Subgroups — C₉×#2480 #11767201

Order 1152.

996 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#379	C₂	1	1	yes	maximal, characteristic
14	C₉×#379	C₂	1	1	yes	maximal, characteristic
15	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2480	C₃	1	1	yes	maximal, characteristic
17	C₂⁵×C₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₉×#126	—	2	4	no	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₉×C₂²⋊C₄	—	2	4	no	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₂²⋊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×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
46	C₉×#95	C₂²	1	1	yes	characteristic, complemented
47	C₉×#95	C₂²	1	1	yes	characteristic, complemented
48	C₉×#95	C₂²	1	1	yes	characteristic, complemented
49	C₉×#95	C₂²	1	1	yes	characteristic, complemented
50	C₉×#95	C₂²	1	1	yes	characteristic, complemented
51	C₉×#95	C₂²	1	1	yes	characteristic, complemented
52	C₉×#95	C₂²	1	1	yes	characteristic, complemented
53	C₉×#95	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×#126	C₂×C₃	1	1	yes	characteristic
55	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
56	C₃×#397	C₂×C₃	1	1	yes	characteristic
57	C₃×#397	C₂×C₃	1	1	yes	characteristic
58	C₃×#397	C₂×C₃	1	1	yes	characteristic
59	C₃×#396	C₂×C₃	1	1	yes	characteristic
60	C₃×#388	C₂×C₃	1	1	yes	characteristic
61	C₃×#388	C₂×C₃	1	1	yes	characteristic
62	C₃×#388	C₂×C₃	1	1	yes	characteristic
63	C₃×#385	C₂×C₃	1	1	yes	characteristic
64	C₃×#385	C₂×C₃	1	1	yes	characteristic
65	C₃×#380	C₂×C₃	1	1	yes	characteristic
66	C₃×#379	C₂×C₃	1	1	yes	characteristic
67	C₃×#379	C₂×C₃	1	1	yes	characteristic
68	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₂⁴×C₉	—	2	2	no	—
70	C₂⁴×C₉	—	2	2	no	—
71	C₂⁴×C₉	—	2	2	no	—
72	C₂⁴×C₉	—	2	2	no	—
73	C₂⁴×C₉	—	2	2	no	—
74	C₂⁴×C₉	—	4	1	no	—
75	C₂⁴×C₉	—	4	1	no	—
76	C₂⁴×C₉	C₂³	1	1	yes	characteristic
77	C₂⁴×C₉	C₂³	1	1	yes	characteristic
78	C₂⁴×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	—	2	2	no	—
80	C₂²×C₄×C₉	—	2	2	no	—
81	C₂²×C₄×C₉	—	2	2	no	—
82	C₂²×C₄×C₉	—	2	2	no	—
83	C₂²×C₄×C₉	—	4	1	no	—
84	C₂²×C₄×C₉	—	4	1	no	—
85	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₉×C₄⋊C₄	—	2	2	no	—
98	C₉×C₄⋊C₄	—	2	2	no	—
99	C₉×C₄⋊C₄	—	2	2	no	—
100	C₉×C₄⋊C₄	—	4	1	no	—
101	C₉×C₄⋊C₄	—	4	1	no	—
102	C₉×C₄⋊C₄	—	4	1	no	—
103	C₉×C₂²⋊C₄	—	2	2	no	—
104	C₉×C₂²⋊C₄	—	2	2	no	—
105	C₉×C₂²⋊C₄	—	2	2	no	—
106	C₉×C₂²⋊C₄	—	2	2	no	—
107	C₉×C₂²⋊C₄	—	2	2	no	—
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	—	2	2	no	—
110	C₉×C₂²⋊C₄	—	2	2	no	—
111	C₉×C₂²⋊C₄	—	2	2	no	—
112	C₉×C₂²⋊C₄	—	2	2	no	—
113	C₉×C₂²⋊C₄	—	2	2	no	—
114	C₉×C₂²⋊C₄	—	4	1	no	—
115	C₉×C₂²⋊C₄	—	4	1	no	—
116	C₉×C₂²⋊C₄	—	4	1	no	—
117	C₉×C₂²⋊C₄	—	4	1	no	—
118	C₉×C₂²⋊C₄	D₄	1	4	yes	—
119	C₄²×C₉	—	2	2	no	—
120	C₄²×C₉	—	4	1	no	—
121	#2480	C₉	1	1	yes	characteristic, direct product factor, Sylow
122	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃×#126	—	2	4	no	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
151	C₃×#95	C₂²×C₃	1	1	yes	characteristic
152	C₃×#95	C₂²×C₃	1	1	yes	characteristic
153	C₃×#95	C₂²×C₃	1	1	yes	characteristic
