Subgroups — C₉×#2554 #11767275

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 654 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	C₂×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#392	C₂	1	1	yes	maximal, characteristic
7	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#390	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×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2554	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	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₉×#126	—	2	4	no	—
22	C₉×#123	—	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×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
45	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₉	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	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic
56	C₃×#398	C₂×C₃	1	1	yes	characteristic
57	C₃×#396	C₂×C₃	1	1	yes	characteristic
58	C₃×#394	C₂×C₃	1	1	yes	characteristic
59	C₃×#392	C₂×C₃	1	1	yes	characteristic
60	C₃×#390	C₂×C₃	1	1	yes	characteristic
61	C₃×#390	C₂×C₃	1	1	yes	characteristic
62	C₃×#390	C₂×C₃	1	1	yes	characteristic
63	C₃×#388	C₂×C₃	1	1	yes	characteristic
64	C₃×#388	C₂×C₃	1	1	yes	characteristic
65	C₃×#388	C₂×C₃	1	1	yes	characteristic
66	C₃×#386	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×C₄⋊C₄	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	C₂⁴×C₉	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₉	—	2	2	no	—
73	C₂×D₄×C₉	—	2	2	no	—
74	C₂×D₄×C₉	—	2	2	no	—
75	C₂×D₄×C₉	—	2	2	no	—
76	C₂×D₄×C₉	—	2	2	no	—
77	C₂×D₄×C₉	—	4	1	no	—
78	C₂×D₄×C₉	—	4	1	no	—
79	C₂×D₄×C₉	—	4	1	no	—
80	C₂×D₄×C₉	—	4	1	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	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	—	4	1	no	—
101	C₉×C₄⋊C₄	—	4	1	no	—
102	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
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	C₄²×C₉	—	2	2	no	—
118	C₄²×C₉	—	2	2	no	—
119	C₄²×C₉	—	4	1	no	—
120	C₄²×C₉	—	4	1	no	—
121	#2554	C₉	1	1	yes	characteristic, direct product factor, Sylow
122	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
124	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃×#126	—	2	4	no	—
127	C₃×#123	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₄⋊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	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×C₄²	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	1	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	—	2	1	no	—
177	C₂³×C₉	—	2	1	no	—
178	C₂³×C₉	—	2	1	no	—
179	C₂³×C₉	#41	1	2	yes	—
180	C₂³×C₉	C₂⁴	1	1	yes	characteristic
181	D₄×C₉	—	4	4	no	—
182	D₄×C₉	—	4	4	no	—
183	D₄×C₉	—	4	4	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	—	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	—	4	4	no	—
215	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
216	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
217	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
218	C₂×C₄×C₉	#41	1	2	yes	—
219	C₂×C₄×C₉	#41	1	2	yes	—
220	C₂×C₄×C₉	#41	1	2	yes	—
221	C₂×#126	C₂×C₉	1	1	yes	characteristic, complemented
222	C₂×#123	C₂×C₉	1	1	yes	characteristic, complemented
223	#398	C₂×C₉	1	1	yes	characteristic, complemented
224	#396	C₂×C₉	1	1	yes	characteristic, complemented
225	#394	C₂×C₉	1	1	yes	characteristic, complemented
226	#392	C₂×C₉	1	1	yes	characteristic
227	#390	C₂×C₉	1	1	yes	characteristic, complemented
228	#390	C₂×C₉	1	1	yes	characteristic, complemented
229	#390	C₂×C₉	1	1	yes	characteristic, complemented
230	#388	C₂×C₉	1	1	yes	characteristic, complemented
231	#388	C₂×C₉	1	1	yes	characteristic, complemented
232	#388	C₂×C₉	1	1	yes	characteristic, complemented
233	#386	C₂×C₉	1	1	yes	characteristic, complemented
234	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
235	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
236	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
237	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
238	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃×D₄	—	2	2	no	—
240	C₂×C₃×D₄	—	2	2	no	—
241	C₂×C₃×D₄	—	2	2	no	—
242	C₂×C₃×D₄	—	2	2	no	—
243	C₂×C₃×D₄	—	2	2	no	—
244	C₂×C₃×D₄	—	4	1	no	—
