Subgroups — C₉×#2464 #11767185

Order 1152.

1065 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#392	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2464	C₃	1	1	yes	maximal, characteristic
17	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
26	C₉×#123	—	2	4	no	—
27	C₉×#121	—	2	4	no	—
28	C₉×#121	—	2	4	no	—
29	C₄×D₄×C₉	—	2	4	no	—
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
50	C₉×#95	C₂²	1	1	yes	characteristic
51	C₉×#95	C₂²	1	1	yes	characteristic
52	C₉×#95	C₂²	1	1	yes	characteristic
53	C₉×#95	C₂²	1	1	yes	characteristic
54	C₉×#95	C₂²	1	1	yes	characteristic
55	C₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
59	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
60	C₃×#398	C₂×C₃	1	1	yes	characteristic
61	C₃×#394	C₂×C₃	1	1	yes	characteristic
62	C₃×#392	C₂×C₃	1	1	yes	characteristic
63	C₃×#392	C₂×C₃	1	1	yes	characteristic
64	C₃×#390	C₂×C₃	1	1	yes	characteristic
65	C₃×#388	C₂×C₃	1	1	yes	characteristic
66	C₃×#388	C₂×C₃	1	1	yes	characteristic
67	C₃×#386	C₂×C₃	1	1	yes	characteristic
68	C₃×#386	C₂×C₃	1	1	yes	characteristic
69	C₃×#385	C₂×C₃	1	1	yes	characteristic
70	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
71	C₂⁴×C₉	C₂³	1	1	yes	characteristic
72	C₂⁴×C₉	C₂³	1	1	yes	characteristic
73	C₂⁴×C₉	C₂³	1	1	yes	characteristic
74	C₂⁴×C₉	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₉	—	2	2	no	—
76	C₂×D₄×C₉	—	2	2	no	—
77	C₂×D₄×C₉	—	2	2	no	—
78	C₂×D₄×C₉	—	2	2	no	—
79	C₂×D₄×C₉	—	2	2	no	—
80	C₂×D₄×C₉	—	2	2	no	—
81	C₂×D₄×C₉	—	2	2	no	—
82	C₂×D₄×C₉	—	2	2	no	—
83	C₂×D₄×C₉	—	2	2	no	—
84	C₂×D₄×C₉	—	2	2	no	—
85	C₂×D₄×C₉	—	2	2	no	—
86	C₂×D₄×C₉	—	2	2	no	—
87	C₂×D₄×C₉	—	2	2	no	—
88	C₂×D₄×C₉	—	4	1	no	—
89	C₂×D₄×C₉	—	4	1	no	—
90	C₂×D₄×C₉	—	4	1	no	—
91	C₂×D₄×C₉	—	4	1	no	—
92	C₂×D₄×C₉	—	4	1	no	—
93	C₂²×C₄×C₉	—	2	2	no	—
94	C₂²×C₄×C₉	—	2	2	no	—
95	C₂²×C₄×C₉	—	2	2	no	—
96	C₂²×C₄×C₉	—	2	2	no	—
97	C₂²×C₄×C₉	—	2	2	no	—
98	C₂²×C₄×C₉	—	2	2	no	—
99	C₂²×C₄×C₉	—	4	1	no	—
100	C₂²×C₄×C₉	—	4	1	no	—
101	C₂²×C₄×C₉	—	4	1	no	—
102	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
113	C₉×C₄⋊C₄	—	2	2	no	—
114	C₉×C₄⋊C₄	—	2	2	no	—
115	C₉×C₄⋊C₄	—	2	2	no	—
116	C₉×C₄⋊C₄	—	2	2	no	—
117	C₉×C₄⋊C₄	—	2	2	no	—
118	C₉×C₂²⋊C₄	—	2	2	no	—
119	C₉×C₂²⋊C₄	—	2	2	no	—
120	C₉×C₂²⋊C₄	—	2	2	no	—
121	C₉×C₂²⋊C₄	—	2	2	no	—
122	C₉×C₂²⋊C₄	—	2	2	no	—
123	C₉×C₂²⋊C₄	—	2	2	no	—
124	C₉×C₂²⋊C₄	—	2	2	no	—
125	C₉×C₂²⋊C₄	—	2	2	no	—
126	C₉×C₂²⋊C₄	—	4	1	no	—
127	C₉×C₂²⋊C₄	—	4	1	no	—
128	C₉×C₂²⋊C₄	—	4	1	no	—
129	C₉×C₂²⋊C₄	D₄	1	4	yes	complemented
130	C₉×C₂²⋊C₄	D₄	1	4	yes	complemented
131	C₄²×C₉	—	2	2	no	—
132	C₄²×C₉	—	4	1	no	—
133	#2464	C₉	1	1	yes	characteristic, direct product factor, Sylow
134	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
135	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
