Subgroups — C₉×#2481 #11767202

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 603 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×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#400	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×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#386	C₂	1	1	yes	maximal, characteristic
11	C₉×#386	C₂	1	1	yes	maximal, characteristic
12	C₉×#386	C₂	1	1	yes	maximal, characteristic
13	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2481	C₃	1	1	yes	maximal, characteristic
17	C₂²×D₄×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	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₉×#126	—	2	4	no	—
22	C₂×C₉×C₄⋊C₄	—	2	4	no	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊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×C₄²×C₉	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
42	C₉×#95	C₂²	1	1	yes	characteristic
43	C₉×#95	C₂²	1	1	yes	characteristic
44	C₉×#95	C₂²	1	1	yes	characteristic
45	C₉×#95	C₂²	1	1	yes	characteristic
46	C₉×#95	C₂²	1	1	yes	characteristic
47	C₉×#95	C₂²	1	1	yes	characteristic
48	C₉×#95	C₂²	1	1	yes	characteristic
49	C₉×#95	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	C₂×C₃×#126	C₂×C₃	1	1	yes	characteristic
55	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
56	C₃×#400	C₂×C₃	1	1	yes	characteristic
57	C₃×#400	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×#387	C₂×C₃	1	1	yes	characteristic
62	C₃×#387	C₂×C₃	1	1	yes	characteristic
63	C₃×#386	C₂×C₃	1	1	yes	characteristic
64	C₃×#386	C₂×C₃	1	1	yes	characteristic
65	C₃×#386	C₂×C₃	1	1	yes	characteristic
66	C₃×#385	C₂×C₃	1	1	yes	characteristic
67	C₃×#380	C₂×C₃	1	1	yes	characteristic
68	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₂⁴×C₉	C₂³	1	1	yes	characteristic
70	C₂⁴×C₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₉	—	2	2	no	—
72	C₂×D₄×C₉	—	2	2	no	—
73	C₂×D₄×C₉	—	2	2	no	—
74	C₂²×C₄×C₉	—	2	2	no	—
75	C₂²×C₄×C₉	—	2	2	no	—
76	C₂²×C₄×C₉	—	2	2	no	—
77	C₂²×C₄×C₉	—	2	2	no	—
78	C₂²×C₄×C₉	—	2	2	no	—
79	C₂²×C₄×C₉	—	2	2	no	—
80	C₂²×C₄×C₉	—	2	2	no	—
81	C₂²×C₄×C₉	—	4	1	no	—
82	C₂²×C₄×C₉	—	4	1	no	—
83	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₉×C₄⋊C₄	—	2	2	no	—
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	—	2	2	no	—
101	C₉×C₄⋊C₄	—	2	2	no	—
102	C₉×C₄⋊C₄	—	4	1	no	—
103	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
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	—	4	1	no	—
112	C₉×C₂²⋊C₄	—	4	1	no	—
113	C₄²×C₉	—	2	2	no	—
114	C₄²×C₉	—	4	1	no	—
115	#2481	C₉	1	1	yes	characteristic, direct product factor, Sylow
116	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
120	C₃×#126	—	2	4	no	—
121	C₂×C₃×C₄⋊C₄	—	2	4	no	—
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₄²	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
141	C₃×#95	C₂²×C₃	1	1	yes	characteristic
142	C₃×#95	C₂²×C₃	1	1	yes	characteristic
143	C₃×#95	C₂²×C₃	1	1	yes	characteristic
144	C₃×#95	C₂²×C₃	1	1	yes	characteristic
145	C₃×#95	C₂²×C₃	1	1	yes	characteristic
146	C₃×#95	C₂²×C₃	1	1	yes	characteristic
147	C₃×#95	C₂²×C₃	1	1	yes	characteristic
148	C₃×#95	C₂²×C₃	1	1	yes	characteristic
149	C₃×#95	C₂²×C₃	1	1	yes	characteristic
