Subgroups — C₉×#5611 #13152830

Order 1728.

970 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#935	C₂	1	2	yes	maximal, complemented
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#883	C₂	1	2	yes	maximal, complemented
11	C₉×#878	C₂	1	2	yes	maximal, complemented
12	C₃×#5611	C₃	1	1	yes	maximal, characteristic
13	C₉×#547	—	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	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
20	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
21	C₉×#237	—	2	8	no	—
22	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₉×Dic₆	C₂²	1	2	yes	—
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₉×#217	C₂²	1	1	yes	characteristic
28	C₉×#217	C₂²	1	2	yes	—
29	C₉×#217	C₂²	1	2	yes	—
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₃×#237	C₂×C₃	1	2	yes	—
39	C₃²×#121	C₂×C₃	1	1	yes	characteristic
40	C₃×#938	C₂×C₃	1	1	yes	characteristic
41	C₃×#935	C₂×C₃	1	2	yes	—
42	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
43	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
44	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
45	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
46	C₃×#888	C₂×C₃	1	1	yes	characteristic
47	C₃×#883	C₂×C₃	1	2	yes	—
48	C₃×#878	C₂×C₃	1	2	yes	—
49	C₂×C₉×#41	—	3	2	no	—
50	C₉×C₄⋊Q₈	—	3	1	no	—
51	C₉×#123	—	3	2	no	—
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	2	no	—
54	C₉×#121	—	2	1	no	—
55	C₉×#121	—	3	1	no	—
56	C₉×#121	D₃	1	1	yes	characteristic, complemented
57	C₄×D₄×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂×C₉×C₄⋊C₄	—	3	1	no	—
61	C₂³×C₃×C₉	C₂³	1	2	yes	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
64	C₃×D₄×C₉	—	2	4	no	—
65	C₃×D₄×C₉	—	2	2	no	—
66	C₂×C₃×C₄×C₉	—	2	2	no	—
67	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×#67	—	2	4	no	—
71	C₉×#67	D₄	1	4	yes	complemented
72	C₂×C₉×Dic₃	—	2	4	no	—
73	C₂×C₉×Dic₃	—	2	4	no	—
74	C₂×C₉×Dic₃	C₂³	1	2	yes	—
75	C₂×C₉×Dic₃	C₂³	1	2	yes	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₄×D₃×C₉	—	2	4	no	—
80	C₄×D₃×C₉	—	2	2	no	—
81	C₉×Dic₆	—	2	4	no	—
82	C₃×#547	—	3	1	no	—
83	#5611	C₉	1	1	yes	characteristic, direct product factor
84	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
86	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
88	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
90	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
91	C₃×#237	—	2	8	no	—
92	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
95	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×#217	C₂²×C₃	1	2	yes	—
98	C₃×#217	C₂²×C₃	1	2	yes	—
99	C₃×#217	C₂²×C₃	1	1	yes	characteristic
100	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
102	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
108	C₉×#41	—	6	8	no	—
109	C₂×Q₈×C₉	—	3	2	no	—
110	C₂×D₄×C₉	—	2	1	no	—
111	C₂×D₄×C₉	—	2	2	no	—
112	C₂×D₄×C₉	—	3	1	no	—
113	C₂×D₄×C₉	—	3	2	no	—
114	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
115	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
116	C₂²×C₄×C₉	—	2	1	no	—
117	C₂²×C₄×C₉	—	3	2	no	—
118	C₂²×C₄×C₉	—	3	2	no	—
119	C₂²×C₄×C₉	—	3	1	no	—
120	C₂²×C₄×C₉	—	3	2	no	—
121	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
122	C₉×C₄⋊C₄	—	2	1	no	—
123	C₉×C₄⋊C₄	—	3	1	no	—
124	C₉×C₄⋊C₄	—	3	1	no	—
125	C₉×C₄⋊C₄	—	3	2	no	—
126	C₉×C₄⋊C₄	—	3	2	no	—
127	C₉×C₄⋊C₄	—	3	1	no	—
128	C₉×C₄⋊C₄	—	3	2	no	—
129	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₉×C₂²⋊C₄	—	2	2	no	—