154	C₃×#95	C₂²×C₃	1	1	yes	characteristic
155	C₃×#95	C₂²×C₃	1	1	yes	characteristic
156	C₃×#95	C₂²×C₃	1	1	yes	characteristic
157	C₃×#95	C₂²×C₃	1	1	yes	characteristic
158	C₃×#95	C₂²×C₃	1	1	yes	characteristic
159	C₂³×C₉	—	2	1	no	—
160	C₂³×C₉	—	2	1	no	—
161	C₂³×C₉	—	2	1	no	—
162	C₂³×C₉	—	2	1	no	—
163	C₂³×C₉	—	2	8	no	—
164	C₂³×C₉	—	2	1	no	—
165	C₂³×C₉	—	2	1	no	—
166	C₂³×C₉	—	2	1	no	—
167	C₂³×C₉	—	2	1	no	—
168	C₂³×C₉	—	2	1	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	2	1	no	—
171	C₂³×C₉	—	2	1	no	—
172	C₂³×C₉	—	2	1	no	—
173	C₂³×C₉	—	2	1	no	—
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	—	2	1	no	—
176	C₂³×C₉	—	4	4	no	—
177	C₂³×C₉	—	4	4	no	—
178	C₂³×C₉	—	4	4	no	—
179	C₂³×C₉	—	4	4	no	—
180	C₂³×C₉	—	4	4	no	—
181	C₂³×C₉	—	4	4	no	—
182	C₂³×C₉	C₂×D₄	1	2	yes	—
183	C₂³×C₉	#41	1	2	yes	—
184	C₂³×C₉	#41	1	2	yes	—
185	C₂³×C₉	#41	1	2	yes	—
186	C₂³×C₉	#41	1	2	yes	—
187	C₂³×C₉	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	—	2	1	no	—
206	C₂×C₄×C₉	—	2	1	no	—
207	C₂×C₄×C₉	—	2	1	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	—	4	4	no	—
223	C₂×C₄×C₉	—	4	4	no	—
224	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
225	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
226	C₂×#126	C₂×C₉	1	1	yes	characteristic, complemented
227	C₂²×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
228	#397	C₂×C₉	1	1	yes	characteristic, complemented
229	#397	C₂×C₉	1	1	yes	characteristic, complemented
230	#397	C₂×C₉	1	1	yes	characteristic, complemented
231	#396	C₂×C₉	1	1	yes	characteristic, complemented
232	#388	C₂×C₉	1	1	yes	characteristic, complemented
233	#388	C₂×C₉	1	1	yes	characteristic, complemented
234	#388	C₂×C₉	1	1	yes	characteristic, complemented
235	#385	C₂×C₉	1	1	yes	characteristic, complemented
236	#385	C₂×C₉	1	1	yes	characteristic, complemented
237	#380	C₂×C₉	1	1	yes	characteristic, complemented
238	#379	C₂×C₉	1	1	yes	characteristic
239	#379	C₂×C₉	1	1	yes	characteristic
240	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
241	C₂⁴×C₃	—	2	2	no	—
242	C₂⁴×C₃	—	2	2	no	—
243	C₂⁴×C₃	—	2	2	no	—
244	C₂⁴×C₃	—	2	2	no	—
245	C₂⁴×C₃	—	2	2	no	—
246	C₂⁴×C₃	—	4	1	no	—
247	C₂⁴×C₃	—	4	1	no	—
248	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
249	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
250	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	2	no	—
253	C₂²×C₃×C₄	—	2	2	no	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	—	4	1	no	—
256	C₂²×C₃×C₄	—	4	1	no	—
257	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
269	C₃×C₄⋊C₄	—	2	2	no	—
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	2	no	—
272	C₃×C₄⋊C₄	—	4	1	no	—
273	C₃×C₄⋊C₄	—	4	1	no	—
274	C₃×C₄⋊C₄	—	4	1	no	—
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	2	2	no	—
278	C₃×C₂²⋊C₄	—	2	2	no	—
279	C₃×C₂²⋊C₄	—	2	2	no	—
280	C₃×C₂²⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	—	2	2	no	—
282	C₃×C₂²⋊C₄	—	2	2	no	—
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₂²⋊C₄	—	2	2	no	—
286	C₃×C₂²⋊C₄	—	4	1	no	—
287	C₃×C₂²⋊C₄	—	4	1	no	—
288	C₃×C₂²⋊C₄	—	4	1	no	—
289	C₃×C₂²⋊C₄	—	4	1	no	—
