×C₉	C₃×C₄²×C₈	direct (N × H)
384. C₄×C₉	C₂²×C₃×C₄×C₈	direct (N × H)
393. C₂²×C₈	C₃×C₄²×C₉	direct (N × H)
397. C₂×C₄²	C₂×C₃×C₈×C₉	direct (N × H)
402. C₄×C₈	C₂²×C₃×C₄×C₉	direct (N × H)
403. C₃×C₉	C₂²×C₄²×C₈	direct (N × H)
415. C₂×C₃×C₄	C₂×C₄×C₈×C₉	direct (N × H)
428. C₃×C₈	C₂²×C₄²×C₉	direct (N × H)
433. C₂×C₉	C₂×C₃×C₄²×C₈	direct (N × H)
439. C₂²×C₄	C₃×C₄×C₈×C₉	direct (N × H)
448. C₂×C₈	C₂×C₃×C₄²×C₉	direct (N × H)
451. C₄²	C₂²×C₃×C₈×C₉	direct (N × H)
453. C₂²×C₃	C₄²×C₈×C₉	direct (N × H)
464. C₃×C₄	C₂²×C₄×C₈×C₉	direct (N × H)
470. C₉	C₂²×C₃×C₄²×C₈	direct (N × H)
477. C₂×C₄	C₂×C₃×C₄×C₈×C₉	direct (N × H)
483. C₈	C₂²×C₃×C₄²×C₉	direct (N × H)
484. C₂×C₃	C₂×C₄²×C₈×C₉	direct (N × H)
490. C₂²	C₃×C₄²×C₈×C₉	direct (N × H)
495. C₄	C₂²×C₃×C₄×C₈×C₉	direct (N × H)
498. C₃	C₂²×C₄²×C₈×C₉	direct (N × H)
500. C₂	C₂×C₃×C₄²×C₈×C₉	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×C₄³×C₉	2
C₂³×C₃×C₄×C₈×C₉	2
C₂×C₃×C₄²×C₈×C₉	2
C₂²×C₃²×C₄²×C₈	3
C₂²×C₄²×C₈×C₉	3

Subgroups — C22×C3×C42×C8×C9 #72192049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄²×C₈×C₉ #72192049