150	C₃×#95	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	C₂³×C₉	—	2	1	no	—
154	C₂³×C₉	—	2	1	no	—
155	C₂³×C₉	—	2	1	no	—
156	C₂³×C₉	—	2	1	no	—
157	C₂³×C₉	—	2	1	no	—
158	C₂³×C₉	—	2	1	no	—
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	1	no	—
164	C₂³×C₉	#41	1	2	yes	—
165	C₂³×C₉	#41	1	2	yes	—
166	C₂³×C₉	#41	1	2	yes	—
167	C₂³×C₉	C₂⁴	1	1	yes	characteristic
168	D₄×C₉	—	4	4	no	—
169	C₂×C₄×C₉	—	2	8	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	1	no	—
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	—	4	4	no	—
206	C₂×C₄×C₉	—	4	4	no	—
207	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
208	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
209	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
210	C₂×C₄×C₉	#41	1	2	yes	—
211	C₂×#126	C₂×C₉	1	1	yes	characteristic, complemented
212	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
213	#400	C₂×C₉	1	1	yes	characteristic, complemented
214	#400	C₂×C₉	1	1	yes	characteristic, complemented
215	#397	C₂×C₉	1	1	yes	characteristic, complemented
216	#396	C₂×C₉	1	1	yes	characteristic, complemented
217	#388	C₂×C₉	1	1	yes	characteristic, complemented
218	#387	C₂×C₉	1	1	yes	characteristic, complemented
219	#387	C₂×C₉	1	1	yes	characteristic, complemented
220	#386	C₂×C₉	1	1	yes	characteristic
221	#386	C₂×C₉	1	1	yes	characteristic
222	#386	C₂×C₉	1	1	yes	characteristic
223	#385	C₂×C₉	1	1	yes	characteristic, complemented
224	#380	C₂×C₉	1	1	yes	characteristic, complemented
225	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
226	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
227	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
228	C₂×C₃×D₄	—	2	2	no	—
229	C₂×C₃×D₄	—	2	2	no	—
230	C₂×C₃×D₄	—	2	2	no	—
231	C₂²×C₃×C₄	—	2	2	no	—
232	C₂²×C₃×C₄	—	2	2	no	—
233	C₂²×C₃×C₄	—	2	2	no	—
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	—	4	1	no	—
239	C₂²×C₃×C₄	—	4	1	no	—
240	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	4	1	no	—
260	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
261	C₃×C₂²⋊C₄	—	2	2	no	—
262	C₃×C₂²⋊C₄	—	2	2	no	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	2	2	no	—
265	C₃×C₂²⋊C₄	—	2	2	no	—
266	C₃×C₂²⋊C₄	—	2	2	no	—
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	—	4	1	no	—
269	C₃×C₂²⋊C₄	—	4	1	no	—
270	C₃×C₄²	—	2	2	no	—
271	C₃×C₄²	—	4	1	no	—
272	C₂²×C₉	—	2	2	no	—
273	C₂²×C₉	—	2	2	no	—
274	C₂²×C₉	—	2	2	no	—
275	C₂²×C₉	—	2	2	no	—
276	C₂²×C₉	—	2	2	no	—
277	C₂²×C₉	—	2	2	no	—
278	C₂²×C₉	—	4	1	no	—
279	C₂²×C₉	—	4	1	no	—
280	C₂²×C₉	—	4	1	no	—
281	C₂²×C₉	—	4	1	no	—
282	C₂²×C₉	—	4	1	no	—
283	C₂²×C₉	—	4	1	no	—
284	C₂²×C₉	—	4	1	no	—
285	C₂²×C₉	#126	1	4	yes	complemented
286	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
287	C₂²×C₉	C₂×#41	1	1	yes	characteristic
288	C₂²×C₉	C₂×#41	1	1	yes	characteristic
289	C₂²×C₉	C₂×#41	1	1	yes	characteristic
290	C₂²×C₉	C₂×#41	1	1	yes	characteristic
291	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
293	C₄×C₉	—	2	2	no	—
294	C₄×C₉	—	2	2	no	—
295	C₄×C₉	—	2	2	no	—
296	C₄×C₉	—	2	2	no	—
297	C₄×C₉	—	4	1	no	—
298	C₄×C₉	—	4	1	no	—
299	C₄×C₉	—	4	1	no	—
300	C₄×C₉	—	4	1	no	—
301	C₄×C₉	—	4	1	no	—
302	C₄×C₉	—	4	1	no	—
303	C₄×C₉	—	4	1	no	—