245	C₂×C₃×D₄	—	4	1	no	—
246	C₂×C₃×D₄	—	4	1	no	—
247	C₂×C₃×D₄	—	4	1	no	—
248	C₂²×C₃×C₄	—	2	2	no	—
249	C₂²×C₃×C₄	—	2	2	no	—
250	C₂²×C₃×C₄	—	4	1	no	—
251	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
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	C₃×C₄⋊C₄	—	2	2	no	—
264	C₃×C₄⋊C₄	—	2	2	no	—
265	C₃×C₄⋊C₄	—	2	2	no	—
266	C₃×C₄⋊C₄	—	2	2	no	—
267	C₃×C₄⋊C₄	—	4	1	no	—
268	C₃×C₄⋊C₄	—	4	1	no	—
269	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	2	2	no	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₂²⋊C₄	—	2	2	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	—	4	1	no	—
282	C₃×C₂²⋊C₄	—	4	1	no	—
283	C₃×C₂²⋊C₄	—	4	1	no	—
284	C₃×C₄²	—	2	2	no	—
285	C₃×C₄²	—	2	2	no	—
286	C₃×C₄²	—	4	1	no	—
287	C₃×C₄²	—	4	1	no	—
288	C₂²×C₉	—	2	2	no	—
289	C₂²×C₉	—	2	2	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	—	4	1	no	—
292	C₂²×C₉	—	4	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	1	no	—
295	C₂²×C₉	—	4	1	no	—
296	C₂²×C₉	—	4	1	no	—
297	C₂²×C₉	—	4	1	no	—
298	C₂²×C₉	—	4	1	no	—
299	C₂²×C₉	—	4	1	no	—
300	C₂²×C₉	—	4	1	no	—
301	C₂²×C₉	—	4	1	no	—
302	C₂²×C₉	—	4	1	no	—
303	C₂²×C₉	—	4	1	no	—
304	C₂²×C₉	—	4	1	no	—
305	C₂²×C₉	—	4	1	no	—
306	C₂²×C₉	—	4	1	no	—
307	C₂²×C₉	—	4	1	no	—
308	C₂²×C₉	—	4	1	no	—
309	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
310	C₂²×C₉	C₂×#41	1	1	yes	characteristic
311	C₂²×C₉	C₂×#41	1	1	yes	characteristic
312	C₂²×C₉	C₂×#41	1	1	yes	characteristic
313	C₂²×C₉	C₂×#41	1	1	yes	characteristic
314	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
316	C₄×C₉	—	2	2	no	—
317	C₄×C₉	—	2	2	no	—
318	C₄×C₉	—	2	2	no	—
319	C₄×C₉	—	2	2	no	—
320	C₄×C₉	—	2	2	no	—
321	C₄×C₉	—	2	2	no	—
322	C₄×C₉	—	4	1	no	—
323	C₄×C₉	—	4	1	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	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
329	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
330	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
331	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
332	#126	—	2	4	no	—
333	#123	—	2	4	no	—
334	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
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×C₄²	C₂²×C₉	1	1	yes	characteristic
356	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
357	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
358	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
359	#95	C₂²×C₉	1	1	yes	characteristic
360	#95	C₂²×C₉	1	1	yes	characteristic
361	#95	C₂²×C₉	1	1	yes	characteristic
362	#95	C₂²×C₉	1	1	yes	characteristic
363	#95	C₂²×C₉	1	1	yes	characteristic
364	#95	C₂²×C₉	1	1	yes	characteristic
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	—	2	1	no	—
370	C₂³×C₃	—	2	1	no	—
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	1	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	C₃×#41	1	2	yes	—
386	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
387	C₃×D₄	—	4	4	no	—
388	C₃×D₄	—	4	4	no	—
389	C₃×D₄	—	4	4	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	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
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	—	4	4	no	—
421	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
423	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
424	C₂×C₃×C₄	C₃×#41	1	2	yes	—
425	C₂×C₃×C₄	C₃×#41	1	2	yes	—
426	C₂×C₃×C₄	C₃×#41	1	2	yes	—
427	C₂×C₉	—	4	2	no	—
428	C₂×C₉	—	8	1	no	—
429	C₂×C₉	—	8	1	no	—
430	C₂×C₉	#529	1	1	yes	characteristic
431	C₂×C₉	#532	1	1	yes	characteristic
432	C₂×C₉	#538	1	1	yes	characteristic
433	C₂×C₉	#546	1	1	yes	characteristic
434	C₂×C₉	#550	1	1	yes	characteristic
435	C₂×C₉	#551	1	1	yes	characteristic
436	C₂×C₉	#553	1	1	yes	characteristic
437	C₂⁴	C₂³×C₉	1	1	yes	characteristic
438	C₂⁴	C₂³×C₉	1	1	yes	characteristic
439	C₂⁴	C₂³×C₉	1	1	yes	characteristic
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
453	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
454	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
455	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
456	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
457	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
458	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
