Subgroups — C₉×#2445 #11767166

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#123	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#394	C₂	1	2	yes	maximal, complemented
5	C₉×#394	C₂	1	2	yes	maximal, complemented
6	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#386	C₂	1	2	yes	maximal, complemented
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2445	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	2	yes	—
15	C₂²×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	2	yes	—
18	C₉×#127	—	2	4	no	—
19	C₉×#123	—	2	8	no	—
20	C₄×D₄×C₉	—	2	4	no	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
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×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×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	1	yes	characteristic
37	C₉×#95	C₂²	1	1	yes	characteristic
38	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#123	C₂×C₃	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
42	C₃×#394	C₂×C₃	1	2	yes	—
43	C₃×#394	C₂×C₃	1	2	yes	—
44	C₃×#390	C₂×C₃	1	1	yes	characteristic
45	C₃×#390	C₂×C₃	1	1	yes	characteristic
46	C₃×#390	C₂×C₃	1	1	yes	characteristic
47	C₃×#389	C₂×C₃	1	1	yes	characteristic
48	C₃×#386	C₂×C₃	1	2	yes	—
49	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	2	yes	—
51	C₂⁴×C₉	C₂³	1	2	yes	—
52	C₂×D₄×C₉	—	2	4	no	—
53	C₂×D₄×C₉	—	2	4	no	—
54	C₂×D₄×C₉	—	2	4	no	—
55	C₂×D₄×C₉	—	2	2	no	—
56	C₂×D₄×C₉	—	2	2	no	—
57	C₂×D₄×C₉	—	2	2	no	—
58	C₂×D₄×C₉	—	2	4	no	—
59	C₂×D₄×C₉	—	2	2	no	—
60	C₂×D₄×C₉	—	2	2	no	—
61	C₂×D₄×C₉	—	4	2	no	—
62	C₂×D₄×C₉	—	4	2	no	—
63	C₂×D₄×C₉	D₄	1	4	yes	—
64	C₂²×C₄×C₉	—	2	4	no	—
65	C₂²×C₄×C₉	—	2	4	no	—
66	C₂²×C₄×C₉	—	4	2	no	—
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	2	yes	—
70	C₂²×C₄×C₉	C₂³	1	2	yes	—
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	2	4	no	—
78	C₉×C₄⋊C₄	—	2	2	no	—
79	C₉×C₄⋊C₄	—	2	2	no	—
80	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
81	C₉×C₂²⋊C₄	—	2	4	no	—
82	C₉×C₂²⋊C₄	—	2	4	no	—
83	C₉×C₂²⋊C₄	—	2	4	no	—
84	C₉×C₂²⋊C₄	—	2	4	no	—
85	C₉×C₂²⋊C₄	—	4	2	no	—
86	C₉×C₂²⋊C₄	—	4	2	no	—
87	C₉×C₂²⋊C₄	—	4	2	no	—
88	C₄²×C₉	—	2	2	no	—
89	C₄²×C₉	—	2	2	no	—
90	C₄²×C₉	—	2	2	no	—
91	#2445	C₉	1	1	yes	characteristic, direct product factor, Sylow
92	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
95	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
97	C₃×#127	—	2	4	no	—
98	C₃×#123	—	2	8	no	—
99	C₃×C₄×D₄	—	2	4	no	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
115	C₃×#95	C₂²×C₃	1	1	yes	characteristic
116	C₃×#95	C₂²×C₃	1	1	yes	characteristic
117	C₃×#95	C₂²×C₃	1	2	yes	—
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	—	2	2	no	—
125	C₂³×C₉	—	2	2	no	—
126	C₂³×C₉	—	2	2	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	—	2	2	no	—
129	C₂³×C₉	—	2	2	no	—
130	C₂³×C₉	—	2	2	no	—
131	C₂³×C₉	C₂×D₄	1	4	yes	—
132	C₂³×C₉	C₂⁴	1	1	yes	characteristic
133	D₄×C₉	—	2	8	no	—
134	D₄×C₉	—	4	8	no	—
135	D₄×C₉	—	4	8	no	—
136	D₄×C₉	—	4	4	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	4	8	no	—
158	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
159	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
162	C₂×C₄×C₉	#41	1	2	yes	—
163	C₂×C₄×C₉	#41	1	2	yes	—
164	C₂×C₄×C₉	#41	1	2	yes	—
165	C₂×#127	C₂×C₉	1	1	yes	characteristic
166	C₂×#123	C₂×C₉	1	2	yes	complemented
167	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
168	#394	C₂×C₉	1	2	yes	complemented
169	#394	C₂×C₉	1	2	yes	complemented
170	#390	C₂×C₉	1	1	yes	characteristic, complemented
171	#390	C₂×C₉	1	1	yes	characteristic, complemented
172	#390	C₂×C₉	1	1	yes	characteristic, complemented