290	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
291	C₃×C₄²	—	2	2	no	—
292	C₃×C₄²	—	4	1	no	—
293	C₂²×C₉	—	2	2	no	—
294	C₂²×C₉	—	2	2	no	—
295	C₂²×C₉	—	2	2	no	—
296	C₂²×C₉	—	2	2	no	—
297	C₂²×C₉	—	2	2	no	—
298	C₂²×C₉	—	2	2	no	—
299	C₂²×C₉	—	2	2	no	—
300	C₂²×C₉	—	2	2	no	—
301	C₂²×C₉	—	2	2	no	—
302	C₂²×C₉	—	2	2	no	—
303	C₂²×C₉	—	2	2	no	—
304	C₂²×C₉	—	2	2	no	—
305	C₂²×C₉	—	4	16	no	—
306	C₂²×C₉	—	4	1	no	—
307	C₂²×C₉	—	4	1	no	—
308	C₂²×C₉	—	4	1	no	—
309	C₂²×C₉	—	4	1	no	—
310	C₂²×C₉	—	4	1	no	—
311	C₂²×C₉	—	4	1	no	—
312	C₂²×C₉	—	4	1	no	—
313	C₂²×C₉	—	4	1	no	—
314	C₂²×C₉	#126	1	4	yes	complemented
315	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
316	C₂²×C₉	C₂×#41	1	1	yes	characteristic
317	C₂²×C₉	C₂×#41	1	1	yes	characteristic
318	C₂²×C₉	C₂×#41	1	1	yes	characteristic
319	C₂²×C₉	C₂×#41	1	1	yes	characteristic
320	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
322	C₄×C₉	—	2	2	no	—
323	C₄×C₉	—	2	2	no	—
324	C₄×C₉	—	4	1	no	—
325	C₄×C₉	—	4	1	no	—
326	C₄×C₉	—	4	1	no	—
327	C₄×C₉	—	4	1	no	—
328	C₄×C₉	—	4	1	no	—
329	C₄×C₉	—	4	1	no	—
330	C₄×C₉	—	4	1	no	—
331	C₄×C₉	—	4	1	no	—
332	C₄×C₉	—	4	1	no	—
333	C₄×C₉	—	4	1	no	—
334	C₂⁵	C₂²×C₉	1	1	yes	characteristic
335	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
336	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
337	#126	—	2	4	no	—
338	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
339	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
340	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
341	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
342	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
343	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
361	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
362	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
363	#95	C₂²×C₉	1	1	yes	characteristic, complemented
364	#95	C₂²×C₉	1	1	yes	characteristic, complemented
365	#95	C₂²×C₉	1	1	yes	characteristic, complemented
366	#95	C₂²×C₉	1	1	yes	characteristic, complemented
367	#95	C₂²×C₉	1	1	yes	characteristic, complemented
368	#95	C₂²×C₉	1	1	yes	characteristic, complemented
369	#95	C₂²×C₉	1	1	yes	characteristic, complemented
370	#95	C₂²×C₉	1	1	yes	characteristic, complemented
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	2	1	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	—	2	8	no	—
376	C₂³×C₃	—	2	1	no	—
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	—	2	1	no	—
379	C₂³×C₃	—	2	1	no	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	—	2	1	no	—
384	C₂³×C₃	—	2	1	no	—
385	C₂³×C₃	—	2	1	no	—
386	C₂³×C₃	—	2	1	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	4	4	no	—
389	C₂³×C₃	—	4	4	no	—
390	C₂³×C₃	—	4	4	no	—
391	C₂³×C₃	—	4	4	no	—
392	C₂³×C₃	—	4	4	no	—
393	C₂³×C₃	—	4	4	no	—
394	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
395	C₂³×C₃	C₃×#41	1	2	yes	—
396	C₂³×C₃	C₃×#41	1	2	yes	—
397	C₂³×C₃	C₃×#41	1	2	yes	—
398	C₂³×C₃	C₃×#41	1	2	yes	—
399	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	2	1	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	4	4	no	—
