Subgroups — C₉×#5600 #13152801

Order 1728.

796 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#935	C₂	1	2	yes	maximal, complemented
4	D₄×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#879	C₂	1	2	yes	maximal, complemented
11	C₉×#877	C₂	1	2	yes	maximal, complemented
12	C₃×#5600	C₃	1	1	yes	maximal, characteristic
13	C₉×#529	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	2	yes	—
24	C₉×#217	C₂²	1	2	yes	—
25	C₉×#217	C₂²	1	2	yes	—
26	C₉×#217	C₂²	1	2	yes	—
27	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
28	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
33	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×#121	C₂×C₃	1	1	yes	characteristic
38	C₃×#936	C₂×C₃	1	1	yes	characteristic
39	C₃×#935	C₂×C₃	1	2	yes	—
40	C₃×D₄×Dic₃	C₂×C₃	1	2	yes	—
41	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#924	C₂×C₃	1	1	yes	characteristic
43	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
44	C₃×#890	C₂×C₃	1	1	yes	characteristic
45	C₃×#887	C₂×C₃	1	1	yes	characteristic
46	C₃×#879	C₂×C₃	1	2	yes	—
47	C₃×#877	C₂×C₃	1	2	yes	—
48	C₉×#126	—	3	2	no	—
49	C₉×#125	—	3	1	no	—
50	C₉×#124	—	3	1	no	—
51	C₉×#123	—	3	2	no	—
52	C₉×C₂²⋊Q₈	—	3	1	no	—
53	C₉×#121	—	2	1	no	—
54	C₉×#121	D₃	1	1	yes	characteristic
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	2	no	—
58	C₉×#117	—	3	2	no	—
59	C₂×C₄²×C₉	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
62	C₃×D₄×C₉	—	2	4	no	—
63	C₃×D₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	—	2	2	no	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₉×Dic₃	—	2	2	no	—
69	C₂×C₉×Dic₃	—	2	2	no	—
70	C₂×C₉×Dic₃	—	2	4	no	—
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₉×Dic₃	C₂³	1	2	yes	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₉×Dic₆	—	2	2	no	—
78	C₃×#529	—	3	1	no	—
79	#5600	C₉	1	1	yes	characteristic, direct product factor
80	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
81	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
84	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃×#217	C₂²×C₃	1	2	yes	—
90	C₃×#217	C₂²×C₃	1	2	yes	—
91	C₃×#217	C₂²×C₃	1	2	yes	—
92	C₃×#217	C₂²×C₃	1	2	yes	—
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
103	C₂×Q₈×C₉	—	3	1	no	—
104	C₂×D₄×C₉	—	2	1	no	—
105	C₂×D₄×C₉	—	2	2	no	—
106	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
107	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₄×C₉	—	2	1	no	—
109	C₂²×C₄×C₉	—	3	1	no	—
110	C₂²×C₄×C₉	—	3	1	no	—
111	C₂²×C₄×C₉	—	3	2	no	—
112	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
113	C₉×C₄⋊C₄	—	2	1	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	1	no	—
117	C₉×C₄⋊C₄	—	3	2	no	—
118	C₉×C₄⋊C₄	—	3	2	no	—
119	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
120	C₉×C₂²⋊C₄	—	2	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
126	C₄²×C₉	—	3	1	no	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	1	no	—
129	C₄²×C₉	—	3	1	no	—
130	C₄²×C₉	—	3	2	no	—
131	C₂²×C₃×C₉	—	2	1	no	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	—	2	2	no	—
134	C₂²×C₃×C₉	—	2	2	no	—
135	C₂²×C₃×C₉	—	2	2	no	—
136	C₂²×C₃×C₉	#41	1	2	yes	—
137	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
138	C₃×C₄×C₉	—	2	1	no	—
139	C₃×C₄×C₉	—	2	2	no	—
140	C₃×C₄×C₉	#41	1	2	yes	—
141	C₉×Dic₃	—	2	2	no	—
142	C₉×Dic₃	—	2	1	no	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	1	no	—
145	C₉×Dic₃	—	2	2	no	—
146	C₉×Dic₃	#41	1	2	yes	—
147	C₃×#126	—	3	2	no	—
148	C₃×#125	—	3	1	no	—
149	C₃×#124	—	3	1	no	—
150	C₃×#123	—	3	2	no	—
151	C₃×C₂²⋊Q₈	—	3	1	no	—
152	C₃×#121	—	2	1	no	—
153	C₃×#121	C₂×C₉	1	1	yes	characteristic
154	C₃×#121	C₃×D₃	1	1	yes	characteristic
155	C₃×C₄×Q₈	—	3	1	no	—
156	C₃×C₄×D₄	—	3	1	no	—
157	C₃×C₄×D₄	—	3	2	no	—
158	C₃×#117	—	3	2	no	—