173	#389	C₂×C₉	1	1	yes	characteristic, complemented
174	#386	C₂×C₉	1	2	yes	complemented
175	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
176	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
177	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	—	2	4	no	—
181	C₂×C₃×D₄	—	2	2	no	—
182	C₂×C₃×D₄	—	2	2	no	—
183	C₂×C₃×D₄	—	2	2	no	—
184	C₂×C₃×D₄	—	2	4	no	—
185	C₂×C₃×D₄	—	2	2	no	—
186	C₂×C₃×D₄	—	2	2	no	—
187	C₂×C₃×D₄	—	4	2	no	—
188	C₂×C₃×D₄	—	4	2	no	—
189	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	—	4	2	no	—
193	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
197	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₄⋊C₄	—	2	4	no	—
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	—	2	2	no	—
206	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
207	C₃×C₂²⋊C₄	—	2	4	no	—
208	C₃×C₂²⋊C₄	—	2	4	no	—
209	C₃×C₂²⋊C₄	—	2	4	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	4	2	no	—
212	C₃×C₂²⋊C₄	—	4	2	no	—
213	C₃×C₂²⋊C₄	—	4	2	no	—
214	C₃×C₄²	—	2	2	no	—
215	C₃×C₄²	—	2	2	no	—
216	C₃×C₄²	—	2	2	no	—
217	C₂²×C₉	—	2	4	no	—
218	C₂²×C₉	—	2	4	no	—
219	C₂²×C₉	—	2	4	no	—
220	C₂²×C₉	—	4	2	no	—
221	C₂²×C₉	—	4	2	no	—
222	C₂²×C₉	—	4	2	no	—
223	C₂²×C₉	—	4	2	no	—
224	C₂²×C₉	—	4	2	no	—
225	C₂²×C₉	—	4	2	no	—
226	C₂²×C₉	—	4	2	no	—
227	C₂²×C₉	—	4	2	no	—
228	C₂²×C₉	—	4	2	no	—
229	C₂²×C₉	—	4	2	no	—
230	C₂²×C₉	—	4	2	no	—
231	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
232	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
233	C₂²×C₉	C₂×#41	1	1	yes	characteristic
234	C₂²×C₉	C₂×#41	1	1	yes	characteristic
235	C₂²×C₉	C₂×#41	1	1	yes	characteristic
236	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₄×C₉	—	2	2	no	—
239	C₄×C₉	—	2	2	no	—
240	C₄×C₉	—	2	2	no	—
241	C₄×C₉	—	2	2	no	—
242	C₄×C₉	—	4	1	no	—
243	C₄×C₉	—	4	2	no	—
244	C₄×C₉	—	4	1	no	—
245	C₄×C₉	—	4	2	no	—
246	C₄×C₉	#123	1	4	yes	complemented
247	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
248	C₂²×D₄	C₂²×C₉	1	2	yes	—
249	C₂²×D₄	C₂²×C₉	1	2	yes	—
250	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
251	C₂³×C₄	C₂²×C₉	1	2	yes	—
252	#127	—	2	4	no	—
253	#123	—	2	8	no	—
254	C₄×D₄	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
267	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
268	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
269	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
270	#95	C₂²×C₉	1	1	yes	characteristic
271	#95	C₂²×C₉	1	1	yes	characteristic
272	#95	C₂²×C₉	1	2	yes	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	2	2	no	—
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
287	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
288	C₃×D₄	—	2	8	no	—
289	C₃×D₄	—	4	8	no	—
290	C₃×D₄	—	4	8	no	—
291	C₃×D₄	—	4	4	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	4	8	no	—
313	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
314	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
315	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
316	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
317	C₂×C₃×C₄	C₃×#41	1	2	yes	—
318	C₂×C₃×C₄	C₃×#41	1	2	yes	—
319	C₂×C₃×C₄	C₃×#41	1	2	yes	—
320	C₂×C₉	—	4	4	no	—
321	C₂×C₉	—	8	2	no	—
322	C₂×C₉	C₂×#123	1	1	yes	characteristic
323	C₂×C₉	#532	1	1	yes	characteristic
324	C₂×C₉	#540	1	1	yes	characteristic
325	C₂×C₉	D₄²	1	1	yes	characteristic
326	C₂×C₉	#546	1	1	yes	characteristic
327	C₂×C₉	#550	1	1	yes	characteristic
328	C₂×C₉	#559	1	1	yes	characteristic
329	C₂⁴	C₂³×C₉	1	2	yes	—
330	C₂⁴	C₂³×C₉	1	2	yes	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	D₄×C₉	1	4	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