435	C₂×C₃×C₄	—	4	4	no	—
436	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
437	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
438	C₂×C₉	—	2	4	no	—
439	C₂×C₉	—	4	2	no	—
440	C₂×C₉	—	4	2	no	—
441	C₂×C₉	#525	1	1	yes	characteristic
442	C₂×C₉	C₂×#126	1	1	yes	characteristic
443	C₂×C₉	#538	1	1	yes	characteristic
444	C₂×C₉	#546	1	1	yes	characteristic
445	C₂×C₉	#546	1	1	yes	characteristic
446	C₂×C₉	#551	1	1	yes	characteristic
447	C₂×C₉	#551	1	1	yes	characteristic
448	C₂⁴	—	2	2	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	4	1	no	—
454	C₂⁴	—	4	1	no	—
455	C₂⁴	C₂³×C₉	1	1	yes	characteristic
456	C₂⁴	C₂³×C₉	1	1	yes	characteristic
457	C₂⁴	C₂³×C₉	1	1	yes	characteristic
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
465	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
466	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
467	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
469	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
470	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
471	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
472	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
473	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
474	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
475	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	D₄×C₉	1	4	yes	—
498	C₄²	—	2	2	no	—
499	C₄²	—	4	1	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	2	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	2	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	4	16	no	—
513	C₂²×C₃	—	4	1	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	4	1	no	—
518	C₂²×C₃	—	4	1	no	—
519	C₂²×C₃	—	4	1	no	—
520	C₂²×C₃	—	4	1	no	—
521	C₂²×C₃	C₃×#126	1	4	yes	—
522	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
523	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
524	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
525	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
526	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
527	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
529	C₃×C₄	—	2	2	no	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	4	1	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	—	4	1	no	—
536	C₃×C₄	—	4	1	no	—
537	C₃×C₄	—	4	1	no	—
538	C₃×C₄	—	4	1	no	—
539	C₃×C₄	—	4	1	no	—
540	C₃×C₄	—	4	1	no	—
541	C₉	#2480	1	1	yes	characteristic, direct product factor, Sylow
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	8	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	4	4	no	—
560	C₂³	—	4	4	no	—
561	C₂³	—	4	4	no	—
562	C₂³	—	4	4	no	—
563	C₂³	—	4	4	no	—
564	C₂³	—	4	4	no	—
565	C₂³	C₂×D₄×C₉	1	2	yes	—
566	C₂³	C₉×#41	1	2	yes	—
567	C₂³	C₉×#41	1	2	yes	—
568	C₂³	C₉×#41	1	2	yes	—
569	C₂³	C₉×#41	1	2	yes	—
570	C₂³	C₂⁴×C₉	1	1	yes	characteristic
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
608	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
609	C₂×C₃	—	2	4	no	—
610	C₂×C₃	—	4	2	no	—
611	C₂×C₃	—	4	2	no	—
612	C₂×C₃	C₃×#525	1	1	yes	characteristic
613	C₂×C₃	C₂×C₃×#126	1	1	yes	characteristic
