Subgroups — C₉×#2485 #11767206

Order 1152.

810 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#397	C₂	1	2	yes	maximal, complemented
4	C₉×#394	C₂	1	2	yes	maximal
5	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	2	yes	maximal, complemented
8	C₉×#387	C₂	1	2	yes	maximal, complemented
9	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2485	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₄×D₄×C₉	—	2	4	no	—
17	C₉×#117	—	2	4	no	—
18	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₄²×C₉	C₂²	1	2	yes	—
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	2	yes	—
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
40	C₃×#397	C₂×C₃	1	2	yes	—
41	C₃×#394	C₂×C₃	1	2	yes	—
42	C₃×#389	C₂×C₃	1	1	yes	characteristic
43	C₃×#389	C₂×C₃	1	1	yes	characteristic
44	C₃×#388	C₂×C₃	1	2	yes	—
45	C₃×#387	C₂×C₃	1	2	yes	—
46	C₃×#380	C₂×C₃	1	1	yes	characteristic
47	C₃×#380	C₂×C₃	1	1	yes	characteristic
48	C₃×#380	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×D₄×C₉	—	2	2	no	—
52	C₂×D₄×C₉	—	2	2	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂²×C₄×C₉	—	2	2	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	—	2	2	no	—
57	C₂²×C₄×C₉	—	2	2	no	—
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	D₄	1	4	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₉×C₄⋊C₄	—	2	2	no	—
70	C₉×C₄⋊C₄	—	2	2	no	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	2	4	no	—
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	—	4	2	no	—
76	C₉×C₂²⋊C₄	—	2	4	no	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	2	4	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	4	2	no	—
81	C₉×C₂²⋊C₄	—	4	2	no	—
82	C₄²×C₉	—	2	4	no	—
83	C₄²×C₉	—	2	2	no	—
84	#2485	C₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄×D₄	—	2	4	no	—
89	C₃×#117	—	2	4	no	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
105	C₃×#95	C₂²×C₃	1	2	yes	—
106	C₃×#95	C₂²×C₃	1	2	yes	—
107	C₃×#95	C₂²×C₃	1	2	yes	—
108	C₃×#95	C₂²×C₃	1	2	yes	—
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₂³×C₉	—	2	1	no	—
111	C₂³×C₉	—	2	1	no	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	—	2	1	no	—
117	C₂³×C₉	—	2	1	no	—
118	C₂³×C₉	—	2	1	no	—
119	C₂³×C₉	—	2	1	no	—
120	C₂³×C₉	—	2	1	no	—
121	C₂³×C₉	—	2	1	no	—
122	C₂³×C₉	C₂×D₄	1	2	yes	—
123	C₂³×C₉	#41	1	2	yes	—
124	C₂³×C₉	C₂⁴	1	1	yes	characteristic
125	D₄×C₉	—	2	8	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	8	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	4	4	no	—
150	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
151	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
152	C₂×C₄×C₉	#41	1	2	yes	—
153	C₂×C₄×C₉	#41	1	2	yes	—
154	C₂×C₄×C₉	#41	1	2	yes	—
155	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
156	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
157	#397	C₂×C₉	1	2	yes	complemented
158	#394	C₂×C₉	1	2	yes	—
159	#389	C₂×C₉	1	1	yes	characteristic, complemented
160	#389	C₂×C₉	1	1	yes	characteristic, complemented
161	#388	C₂×C₉	1	2	yes	complemented
162	#387	C₂×C₉	1	2	yes	complemented
163	#380	C₂×C₉	1	1	yes	characteristic, complemented
164	#380	C₂×C₉	1	1	yes	characteristic, complemented
165	#380	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
167	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₃×D₄	—	2	2	no	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	2	2	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	2	2	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	2	4	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	4	2	no	—
193	C₃×C₂²⋊C₄	—	2	4	no	—
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	—	2	4	no	—
196	C₃×C₂²⋊C₄	—	2	2	no	—
197	C₃×C₂²⋊C₄	—	4	2	no	—
198	C₃×C₂²⋊C₄	—	4	2	no	—
199	C₃×C₄²	—	2	4	no	—
200	C₃×C₄²	—	2	2	no	—
201	C₂²×C₉	—	2	2	no	—
202	C₂²×C₉	—	2	2	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	2	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	4	1	no	—
208	C₂²×C₉	—	4	1	no	—
209	C₂²×C₉	—	4	1	no	—
210	C₂²×C₉	—	4	1	no	—
211	C₂²×C₉	—	4	1	no	—
212	C₂²×C₉	—	4	1	no	—
213	C₂²×C₉	—	4	1	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
216	C₂²×C₉	C₂×#41	1	1	yes	characteristic
217	C₂²×C₉	C₂×#41	1	1	yes	characteristic
218	C₂²×C₉	C₂×#41	1	1	yes	characteristic
219	C₂²×C₉	C₂×#41	1	1	yes	characteristic
220	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
222	C₄×C₉	—	2	2	no	—
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	4	1	no	—
225	C₄×C₉	—	4	2	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	2	no	—
228	C₄×C₉	—	4	2	no	—
229	C₄×C₉	—	4	2	no	—
230	C₄×C₉	#123	1	4	yes	—
231	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
233	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