347	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
348	C₂²×C₄	C₂³×C₉	1	2	yes	—
349	C₂²×C₄	C₂³×C₉	1	2	yes	—
350	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
351	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
352	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
353	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₂²×C₃	—	2	4	no	—
371	C₂²×C₃	—	2	4	no	—
372	C₂²×C₃	—	2	4	no	—
373	C₂²×C₃	—	4	2	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	—	4	2	no	—
378	C₂²×C₃	—	4	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	—	4	2	no	—
384	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
386	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
387	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
388	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
389	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	4	1	no	—
396	C₃×C₄	—	4	2	no	—
397	C₃×C₄	—	4	1	no	—
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	C₃×#123	1	4	yes	—
400	C₉	#2445	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂×D₄×C₉	1	4	yes	—
415	C₂³	C₂⁴×C₉	1	1	yes	characteristic
416	D₄	—	2	8	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	8	no	—
419	D₄	—	4	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
442	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
443	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
444	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
445	C₂×C₄	C₉×#41	1	2	yes	—
446	C₂×C₄	C₉×#41	1	2	yes	—
447	C₂×C₄	C₉×#41	1	2	yes	—
448	C₂×C₃	—	4	4	no	—
449	C₂×C₃	—	8	2	no	—
450	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
451	C₂×C₃	C₃×#532	1	1	yes	characteristic
452	C₂×C₃	C₃×#540	1	1	yes	characteristic
453	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
454	C₂×C₃	C₃×#546	1	1	yes	characteristic
455	C₂×C₃	C₃×#550	1	1	yes	characteristic
456	C₂×C₃	C₃×#559	1	1	yes	characteristic
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
472	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
473	C₂²	C₂×C₉×#41	1	1	yes	characteristic
474	C₂²	C₂×C₉×#41	1	1	yes	characteristic
475	C₂²	C₂×C₉×#41	1	1	yes	characteristic
476	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	C₉×#123	1	4	yes	complemented
487	C₃	C₃×#2445	1	1	yes	characteristic
488	C₂	—	4	4	no	—
489	C₂	—	8	2	no	—
490	C₂	C₂×C₉×#123	1	1	yes	characteristic
491	C₂	C₉×#532	1	1	yes	characteristic
492	C₂	C₉×#540	1	1	yes	characteristic
493	C₂	D₄²×C₉	1	1	yes	characteristic
494	C₂	C₉×#546	1	1	yes	characteristic
495	C₂	C₉×#550	1	1	yes	characteristic
496	C₂	C₉×#559	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×#127	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
2. C₂×C₉×#123	C₂	semidirect
3. C₂×C₄×D₄×C₉	C₂	semidirect
4. C₉×#394	C₂	semidirect
5. C₉×#394	C₂	semidirect
6. C₉×#390	C₂	semidirect
7. C₉×#390	C₂	semidirect
8. C₉×#390	C₂	semidirect
9. C₉×#389	C₂	semidirect
10. C₉×#386	C₂	semidirect
11. C₄×C₉×C₄⋊C₄	C₂	semidirect
80. C₉×C₄⋊C₄	D₄	semidirect
91. #2445	C₉	direct (N × H)
166. C₂×#123	C₂×C₉	semidirect
167. C₂×C₄×D₄	C₂×C₉	semidirect
168. #394	C₂×C₉	semidirect
169. #394	C₂×C₉	semidirect
170. #390	C₂×C₉	semidirect
171. #390	C₂×C₉	semidirect
172. #390	C₂×C₉	semidirect
173. #389	C₂×C₉	semidirect
174. #386	C₂×C₉	semidirect
175. C₄×C₄⋊C₄	C₂×C₉	semidirect
246. C₄×C₉	#123	semidirect
359. C₄⋊C₄	D₄×C₉	semidirect
400. C₉	#2445	direct (N × H)
486. C₄	C₉×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#127	2
C₂×C₉×#123	2
C₂×C₄×D₄×C₉	2
C₉×#394	2
C₉×#390	2
C₉×#389	2
C₉×#386	2
C₄×C₉×C₄⋊C₄	2
C₃×#2445	3

Subgroups — C9×#2445 #11767166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2445 #11767166