131	C₉×C₂²⋊C₄	—	3	1	no	—
132	C₉×C₂²⋊C₄	—	3	2	no	—
133	C₉×C₂²⋊C₄	—	3	2	no	—
134	C₉×C₂²⋊C₄	—	3	1	no	—
135	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
136	C₄²×C₉	—	3	1	no	—
137	C₂²×C₃×C₉	—	2	1	no	—
138	C₂²×C₃×C₉	—	2	1	no	—
139	C₂²×C₃×C₉	—	2	2	no	—
140	C₂²×C₃×C₉	—	2	2	no	—
141	C₂²×C₃×C₉	—	2	2	no	—
142	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
143	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
144	C₂×D₃×C₉	—	2	1	no	—
145	C₂×D₃×C₉	—	2	1	no	—
146	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
147	C₃×C₄×C₉	—	2	2	no	—
148	C₃×C₄×C₉	—	2	1	no	—
149	C₃×C₄×C₉	#41	1	2	yes	complemented
150	C₉×Dic₃	—	2	2	no	—
151	C₉×Dic₃	—	2	2	no	—
152	C₉×Dic₃	—	2	1	no	—
153	C₉×Dic₃	—	2	1	no	—
154	C₉×Dic₃	C₂×D₄	1	2	yes	—
155	C₂×C₃×#41	—	3	2	no	—
156	C₂×#237	C₂×C₉	1	2	yes	complemented
157	C₃×C₄⋊Q₈	—	3	1	no	—
158	C₃×#123	—	3	2	no	—
159	C₃×#123	—	3	2	no	—
160	C₃×C₂²⋊Q₈	—	3	2	no	—
161	C₃×#121	—	2	1	no	—
162	C₃×#121	—	3	1	no	—
163	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
164	C₃×#121	C₃×D₃	1	1	yes	characteristic
165	C₃×C₄×D₄	—	3	1	no	—
166	C₃×C₄×D₄	—	3	1	no	—
167	C₂×C₃×C₄⋊C₄	—	3	1	no	—
168	C₂×C₃×C₄⋊C₄	—	3	1	no	—
169	#938	C₂×C₉	1	1	yes	characteristic, complemented
170	#935	C₂×C₉	1	2	yes	complemented
171	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
172	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
173	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
174	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
175	#888	C₂×C₉	1	1	yes	characteristic, complemented
176	#883	C₂×C₉	1	2	yes	complemented
177	#878	C₂×C₉	1	2	yes	complemented
178	C₂³×C₃²	C₂³×C₃	1	2	yes	—
179	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
181	C₃²×D₄	—	2	4	no	—
182	C₃²×D₄	—	2	2	no	—
183	C₂×C₃²×C₄	—	2	2	no	—
184	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₃×#67	—	2	4	no	—
188	C₃×#67	C₃×D₄	1	4	yes	—
189	C₂×C₃×Dic₃	—	2	4	no	—
190	C₂×C₃×Dic₃	—	2	4	no	—
191	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
194	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
196	C₃×C₄×D₃	—	2	4	no	—
197	C₃×C₄×D₃	—	2	2	no	—
198	C₃×Dic₆	—	2	4	no	—
199	C₂³×C₉	—	2	1	no	—
200	C₂³×C₉	—	2	2	no	—
201	C₂³×C₉	—	3	1	no	—
202	C₂³×C₉	C₂²×D₃	1	2	yes	—
203	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
204	Q₈×C₉	—	6	4	no	—
205	D₄×C₉	—	2	4	no	—
206	D₄×C₉	—	2	2	no	—
207	D₄×C₉	—	3	4	no	—
208	D₄×C₉	—	4	2	no	—
209	D₄×C₉	—	4	4	no	—
210	D₄×C₉	—	6	4	no	—
211	C₂×C₄×C₉	—	2	2	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	2	no	—
215	C₂×C₄×C₉	—	3	1	no	—
216	C₂×C₄×C₉	—	3	1	no	—
217	C₂×C₄×C₉	—	3	1	no	—
218	C₂×C₄×C₉	—	3	2	no	—
219	C₂×C₄×C₉	—	3	2	no	—
220	C₂×C₄×C₉	—	4	2	no	—
221	C₂×C₄×C₉	—	6	4	no	—
222	C₂×C₄×C₉	—	6	4	no	—
223	C₂×C₄×C₉	—	6	4	no	—
224	C₂×C₄×C₉	—	6	2	no	—
225	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
227	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
228	#547	—	3	1	no	Sylow
229	C₂×C₃×C₉	—	2	2	no	—
230	C₂×C₃×C₉	—	4	2	no	—
231	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
234	D₃×C₉	—	2	2	no	—
235	C₃×#41	—	6	8	no	—
236	C₂×C₃×Q₈	—	3	2	no	—
237	C₂×C₃×D₄	—	2	1	no	—
238	C₂×C₃×D₄	—	2	2	no	—
239	C₂×C₃×D₄	—	3	1	no	—
240	C₂×C₃×D₄	—	3	2	no	—
241	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
243	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
244	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	3	2	no	—
247	C₂²×C₃×C₄	—	3	2	no	—
248	C₂²×C₃×C₄	—	3	1	no	—
249	C₂²×C₃×C₄	—	3	2	no	—