234	C₄×D₄	—	2	4	no	—
235	#117	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
242	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
248	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
249	C₂×C₄²	C₂²×C₉	1	2	yes	—
250	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
251	#95	C₂²×C₉	1	2	yes	—
252	#95	C₂²×C₉	1	2	yes	—
253	#95	C₂²×C₉	1	2	yes	—
254	#95	C₂²×C₉	1	2	yes	—
255	#95	C₂²×C₉	1	2	yes	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	2	1	no	—
258	C₂³×C₃	—	2	1	no	—
259	C₂³×C₃	—	2	1	no	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	1	no	—
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	2	1	no	—
265	C₂³×C₃	—	2	1	no	—
266	C₂³×C₃	—	2	1	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
269	C₂³×C₃	C₃×#41	1	2	yes	—
270	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
271	C₃×D₄	—	2	8	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	4	4	no	—
296	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₃×C₄	C₃×#41	1	2	yes	—
299	C₂×C₃×C₄	C₃×#41	1	2	yes	—
300	C₂×C₃×C₄	C₃×#41	1	2	yes	—
301	C₂×C₉	—	4	2	no	—
302	C₂×C₉	—	4	2	no	—
303	C₂×C₉	C₂×#123	1	1	yes	characteristic
304	C₂×C₉	#525	1	1	yes	characteristic
305	C₂×C₉	#537	1	1	yes	characteristic
306	C₂×C₉	#552	1	1	yes	characteristic
307	C₂×C₉	#553	1	1	yes	characteristic
308	C₂×C₉	#555	1	1	yes	characteristic
309	C₂×C₉	#556	1	1	yes	characteristic
310	C₂⁴	C₂³×C₉	1	1	yes	characteristic
311	C₂⁴	C₂³×C₉	1	1	yes	characteristic
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	D₄×C₉	1	4	yes	—
321	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
322	C₂²×C₄	C₂³×C₉	1	2	yes	—
323	C₂²×C₄	C₂³×C₉	1	2	yes	—
324	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₉	1	2	yes	—
326	C₂²×C₄	C₂³×C₉	1	2	yes	—
327	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	—	4	1	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	—	4	1	no	—
355	C₂²×C₃	—	4	1	no	—
356	C₂²×C₃	—	4	1	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
360	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
361	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
362	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
363	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
364	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	—	4	2	no	—
372	C₃×C₄	—	4	2	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	C₃×#123	1	4	yes	—
375	C₉	#2485	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₂×D₄×C₉	1	2	yes	—
389	C₂³	C₉×#41	1	2	yes	—
390	C₂³	C₂⁴×C₉	1	1	yes	characteristic
391	D₄	—	2	8	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
417	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
418	C₂×C₄	C₉×#41	1	2	yes	—
419	C₂×C₄	C₉×#41	1	2	yes	—
420	C₂×C₄	C₉×#41	1	2	yes	—
421	C₂×C₃	—	4	2	no	—
422	C₂×C₃	—	4	2	no	—
423	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
424	C₂×C₃	C₃×#525	1	1	yes	characteristic
425	C₂×C₃	C₃×#537	1	1	yes	characteristic
426	C₂×C₃	C₃×#552	1	1	yes	characteristic
427	C₂×C₃	C₃×#553	1	1	yes	characteristic
428	C₂×C₃	C₃×#555	1	1	yes	characteristic
429	C₂×C₃	C₃×#556	1	1	yes	characteristic
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
445	C₂²	C₂×C₉×#41	1	1	yes	characteristic
446	C₂²	C₂×C₉×#41	1	1	yes	characteristic
447	C₂²	C₂×C₉×#41	1	1	yes	characteristic
448	C₂²	C₂×C₉×#41	1	1	yes	characteristic
449	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	C₉×#123	1	4	yes	—
460	C₃	C₃×#2485	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	—	4	2	no	—
463	C₂	C₂×C₉×#123	1	1	yes	characteristic
464	C₂	C₉×#525	1	1	yes	characteristic
465	C₂	C₉×#537	1	1	yes	characteristic
466	C₂	C₉×#552	1	1	yes	characteristic
467	C₂	C₉×#553	1	1	yes	characteristic
468	C₂	C₉×#555	1	1	yes	characteristic
469	C₂	C₉×#556	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×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
2. C₂×C₉×#117	C₂	semidirect
3. C₉×#397	C₂	semidirect
5. C₉×#389	C₂	semidirect
6. C₉×#389	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#387	C₂	semidirect
9. C₉×#380	C₂	semidirect
10. C₉×#380	C₂	semidirect
11. C₉×#380	C₂	semidirect
84. #2485	C₉	direct (N × H)
156. C₂×#117	C₂×C₉	semidirect
157. #397	C₂×C₉	semidirect
159. #389	C₂×C₉	semidirect
160. #389	C₂×C₉	semidirect
161. #388	C₂×C₉	semidirect
162. #387	C₂×C₉	semidirect
163. #380	C₂×C₉	semidirect
164. #380	C₂×C₉	semidirect
165. #380	C₂×C₉	semidirect
375. C₉	#2485	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×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₉×#397	2
C₉×#394	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#380	2
C₃×#2485	3

Subgroups — C9×#2485 #11767206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2485 #11767206