Subgroups — C₂×C₃²×C₅²×C₈×C₉ #72209124

Order 32400.

4400 conjugacy classes of subgroups.

The subgroup lattice has 243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×C₅²×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₈×C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃³×C₅²×C₈	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅²×C₈×C₉	C₃	1	12	yes	maximal, direct product factor
5	C₂²×C₃²×C₅²×C₉	C₄	1	1	yes	characteristic
6	C₃²×C₄×C₅²×C₉	C₄	1	1	yes	characteristic
7	C₃²×C₄×C₅²×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₅×C₈×C₉	C₅	1	6	yes	maximal, direct product factor
9	C₂×C₃³×C₄×C₅²	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₄×C₅²×C₉	C₂×C₃	1	12	yes	—
11	C₃³×C₅²×C₈	C₂×C₃	1	2	yes	—
12	C₃×C₅²×C₈×C₉	C₂×C₃	1	24	yes	direct product factor
13	C₂×C₃²×C₅²×C₉	C₈	1	2	yes	direct product factor
14	C₂×C₃²×C₅²×C₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃²×C₅²×C₈	C₉	1	9	yes	direct product factor
16	C₂×C₃²×C₅²×C₈	C₃²	1	4	yes	—
17	C₂×C₅²×C₈×C₉	C₃²	1	9	yes	direct product factor
18	C₂×C₃²×C₄×C₅×C₉	C₂×C₅	1	6	yes	—
19	C₃²×C₅×C₈×C₉	C₂×C₅	1	12	yes	direct product factor
20	C₂²×C₃³×C₅²	C₃×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₅²×C₉	C₃×C₄	1	12	yes	—
22	C₃³×C₄×C₅²	C₃×C₄	1	1	yes	characteristic
23	C₃³×C₄×C₅²	C₂²×C₃	1	1	yes	characteristic
24	C₃×C₄×C₅²×C₉	C₃×C₄	1	12	yes	—
25	C₃×C₄×C₅²×C₉	C₂²×C₃	1	12	yes	—
26	C₂×C₃³×C₅×C₈	C₃×C₅	1	6	yes	—
27	C₂×C₃×C₅×C₈×C₉	C₃×C₅	1	72	yes	direct product factor
28	C₃²×C₅²×C₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃²×C₄×C₅²	C₂×C₉	1	9	yes	—
30	C₂×C₃²×C₄×C₅²	C₂×C₃²	1	4	yes	—
31	C₃²×C₅²×C₈	C₂×C₉	1	18	yes	direct product factor
32	C₃²×C₅²×C₈	C₂×C₃²	1	8	yes	—
33	C₂×C₄×C₅²×C₉	C₂×C₃²	1	9	yes	—
34	C₅²×C₈×C₉	C₂×C₃²	1	18	yes	direct product factor
35	C₂²×C₃²×C₅×C₉	C₄×C₅	1	6	yes	—
36	C₃²×C₄×C₅×C₉	C₄×C₅	1	6	yes	—
37	C₃²×C₄×C₅×C₉	C₂²×C₅	1	6	yes	—
38	C₂×C₃³×C₅²	C₃×C₈	1	2	yes	—