250	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
252	C₂×#67	C₂²×C₉	1	2	yes	—
253	C₂×#67	C₂²×C₉	1	1	yes	characteristic
254	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
255	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
256	#237	—	2	8	no	—
257	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
258	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
259	C₂×Dic₆	C₂²×C₉	1	2	yes	—
260	C₃×C₄⋊C₄	—	2	1	no	—
261	C₃×C₄⋊C₄	—	3	2	no	—
262	C₃×C₄⋊C₄	—	3	1	no	—
263	C₃×C₄⋊C₄	—	3	2	no	—
264	C₃×C₄⋊C₄	—	3	1	no	—
265	C₃×C₄⋊C₄	—	3	1	no	—
266	C₃×C₄⋊C₄	—	3	2	no	—
267	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
269	C₃×C₂²⋊C₄	—	2	2	no	—
270	C₃×C₂²⋊C₄	—	3	1	no	—
271	C₃×C₂²⋊C₄	—	3	2	no	—
272	C₃×C₂²⋊C₄	—	3	2	no	—
273	C₃×C₂²⋊C₄	—	3	1	no	—
274	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
275	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
276	C₃×C₄²	—	3	1	no	—
277	#217	C₂²×C₉	1	2	yes	—
278	#217	C₂²×C₉	1	2	yes	—
279	#217	C₂²×C₉	1	1	yes	characteristic
280	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
281	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
282	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
283	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
284	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
285	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
286	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
287	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
288	C₂²×C₃²	—	2	1	no	—
289	C₂²×C₃²	—	2	1	no	—
290	C₂²×C₃²	—	2	2	no	—
291	C₂²×C₃²	—	2	2	no	—
292	C₂²×C₃²	—	2	2	no	—
293	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
294	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
295	C₂×C₃×D₃	—	2	1	no	—
296	C₂×C₃×D₃	—	2	1	no	—
297	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
298	C₃²×C₄	—	2	2	no	—
299	C₃²×C₄	—	2	1	no	—
300	C₃²×C₄	C₃×#41	1	2	yes	—
301	C₃×Dic₃	—	2	2	no	—
302	C₃×Dic₃	—	2	2	no	—
303	C₃×Dic₃	—	2	1	no	—
304	C₃×Dic₃	—	2	1	no	—
305	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
306	C₂²×C₉	—	2	1	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	2	no	—
309	C₂²×C₉	—	2	2	no	—
310	C₂²×C₉	—	2	2	no	—
311	C₂²×C₉	—	2	1	no	—
312	C₂²×C₉	—	2	2	no	—
313	C₂²×C₉	—	3	2	no	—
314	C₂²×C₉	—	4	1	no	—
315	C₂²×C₉	—	4	1	no	—
316	C₂²×C₉	—	4	2	no	—
317	C₂²×C₉	—	4	2	no	—
318	C₂²×C₉	—	4	2	no	—
319	C₂²×C₉	—	6	1	no	—
320	C₂²×C₉	—	6	1	no	—
321	C₂²×C₉	D₃×D₄	1	2	yes	—
322	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
323	C₄×C₉	—	2	2	no	—
324	C₄×C₉	—	2	1	no	—
325	C₄×C₉	—	2	2	no	—
326	C₄×C₉	—	3	2	no	—
327	C₄×C₉	—	4	1	no	—
328	C₄×C₉	—	4	2	no	—
329	C₄×C₉	—	6	2	no	—
330	C₄×C₉	—	6	2	no	—
331	C₄×C₉	—	6	1	no	—
332	C₄×C₉	—	6	1	no	—
333	C₄×C₉	#237	1	2	yes	complemented
334	C₂×#41	—	3	2	no	—
335	C₄⋊Q₈	—	3	1	no	—
336	#123	—	3	2	no	—
337	#123	—	3	2	no	—
338	C₂²⋊Q₈	—	3	2	no	—
339	#121	—	3	1	no	—
340	#121	D₃×C₉	1	1	yes	characteristic, complemented
341	C₄×D₄	—	3	1	no	—
342	C₄×D₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	1	no	—
345	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
346	C₂³×C₃	—	2	1	no	—
347	C₂³×C₃	—	2	2	no	—
348	C₂³×C₃	—	3	1	no	—
349	C₂³×C₃	C₂³×C₉	1	2	yes	—
350	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
351	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
352	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
353	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
354	C₃×Q₈	—	6	4	no	—