137	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
143	C₃×#123	—	2	4	no	—
144	C₃×#121	—	2	4	no	—
145	C₃×#121	—	2	4	no	—
146	C₃×C₄×D₄	—	2	4	no	—
147	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
167	C₃×#95	C₂²×C₃	1	1	yes	characteristic
168	C₃×#95	C₂²×C₃	1	1	yes	characteristic
169	C₃×#95	C₂²×C₃	1	1	yes	characteristic
170	C₃×#95	C₂²×C₃	1	1	yes	characteristic
171	C₃×#95	C₂²×C₃	1	1	yes	characteristic
172	C₃×#95	C₂²×C₃	1	1	yes	characteristic
173	C₂³×C₉	—	2	1	no	—
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	—	2	1	no	—
176	C₂³×C₉	—	2	1	no	—
177	C₂³×C₉	—	2	1	no	—
178	C₂³×C₉	—	2	1	no	—
179	C₂³×C₉	—	2	1	no	—
180	C₂³×C₉	—	2	1	no	—
181	C₂³×C₉	—	2	1	no	—
182	C₂³×C₉	—	2	1	no	—
183	C₂³×C₉	—	2	1	no	—
184	C₂³×C₉	—	2	1	no	—
185	C₂³×C₉	—	2	1	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	—	2	1	no	—
191	C₂³×C₉	—	2	1	no	—
192	C₂³×C₉	—	2	1	no	—
193	C₂³×C₉	—	2	1	no	—
194	C₂³×C₉	—	2	1	no	—
195	C₂³×C₉	—	2	1	no	—
196	C₂³×C₉	—	2	1	no	—
197	C₂³×C₉	—	2	1	no	—
198	C₂³×C₉	C₂×D₄	1	2	yes	—
199	C₂³×C₉	C₂×D₄	1	2	yes	—
200	C₂³×C₉	#41	1	2	yes	—
201	C₂³×C₉	C₂⁴	1	1	yes	characteristic
202	D₄×C₉	—	2	8	no	—
203	D₄×C₉	—	4	4	no	—
204	D₄×C₉	—	4	4	no	—
205	D₄×C₉	—	4	4	no	—
206	D₄×C₉	—	4	4	no	—
207	D₄×C₉	—	4	4	no	—
208	C₂×C₄×C₉	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	2	1	no	—
216	C₂×C₄×C₉	—	2	1	no	—
217	C₂×C₄×C₉	—	2	1	no	—
218	C₂×C₄×C₉	—	2	1	no	—
219	C₂×C₄×C₉	—	2	1	no	—
220	C₂×C₄×C₉	—	2	1	no	—
221	C₂×C₄×C₉	—	2	1	no	—
222	C₂×C₄×C₉	—	2	1	no	—
223	C₂×C₄×C₉	—	2	1	no	—
224	C₂×C₄×C₉	—	2	1	no	—
225	C₂×C₄×C₉	—	2	1	no	—
226	C₂×C₄×C₉	—	2	1	no	—
227	C₂×C₄×C₉	—	2	1	no	—
228	C₂×C₄×C₉	—	2	1	no	—
229	C₂×C₄×C₉	—	2	1	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	2	1	no	—
232	C₂×C₄×C₉	—	2	1	no	—
233	C₂×C₄×C₉	—	2	1	no	—
234	C₂×C₄×C₉	—	2	1	no	—
235	C₂×C₄×C₉	—	4	4	no	—
236	C₂×C₄×C₉	—	4	4	no	—
237	C₂×C₄×C₉	—	4	4	no	—
238	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
239	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
240	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
241	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
242	C₂×C₄×C₉	#41	1	2	yes	—
243	C₂×C₄×C₉	#41	1	2	yes	—
244	C₂×#123	C₂×C₉	1	1	yes	characteristic, complemented
245	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
246	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
247	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
248	#398	C₂×C₉	1	1	yes	characteristic, complemented
249	#394	C₂×C₉	1	1	yes	characteristic, complemented
250	#392	C₂×C₉	1	1	yes	characteristic, complemented
251	#392	C₂×C₉	1	1	yes	characteristic, complemented
252	#390	C₂×C₉	1	1	yes	characteristic, complemented
253	#388	C₂×C₉	1	1	yes	characteristic, complemented
