Subgroups — C₉×#2490 #11767211

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
3	C₉×#397	C₂	1	2	yes	maximal, complemented
4	C₉×#394	C₂	1	2	yes	maximal, complemented
5	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#390	C₂	1	2	yes	maximal, complemented
8	C₉×#388	C₂	1	2	yes	maximal, complemented
9	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2490	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₉×#125	—	2	4	no	—
17	C₉×#121	—	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	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₉	C₂²	1	2	yes	—
34	C₉×#95	C₂²	1	1	yes	characteristic
35	C₉×#95	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
40	C₃×#397	C₂×C₃	1	2	yes	—
41	C₃×#394	C₂×C₃	1	2	yes	—
42	C₃×#390	C₂×C₃	1	1	yes	characteristic
43	C₃×#390	C₂×C₃	1	1	yes	characteristic
44	C₃×#390	C₂×C₃	1	2	yes	—
45	C₃×#388	C₂×C₃	1	2	yes	—
46	C₃×#380	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	2	yes	—
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×D₄×C₉	—	2	4	no	—
52	C₂×D₄×C₉	—	2	4	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	—	2	2	no	—
55	C₂×D₄×C₉	—	2	2	no	—
56	C₂×D₄×C₉	—	4	2	no	—
57	C₂²×C₄×C₉	—	2	2	no	—
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	—	2	2	no	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₉×C₄⋊C₄	—	2	4	no	—
70	C₉×C₄⋊C₄	—	2	4	no	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	D₄	1	4	yes	—
74	C₉×C₂²⋊C₄	—	2	2	no	—
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₉×C₂²⋊C₄	—	2	2	no	—
77	C₉×C₂²⋊C₄	—	2	4	no	—
78	C₉×C₂²⋊C₄	—	4	2	no	—
79	C₉×C₂²⋊C₄	—	4	2	no	—
80	C₉×C₂²⋊C₄	—	4	2	no	—
81	C₉×C₂²⋊C₄	—	4	2	no	—
82	C₄²×C₉	—	2	2	no	—
83	C₄²×C₉	—	2	2	no	—
84	C₄²×C₉	—	4	2	no	—
85	#2490	C₉	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃×#125	—	2	4	no	—
90	C₃×#121	—	2	4	no	—
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	2	yes	—
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
107	C₃×#95	C₂²×C₃	1	1	yes	characteristic
108	C₃×#95	C₂²×C₃	1	1	yes	characteristic
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₃×#95	C₂²×C₃	1	2	yes	—
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	2	no	—
118	C₂³×C₉	—	2	2	no	—
119	C₂³×C₉	—	2	2	no	—
120	C₂³×C₉	—	2	2	no	—
121	C₂³×C₉	—	2	2	no	—
122	C₂³×C₉	—	2	2	no	—
123	C₂³×C₉	—	2	2	no	—
124	C₂³×C₉	#41	1	2	yes	—
125	C₂³×C₉	C₂⁴	1	1	yes	characteristic
126	D₄×C₉	—	4	8	no	—
127	D₄×C₉	—	4	4	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	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	—	2	1	no	—
150	C₂×C₄×C₉	—	4	4	no	—
151	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
152	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
153	C₂×C₄×C₉	#41	1	2	yes	—
154	C₂×C₄×C₉	#41	1	2	yes	—
155	C₂×C₄×C₉	#41	1	2	yes	—
156	C₂×#125	C₂×C₉	1	1	yes	characteristic, complemented
157	C₂×#121	C₂×C₉	1	1	yes	characteristic
158	#397	C₂×C₉	1	2	yes	complemented
159	#394	C₂×C₉	1	2	yes	complemented
160	#390	C₂×C₉	1	1	yes	characteristic, complemented
161	#390	C₂×C₉	1	1	yes	characteristic, complemented
162	#390	C₂×C₉	1	2	yes	complemented
163	#388	C₂×C₉	1	2	yes	complemented
164	#380	C₂×C₉	1	1	yes	characteristic, complemented
165	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
166	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
168	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	4	2	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
185	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
192	C₃×C₂²⋊C₄	—	2	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	—	4	2	no	—
197	C₃×C₂²⋊C₄	—	4	2	no	—
198	C₃×C₂²⋊C₄	—	4	2	no	—
199	C₃×C₂²⋊C₄	—	4	2	no	—
200	C₃×C₄²	—	2	2	no	—
201	C₃×C₄²	—	2	2	no	—
202	C₃×C₄²	—	4	2	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	2	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	4	1	no	—
207	C₂²×C₉	—	4	1	no	—
208	C₂²×C₉	—	4	1	no	—
209	C₂²×C₉	—	4	1	no	—
210	C₂²×C₉	—	4	2	no	—
211	C₂²×C₉	—	4	2	no	—
212	C₂²×C₉	—	4	2	no	—
213	C₂²×C₉	—	4	2	no	—
214	C₂²×C₉	—	4	2	no	—
215	C₂²×C₉	—	4	2	no	—
216	C₂²×C₉	—	4	2	no	—
217	C₂²×C₉	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
221	C₂²×C₉	C₂×#41	1	1	yes	characteristic
222	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
224	C₄×C₉	—	2	4	no	—
225	C₄×C₉	—	2	2	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	2	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	—	4	1	no	—
230	C₄×C₉	—	4	2	no	—
231	C₄×C₉	—	4	1	no	—
232	C₄×C₉	#124	1	4	yes	—
233	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
234	C₂²×D₄	C₂²×C₉	1	2	yes	—
235	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
236	#125	—	2	4	no	—
237	#121	—	2	4	no	—
238	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
