Subgroups — C₉×#4665 #13141323

Order 1728.

934 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4665	C₃	1	1	yes	maximal, characteristic
9	C₉×#386	—	3	1	no	maximal
10	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₉×D₁₂	—	2	2	no	—
18	C₂×C₉×D₁₂	—	2	2	no	—
19	C₂×C₉×D₁₂	C₄	1	4	yes	complemented
20	C₂×C₄×D₃×C₉	—	2	2	no	—
21	C₂×C₄×D₃×C₉	—	2	2	no	—
22	C₂×C₄×D₃×C₉	—	2	2	no	—
23	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
24	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
25	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
26	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
27	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂²×D₄×C₉	—	3	1	no	—
32	C₂³×C₄×C₉	—	3	1	no	—
33	C₃²×#95	C₂×C₃	1	1	yes	characteristic
34	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
35	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
36	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
37	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
38	C₉×#95	—	2	1	no	—
39	C₉×#95	—	3	1	no	—
40	C₉×#95	D₃	1	1	yes	characteristic, complemented
41	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
42	C₂²×D₃×C₉	—	2	1	no	—
43	C₂²×D₃×C₉	—	2	1	no	—
44	C₂²×D₃×C₉	—	2	1	no	—
45	C₂²×D₃×C₉	—	2	1	no	—
46	C₂²×D₃×C₉	—	2	1	no	—
47	C₂²×D₃×C₉	—	2	1	no	—
48	C₂²×D₃×C₉	—	2	1	no	—
49	C₂²×D₃×C₉	—	2	1	no	—
50	C₂²×D₃×C₉	—	2	1	no	—
51	C₂²×D₃×C₉	—	2	1	no	—
52	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
53	C₂²×D₃×C₉	C₂×C₄	1	2	yes	complemented
54	C₂²×D₃×C₉	D₄	1	2	yes	—
55	C₂²×D₃×C₉	D₄	1	2	yes	—
56	C₂×C₃×C₄×C₉	—	2	1	no	—
57	C₂×C₃×C₄×C₉	—	2	1	no	—
58	C₂×C₃×C₄×C₉	—	2	1	no	—
59	C₂×C₃×C₄×C₉	—	2	1	no	—
60	C₂×C₃×C₄×C₉	—	2	1	no	—
61	C₂×C₃×C₄×C₉	—	2	1	no	—
62	C₂×C₃×C₄×C₉	—	2	1	no	—
63	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	complemented
64	C₂×C₃×C₄×C₉	D₄	1	2	yes	complemented
65	C₂×C₉×Dic₃	—	2	1	no	—
66	C₂×C₉×Dic₃	—	2	1	no	—
67	C₂×C₉×Dic₃	—	2	1	no	—
68	C₂×C₉×Dic₃	—	2	1	no	—
69	C₂×C₉×Dic₃	—	2	1	no	—
70	C₂×C₉×Dic₃	D₄	1	2	yes	complemented
71	C₉×D₁₂	—	2	8	no	—
72	C₄×D₃×C₉	—	2	8	no	—
73	C₃×#386	—	3	1	no	—
74	#4665	C₉	1	1	yes	characteristic, direct product factor
75	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×D₁₂	—	2	2	no	—
83	C₂×C₃×D₁₂	—	2	2	no	—
84	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	—
85	C₂×C₃×C₄×D₃	—	2	2	no	—
86	C₂×C₃×C₄×D₃	—	2	2	no	—
87	C₂×C₃×C₄×D₃	—	2	2	no	—
88	C₂⁴×C₉	—	3	1	no	—
89	C₂⁴×C₉	—	3	1	no	—
90	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
91	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
92	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
93	C₂×D₄×C₉	—	3	4	no	—
94	C₂×D₄×C₉	—	6	2	no	—
95	C₂×D₄×C₉	—	6	2	no	—
96	C₂²×C₄×C₉	—	2	1	no	—