39	C₂×C₃³×C₅²	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂×C₃×C₅²×C₉	C₃×C₈	1	24	yes	direct product factor
41	C₂×C₃×C₅²×C₉	C₂×C₃×C₄	1	12	yes	—
42	C₂×C₃²×C₈×C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₅²×C₈	C₃×C₉	1	12	yes	direct product factor
44	C₂×C₃×C₅²×C₈	C₃³	1	1	yes	characteristic
45	C₂×C₃³×C₄×C₅	C₂×C₃×C₅	1	6	yes	—
46	C₃³×C₅×C₈	C₂×C₃×C₅	1	12	yes	—
47	C₂×C₃×C₄×C₅×C₉	C₂×C₃×C₅	1	72	yes	—
48	C₃×C₅×C₈×C₉	C₂×C₃×C₅	1	144	yes	direct product factor
49	C₂²×C₃²×C₅²	C₄×C₉	1	9	yes	—
50	C₂²×C₃²×C₅²	C₃²×C₄	1	4	yes	—
51	C₃²×C₄×C₅²	C₄×C₉	1	9	yes	—
52	C₃²×C₄×C₅²	C₂²×C₉	1	9	yes	—
53	C₃²×C₄×C₅²	C₃²×C₄	1	4	yes	—
54	C₃²×C₄×C₅²	C₂²×C₃²	1	4	yes	—
55	C₂²×C₅²×C₉	C₃²×C₄	1	9	yes	—
56	C₄×C₅²×C₉	C₃²×C₄	1	9	yes	—
57	C₄×C₅²×C₉	C₂²×C₃²	1	9	yes	—
58	C₂×C₃²×C₅×C₉	C₅×C₈	1	12	yes	direct product factor
59	C₂×C₃²×C₅×C₉	C₂×C₄×C₅	1	6	yes	—
60	C₂×C₃²×C₅×C₈	C₅×C₉	1	54	yes	direct product factor
61	C₂×C₃²×C₅×C₈	C₃²×C₅	1	24	yes	—
62	C₂×C₅×C₈×C₉	C₃²×C₅	1	54	yes	direct product factor
63	C₃³×C₅²	C₂×C₃×C₈	1	1	yes	characteristic
64	C₃×C₅²×C₉	C₂×C₃×C₈	1	12	yes	direct product factor
65	C₂×C₃²×C₄×C₉	C₂×C₅²	1	1	yes	characteristic
66	C₃²×C₈×C₉	C₂×C₅²	1	2	yes	direct product factor
67	C₂×C₃×C₄×C₅²	C₂×C₃×C₉	1	12	yes	—
68	C₂×C₃×C₄×C₅²	C₂×C₃³	1	1	yes	characteristic
69	C₃×C₅²×C₈	C₂×C₃×C₉	1	24	yes	direct product factor
70	C₃×C₅²×C₈	C₂×C₃³	1	2	yes	—
71	C₂²×C₃³×C₅	C₃×C₄×C₅	1	6	yes	—
72	C₃³×C₄×C₅	C₃×C₄×C₅	1	6	yes	—
73	C₃³×C₄×C₅	C₂²×C₃×C₅	1	6	yes	—
74	C₂²×C₃×C₅×C₉	C₃×C₄×C₅	1	72	yes	—
75	C₃×C₄×C₅×C₉	C₃×C₄×C₅	1	72	yes	—
76	C₃×C₄×C₅×C₉	C₂²×C₃×C₅	1	72	yes	—
77	C₂×C₃²×C₅²	C₈×C₉	1	18	yes	direct product factor
78	C₂×C₃²×C₅²	C₂×C₄×C₉	1	9	yes	—
79	C₂×C₃²×C₅²	C₃²×C₈	1	8	yes	—
80	C₂×C₃²×C₅²	C₂×C₃²×C₄	1	4	yes	—
81	C₂×C₅²×C₉	C₃²×C₈	1	18	yes	direct product factor
82	C₂×C₅²×C₉	C₂×C₃²×C₄	1	9	yes	—
83	C₂×C₃³×C₈	C₃×C₅²	1	1	yes	characteristic
84	C₂×C₃×C₈×C₉	C₃×C₅²	1	12	yes	direct product factor
85	C₃²×C₅×C₉	C₂×C₅×C₈	1	6	yes	direct product factor
86	C₂×C₅²×C₈	C₃²×C₉	1	1	yes	characteristic, direct product factor, Hall