254	#388	C₂×C₉	1	1	yes	characteristic, complemented
255	#386	C₂×C₉	1	1	yes	characteristic, complemented
256	#386	C₂×C₉	1	1	yes	characteristic, complemented
257	#385	C₂×C₉	1	1	yes	characteristic, complemented
258	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
259	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
260	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
261	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
262	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃×D₄	—	2	2	no	—
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	—	2	2	no	—
268	C₂×C₃×D₄	—	2	2	no	—
269	C₂×C₃×D₄	—	2	2	no	—
270	C₂×C₃×D₄	—	2	2	no	—
271	C₂×C₃×D₄	—	2	2	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	—	2	2	no	—
275	C₂×C₃×D₄	—	2	2	no	—
276	C₂×C₃×D₄	—	4	1	no	—
277	C₂×C₃×D₄	—	4	1	no	—
278	C₂×C₃×D₄	—	4	1	no	—
279	C₂×C₃×D₄	—	4	1	no	—
280	C₂×C₃×D₄	—	4	1	no	—
281	C₂²×C₃×C₄	—	2	2	no	—
282	C₂²×C₃×C₄	—	2	2	no	—
283	C₂²×C₃×C₄	—	2	2	no	—
284	C₂²×C₃×C₄	—	2	2	no	—
285	C₂²×C₃×C₄	—	2	2	no	—
286	C₂²×C₃×C₄	—	2	2	no	—
287	C₂²×C₃×C₄	—	4	1	no	—
288	C₂²×C₃×C₄	—	4	1	no	—
289	C₂²×C₃×C₄	—	4	1	no	—
290	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
301	C₃×C₄⋊C₄	—	2	2	no	—
302	C₃×C₄⋊C₄	—	2	2	no	—
303	C₃×C₄⋊C₄	—	2	2	no	—
304	C₃×C₄⋊C₄	—	2	2	no	—
305	C₃×C₄⋊C₄	—	2	2	no	—
306	C₃×C₂²⋊C₄	—	2	2	no	—
307	C₃×C₂²⋊C₄	—	2	2	no	—
308	C₃×C₂²⋊C₄	—	2	2	no	—
309	C₃×C₂²⋊C₄	—	2	2	no	—
310	C₃×C₂²⋊C₄	—	2	2	no	—
311	C₃×C₂²⋊C₄	—	2	2	no	—
312	C₃×C₂²⋊C₄	—	2	2	no	—
313	C₃×C₂²⋊C₄	—	2	2	no	—
314	C₃×C₂²⋊C₄	—	4	1	no	—
315	C₃×C₂²⋊C₄	—	4	1	no	—
316	C₃×C₂²⋊C₄	—	4	1	no	—
317	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
318	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
319	C₃×C₄²	—	2	2	no	—
320	C₃×C₄²	—	4	1	no	—
321	C₂²×C₉	—	2	2	no	—
322	C₂²×C₉	—	2	2	no	—
323	C₂²×C₉	—	2	2	no	—
324	C₂²×C₉	—	2	2	no	—
325	C₂²×C₉	—	2	2	no	—
326	C₂²×C₉	—	2	2	no	—
327	C₂²×C₉	—	2	2	no	—
328	C₂²×C₉	—	2	2	no	—
329	C₂²×C₉	—	2	2	no	—
330	C₂²×C₉	—	4	1	no	—
331	C₂²×C₉	—	4	1	no	—
332	C₂²×C₉	—	4	1	no	—
333	C₂²×C₉	—	4	1	no	—
334	C₂²×C₉	—	4	1	no	—
335	C₂²×C₉	—	4	1	no	—
336	C₂²×C₉	—	4	1	no	—
337	C₂²×C₉	—	4	1	no	—
338	C₂²×C₉	—	4	1	no	—
339	C₂²×C₉	—	4	1	no	—
340	C₂²×C₉	—	4	1	no	—
341	C₂²×C₉	—	4	1	no	—
342	C₂²×C₉	—	4	1	no	—
343	C₂²×C₉	—	4	1	no	—
344	C₂²×C₉	—	4	1	no	—
345	C₂²×C₉	—	4	1	no	—
346	C₂²×C₉	—	4	1	no	—
347	C₂²×C₉	—	4	1	no	—
348	C₂²×C₉	—	4	1	no	—
349	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
350	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
351	C₂²×C₉	C₂×#41	1	1	yes	characteristic
352	C₂²×C₉	C₂×#41	1	1	yes	characteristic
353	C₂²×C₉	C₂×#41	1	1	yes	characteristic
354	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
356	C₄×C₉	—	2	2	no	—
357	C₄×C₉	—	2	2	no	—
358	C₄×C₉	—	2	2	no	—
359	C₄×C₉	—	2	2	no	—