97	C₂²×C₄×C₉	—	2	1	no	—
98	C₂²×C₄×C₉	—	2	1	no	—
99	C₂²×C₄×C₉	—	3	1	no	—
100	C₂²×C₄×C₉	—	3	1	no	—
101	C₂²×C₄×C₉	—	6	2	no	—
102	C₂²×C₄×C₉	—	6	2	no	—
103	C₂²×C₄×C₉	—	6	2	no	—
104	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
107	C₉×C₂²⋊C₄	—	6	2	no	—
108	C₉×C₂²⋊C₄	—	6	2	no	—
109	C₉×C₂²⋊C₄	—	6	2	no	—
110	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₃×C₉	#41	1	1	yes	characteristic
116	C₂²×C₃×C₉	#41	1	1	yes	characteristic
117	C₂×D₃×C₉	—	2	2	no	—
118	C₂×D₃×C₉	—	2	2	no	—
119	C₂×D₃×C₉	—	2	2	no	—
120	C₂×D₃×C₉	—	2	2	no	—
121	C₂×D₃×C₉	—	2	2	no	—
122	C₂×D₃×C₉	—	2	2	no	—
123	C₂×D₃×C₉	—	2	2	no	—
124	C₂×D₃×C₉	—	2	2	no	—
125	C₂×D₃×C₉	—	2	2	no	—
126	C₂×D₃×C₉	—	4	1	no	—
127	C₂×D₃×C₉	—	4	1	no	—
128	C₂×D₃×C₉	—	4	1	no	—
129	C₂×D₃×C₉	—	4	1	no	—
130	C₂×D₃×C₉	C₂²⋊C₄	1	4	yes	complemented
131	C₃×C₄×C₉	—	2	2	no	—
132	C₃×C₄×C₉	—	2	2	no	—
133	C₃×C₄×C₉	—	4	1	no	—
134	C₉×Dic₃	—	2	2	no	—
135	C₉×Dic₃	—	4	1	no	—
136	C₂²×C₃×D₄	—	3	1	no	—
137	C₂³×C₃×C₄	—	3	1	no	—
138	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic
139	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
140	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
141	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
143	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
144	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
145	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
146	C₃×#95	—	2	1	no	—
147	C₃×#95	—	3	1	no	—
148	C₃×#95	C₂×C₉	1	1	yes	characteristic, complemented
149	C₃×#95	C₃×D₃	1	1	yes	characteristic
150	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
151	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₃×D₃	—	2	1	no	—
153	C₂²×C₃×D₃	—	2	1	no	—
154	C₂²×C₃×D₃	—	2	1	no	—
155	C₂²×C₃×D₃	—	2	1	no	—
156	C₂²×C₃×D₃	—	2	1	no	—
157	C₂²×C₃×D₃	—	2	1	no	—
158	C₂²×C₃×D₃	—	2	1	no	—
159	C₂²×C₃×D₃	—	2	1	no	—
160	C₂²×C₃×D₃	—	2	1	no	—
161	C₂²×C₃×D₃	—	2	1	no	—
162	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
163	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
164	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
165	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
166	C₂×C₃²×C₄	—	2	1	no	—
167	C₂×C₃²×C₄	—	2	1	no	—
168	C₂×C₃²×C₄	—	2	1	no	—
169	C₂×C₃²×C₄	—	2	1	no	—
170	C₂×C₃²×C₄	—	2	1	no	—
171	C₂×C₃²×C₄	—	2	1	no	—
172	C₂×C₃²×C₄	—	2	1	no	—
173	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
174	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
175	C₂×C₃×Dic₃	—	2	1	no	—
176	C₂×C₃×Dic₃	—	2	1	no	—
177	C₂×C₃×Dic₃	—	2	1	no	—
178	C₂×C₃×Dic₃	—	2	1	no	—
179	C₂×C₃×Dic₃	—	2	1	no	—
180	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
181	C₃×D₁₂	—	2	8	no	—
182	C₃×C₄×D₃	—	2	8	no	—