304	C₄×C₉	—	4	1	no	—
305	C₄×C₉	—	4	1	no	—
306	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
307	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
308	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
309	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
310	#126	—	2	4	no	—
311	C₂×C₄⋊C₄	—	2	4	no	—
312	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
329	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
330	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
331	#95	C₂²×C₉	1	1	yes	characteristic
332	#95	C₂²×C₉	1	1	yes	characteristic
333	#95	C₂²×C₉	1	1	yes	characteristic
334	#95	C₂²×C₉	1	1	yes	characteristic
335	#95	C₂²×C₉	1	1	yes	characteristic
336	#95	C₂²×C₉	1	1	yes	characteristic
337	#95	C₂²×C₉	1	1	yes	characteristic
338	#95	C₂²×C₉	1	1	yes	characteristic
339	#95	C₂²×C₉	1	1	yes	characteristic
340	#95	C₂²×C₉	1	1	yes	characteristic
341	#95	C₂²×C₉	1	1	yes	characteristic
342	#95	C₂²×C₉	1	1	yes	characteristic
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	2	1	no	—
345	C₂³×C₃	—	2	1	no	—
346	C₂³×C₃	—	2	1	no	—
347	C₂³×C₃	—	2	1	no	—
348	C₂³×C₃	—	2	1	no	—
349	C₂³×C₃	—	2	1	no	—
350	C₂³×C₃	—	2	1	no	—
351	C₂³×C₃	—	2	1	no	—
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	C₃×#41	1	2	yes	—
355	C₂³×C₃	C₃×#41	1	2	yes	—
356	C₂³×C₃	C₃×#41	1	2	yes	—
357	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
358	C₃×D₄	—	4	4	no	—
359	C₂×C₃×C₄	—	2	8	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	4	4	no	—
396	C₂×C₃×C₄	—	4	4	no	—
397	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
398	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
399	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
400	C₂×C₃×C₄	C₃×#41	1	2	yes	—
401	C₂×C₉	—	2	4	no	—
402	C₂×C₉	—	8	1	no	—
403	C₂×C₉	#525	1	1	yes	characteristic
404	C₂×C₉	C₂×#126	1	1	yes	characteristic
405	C₂×C₉	#539	1	1	yes	characteristic
406	C₂×C₉	#546	1	1	yes	characteristic
407	C₂×C₉	#548	1	1	yes	characteristic
408	C₂×C₉	#552	1	1	yes	characteristic
409	C₂×C₉	#553	1	1	yes	characteristic
410	C₂⁴	C₂³×C₉	1	1	yes	characteristic
411	C₂⁴	C₂³×C₉	1	1	yes	characteristic
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
425	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
426	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
427	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
430	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
431	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
432	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
433	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
434	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
435	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
436	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	4	1	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	4	1	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	4	1	no	—
464	C₂²×C₃	—	4	1	no	—
465	C₂²×C₃	—	4	1	no	—
466	C₂²×C₃	—	4	1	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	—	4	1	no	—
469	C₂²×C₃	C₃×#126	1	4	yes	—
470	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
471	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