87	C₂×C₃²×C₄×C₅	C₂×C₅×C₉	1	54	yes	—
88	C₂×C₃²×C₄×C₅	C₂×C₃²×C₅	1	24	yes	—
89	C₃²×C₅×C₈	C₂×C₅×C₉	1	108	yes	direct product factor
90	C₃²×C₅×C₈	C₂×C₃²×C₅	1	48	yes	—
91	C₂×C₄×C₅×C₉	C₂×C₃²×C₅	1	54	yes	—
92	C₅×C₈×C₉	C₂×C₃²×C₅	1	108	yes	direct product factor
93	C₂²×C₃²×C₉	C₄×C₅²	1	1	yes	characteristic
94	C₃²×C₄×C₉	C₄×C₅²	1	1	yes	characteristic
95	C₃²×C₄×C₉	C₂²×C₅²	1	1	yes	characteristic
96	C₂²×C₃×C₅²	C₃×C₄×C₉	1	12	yes	—
97	C₂²×C₃×C₅²	C₃³×C₄	1	1	yes	characteristic
98	C₃×C₄×C₅²	C₃×C₄×C₉	1	12	yes	—
99	C₃×C₄×C₅²	C₂²×C₃×C₉	1	12	yes	—
100	C₃×C₄×C₅²	C₃³×C₄	1	1	yes	characteristic
101	C₃×C₄×C₅²	C₂²×C₃³	1	1	yes	characteristic
102	C₂×C₃³×C₅	C₃×C₅×C₈	1	12	yes	—
103	C₂×C₃³×C₅	C₂×C₃×C₄×C₅	1	6	yes	—
104	C₂×C₃×C₅×C₉	C₃×C₅×C₈	1	144	yes	direct product factor
105	C₂×C₃×C₅×C₉	C₂×C₃×C₄×C₅	1	72	yes	—
106	C₂×C₃×C₅×C₈	C₃×C₅×C₉	1	72	yes	direct product factor
107	C₂×C₃×C₅×C₈	C₃³×C₅	1	6	yes	—
108	C₃²×C₅²	C₂×C₈×C₉	1	9	yes	direct product factor
109	C₃²×C₅²	C₂×C₃²×C₈	1	4	yes	—
110	C₅²×C₉	C₂×C₃²×C₈	1	9	yes	direct product factor
111	C₂×C₃³×C₄	C₂×C₃×C₅²	1	1	yes	characteristic
112	C₃³×C₈	C₂×C₃×C₅²	1	2	yes	—
113	C₂×C₃×C₄×C₉	C₂×C₃×C₅²	1	12	yes	—
114	C₃×C₈×C₉	C₂×C₃×C₅²	1	24	yes	direct product factor
115	C₂×C₄×C₅²	C₂×C₃²×C₉	1	1	yes	characteristic
116	C₅²×C₈	C₂×C₃²×C₉	1	2	yes	direct product factor
117	C₂²×C₃²×C₅	C₄×C₅×C₉	1	54	yes	—
118	C₂²×C₃²×C₅	C₃²×C₄×C₅	1	24	yes	—
119	C₃²×C₄×C₅	C₄×C₅×C₉	1	54	yes	—
120	C₃²×C₄×C₅	C₂²×C₅×C₉	1	54	yes	—
121	C₃²×C₄×C₅	C₃²×C₄×C₅	1	24	yes	—
122	C₃²×C₄×C₅	C₂²×C₃²×C₅	1	24	yes	—
123	C₂²×C₅×C₉	C₃²×C₄×C₅	1	54	yes	—
124	C₄×C₅×C₉	C₃²×C₄×C₅	1	54	yes	—
125	C₄×C₅×C₉	C₂²×C₃²×C₅	1	54	yes	—
126	C₂×C₃²×C₉	C₅²×C₈	1	2	yes	direct product factor
127	C₂×C₃²×C₉	C₂×C₄×C₅²	1	1	yes	characteristic
128	C₂×C₃×C₅²	C₃×C₈×C₉	1	24	yes	direct product factor
129	C₂×C₃×C₅²	C₂×C₃×C₄×C₉	1	12	yes	—
130	C₂×C₃×C₅²	C₃³×C₈	1	2	yes	—
131	C₂×C₃×C₅²	C₂×C₃³×C₄	1	1	yes	characteristic
132	C₂×C₃²×C₈	C₅²×C₉	1	9	yes	direct product factor