183	C₂³×C₉	—	2	1	no	—
184	C₂³×C₉	—	3	2	no	—
185	C₂³×C₉	—	3	2	no	—
186	C₂³×C₉	—	3	2	no	—
187	C₂³×C₉	—	3	2	no	—
188	C₂³×C₉	—	6	1	no	—
189	C₂³×C₉	—	6	1	no	—
190	C₂³×C₉	—	6	1	no	—
191	C₂³×C₉	—	6	1	no	—
192	C₂³×C₉	—	6	1	no	—
193	C₂³×C₉	—	6	1	no	—
194	C₂³×C₉	—	6	1	no	—
195	C₂³×C₉	—	6	1	no	—
196	C₂³×C₉	—	6	1	no	—
197	C₂³×C₉	—	6	1	no	—
198	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
199	D₄×C₉	—	6	8	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	2	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	2	no	—
209	C₂×C₄×C₉	—	2	2	no	—
210	C₂×C₄×C₉	—	3	2	no	—
211	C₂×C₄×C₉	—	4	1	no	—
212	C₂×C₄×C₉	—	4	1	no	—
213	C₂×C₄×C₉	—	4	1	no	—
214	C₂×C₄×C₉	—	4	1	no	—
215	C₂×C₄×C₉	—	4	1	no	—
216	C₂×C₄×C₉	—	4	1	no	—
217	C₂×C₄×C₉	—	6	8	no	—
218	C₂×C₄×C₉	—	6	1	no	—
219	C₂×C₄×C₉	—	6	1	no	—
220	C₂×C₄×C₉	—	6	1	no	—
221	C₂×C₄×C₉	—	6	1	no	—
222	C₂×C₄×C₉	—	6	1	no	—
223	C₂×C₄×C₉	C₄×D₃	1	2	yes	complemented
224	C₂×C₄×C₉	D₁₂	1	2	yes	complemented
225	#386	—	3	1	no	Sylow
226	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₃×C₉	#120	1	1	yes	characteristic
230	C₂×C₃×C₉	#121	1	1	yes	characteristic
231	C₂×C₃×C₉	#121	1	1	yes	characteristic
232	C₂×C₃×C₉	#123	1	1	yes	characteristic
233	D₃×C₉	—	2	4	no	—
234	D₃×C₉	—	4	2	no	—
235	C₂⁴×C₃	—	3	1	no	—
236	C₂⁴×C₃	—	3	1	no	—
237	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
238	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
239	C₂×C₃×D₄	—	3	4	no	—
240	C₂×C₃×D₄	—	6	2	no	—
241	C₂×C₃×D₄	—	6	2	no	—
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	3	1	no	—
246	C₂²×C₃×C₄	—	3	1	no	—
247	C₂²×C₃×C₄	—	6	2	no	—
248	C₂²×C₃×C₄	—	6	2	no	—
249	C₂²×C₃×C₄	—	6	2	no	—
250	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
256	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
257	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
258	C₂×D₁₂	—	2	2	no	—
259	C₂×D₁₂	—	2	2	no	—
260	C₂×D₁₂	C₄×C₉	1	4	yes	complemented
261	C₂×C₄×D₃	—	2	2	no	—
262	C₂×C₄×D₃	—	2	2	no	—
263	C₂×C₄×D₃	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	6	2	no	—
265	C₃×C₂²⋊C₄	—	6	2	no	—
266	C₃×C₂²⋊C₄	—	6	2	no	—
267	(C₂×D₃)⋊C₄	—	2	2	no	—
268	(C₂×D₃)⋊C₄	—	2	2	no	—
269	(C₂×D₃)⋊C₄	—	2	2	no	—
270	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
271	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
275	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
276	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
277	C₂×C₃×D₃	—	2	2	no	—
278	C₂×C₃×D₃	—	2	2	no	—
279	C₂×C₃×D₃	—	2	2	no	—
280	C₂×C₃×D₃	—	2	2	no	—
281	C₂×C₃×D₃	—	2	2	no	—
282	C₂×C₃×D₃	—	2	2	no	—
283	C₂×C₃×D₃	—	2	2	no	—
284	C₂×C₃×D₃	—	2	2	no	—
285	C₂×C₃×D₃	—	2	2	no	—
286	C₂×C₃×D₃	—	4	1	no	—
287	C₂×C₃×D₃	—	4	1	no	—