472	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
473	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
474	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
475	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
477	C₃×C₄	—	2	2	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	4	1	no	—
482	C₃×C₄	—	4	1	no	—
483	C₃×C₄	—	4	1	no	—
484	C₃×C₄	—	4	1	no	—
485	C₃×C₄	—	4	1	no	—
486	C₃×C₄	—	4	1	no	—
487	C₃×C₄	—	4	1	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	1	no	—
490	C₉	#2481	1	1	yes	characteristic, direct product factor, Sylow
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	C₉×#41	1	2	yes	—
503	C₂³	C₉×#41	1	2	yes	—
504	C₂³	C₉×#41	1	2	yes	—
505	C₂³	C₂⁴×C₉	1	1	yes	characteristic
506	D₄	—	4	4	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
546	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
547	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
548	C₂×C₄	C₉×#41	1	2	yes	—
549	C₂×C₃	—	2	4	no	—
550	C₂×C₃	—	8	1	no	—
551	C₂×C₃	C₃×#525	1	1	yes	characteristic
552	C₂×C₃	C₂×C₃×#126	1	1	yes	characteristic
553	C₂×C₃	C₃×#539	1	1	yes	characteristic
554	C₂×C₃	C₃×#546	1	1	yes	characteristic
555	C₂×C₃	C₃×#548	1	1	yes	characteristic
556	C₂×C₃	C₃×#552	1	1	yes	characteristic
557	C₂×C₃	C₃×#553	1	1	yes	characteristic
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	C₉×#126	1	4	yes	complemented
572	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
573	C₂²	C₂×C₉×#41	1	1	yes	characteristic
574	C₂²	C₂×C₉×#41	1	1	yes	characteristic
575	C₂²	C₂×C₉×#41	1	1	yes	characteristic
576	C₂²	C₂×C₉×#41	1	1	yes	characteristic
577	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₃	C₃×#2481	1	1	yes	characteristic
593	C₂	—	2	4	no	—
594	C₂	—	8	1	no	—
595	C₂	C₉×#525	1	1	yes	characteristic
596	C₂	C₂×C₉×#126	1	1	yes	characteristic
597	C₂	C₉×#539	1	1	yes	characteristic
598	C₂	C₉×#546	1	1	yes	characteristic
599	C₂	C₉×#548	1	1	yes	characteristic
600	C₂	C₉×#552	1	1	yes	characteristic
601	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	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
1. C₂×C₉×#126	C₂	semidirect
2. C₂²×C₉×C₄⋊C₄	C₂	semidirect
3. C₉×#400	C₂	semidirect
4. C₉×#400	C₂	semidirect
5. C₉×#397	C₂	semidirect
6. C₉×#396	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#387	C₂	semidirect
9. C₉×#387	C₂	semidirect
13. C₉×#385	C₂	semidirect
14. C₉×#380	C₂	semidirect
15. C₄×C₉×C₂²⋊C₄	C₂	semidirect
103. C₉×C₄⋊C₄	D₄	semidirect
115. #2481	C₉	direct (N × H)
211. C₂×#126	C₂×C₉	semidirect
212. C₂²×C₄⋊C₄	C₂×C₉	semidirect
213. #400	C₂×C₉	semidirect
214. #400	C₂×C₉	semidirect
215. #397	C₂×C₉	semidirect
216. #396	C₂×C₉	semidirect
217. #388	C₂×C₉	semidirect
218. #387	C₂×C₉	semidirect
219. #387	C₂×C₉	semidirect
223. #385	C₂×C₉	semidirect
224. #380	C₂×C₉	semidirect
225. C₄×C₂²⋊C₄	C₂×C₉	semidirect
285. C₂²×C₉	#126	semidirect
444. C₄⋊C₄	D₄×C₉	semidirect
490. C₉	#2481	direct (N × H)
571. 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×C₄⋊C₄	2
C₉×#400	2
C₉×#397	2
C₉×#396	2
C₉×#388	2
C₉×#387	2
C₉×#386	2
C₉×#385	2
C₉×#380	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2481	3

Subgroups — C9×#2481 #11767202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2481 #11767202