240	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
241	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
251	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²×C₉	1	2	yes	—
254	#95	C₂²×C₉	1	1	yes	characteristic
255	#95	C₂²×C₉	1	1	yes	characteristic
256	#95	C₂²×C₉	1	2	yes	—
257	#95	C₂²×C₉	1	2	yes	—
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	2	no	—
265	C₂³×C₃	—	2	2	no	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	—	2	2	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	2	no	—
271	C₂³×C₃	C₃×#41	1	2	yes	—
272	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
273	C₃×D₄	—	4	8	no	—
274	C₃×D₄	—	4	4	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	4	4	no	—
298	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
299	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₃×#41	1	2	yes	—
301	C₂×C₃×C₄	C₃×#41	1	2	yes	—
302	C₂×C₃×C₄	C₃×#41	1	2	yes	—
303	C₂×C₉	—	4	2	no	—
304	C₂×C₉	—	8	2	no	—
305	C₂×C₉	C₂×#124	1	1	yes	characteristic
306	C₂×C₉	#529	1	1	yes	characteristic
307	C₂×C₉	#540	1	1	yes	characteristic
308	C₂×C₉	#546	1	1	yes	characteristic
309	C₂×C₉	#550	1	1	yes	characteristic
310	C₂×C₉	#553	1	1	yes	characteristic
311	C₂×C₉	#553	1	1	yes	characteristic
312	C₂⁴	C₂³×C₉	1	2	yes	—
313	C₂⁴	C₂³×C₉	1	1	yes	characteristic
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₉	1	2	yes	—
326	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₉	1	2	yes	—
329	C₂²×C₄	C₂³×C₉	1	2	yes	—
330	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	D₄×C₉	1	4	yes	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	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	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	2	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
364	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
365	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
366	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
367	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	4	1	no	—
372	C₃×C₄	—	4	2	no	—
373	C₃×C₄	—	4	1	no	—
374	C₃×C₄	—	4	1	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	—	4	1	no	—
377	C₃×C₄	C₃×#124	1	4	yes	—
378	C₉	#2490	1	1	yes	characteristic, direct product factor, Sylow
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	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	C₉×#41	1	2	yes	—
393	C₂³	C₂⁴×C₉	1	1	yes	characteristic
394	D₄	—	4	8	no	—
395	D₄	—	4	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
420	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
421	C₂×C₄	C₉×#41	1	2	yes	—
422	C₂×C₄	C₉×#41	1	2	yes	—
423	C₂×C₄	C₉×#41	1	2	yes	—
424	C₂×C₃	—	4	2	no	—
425	C₂×C₃	—	8	2	no	—
426	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
427	C₂×C₃	C₃×#529	1	1	yes	characteristic
428	C₂×C₃	C₃×#540	1	1	yes	characteristic
429	C₂×C₃	C₃×#546	1	1	yes	characteristic
430	C₂×C₃	C₃×#550	1	1	yes	characteristic
431	C₂×C₃	C₃×#553	1	1	yes	characteristic
432	C₂×C₃	C₃×#553	1	1	yes	characteristic
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	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
448	C₂²	C₂×C₉×#41	1	1	yes	characteristic
449	C₂²	C₂×C₉×#41	1	1	yes	characteristic
450	C₂²	C₂×C₉×#41	1	1	yes	characteristic
451	C₂²	C₂×C₉×#41	1	1	yes	characteristic
452	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	1	no	—
462	C₄	C₉×#124	1	4	yes	—
463	C₃	C₃×#2490	1	1	yes	characteristic
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₂×C₉×#124	1	1	yes	characteristic
467	C₂	C₉×#529	1	1	yes	characteristic
468	C₂	C₉×#540	1	1	yes	characteristic
469	C₂	C₉×#546	1	1	yes	characteristic
470	C₂	C₉×#550	1	1	yes	characteristic
471	C₂	C₉×#553	1	1	yes	characteristic
472	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	C₂×C₃×#121	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×#125	C₂	semidirect
3. C₉×#397	C₂	semidirect
4. C₉×#394	C₂	semidirect
5. C₉×#390	C₂	semidirect
6. C₉×#390	C₂	semidirect
7. C₉×#390	C₂	semidirect
8. C₉×#388	C₂	semidirect
9. C₉×#380	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
11. C₄×C₉×C₂²⋊C₄	C₂	semidirect
85. #2490	C₉	direct (N × H)
156. C₂×#125	C₂×C₉	semidirect
158. #397	C₂×C₉	semidirect
159. #394	C₂×C₉	semidirect
160. #390	C₂×C₉	semidirect
161. #390	C₂×C₉	semidirect
162. #390	C₂×C₉	semidirect
163. #388	C₂×C₉	semidirect
164. #380	C₂×C₉	semidirect
165. C₄×C₄⋊C₄	C₂×C₉	semidirect
166. C₄×C₂²⋊C₄	C₂×C₉	semidirect
378. C₉	#2490	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×#125	2
C₂×C₉×#121	2
C₉×#397	2
C₉×#394	2
C₉×#390	2
C₉×#388	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2490	3

Subgroups — C9×#2490 #11767211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2490 #11767211