288	C₂×C₃×D₃	—	4	1	no	—
289	C₂×C₃×D₃	—	4	1	no	—
290	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	4	yes	—
291	C₃²×C₄	—	2	2	no	—
292	C₃²×C₄	—	2	2	no	—
293	C₃²×C₄	—	4	1	no	—
294	C₃×Dic₃	—	2	2	no	—
295	C₃×Dic₃	—	4	1	no	—
296	C₂²×C₉	—	2	1	no	—
297	C₂²×C₉	—	2	1	no	—
298	C₂²×C₉	—	2	1	no	—
299	C₂²×C₉	—	2	1	no	—
300	C₂²×C₉	—	2	1	no	—
301	C₂²×C₉	—	2	1	no	—
302	C₂²×C₉	—	2	1	no	—
303	C₂²×C₉	—	3	4	no	—
304	C₂²×C₉	—	6	2	no	—
305	C₂²×C₉	—	6	2	no	—
306	C₂²×C₉	—	6	2	no	—
307	C₂²×C₉	—	6	2	no	—
308	C₂²×C₉	—	6	2	no	—
309	C₂²×C₉	—	6	2	no	—
310	C₂²×C₉	—	6	2	no	—
311	C₂²×C₉	—	6	2	no	—
312	C₂²×C₉	—	6	2	no	—
313	C₂²×C₉	—	12	1	no	—
314	C₂²×C₉	—	12	1	no	—
315	C₂²×C₉	—	12	1	no	—
316	C₂²×C₉	—	12	1	no	—
317	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
318	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
319	C₂²×C₉	#235	1	1	yes	characteristic
320	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
321	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
322	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
323	C₂²×C₉	#239	1	1	yes	characteristic
324	C₄×C₉	—	2	2	no	—
325	C₄×C₉	—	2	2	no	—
326	C₄×C₉	—	4	2	no	—
327	C₄×C₉	—	4	2	no	—
328	C₄×C₉	—	4	2	no	—
329	C₄×C₉	—	4	1	no	—
330	C₄×C₉	—	6	2	no	—
331	C₄×C₉	—	12	1	no	—
332	C₂²×D₄	—	3	1	no	—
333	C₂³×C₄	—	3	1	no	—
334	C₂×C₂²⋊C₄	—	3	1	no	—
335	C₂×C₂²⋊C₄	—	3	1	no	—
336	C₂×C₂²⋊C₄	—	3	1	no	—
337	#95	—	3	1	no	—
338	#95	D₃×C₉	1	1	yes	characteristic, complemented
339	C₃×C₉	#386	1	1	yes	characteristic, complemented, Sylow
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	—	3	2	no	—
342	C₂³×C₃	—	3	2	no	—
343	C₂³×C₃	—	3	2	no	—
344	C₂³×C₃	—	3	2	no	—
345	C₂³×C₃	—	6	1	no	—
346	C₂³×C₃	—	6	1	no	—
347	C₂³×C₃	—	6	1	no	—
348	C₂³×C₃	—	6	1	no	—
349	C₂³×C₃	—	6	1	no	—
350	C₂³×C₃	—	6	1	no	—
351	C₂³×C₃	—	6	1	no	—
352	C₂³×C₃	—	6	1	no	—
353	C₂³×C₃	—	6	1	no	—
354	C₂³×C₃	—	6	1	no	—
355	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
356	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂²×D₃	—	2	1	no	—
358	C₂²×D₃	—	2	1	no	—
359	C₂²×D₃	—	2	1	no	—
360	C₂²×D₃	—	2	1	no	—
361	C₂²×D₃	—	2	1	no	—
362	C₂²×D₃	—	2	1	no	—
363	C₂²×D₃	—	2	1	no	—
364	C₂²×D₃	—	2	1	no	—
365	C₂²×D₃	—	2	1	no	—
366	C₂²×D₃	—	2	1	no	—
367	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
368	C₂²×D₃	C₂×C₄×C₉	1	2	yes	complemented
369	C₂²×D₃	D₄×C₉	1	2	yes	—
370	C₂²×D₃	D₄×C₉	1	2	yes	—
371	C₃×D₄	—	6	8	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	2	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	2	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	3	2	no	—
390	C₂×C₃×C₄	—	4	1	no	—
391	C₂×C₃×C₄	—	4	1	no	—
392	C₂×C₃×C₄	—	4	1	no	—
393	C₂×C₃×C₄	—	4	1	no	—
394	C₂×C₃×C₄	—	4	1	no	—
395	C₂×C₃×C₄	—	4	1	no	—