360	C₄×C₉	—	2	2	no	—
361	C₄×C₉	—	2	2	no	—
362	C₄×C₉	—	4	1	no	—
363	C₄×C₉	—	4	1	no	—
364	C₄×C₉	—	4	1	no	—
365	C₄×C₉	—	4	1	no	—
366	C₄×C₉	—	4	1	no	—
367	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
368	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
369	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
370	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
371	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
372	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
373	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
374	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
375	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
376	#123	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	4	no	—
379	C₄×D₄	—	2	4	no	—
380	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
398	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
399	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
400	#95	C₂²×C₉	1	1	yes	characteristic
401	#95	C₂²×C₉	1	1	yes	characteristic
402	#95	C₂²×C₉	1	1	yes	characteristic
403	#95	C₂²×C₉	1	1	yes	characteristic
404	#95	C₂²×C₉	1	1	yes	characteristic
405	#95	C₂²×C₉	1	1	yes	characteristic
406	C₂³×C₃	—	2	1	no	—
407	C₂³×C₃	—	2	1	no	—
408	C₂³×C₃	—	2	1	no	—
409	C₂³×C₃	—	2	1	no	—
410	C₂³×C₃	—	2	1	no	—
411	C₂³×C₃	—	2	1	no	—
412	C₂³×C₃	—	2	1	no	—
413	C₂³×C₃	—	2	1	no	—
414	C₂³×C₃	—	2	1	no	—
415	C₂³×C₃	—	2	1	no	—
416	C₂³×C₃	—	2	1	no	—
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	—	2	1	no	—
419	C₂³×C₃	—	2	1	no	—
420	C₂³×C₃	—	2	1	no	—
421	C₂³×C₃	—	2	1	no	—
422	C₂³×C₃	—	2	1	no	—
423	C₂³×C₃	—	2	1	no	—
424	C₂³×C₃	—	2	1	no	—
425	C₂³×C₃	—	2	1	no	—
426	C₂³×C₃	—	2	1	no	—
427	C₂³×C₃	—	2	1	no	—
428	C₂³×C₃	—	2	1	no	—
429	C₂³×C₃	—	2	1	no	—
430	C₂³×C₃	—	2	1	no	—
431	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
432	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
433	C₂³×C₃	C₃×#41	1	2	yes	—
434	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
435	C₃×D₄	—	2	8	no	—
436	C₃×D₄	—	4	4	no	—
437	C₃×D₄	—	4	4	no	—
438	C₃×D₄	—	4	4	no	—
439	C₃×D₄	—	4	4	no	—
440	C₃×D₄	—	4	4	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	4	4	no	—
469	C₂×C₃×C₄	—	4	4	no	—
470	C₂×C₃×C₄	—	4	4	no	—
471	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
472	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
473	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
474	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
475	C₂×C₃×C₄	C₃×#41	1	2	yes	—
476	C₂×C₃×C₄	C₃×#41	1	2	yes	—
477	C₂×C₉	—	4	2	no	—
478	C₂×C₉	—	4	2	no	—
479	C₂×C₉	—	4	2	no	—
480	C₂×C₉	—	8	1	no	—
481	C₂×C₉	#525	1	1	yes	characteristic
482	C₂×C₉	#532	1	1	yes	characteristic
483	C₂×C₉	#540	1	1	yes	characteristic
484	C₂×C₉	D₄²	1	1	yes	characteristic