133	C₂×C₃²×C₈	C₃²×C₅²	1	4	yes	—
134	C₂×C₈×C₉	C₃²×C₅²	1	9	yes	direct product factor
135	C₃³×C₅	C₂×C₃×C₅×C₈	1	6	yes	—
136	C₃×C₅×C₉	C₂×C₃×C₅×C₈	1	72	yes	direct product factor
137	C₂×C₃×C₄×C₅	C₂×C₃×C₅×C₉	1	72	yes	—
138	C₂×C₃×C₄×C₅	C₂×C₃³×C₅	1	6	yes	—
139	C₃×C₅×C₈	C₂×C₃×C₅×C₉	1	144	yes	direct product factor
140	C₃×C₅×C₈	C₂×C₃³×C₅	1	12	yes	—
141	C₂²×C₃³	C₃×C₄×C₅²	1	1	yes	characteristic
142	C₃³×C₄	C₃×C₄×C₅²	1	1	yes	characteristic
143	C₃³×C₄	C₂²×C₃×C₅²	1	1	yes	characteristic
144	C₂²×C₃×C₉	C₃×C₄×C₅²	1	12	yes	—
145	C₃×C₄×C₉	C₃×C₄×C₅²	1	12	yes	—
146	C₃×C₄×C₉	C₂²×C₃×C₅²	1	12	yes	—
147	C₂²×C₅²	C₃²×C₄×C₉	1	1	yes	characteristic
148	C₄×C₅²	C₃²×C₄×C₉	1	1	yes	characteristic
149	C₄×C₅²	C₂²×C₃²×C₉	1	1	yes	characteristic
150	C₂×C₃²×C₅	C₅×C₈×C₉	1	108	yes	direct product factor
151	C₂×C₃²×C₅	C₂×C₄×C₅×C₉	1	54	yes	—
152	C₂×C₃²×C₅	C₃²×C₅×C₈	1	48	yes	—
153	C₂×C₃²×C₅	C₂×C₃²×C₄×C₅	1	24	yes	—
154	C₂×C₅×C₉	C₃²×C₅×C₈	1	108	yes	direct product factor
155	C₂×C₅×C₉	C₂×C₃²×C₄×C₅	1	54	yes	—
156	C₃²×C₉	C₂×C₅²×C₈	1	1	yes	characteristic, direct product factor, Sylow
157	C₂×C₅×C₈	C₃²×C₅×C₉	1	6	yes	direct product factor
158	C₃×C₅²	C₂×C₃×C₈×C₉	1	12	yes	direct product factor
159	C₃×C₅²	C₂×C₃³×C₈	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₂×C₅²×C₉	1	9	yes	—
161	C₂×C₃²×C₄	C₂×C₃²×C₅²	1	4	yes	—
162	C₃²×C₈	C₂×C₅²×C₉	1	18	yes	direct product factor
163	C₃²×C₈	C₂×C₃²×C₅²	1	8	yes	—
164	C₂×C₄×C₉	C₂×C₃²×C₅²	1	9	yes	—
165	C₈×C₉	C₂×C₃²×C₅²	1	18	yes	direct product factor
166	C₂²×C₃×C₅	C₃×C₄×C₅×C₉	1	72	yes	—
167	C₂²×C₃×C₅	C₃³×C₄×C₅	1	6	yes	—
168	C₃×C₄×C₅	C₃×C₄×C₅×C₉	1	72	yes	—
169	C₃×C₄×C₅	C₂²×C₃×C₅×C₉	1	72	yes	—
170	C₃×C₄×C₅	C₃³×C₄×C₅	1	6	yes	—
171	C₃×C₄×C₅	C₂²×C₃³×C₅	1	6	yes	—
172	C₂×C₃³	C₃×C₅²×C₈	1	2	yes	—
173	C₂×C₃³	C₂×C₃×C₄×C₅²	1	1	yes	characteristic
174	C₂×C₃×C₉	C₃×C₅²×C₈	1	24	yes	direct product factor
175	C₂×C₃×C₉	C₂×C₃×C₄×C₅²	1	12	yes	—
176	C₂×C₅²	C₃²×C₈×C₉	1	2	yes	direct product factor
177	C₂×C₅²	C₂×C₃²×C₄×C₉	1	1	yes	characteristic