396	C₂×C₃×C₄	—	6	8	no	—
397	C₂×C₃×C₄	—	6	1	no	—
398	C₂×C₃×C₄	—	6	1	no	—
399	C₂×C₃×C₄	—	6	1	no	—
400	C₂×C₃×C₄	—	6	1	no	—
401	C₂×C₃×C₄	—	6	1	no	—
402	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	complemented
403	C₂×C₃×C₄	D₄×C₉	1	2	yes	complemented
404	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
405	C₂×C₃×C₄	C₃×D₁₂	1	2	yes	—
406	C₂×Dic₃	—	2	1	no	—
407	C₂×Dic₃	—	2	1	no	—
408	C₂×Dic₃	—	2	1	no	—
409	C₂×Dic₃	—	2	1	no	—
410	C₂×Dic₃	—	2	1	no	—
411	C₂×Dic₃	D₄×C₉	1	2	yes	complemented
412	D₁₂	—	2	8	no	—
413	C₄×D₃	—	2	8	no	—
414	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
415	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
416	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
417	C₂×C₃²	C₃×#120	1	1	yes	characteristic
418	C₂×C₃²	C₃×#121	1	1	yes	characteristic
419	C₂×C₃²	C₃×#121	1	1	yes	characteristic
420	C₂×C₃²	C₃×#123	1	1	yes	characteristic
421	C₃×D₃	—	2	4	no	—
422	C₃×D₃	—	4	2	no	—
423	C₂×C₉	—	2	1	no	—
424	C₂×C₉	—	2	1	no	—
425	C₂×C₉	—	2	1	no	—
426	C₂×C₉	—	2	1	no	—
427	C₂×C₉	—	2	1	no	—
428	C₂×C₉	—	2	1	no	—
429	C₂×C₉	—	2	1	no	—
430	C₂×C₉	—	6	4	no	—
431	C₂×C₉	—	12	2	no	—
432	C₂×C₉	C₄×D₁₂	1	1	yes	characteristic
433	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
434	C₂×C₉	#882	1	1	yes	characteristic
435	C₂×C₉	#884	1	1	yes	characteristic
436	C₂×C₉	#893	1	1	yes	characteristic
437	C₂×C₉	#894	1	1	yes	characteristic
438	C₂×C₉	#895	1	1	yes	characteristic
439	C₂⁴	—	3	1	no	—
440	C₂⁴	—	3	1	no	—
441	C₂×D₄	—	3	4	no	—
442	C₂×D₄	—	6	2	no	—
443	C₂×D₄	—	6	2	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	6	2	no	—
447	C₂²×C₄	—	6	2	no	—
448	C₂²×C₄	—	6	2	no	—
449	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
452	C₂²⋊C₄	—	6	2	no	—
453	C₂²⋊C₄	—	6	2	no	—
454	C₂²⋊C₄	—	6	2	no	—
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	—	2	1	no	—
458	C₂²×C₃	—	2	1	no	—
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	3	4	no	—
463	C₂²×C₃	—	6	2	no	—
464	C₂²×C₃	—	6	2	no	—
465	C₂²×C₃	—	6	2	no	—
466	C₂²×C₃	—	6	2	no	—
467	C₂²×C₃	—	6	2	no	—
468	C₂²×C₃	—	6	2	no	—
469	C₂²×C₃	—	6	2	no	—
470	C₂²×C₃	—	6	2	no	—
471	C₂²×C₃	—	6	2	no	—
472	C₂²×C₃	—	12	1	no	—
473	C₂²×C₃	—	12	1	no	—
474	C₂²×C₃	—	12	1	no	—
475	C₂²×C₃	—	12	1	no	—
476	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
477	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
478	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
479	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
480	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
481	C₂²×C₃	C₉×#41	1	1	yes	characteristic
482	C₂²×C₃	C₉×#41	1	1	yes	characteristic
483	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