459	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
460	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
461	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
462	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
463	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	4	1	no	—
488	C₄²	—	4	1	no	—
489	C₂²×C₃	—	2	2	no	—
490	C₂²×C₃	—	2	2	no	—
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	1	no	—
496	C₂²×C₃	—	4	1	no	—
497	C₂²×C₃	—	4	1	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	4	1	no	—
500	C₂²×C₃	—	4	1	no	—
501	C₂²×C₃	—	4	1	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	—	4	1	no	—
504	C₂²×C₃	—	4	1	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	1	no	—
507	C₂²×C₃	—	4	1	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	—	4	1	no	—
510	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
511	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
512	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
513	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
514	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
515	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	2	2	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	2	no	—
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	4	1	no	—
524	C₃×C₄	—	4	1	no	—
525	C₃×C₄	—	4	1	no	—
526	C₃×C₄	—	4	1	no	—
527	C₃×C₄	—	4	1	no	—
528	C₃×C₄	—	4	1	no	—
529	C₉	#2554	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	C₉×#41	1	2	yes	—
551	C₂³	C₂⁴×C₉	1	1	yes	characteristic
552	D₄	—	4	4	no	—
553	D₄	—	4	4	no	—
554	D₄	—	4	4	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
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	—	4	4	no	—
586	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
587	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
588	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
589	C₂×C₄	C₉×#41	1	2	yes	—
590	C₂×C₄	C₉×#41	1	2	yes	—
591	C₂×C₄	C₉×#41	1	2	yes	—
592	C₂×C₃	—	4	2	no	—
593	C₂×C₃	—	8	1	no	—
594	C₂×C₃	—	8	1	no	—
595	C₂×C₃	C₃×#529	1	1	yes	characteristic
596	C₂×C₃	C₃×#532	1	1	yes	characteristic
597	C₂×C₃	C₃×#538	1	1	yes	characteristic
598	C₂×C₃	C₃×#546	1	1	yes	characteristic
599	C₂×C₃	C₃×#550	1	1	yes	characteristic
600	C₂×C₃	C₃×#551	1	1	yes	characteristic
601	C₂×C₃	C₃×#553	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
624	C₂²	C₂×C₉×#41	1	1	yes	characteristic
625	C₂²	C₂×C₉×#41	1	1	yes	characteristic
626	C₂²	C₂×C₉×#41	1	1	yes	characteristic
627	C₂²	C₂×C₉×#41	1	1	yes	characteristic
628	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₃	C₃×#2554	1	1	yes	characteristic
643	C₂	—	4	2	no	—
644	C₂	—	8	1	no	—
645	C₂	—	8	1	no	—
646	C₂	C₉×#529	1	1	yes	characteristic
647	C₂	C₉×#532	1	1	yes	characteristic
648	C₂	C₉×#538	1	1	yes	characteristic
649	C₂	C₉×#546	1	1	yes	characteristic
650	C₂	C₉×#550	1	1	yes	characteristic
651	C₂	C₉×#551	1	1	yes	characteristic
652	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×#392	C₂×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. C₂×C₉×#123	C₂	semidirect
3. C₉×#398	C₂	semidirect
4. C₉×#396	C₂	semidirect
5. C₉×#394	C₂	semidirect
7. C₉×#390	C₂	semidirect
8. C₉×#390	C₂	semidirect
9. C₉×#390	C₂	semidirect
10. C₉×#388	C₂	semidirect
11. C₉×#388	C₂	semidirect
12. C₉×#388	C₂	semidirect
13. C₉×#386	C₂	semidirect
14. C₄×C₉×C₄⋊C₄	C₂	semidirect
15. C₄×C₉×C₂²⋊C₄	C₂	semidirect
102. C₉×C₄⋊C₄	D₄	semidirect
121. #2554	C₉	direct (N × H)
221. C₂×#126	C₂×C₉	semidirect
222. C₂×#123	C₂×C₉	semidirect
223. #398	C₂×C₉	semidirect
224. #396	C₂×C₉	semidirect
225. #394	C₂×C₉	semidirect
227. #390	C₂×C₉	semidirect
228. #390	C₂×C₉	semidirect
229. #390	C₂×C₉	semidirect
230. #388	C₂×C₉	semidirect
231. #388	C₂×C₉	semidirect
232. #388	C₂×C₉	semidirect
233. #386	C₂×C₉	semidirect
234. C₄×C₄⋊C₄	C₂×C₉	semidirect
235. C₄×C₂²⋊C₄	C₂×C₉	semidirect
470. C₄⋊C₄	D₄×C₉	semidirect
529. C₉	#2554	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×#126	2
C₂×C₉×#123	2
C₉×#398	2
C₉×#396	2
C₉×#394	2
C₉×#392	2
C₉×#390	2
C₉×#388	2
C₉×#386	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2554	3

Subgroups — C9×#2554 #11767275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2554 #11767275