178	C₂×C₃×C₈	C₃×C₅²×C₉	1	12	yes	direct product factor
179	C₂×C₃×C₈	C₃³×C₅²	1	1	yes	characteristic
180	C₃²×C₅	C₂×C₅×C₈×C₉	1	54	yes	direct product factor
181	C₃²×C₅	C₂×C₃²×C₅×C₈	1	24	yes	—
182	C₅×C₉	C₂×C₃²×C₅×C₈	1	54	yes	direct product factor
183	C₂×C₄×C₅	C₂×C₃²×C₅×C₉	1	6	yes	—
184	C₅×C₈	C₂×C₃²×C₅×C₉	1	12	yes	direct product factor
185	C₂²×C₃²	C₄×C₅²×C₉	1	9	yes	—
186	C₂²×C₃²	C₃²×C₄×C₅²	1	4	yes	—
187	C₃²×C₄	C₄×C₅²×C₉	1	9	yes	—
188	C₃²×C₄	C₂²×C₅²×C₉	1	9	yes	—
189	C₃²×C₄	C₃²×C₄×C₅²	1	4	yes	—
190	C₃²×C₄	C₂²×C₃²×C₅²	1	4	yes	—
191	C₂²×C₉	C₃²×C₄×C₅²	1	9	yes	—
192	C₄×C₉	C₃²×C₄×C₅²	1	9	yes	—
193	C₄×C₉	C₂²×C₃²×C₅²	1	9	yes	—
194	C₂×C₃×C₅	C₃×C₅×C₈×C₉	1	144	yes	direct product factor
195	C₂×C₃×C₅	C₂×C₃×C₄×C₅×C₉	1	72	yes	—
196	C₂×C₃×C₅	C₃³×C₅×C₈	1	12	yes	—
197	C₂×C₃×C₅	C₂×C₃³×C₄×C₅	1	6	yes	—
198	C₃³	C₂×C₃×C₅²×C₈	1	1	yes	characteristic
199	C₃×C₉	C₂×C₃×C₅²×C₈	1	12	yes	direct product factor
200	C₅²	C₂×C₃²×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
201	C₂×C₃×C₄	C₂×C₃×C₅²×C₉	1	12	yes	—
202	C₂×C₃×C₄	C₂×C₃³×C₅²	1	1	yes	characteristic
203	C₃×C₈	C₂×C₃×C₅²×C₉	1	24	yes	direct product factor
204	C₃×C₈	C₂×C₃³×C₅²	1	2	yes	—
205	C₂²×C₅	C₃²×C₄×C₅×C₉	1	6	yes	—
206	C₄×C₅	C₃²×C₄×C₅×C₉	1	6	yes	—
207	C₄×C₅	C₂²×C₃²×C₅×C₉	1	6	yes	—
208	C₂×C₃²	C₅²×C₈×C₉	1	18	yes	direct product factor
209	C₂×C₃²	C₂×C₄×C₅²×C₉	1	9	yes	—
210	C₂×C₃²	C₃²×C₅²×C₈	1	8	yes	—
211	C₂×C₃²	C₂×C₃²×C₄×C₅²	1	4	yes	—
212	C₂×C₉	C₃²×C₅²×C₈	1	18	yes	direct product factor
213	C₂×C₉	C₂×C₃²×C₄×C₅²	1	9	yes	—
214	C₂×C₈	C₃²×C₅²×C₉	1	1	yes	characteristic, direct product factor, Sylow
215	C₃×C₅	C₂×C₃×C₅×C₈×C₉	1	72	yes	direct product factor
216	C₃×C₅	C₂×C₃³×C₅×C₈	1	6	yes	—
217	C₂²×C₃	C₃×C₄×C₅²×C₉	1	12	yes	—
218	C₂²×C₃	C₃³×C₄×C₅²	1	1	yes	characteristic
219	C₃×C₄	C₃×C₄×C₅²×C₉	1	12	yes	—
220	C₃×C₄	C₃³×C₄×C₅²	1	1	yes	characteristic
221	C₃×C₄	C₂²×C₃×C₅²×C₉	1	12	yes	—
222	C₃×C₄	C₂²×C₃³×C₅²	1	1	yes	characteristic
223	C₂×C₅	C₃²×C₅×C₈×C₉	1	12	yes	direct product factor