484	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
485	C₂²×C₃	C₃×#235	1	1	yes	characteristic
486	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
487	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
488	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
489	C₂²×C₃	C₃×#239	1	1	yes	characteristic
490	C₂×D₃	—	2	2	no	—
491	C₂×D₃	—	2	2	no	—
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	2	2	no	—
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	2	2	no	—
496	C₂×D₃	—	2	2	no	—
497	C₂×D₃	—	2	2	no	—
498	C₂×D₃	—	2	2	no	—
499	C₂×D₃	—	4	1	no	—
500	C₂×D₃	—	4	1	no	—
501	C₂×D₃	—	4	1	no	—
502	C₂×D₃	—	4	1	no	—
503	C₂×D₃	C₉×C₂²⋊C₄	1	4	yes	complemented
504	C₃×C₄	—	2	2	no	—
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	2	no	—
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	4	2	no	—
509	C₃×C₄	—	4	2	no	—
510	C₃×C₄	—	4	2	no	—
511	C₃×C₄	—	4	1	no	—
512	C₃×C₄	—	4	1	no	—
513	C₃×C₄	—	6	2	no	—
514	C₃×C₄	—	12	1	no	—
515	Dic₃	—	2	2	no	—
516	Dic₃	—	4	1	no	—
517	C₃²	C₃×#386	1	1	yes	characteristic
518	C₉	—	2	1	no	—
519	C₉	#4665	1	1	yes	characteristic, direct product factor
520	C₂³	—	3	2	no	—
521	C₂³	—	3	2	no	—
522	C₂³	—	3	2	no	—
523	C₂³	—	3	2	no	—
524	C₂³	—	6	1	no	—
525	C₂³	—	6	1	no	—
526	C₂³	—	6	1	no	—
527	C₂³	—	6	1	no	—
528	C₂³	—	6	1	no	—
529	C₂³	—	6	1	no	—
530	C₂³	—	6	1	no	—
531	C₂³	—	6	1	no	—
532	C₂³	—	6	1	no	—
533	C₂³	—	6	1	no	—
534	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
535	D₄	—	6	8	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	—	3	2	no	—
544	C₂×C₄	—	6	8	no	—
545	C₂×C₄	—	6	1	no	—
546	C₂×C₄	—	6	1	no	—
547	C₂×C₄	—	6	1	no	—
548	C₂×C₄	—	6	1	no	—
549	C₂×C₄	—	6	1	no	—
550	C₂×C₄	C₄×D₃×C₉	1	2	yes	complemented
551	C₂×C₄	C₉×D₁₂	1	2	yes	complemented
552	C₂×C₃	—	2	1	no	—
553	C₂×C₃	—	2	1	no	—
554	C₂×C₃	—	2	1	no	—
555	C₂×C₃	—	2	1	no	—
556	C₂×C₃	—	2	1	no	—
557	C₂×C₃	—	2	1	no	—
558	C₂×C₃	—	2	1	no	—
559	C₂×C₃	—	6	4	no	—
560	C₂×C₃	—	12	2	no	—
561	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
563	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
564	C₂×C₃	C₉×#120	1	1	yes	characteristic
565	C₂×C₃	C₉×#121	1	1	yes	characteristic
566	C₂×C₃	C₉×#121	1	1	yes	characteristic
567	C₂×C₃	C₉×#123	1	1	yes	characteristic
568	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
569	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
570	C₂×C₃	C₃×#882	1	1	yes	characteristic
571	C₂×C₃	C₃×#884	1	1	yes	characteristic
572	C₂×C₃	C₃×#893	1	1	yes	characteristic
573	C₂×C₃	C₃×#894	1	1	yes	characteristic
574	C₂×C₃	C₃×#895	1	1	yes	characteristic
575	D₃	—	2	4	no	—
576	D₃	—	4	2	no	—
577	C₂²	—	3	4	no	—
578	C₂²	—	6	2	no	—
579	C₂²	—	6	2	no	—
580	C₂²	—	6	2	no	—
581	C₂²	—	6	2	no	—
582	C₂²	—	6	2	no	—