355	C₃×D₄	—	2	4	no	—
356	C₃×D₄	—	2	4	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	3	4	no	—
360	C₃×D₄	—	4	2	no	—
361	C₃×D₄	—	4	4	no	—
362	C₃×D₄	—	6	4	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	3	1	no	—
369	C₂×C₃×C₄	—	3	1	no	—
370	C₂×C₃×C₄	—	3	1	no	—
371	C₂×C₃×C₄	—	3	2	no	—
372	C₂×C₃×C₄	—	3	2	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	—	6	4	no	—
375	C₂×C₃×C₄	—	6	4	no	—
376	C₂×C₃×C₄	—	6	4	no	—
377	C₂×C₃×C₄	—	6	2	no	—
378	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
379	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
383	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
384	#67	—	2	4	no	—
385	#67	D₄×C₉	1	4	yes	complemented
386	C₂×Dic₃	—	2	4	no	—
387	C₂×Dic₃	—	2	4	no	—
388	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
389	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
390	C₂×Dic₃	C₂³×C₉	1	2	yes	—
391	C₂×Dic₃	C₂³×C₉	1	2	yes	—
392	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
393	C₄×D₃	—	2	4	no	—
394	C₄×D₃	—	2	2	no	—
395	Dic₆	—	2	4	no	—
396	C₂×C₃²	—	2	2	no	—
397	C₂×C₃²	—	4	2	no	—
398	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
399	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
400	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
401	C₃×D₃	—	2	2	no	—
402	C₂×C₉	—	2	2	no	—
403	C₂×C₉	—	2	1	no	—
404	C₂×C₉	—	2	1	no	—
405	C₂×C₉	—	2	1	no	—
406	C₂×C₉	—	4	2	no	—
407	C₂×C₉	—	4	2	no	—
408	C₂×C₉	—	6	2	no	—
409	C₂×C₉	—	8	2	no	—
410	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
411	C₂×C₉	C₂×#237	1	1	yes	characteristic
412	C₂×C₉	#1010	1	1	yes	characteristic
413	#41	—	6	8	no	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×D₄	—	3	1	no	—
416	C₂×D₄	—	3	2	no	—
417	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
418	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
419	C₂²×C₄	—	3	2	no	—
420	C₂²×C₄	—	3	2	no	—
421	C₂²×C₄	—	3	1	no	—
422	C₂²×C₄	—	3	2	no	—
423	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
424	C₄⋊C₄	—	3	1	no	—
425	C₄⋊C₄	—	3	1	no	—
426	C₄⋊C₄	—	3	2	no	—
427	C₄⋊C₄	—	3	2	no	—
428	C₄⋊C₄	—	3	1	no	—
429	C₄⋊C₄	—	3	2	no	—
430	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
431	C₂²⋊C₄	—	3	1	no	—
432	C₂²⋊C₄	—	3	2	no	—
433	C₂²⋊C₄	—	3	2	no	—
434	C₂²⋊C₄	—	3	1	no	—
435	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
436	C₄²	—	3	1	no	—
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	1	no	—
439	C₂²×C₃	—	2	1	no	—
440	C₂²×C₃	—	2	1	no	—
441	C₂²×C₃	—	2	2	no	—
442	C₂²×C₃	—	2	2	no	—
443	C₂²×C₃	—	2	2	no	—
444	C₂²×C₃	—	2	2	no	—
445	C₂²×C₃	—	2	2	no	—
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	3	2	no	—
450	C₂²×C₃	—	4	1	no	—
451	C₂²×C₃	—	4	1	no	—
452	C₂²×C₃	—	4	2	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	4	2	no	—
455	C₂²×C₃	—	6	1	no	—
456	C₂²×C₃	—	6	1	no	—
457	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
458	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
459	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
460	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
461	C₂×D₃	—	2	1	no	—
462	C₂×D₃	—	2	1	no	—
463	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
464	C₃×C₄	—	2	2	no	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	2	1	no	—
468	C₃×C₄	—	2	2	no	—
469	C₃×C₄	—	3	2	no	—
470	C₃×C₄	—	4	1	no	—
471	C₃×C₄	—	4	2	no	—
472	C₃×C₄	—	6	2	no	—
473	C₃×C₄	—	6	2	no	—
474	C₃×C₄	—	6	1	no	—
475	C₃×C₄	—	6	1	no	—
476	C₃×C₄	C₉×#41	1	2	yes	complemented
477	C₃×C₄	C₃×#237	1	2	yes	—