224	C₂×C₅	C₂×C₃²×C₄×C₅×C₉	1	6	yes	—
225	C₃²	C₂×C₅²×C₈×C₉	1	9	yes	direct product factor
226	C₃²	C₂×C₃²×C₅²×C₈	1	4	yes	—
227	C₉	C₂×C₃²×C₅²×C₈	1	9	yes	direct product factor
228	C₂×C₄	C₂×C₃²×C₅²×C₉	1	1	yes	characteristic
229	C₈	C₂×C₃²×C₅²×C₉	1	2	yes	direct product factor
230	C₂×C₃	C₃×C₅²×C₈×C₉	1	24	yes	direct product factor
231	C₂×C₃	C₃³×C₅²×C₈	1	2	yes	—
232	C₂×C₃	C₂×C₃×C₄×C₅²×C₉	1	12	yes	—
233	C₂×C₃	C₂×C₃³×C₄×C₅²	1	1	yes	characteristic
234	C₅	C₂×C₃²×C₅×C₈×C₉	1	6	yes	direct product factor
235	C₂²	C₃²×C₄×C₅²×C₉	1	1	yes	characteristic
236	C₄	C₃²×C₄×C₅²×C₉	1	1	yes	characteristic
237	C₄	C₂²×C₃²×C₅²×C₉	1	1	yes	characteristic
238	C₃	C₂×C₃×C₅²×C₈×C₉	1	12	yes	direct product factor
239	C₃	C₂×C₃³×C₅²×C₈	1	1	yes	characteristic
240	C₂	C₃²×C₅²×C₈×C₉	1	2	yes	direct product factor
241	C₂	C₂×C₃²×C₄×C₅²×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃³×C₅²
socle, prime radical	C₂²×C₃³×C₅²	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₈×C₉	C₂	direct (N × H)
4. C₂×C₃×C₅²×C₈×C₉	C₃	direct (N × H)
8. C₂×C₃²×C₅×C₈×C₉	C₅	direct (N × H)
12. C₃×C₅²×C₈×C₉	C₂×C₃	direct (N × H)
13. C₂×C₃²×C₅²×C₉	C₈	direct (N × H)
15. C₂×C₃²×C₅²×C₈	C₉	direct (N × H)
17. C₂×C₅²×C₈×C₉	C₃²	direct (N × H)
19. C₃²×C₅×C₈×C₉	C₂×C₅	direct (N × H)
27. C₂×C₃×C₅×C₈×C₉	C₃×C₅	direct (N × H)
28. C₃²×C₅²×C₉	C₂×C₈	direct (N × H)
31. C₃²×C₅²×C₈	C₂×C₉	direct (N × H)
34. C₅²×C₈×C₉	C₂×C₃²	direct (N × H)
40. C₂×C₃×C₅²×C₉	C₃×C₈	direct (N × H)
42. C₂×C₃²×C₈×C₉	C₅²	direct (N × H)
43. C₂×C₃×C₅²×C₈	C₃×C₉	direct (N × H)
48. C₃×C₅×C₈×C₉	C₂×C₃×C₅	direct (N × H)
58. C₂×C₃²×C₅×C₉	C₅×C₈	direct (N × H)
60. C₂×C₃²×C₅×C₈	C₅×C₉	direct (N × H)
62. C₂×C₅×C₈×C₉	C₃²×C₅	direct (N × H)
64. C₃×C₅²×C₉	C₂×C₃×C₈	direct (N × H)
66. C₃²×C₈×C₉	C₂×C₅²	direct (N × H)
69. C₃×C₅²×C₈	C₂×C₃×C₉	direct (N × H)
77. C₂×C₃²×C₅²	C₈×C₉	direct (N × H)
81. C₂×C₅²×C₉	C₃²×C₈	direct (N × H)
84. C₂×C₃×C₈×C₉	C₃×C₅²	direct (N × H)
85. C₃²×C₅×C₉	C₂×C₅×C₈	direct (N × H)