583	C₂²	—	6	2	no	—
584	C₂²	—	6	2	no	—
585	C₂²	—	6	2	no	—
586	C₂²	—	6	2	no	—
587	C₂²	—	12	1	no	—
588	C₂²	—	12	1	no	—
589	C₂²	—	12	1	no	—
590	C₂²	—	12	1	no	—
591	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
592	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
593	C₂²	C₉×#235	1	1	yes	characteristic
594	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
595	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
596	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
597	C₂²	C₉×#239	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	4	1	no	—
601	C₄	—	6	2	no	—
602	C₄	—	12	1	no	—
603	C₃	—	2	1	no	—
604	C₃	C₉×#386	1	1	yes	characteristic, complemented
605	C₃	C₃×#4665	1	1	yes	characteristic
606	C₂	—	6	4	no	—
607	C₂	—	12	2	no	—
608	C₂	C₄×C₉×D₁₂	1	1	yes	characteristic
609	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
610	C₂	C₉×#882	1	1	yes	characteristic
611	C₂	C₉×#884	1	1	yes	characteristic
612	C₂	C₉×#893	1	1	yes	characteristic
613	C₂	C₉×#894	1	1	yes	characteristic
614	C₂	C₉×#895	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₃×C₉×#95	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×D₁₂	C₂×C₃
hypercenter	C₉×#95	D₃
hypocenter	C₃	C₉×#386
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₉×#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
4. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₃×C₉×#95	C₂	semidirect
7. C₉×C₃⋊#95	C₂	semidirect
19. C₂×C₉×D₁₂	C₄	semidirect
40. C₉×#95	D₃	semidirect
53. C₂²×D₃×C₉	C₂×C₄	semidirect
63. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
64. C₂×C₃×C₄×C₉	D₄	semidirect
70. C₂×C₉×Dic₃	D₄	semidirect
74. #4665	C₉	direct (N × H)
130. C₂×D₃×C₉	C₂²⋊C₄	semidirect
139. C₂²×C₄×D₃	C₂×C₉	semidirect
143. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
144. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
145. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
148. C₃×#95	C₂×C₉	semidirect
150. C₃⋊#95	C₂×C₉	semidirect
223. C₂×C₄×C₉	C₄×D₃	semidirect
224. C₂×C₄×C₉	D₁₂	semidirect
260. C₂×D₁₂	C₄×C₉	semidirect
338. #95	D₃×C₉	semidirect
339. C₃×C₉	#386	semidirect
368. C₂²×D₃	C₂×C₄×C₉	semidirect
402. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
403. C₂×C₃×C₄	D₄×C₉	semidirect
411. C₂×Dic₃	D₄×C₉	semidirect
503. C₂×D₃	C₉×C₂²⋊C₄	semidirect
519. C₉	#4665	direct (N × H)
550. C₂×C₄	C₄×D₃×C₉	semidirect
551. C₂×C₄	C₉×D₁₂	semidirect
604. C₃	C₉×#386	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×D₁₂	2
C₂²×C₄×D₃×C₉	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₃×C₉×#95	2
C₉×C₃⋊#95	2
C₃×#4665	3
C₉×#386	3

Subgroups — C9×#4665 #13141323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4665 #13141323