159	C₂×C₃×C₄²	—	3	1	no	—
160	#936	C₂×C₉	1	1	yes	characteristic, complemented
161	#935	C₂×C₉	1	2	yes	complemented
162	D₄×Dic₃	C₂×C₉	1	2	yes	complemented
163	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
164	#924	C₂×C₉	1	1	yes	characteristic, complemented
165	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
166	#890	C₂×C₉	1	1	yes	characteristic, complemented
167	#887	C₂×C₉	1	1	yes	characteristic, complemented
168	#879	C₂×C₉	1	2	yes	complemented
169	#877	C₂×C₉	1	2	yes	complemented
170	C₂³×C₃²	C₂³×C₃	1	2	yes	—
171	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
172	C₃²×D₄	—	2	4	no	—
173	C₃²×D₄	—	2	2	no	—
174	C₂×C₃²×C₄	—	2	2	no	—
175	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
177	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃×Dic₃	—	2	2	no	—
179	C₂×C₃×Dic₃	—	2	2	no	—
180	C₂×C₃×Dic₃	—	2	4	no	—
181	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
185	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
186	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
187	C₃×Dic₆	—	2	2	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	2	no	—
190	C₂³×C₉	C₂²×D₃	1	2	yes	—
191	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
192	Q₈×C₉	—	6	2	no	—
193	D₄×C₉	—	2	4	no	—
194	D₄×C₉	—	2	2	no	—
195	D₄×C₉	—	4	2	no	—
196	D₄×C₉	—	4	4	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	2	no	—
201	C₂×C₄×C₉	—	3	1	no	—
202	C₂×C₄×C₉	—	3	1	no	—
203	C₂×C₄×C₉	—	3	1	no	—
204	C₂×C₄×C₉	—	3	1	no	—
205	C₂×C₄×C₉	—	3	2	no	—
206	C₂×C₄×C₉	—	3	2	no	—
207	C₂×C₄×C₉	—	4	2	no	—
208	C₂×C₄×C₉	—	6	2	no	—
209	C₂×C₄×C₉	—	6	4	no	—
210	C₂×C₄×C₉	—	6	2	no	—
211	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
212	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
213	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
214	#529	—	3	1	no	Sylow
215	C₂×C₃×C₉	—	2	2	no	—
216	C₂×C₃×C₉	—	4	2	no	—
217	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₃×Q₈	—	3	1	no	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	—	2	1	no	—
223	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
224	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
225	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
226	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	3	1	no	—
229	C₂²×C₃×C₄	—	3	1	no	—
230	C₂²×C₃×C₄	—	3	2	no	—
231	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
233	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
234	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
235	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
236	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
237	C₃×C₄⋊C₄	—	2	1	no	—
238	C₃×C₄⋊C₄	—	3	2	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₄⋊C₄	—	3	2	no	—
241	C₃×C₄⋊C₄	—	3	1	no	—
242	C₃×C₄⋊C₄	—	3	2	no	—
243	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
244	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
245	C₃×C₂²⋊C₄	—	2	2	no	—
246	C₃×C₂²⋊C₄	—	3	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₂²⋊C₄	—	3	2	no	—
249	C₃×C₂²⋊C₄	—	3	2	no	—
250	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
251	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
252	C₃×C₄²	—	3	1	no	—
253	C₃×C₄²	—	3	1	no	—
254	C₃×C₄²	—	3	1	no	—
255	C₃×C₄²	—	3	1	no	—
256	C₃×C₄²	—	3	2	no	—
257	#217	C₂²×C₉	1	2	yes	—
258	#217	C₂²×C₉	1	2	yes	—
259	#217	C₂²×C₉	1	2	yes	—
260	#217	C₂²×C₉	1	2	yes	—
261	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
262	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
263	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
264	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
265	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
266	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×C₉	1	2	yes	—