478	Dic₃	—	2	2	no	—
479	Dic₃	—	2	2	no	—
480	Dic₃	—	2	1	no	—
481	Dic₃	—	2	1	no	—
482	Dic₃	C₂×D₄×C₉	1	2	yes	—
483	C₃²	C₃×#547	1	1	yes	characteristic
484	C₉	—	2	1	no	—
485	C₉	#5611	1	1	yes	characteristic, direct product factor
486	C₂³	—	3	1	no	—
487	C₂³	C₂²×D₃×C₉	1	2	yes	—
488	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
489	Q₈	—	6	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	2	2	no	—
492	D₄	—	3	4	no	—
493	D₄	—	6	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	3	1	no	—
496	C₂×C₄	—	3	1	no	—
497	C₂×C₄	—	3	1	no	—
498	C₂×C₄	—	3	2	no	—
499	C₂×C₄	—	3	2	no	—
500	C₂×C₄	—	6	4	no	—
501	C₂×C₄	—	6	4	no	—
502	C₂×C₄	—	6	4	no	—
503	C₂×C₄	—	6	2	no	—
504	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
506	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
507	C₂×C₃	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	2	1	no	—
510	C₂×C₃	—	2	1	no	—
511	C₂×C₃	—	2	1	no	—
512	C₂×C₃	—	4	2	no	—
513	C₂×C₃	—	4	2	no	—
514	C₂×C₃	—	4	2	no	—
515	C₂×C₃	—	6	2	no	—
516	C₂×C₃	—	8	2	no	—
517	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
518	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
519	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
521	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
522	C₂×C₃	C₃×#1010	1	1	yes	characteristic
523	D₃	—	2	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	3	2	no	—
530	C₂²	—	6	1	no	—
531	C₂²	—	6	1	no	—
532	C₂²	D₃×D₄×C₉	1	2	yes	—
533	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	1	no	—
536	C₄	—	3	2	no	—
537	C₄	—	6	2	no	—
538	C₄	—	6	2	no	—
539	C₄	—	6	1	no	—
540	C₄	—	6	1	no	—
541	C₄	C₉×#237	1	2	yes	complemented
542	C₃	—	2	1	no	—
543	C₃	C₉×#547	1	1	yes	characteristic, complemented
544	C₃	C₃×#5611	1	1	yes	characteristic
545	C₂	—	2	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	6	2	no	—
548	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
549	C₂	C₂×C₉×#237	1	1	yes	characteristic
550	C₂	C₉×#1010	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	C₃×#5611	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#547
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
1. C₂×C₉×#237	C₂	semidirect
2. C₃×C₉×#121	C₂	semidirect
3. C₉×#938	C₂	semidirect
4. C₉×#935	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₄×C₉×#67	C₂	semidirect
7. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
8. D₃×C₉×C₄⋊C₄	C₂	semidirect
9. C₉×#888	C₂	semidirect
10. C₉×#883	C₂	semidirect
11. C₉×#878	C₂	semidirect
56. C₉×#121	D₃	semidirect
71. C₉×#67	D₄	semidirect
83. #5611	C₉	direct (N × H)
149. C₃×C₄×C₉	#41	semidirect
156. C₂×#237	C₂×C₉	semidirect
163. C₃×#121	C₂×C₉	semidirect
169. #938	C₂×C₉	semidirect
170. #935	C₂×C₉	semidirect
171. D₄×Dic₃	C₂×C₉	semidirect
172. C₄×#67	C₂×C₉	semidirect
173. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
174. D₃×C₄⋊C₄	C₂×C₉	semidirect
175. #888	C₂×C₉	semidirect
176. #883	C₂×C₉	semidirect
177. #878	C₂×C₉	semidirect
333. C₄×C₉	#237	semidirect
340. #121	D₃×C₉	semidirect
345. C₃×C₉	#547	semidirect
385. #67	D₄×C₉	semidirect
476. C₃×C₄	C₉×#41	semidirect
485. C₉	#5611	direct (N × H)
541. C₄	C₉×#237	semidirect
543. C₃	C₉×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#237	2
C₃×C₉×#121	2
C₉×#938	2
C₉×#935	2
D₄×C₉×Dic₃	2
C₄×C₉×#67	2
C₂×C₉×C₄⋊Dic₃	2
D₃×C₉×C₄⋊C₄	2
C₉×#888	2
C₉×#883	2
C₉×#878	2
C₃×#5611	3
C₉×#547	3

Subgroups — C9×#5611 #13152830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5611 #13152830