614	C₂×C₃	C₃×#538	1	1	yes	characteristic
615	C₂×C₃	C₃×#546	1	1	yes	characteristic
616	C₂×C₃	C₃×#546	1	1	yes	characteristic
617	C₂×C₃	C₃×#551	1	1	yes	characteristic
618	C₂×C₃	C₃×#551	1	1	yes	characteristic
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	16	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	C₉×#126	1	4	yes	complemented
641	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
642	C₂²	C₂×C₉×#41	1	1	yes	characteristic
643	C₂²	C₂×C₉×#41	1	1	yes	characteristic
644	C₂²	C₂×C₉×#41	1	1	yes	characteristic
645	C₂²	C₂×C₉×#41	1	1	yes	characteristic
646	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₃	C₃×#2480	1	1	yes	characteristic
661	C₂	—	2	4	no	—
662	C₂	—	4	2	no	—
663	C₂	—	4	2	no	—
664	C₂	C₉×#525	1	1	yes	characteristic
665	C₂	C₂×C₉×#126	1	1	yes	characteristic
666	C₂	C₉×#538	1	1	yes	characteristic
667	C₂	C₉×#546	1	1	yes	characteristic
668	C₂	C₉×#546	1	1	yes	characteristic
669	C₂	C₉×#551	1	1	yes	characteristic
670	C₂	C₉×#551	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁵×C₃	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
1. C₂×C₉×#126	C₂	semidirect
3. C₉×#397	C₂	semidirect
4. C₉×#397	C₂	semidirect
5. C₉×#397	C₂	semidirect
6. C₉×#396	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#388	C₂	semidirect
9. C₉×#388	C₂	semidirect
10. C₉×#385	C₂	semidirect
11. C₉×#385	C₂	semidirect
12. C₉×#380	C₂	semidirect
15. C₄×C₉×C₂²⋊C₄	C₂	semidirect
21. C₂×C₉×C₄⋊C₄	C₂²	semidirect
22. C₂×C₉×C₄⋊C₄	C₂²	semidirect
23. C₂×C₉×C₄⋊C₄	C₂²	semidirect
24. C₂×C₉×C₄⋊C₄	C₂²	semidirect
25. C₂×C₉×C₄⋊C₄	C₂²	semidirect
26. C₂×C₉×C₄⋊C₄	C₂²	semidirect
44. C₂×C₄²×C₉	C₂²	semidirect
45. C₂×C₄²×C₉	C₂²	semidirect
46. C₉×#95	C₂²	semidirect
47. C₉×#95	C₂²	semidirect
48. C₉×#95	C₂²	semidirect
49. C₉×#95	C₂²	semidirect
50. C₉×#95	C₂²	semidirect
51. C₉×#95	C₂²	semidirect
52. C₉×#95	C₂²	semidirect
53. C₉×#95	C₂²	semidirect
121. #2480	C₉	direct (N × H)
226. C₂×#126	C₂×C₉	semidirect
228. #397	C₂×C₉	semidirect
229. #397	C₂×C₉	semidirect
230. #397	C₂×C₉	semidirect
231. #396	C₂×C₉	semidirect
232. #388	C₂×C₉	semidirect
233. #388	C₂×C₉	semidirect
234. #388	C₂×C₉	semidirect
235. #385	C₂×C₉	semidirect
236. #385	C₂×C₉	semidirect
237. #380	C₂×C₉	semidirect
240. C₄×C₂²⋊C₄	C₂×C₉	semidirect
314. C₂²×C₉	#126	semidirect
338. C₂×C₄⋊C₄	C₂²×C₉	semidirect
339. C₂×C₄⋊C₄	C₂²×C₉	semidirect
340. C₂×C₄⋊C₄	C₂²×C₉	semidirect
341. C₂×C₄⋊C₄	C₂²×C₉	semidirect
342. C₂×C₄⋊C₄	C₂²×C₉	semidirect
343. C₂×C₄⋊C₄	C₂²×C₉	semidirect
361. C₂×C₄²	C₂²×C₉	semidirect
362. C₂×C₄²	C₂²×C₉	semidirect
363. #95	C₂²×C₉	semidirect
364. #95	C₂²×C₉	semidirect
365. #95	C₂²×C₉	semidirect
366. #95	C₂²×C₉	semidirect
367. #95	C₂²×C₉	semidirect
368. #95	C₂²×C₉	semidirect
369. #95	C₂²×C₉	semidirect
370. #95	C₂²×C₉	semidirect
541. C₉	#2480	direct (N × H)
640. C₂²	C₉×#126	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#126	2
C₂²×C₉×C₂²⋊C₄	2
C₉×#397	2
C₉×#396	2
C₉×#388	2
C₉×#385	2
C₉×#380	2
C₉×#379	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2480	3

Subgroups — C9×#2480 #11767201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2480 #11767201