485	C₂×C₉	#546	1	1	yes	characteristic
486	C₂×C₉	#546	1	1	yes	characteristic
487	C₂×C₉	#553	1	1	yes	characteristic
488	C₂⁴	C₂³×C₉	1	1	yes	characteristic
489	C₂⁴	C₂³×C₉	1	1	yes	characteristic
490	C₂⁴	C₂³×C₉	1	1	yes	characteristic
491	C₂⁴	C₂³×C₉	1	1	yes	characteristic
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	4	1	no	—
506	C₂×D₄	—	4	1	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	1	no	—
509	C₂×D₄	—	4	1	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	4	1	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
520	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
521	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
522	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
523	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
524	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
525	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
526	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
527	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
528	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
529	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	D₄×C₉	1	4	yes	complemented
547	C₂²⋊C₄	D₄×C₉	1	4	yes	complemented
548	C₄²	—	2	2	no	—
549	C₄²	—	4	1	no	—
550	C₂²×C₃	—	2	2	no	—
551	C₂²×C₃	—	2	2	no	—
552	C₂²×C₃	—	2	2	no	—
553	C₂²×C₃	—	2	2	no	—
554	C₂²×C₃	—	2	2	no	—
555	C₂²×C₃	—	2	2	no	—
556	C₂²×C₃	—	2	2	no	—
557	C₂²×C₃	—	2	2	no	—
558	C₂²×C₃	—	2	2	no	—
559	C₂²×C₃	—	4	1	no	—
560	C₂²×C₃	—	4	1	no	—
561	C₂²×C₃	—	4	1	no	—
562	C₂²×C₃	—	4	1	no	—
563	C₂²×C₃	—	4	1	no	—
564	C₂²×C₃	—	4	1	no	—
565	C₂²×C₃	—	4	1	no	—
566	C₂²×C₃	—	4	1	no	—
567	C₂²×C₃	—	4	1	no	—
568	C₂²×C₃	—	4	1	no	—
569	C₂²×C₃	—	4	1	no	—
570	C₂²×C₃	—	4	1	no	—
571	C₂²×C₃	—	4	1	no	—
572	C₂²×C₃	—	4	1	no	—
573	C₂²×C₃	—	4	1	no	—
574	C₂²×C₃	—	4	1	no	—
575	C₂²×C₃	—	4	1	no	—
576	C₂²×C₃	—	4	1	no	—
577	C₂²×C₃	—	4	1	no	—
578	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
579	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
580	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
581	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
582	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
583	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	2	2	no	—
588	C₃×C₄	—	2	2	no	—
589	C₃×C₄	—	2	2	no	—
590	C₃×C₄	—	2	2	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	—	4	1	no	—
596	C₉	#2464	1	1	yes	characteristic, direct product factor, Sylow
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	C₂×D₄×C₉	1	2	yes	—
623	C₂³	C₂×D₄×C₉	1	2	yes	—
624	C₂³	C₉×#41	1	2	yes	—
625	C₂³	C₂⁴×C₉	1	1	yes	characteristic
626	D₄	—	2	8	no	—
627	D₄	—	4	4	no	—
628	D₄	—	4	4	no	—
629	D₄	—	4	4	no	—
630	D₄	—	4	4	no	—
631	D₄	—	4	4	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