268	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
269	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
270	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
271	C₂²×C₃²	—	2	1	no	—
272	C₂²×C₃²	—	2	1	no	—
273	C₂²×C₃²	—	2	2	no	—
274	C₂²×C₃²	—	2	2	no	—
275	C₂²×C₃²	—	2	2	no	—
276	C₂²×C₃²	C₃×#41	1	2	yes	—
277	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
278	C₃²×C₄	—	2	1	no	—
279	C₃²×C₄	—	2	2	no	—
280	C₃²×C₄	C₃×#41	1	2	yes	—
281	C₃×Dic₃	—	2	2	no	—
282	C₃×Dic₃	—	2	1	no	—
283	C₃×Dic₃	—	2	1	no	—
284	C₃×Dic₃	—	2	1	no	—
285	C₃×Dic₃	—	2	2	no	—
286	C₃×Dic₃	C₃×#41	1	2	yes	—
287	C₂²×C₉	—	2	1	no	—
288	C₂²×C₉	—	2	1	no	—
289	C₂²×C₉	—	2	2	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	—	2	2	no	—
292	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	2	2	no	—
294	C₂²×C₉	—	4	1	no	—
295	C₂²×C₉	—	4	1	no	—
296	C₂²×C₉	—	4	2	no	—
297	C₂²×C₉	—	4	2	no	—
298	C₂²×C₉	—	4	2	no	—
299	C₂²×C₉	#237	1	2	yes	—
300	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
301	C₄×C₉	—	2	1	no	—
302	C₄×C₉	—	2	2	no	—
303	C₄×C₉	—	2	2	no	—
304	C₄×C₉	—	3	2	no	—
305	C₄×C₉	—	4	1	no	—
306	C₄×C₉	—	4	2	no	—
307	C₄×C₉	—	6	1	no	—
308	C₄×C₉	—	6	1	no	—
309	C₄×C₉	—	6	2	no	—
310	C₄×C₉	—	6	1	no	—
311	C₄×C₉	—	6	2	no	—
312	C₄×C₉	#237	1	2	yes	—
313	#126	—	3	2	no	—
314	#125	—	3	1	no	—
315	#124	—	3	1	no	—
316	#123	—	3	2	no	—
317	C₂²⋊Q₈	—	3	1	no	—
318	#121	D₃×C₉	1	1	yes	characteristic
319	C₄×Q₈	—	3	1	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	2	no	—
322	#117	—	3	2	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₃×C₉	#529	1	1	yes	characteristic, complemented, Sylow
325	C₂³×C₃	—	2	1	no	—
326	C₂³×C₃	—	2	2	no	—
327	C₂³×C₃	C₂³×C₉	1	2	yes	—
328	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
329	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
330	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
331	C₃×Q₈	—	6	2	no	—
332	C₃×D₄	—	2	4	no	—
333	C₃×D₄	—	2	4	no	—
334	C₃×D₄	—	2	2	no	—
335	C₃×D₄	—	2	2	no	—
336	C₃×D₄	—	4	2	no	—
337	C₃×D₄	—	4	4	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	3	1	no	—
344	C₂×C₃×C₄	—	3	1	no	—
345	C₂×C₃×C₄	—	3	1	no	—
346	C₂×C₃×C₄	—	3	1	no	—
347	C₂×C₃×C₄	—	3	2	no	—
348	C₂×C₃×C₄	—	3	2	no	—
349	C₂×C₃×C₄	—	4	2	no	—
350	C₂×C₃×C₄	—	6	2	no	—
351	C₂×C₃×C₄	—	6	4	no	—
352	C₂×C₃×C₄	—	6	2	no	—
353	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
355	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
358	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
359	C₂×Dic₃	—	2	2	no	—
360	C₂×Dic₃	—	2	2	no	—
361	C₂×Dic₃	—	2	4	no	—
362	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
363	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
364	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
365	C₂×Dic₃	C₂³×C₉	1	2	yes	—
366	C₂×Dic₃	C₂³×C₉	1	2	yes	—
367	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
368	Dic₆	—	2	2	no	—
369	C₂×C₃²	—	2	2	no	—
370	C₂×C₃²	—	4	2	no	—
371	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
372	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
373	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
374	C₂×C₉	—	2	2	no	—
375	C₂×C₉	—	2	1	no	—
376	C₂×C₉	—	2	1	no	—
377	C₂×C₉	—	2	1	no	—
378	C₂×C₉	—	4	2	no	—
379	C₂×C₉	—	4	2	no	—
380	C₂×C₉	—	8	2	no	—
381	C₂×C₉	C₂×#237	1	1	yes	characteristic
382	C₂×C₉	C₂×#237	1	1	yes	characteristic
383	C₂×C₉	D₃×#41	1	1	yes	characteristic
384	C₂×Q₈	—	3	1	no	—
385	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
386	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	1	no	—
389	C₂²×C₄	—	3	2	no	—
390	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
391	C₄⋊C₄	—	3	2	no	—
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	—	3	1	no	—
394	C₄⋊C₄	—	3	2	no	—
395	C₄⋊C₄	—	3	2	no	—