86. C₂×C₅²×C₈	C₃²×C₉	direct (N × H)
89. C₃²×C₅×C₈	C₂×C₅×C₉	direct (N × H)
92. C₅×C₈×C₉	C₂×C₃²×C₅	direct (N × H)
104. C₂×C₃×C₅×C₉	C₃×C₅×C₈	direct (N × H)
106. C₂×C₃×C₅×C₈	C₃×C₅×C₉	direct (N × H)
108. C₃²×C₅²	C₂×C₈×C₉	direct (N × H)
110. C₅²×C₉	C₂×C₃²×C₈	direct (N × H)
114. C₃×C₈×C₉	C₂×C₃×C₅²	direct (N × H)
116. C₅²×C₈	C₂×C₃²×C₉	direct (N × H)
126. C₂×C₃²×C₉	C₅²×C₈	direct (N × H)
128. C₂×C₃×C₅²	C₃×C₈×C₉	direct (N × H)
132. C₂×C₃²×C₈	C₅²×C₉	direct (N × H)
134. C₂×C₈×C₉	C₃²×C₅²	direct (N × H)
136. C₃×C₅×C₉	C₂×C₃×C₅×C₈	direct (N × H)
139. C₃×C₅×C₈	C₂×C₃×C₅×C₉	direct (N × H)
150. C₂×C₃²×C₅	C₅×C₈×C₉	direct (N × H)
154. C₂×C₅×C₉	C₃²×C₅×C₈	direct (N × H)
156. C₃²×C₉	C₂×C₅²×C₈	direct (N × H)
157. C₂×C₅×C₈	C₃²×C₅×C₉	direct (N × H)
158. C₃×C₅²	C₂×C₃×C₈×C₉	direct (N × H)
162. C₃²×C₈	C₂×C₅²×C₉	direct (N × H)
165. C₈×C₉	C₂×C₃²×C₅²	direct (N × H)
174. C₂×C₃×C₉	C₃×C₅²×C₈	direct (N × H)
176. C₂×C₅²	C₃²×C₈×C₉	direct (N × H)
178. C₂×C₃×C₈	C₃×C₅²×C₉	direct (N × H)
180. C₃²×C₅	C₂×C₅×C₈×C₉	direct (N × H)
182. C₅×C₉	C₂×C₃²×C₅×C₈	direct (N × H)
184. C₅×C₈	C₂×C₃²×C₅×C₉	direct (N × H)
194. C₂×C₃×C₅	C₃×C₅×C₈×C₉	direct (N × H)
199. C₃×C₉	C₂×C₃×C₅²×C₈	direct (N × H)
200. C₅²	C₂×C₃²×C₈×C₉	direct (N × H)
203. C₃×C₈	C₂×C₃×C₅²×C₉	direct (N × H)
208. C₂×C₃²	C₅²×C₈×C₉	direct (N × H)
212. C₂×C₉	C₃²×C₅²×C₈	direct (N × H)
214. C₂×C₈	C₃²×C₅²×C₉	direct (N × H)
215. C₃×C₅	C₂×C₃×C₅×C₈×C₉	direct (N × H)
223. C₂×C₅	C₃²×C₅×C₈×C₉	direct (N × H)
225. C₃²	C₂×C₅²×C₈×C₉	direct (N × H)
227. C₉	C₂×C₃²×C₅²×C₈	direct (N × H)
229. C₈	C₂×C₃²×C₅²×C₉	direct (N × H)
230. C₂×C₃	C₃×C₅²×C₈×C₉	direct (N × H)
234. C₅	C₂×C₃²×C₅×C₈×C₉	direct (N × H)
238. C₃	C₂×C₃×C₅²×C₈×C₉	direct (N × H)
240. C₂	C₃²×C₅²×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
C₂×C₃²×C₄×C₅²×C₉	2
C₃²×C₅²×C₈×C₉	2
C₂×C₃³×C₅²×C₈	3
C₂×C₃×C₅²×C₈×C₉	3
C₂×C₃²×C₅×C₈×C₉	5

Subgroups — C2×C32×C52×C8×C9 #72209124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅²×C₈×C₉ #72209124