663	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
664	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
665	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
666	C₂×C₄	C₉×#41	1	2	yes	—
667	C₂×C₄	C₉×#41	1	2	yes	—
668	C₂×C₃	—	4	2	no	—
669	C₂×C₃	—	4	2	no	—
670	C₂×C₃	—	4	2	no	—
671	C₂×C₃	—	8	1	no	—
672	C₂×C₃	C₃×#525	1	1	yes	characteristic
673	C₂×C₃	C₃×#532	1	1	yes	characteristic
674	C₂×C₃	C₃×#540	1	1	yes	characteristic
675	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
676	C₂×C₃	C₃×#546	1	1	yes	characteristic
677	C₂×C₃	C₃×#546	1	1	yes	characteristic
678	C₂×C₃	C₃×#553	1	1	yes	characteristic
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
708	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
709	C₂²	C₂×C₉×#41	1	1	yes	characteristic
710	C₂²	C₂×C₉×#41	1	1	yes	characteristic
711	C₂²	C₂×C₉×#41	1	1	yes	characteristic
712	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₃	C₃×#2464	1	1	yes	characteristic
726	C₂	—	4	2	no	—
727	C₂	—	4	2	no	—
728	C₂	—	4	2	no	—
729	C₂	—	8	1	no	—
730	C₂	C₉×#525	1	1	yes	characteristic
731	C₂	C₉×#532	1	1	yes	characteristic
732	C₂	C₉×#540	1	1	yes	characteristic
733	C₂	D₄²×C₉	1	1	yes	characteristic
734	C₂	C₉×#546	1	1	yes	characteristic
735	C₂	C₉×#546	1	1	yes	characteristic
736	C₂	C₉×#553	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₃×#2464	C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#123	C₂	semidirect
2. C₂×C₉×#121	C₂	semidirect
3. C₂×C₉×#121	C₂	semidirect
4. C₂×C₄×D₄×C₉	C₂	semidirect
5. C₉×#398	C₂	semidirect
6. C₉×#394	C₂	semidirect
7. C₉×#392	C₂	semidirect
8. C₉×#392	C₂	semidirect
9. C₉×#390	C₂	semidirect
10. C₉×#388	C₂	semidirect
11. C₉×#388	C₂	semidirect
12. C₉×#386	C₂	semidirect
13. C₉×#386	C₂	semidirect
14. C₉×#385	C₂	semidirect
15. C₄×C₉×C₂²⋊C₄	C₂	semidirect
129. C₉×C₂²⋊C₄	D₄	semidirect
130. C₉×C₂²⋊C₄	D₄	semidirect
133. #2464	C₉	direct (N × H)
244. C₂×#123	C₂×C₉	semidirect
245. C₂×#121	C₂×C₉	semidirect
246. C₂×#121	C₂×C₉	semidirect
247. C₂×C₄×D₄	C₂×C₉	semidirect
248. #398	C₂×C₉	semidirect
249. #394	C₂×C₉	semidirect
250. #392	C₂×C₉	semidirect
251. #392	C₂×C₉	semidirect
252. #390	C₂×C₉	semidirect
253. #388	C₂×C₉	semidirect
254. #388	C₂×C₉	semidirect
255. #386	C₂×C₉	semidirect
256. #386	C₂×C₉	semidirect
257. #385	C₂×C₉	semidirect
258. C₄×C₂²⋊C₄	C₂×C₉	semidirect
546. C₂²⋊C₄	D₄×C₉	semidirect
547. C₂²⋊C₄	D₄×C₉	semidirect
596. C₉	#2464	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×C₉×#123	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₉×#398	2
C₉×#394	2
C₉×#392	2
C₉×#390	2
C₉×#388	2
C₉×#386	2
C₉×#385	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2464	3

Subgroups — C9×#2464 #11767185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2464 #11767185