396	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	—	3	2	no	—
400	C₂²⋊C₄	—	3	2	no	—
401	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
402	C₄²	—	3	1	no	—
403	C₄²	—	3	1	no	—
404	C₄²	—	3	1	no	—
405	C₄²	—	3	1	no	—
406	C₄²	—	3	2	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	2	no	—
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	1	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	—	4	1	no	—
420	C₂²×C₃	—	4	1	no	—
421	C₂²×C₃	—	4	2	no	—
422	C₂²×C₃	—	4	2	no	—
423	C₂²×C₃	—	4	2	no	—
424	C₂²×C₃	C₉×#41	1	2	yes	—
425	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
426	C₂²×C₃	C₃×#237	1	2	yes	—
427	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	3	2	no	—
434	C₃×C₄	—	4	1	no	—
435	C₃×C₄	—	4	2	no	—
436	C₃×C₄	—	6	1	no	—
437	C₃×C₄	—	6	1	no	—
438	C₃×C₄	—	6	2	no	—
439	C₃×C₄	—	6	1	no	—
440	C₃×C₄	—	6	2	no	—
441	C₃×C₄	C₉×#41	1	2	yes	—
442	C₃×C₄	C₃×#237	1	2	yes	—
443	Dic₃	—	2	2	no	—
444	Dic₃	—	2	1	no	—
445	Dic₃	—	2	1	no	—
446	Dic₃	—	2	1	no	—
447	Dic₃	—	2	2	no	—
448	Dic₃	C₉×#41	1	2	yes	—
449	C₃²	C₃×#529	1	1	yes	characteristic
450	C₉	—	2	1	no	—
451	C₉	#5600	1	1	yes	characteristic, direct product factor
452	C₂³	C₂²×D₃×C₉	1	2	yes	—
453	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
454	Q₈	—	6	2	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	3	1	no	—
459	C₂×C₄	—	3	1	no	—
460	C₂×C₄	—	3	1	no	—
461	C₂×C₄	—	3	1	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	6	2	no	—
465	C₂×C₄	—	6	4	no	—
466	C₂×C₄	—	6	2	no	—
467	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
469	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
470	C₂×C₃	—	2	2	no	—
471	C₂×C₃	—	2	2	no	—
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	2	1	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	4	2	no	—
476	C₂×C₃	—	4	2	no	—
477	C₂×C₃	—	4	2	no	—
478	C₂×C₃	—	8	2	no	—
479	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
480	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
481	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
482	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
483	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
484	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	C₉×#237	1	2	yes	—
491	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	2	no	—
494	C₄	—	3	2	no	—
495	C₄	—	6	1	no	—
496	C₄	—	6	1	no	—
497	C₄	—	6	2	no	—
498	C₄	—	6	1	no	—
499	C₄	—	6	2	no	—
500	C₄	C₉×#237	1	2	yes	—
501	C₃	—	2	1	no	—
502	C₃	C₉×#529	1	1	yes	characteristic, complemented
503	C₃	C₃×#5600	1	1	yes	characteristic
504	C₂	—	2	2	no	—
505	C₂	—	4	2	no	—
506	C₂	C₂×C₉×#237	1	1	yes	characteristic
507	C₂	C₂×C₉×#237	1	1	yes	characteristic
508	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃²×#121	C₂×C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
2. C₉×#936	C₂	semidirect
3. C₉×#935	C₂	semidirect
4. D₄×C₉×Dic₃	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₉×#924	C₂	semidirect
7. C₂×C₄×C₉×Dic₃	C₂	semidirect
8. C₉×#890	C₂	semidirect
9. C₉×#887	C₂	semidirect
10. C₉×#879	C₂	semidirect
11. C₉×#877	C₂	semidirect
79. #5600	C₉	direct (N × H)
160. #936	C₂×C₉	semidirect
161. #935	C₂×C₉	semidirect
162. D₄×Dic₃	C₂×C₉	semidirect
163. D₄×Dic₃	C₂×C₉	semidirect
164. #924	C₂×C₉	semidirect
165. C₂×C₄×Dic₃	C₂×C₉	semidirect
166. #890	C₂×C₉	semidirect
167. #887	C₂×C₉	semidirect
168. #879	C₂×C₉	semidirect
169. #877	C₂×C₉	semidirect
324. C₃×C₉	#529	semidirect
451. C₉	#5600	direct (N × H)
502. C₃	C₉×#529	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#121	2
C₉×#936	2
C₉×#935	2
D₄×C₉×Dic₃	2
C₉×#924	2
C₂×C₄×C₉×Dic₃	2
C₉×#890	2
C₉×#887	2
C₉×#879	2
C₉×#877	2
C₃×#5600	3
C₉×#529	3

Subgroups — C9×#5600 #13152801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5600 #13152801