Subgroups — C₉×#5655 #13153026

Order 1728.

954 conjugacy classes of subgroups.

The subgroup lattice has 766 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	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#894	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×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5655	C₃	1	1	yes	maximal, characteristic
17	C₉×#547	—	3	1	no	maximal
18	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	C₂²	1	1	yes	characteristic
21	C₂×C₉×#67	C₂²	1	1	yes	characteristic
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic
23	C₂×C₉×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
26	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
27	C₉×#237	—	2	4	no	—
28	C₉×#235	—	2	4	no	—
29	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
34	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
35	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
36	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×#217	C₂²	1	1	yes	characteristic
42	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
47	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
55	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
57	C₃²×#123	C₂×C₃	1	1	yes	characteristic
58	C₃×#939	C₂×C₃	1	1	yes	characteristic
59	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
60	C₃×#896	C₂×C₃	1	1	yes	characteristic
61	C₃×#894	C₂×C₃	1	1	yes	characteristic
62	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
63	C₃×#888	C₂×C₃	1	1	yes	characteristic
64	C₃×#886	C₂×C₃	1	1	yes	characteristic
65	C₃×#884	C₂×C₃	1	1	yes	characteristic
66	C₃×#883	C₂×C₃	1	1	yes	characteristic
67	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₃×#878	C₂×C₃	1	1	yes	characteristic
70	C₂×C₉×#41	—	3	1	no	—
71	C₂×C₉×#41	—	3	1	no	—
72	C₉×C₄⋊Q₈	—	3	1	no	—
73	C₉×#123	—	2	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×#123	—	3	1	no	—
76	C₉×#123	—	3	1	no	—
77	C₉×#123	D₃	1	1	yes	characteristic, complemented
78	C₉×C₂²⋊Q₈	—	3	1	no	—
79	C₉×C₂²⋊Q₈	—	3	1	no	—
80	C₉×#121	—	3	1	no	—
81	C₉×#121	—	3	1	no	—
82	C₄×D₄×C₉	—	3	1	no	—
83	C₄×D₄×C₉	—	3	1	no	—
84	C₂×C₉×C₄⋊C₄	—	3	1	no	—
85	C₂×C₉×C₄⋊C₄	—	3	1	no	—
86	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
88	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
89	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
90	C₃×D₄×C₉	—	2	2	no	—
91	C₂×C₃×C₄×C₉	—	2	2	no	—
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₉×#67	—	2	2	no	—
98	C₉×#67	—	2	2	no	—
99	C₉×#67	—	2	2	no	—
100	C₉×#67	D₄	1	4	yes	complemented
101	C₂×C₉×Dic₃	—	2	2	no	—
102	C₂×C₉×Dic₃	—	2	2	no	—
103	C₂×C₉×Dic₃	—	2	2	no	—
104	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
109	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
110	C₉×D₁₂	—	2	2	no	—
111	C₄×D₃×C₉	—	2	2	no	—
112	C₄×D₃×C₉	—	2	2	no	—
113	C₄×D₃×C₉	—	2	2	no	—
114	C₄×D₃×C₉	—	2	2	no	—
115	C₉×Dic₆	—	2	2	no	—
116	C₉×Dic₆	—	2	2	no	—
117	C₃×#547	—	3	1	no	—
118	#5655	C₉	1	1	yes	characteristic, direct product factor
119	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
127	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
128	C₃×#237	—	2	4	no	—
129	C₃×#235	—	2	4	no	—
130	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
137	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₃×#217	C₂²×C₃	1	1	yes	characteristic
143	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
148	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
149	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
156	C₉×#41	—	6	4	no	—
157	C₉×#41	—	6	4	no	—
158	C₂×Q₈×C₉	—	3	1	no	—
159	C₂×Q₈×C₉	—	3	1	no	—
160	C₂×D₄×C₉	—	2	1	no	—
161	C₂×D₄×C₉	—	3	1	no	—
162	C₂×D₄×C₉	—	3	1	no	—
163	C₂×D₄×C₉	—	3	1	no	—
164	C₂×D₄×C₉	—	3	1	no	—
165	C₂×D₄×C₉	—	3	1	no	—
166	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
167	C₂²×C₄×C₉	—	2	1	no	—
168	C₂²×C₄×C₉	—	3	1	no	—
169	C₂²×C₄×C₉	—	3	1	no	—
170	C₂²×C₄×C₉	—	3	1	no	—
171	C₂²×C₄×C₉	—	3	1	no	—
172	C₂²×C₄×C₉	—	3	1	no	—
173	C₂²×C₄×C₉	—	3	1	no	—
174	C₂²×C₄×C₉	—	3	1	no	—
175	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
176	C₉×C₄⋊C₄	—	2	1	no	—
177	C₉×C₄⋊C₄	—	2	1	no	—
178	C₉×C₄⋊C₄	—	3	1	no	—
179	C₉×C₄⋊C₄	—	3	1	no	—
180	C₉×C₄⋊C₄	—	3	1	no	—
181	C₉×C₄⋊C₄	—	3	1	no	—
182	C₉×C₄⋊C₄	—	3	1	no	—
183	C₉×C₄⋊C₄	—	3	1	no	—
184	C₉×C₄⋊C₄	—	3	1	no	—
185	C₉×C₄⋊C₄	—	3	1	no	—
186	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
187	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
188	C₉×C₂²⋊C₄	—	2	1	no	—
189	C₉×C₂²⋊C₄	—	2	1	no	—
190	C₉×C₂²⋊C₄	—	2	1	no	—
191	C₉×C₂²⋊C₄	—	3	1	no	—
192	C₉×C₂²⋊C₄	—	3	1	no	—
193	C₉×C₂²⋊C₄	—	3	1	no	—
194	C₉×C₂²⋊C₄	—	3	1	no	—
195	C₉×C₂²⋊C₄	—	3	1	no	—
196	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
197	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
198	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
199	C₄²×C₉	—	3	1	no	—
200	C₂²×C₃×C₉	—	2	1	no	—
201	C₂²×C₃×C₉	—	2	1	no	—
202	C₂²×C₃×C₉	—	2	1	no	—
203	C₂²×C₃×C₉	—	2	1	no	—
204	C₂²×C₃×C₉	—	2	1	no	—
205	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
206	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
207	C₂×D₃×C₉	—	2	1	no	—
208	C₂×D₃×C₉	—	2	1	no	—
209	C₂×D₃×C₉	—	2	1	no	—
210	C₂×D₃×C₉	—	2	1	no	—
211	C₂×D₃×C₉	—	2	1	no	—
212	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
213	C₃×C₄×C₉	—	2	1	no	—
214	C₃×C₄×C₉	—	2	1	no	—
215	C₃×C₄×C₉	—	2	1	no	—
216	C₃×C₄×C₉	—	2	1	no	—
217	C₃×C₄×C₉	—	2	1	no	—
218	C₉×Dic₃	—	2	1	no	—
219	C₉×Dic₃	—	2	1	no	—
220	C₉×Dic₃	—	2	1	no	—
221	C₉×Dic₃	—	2	1	no	—
222	C₉×Dic₃	C₂×D₄	1	2	yes	—
223	C₉×Dic₃	#41	1	2	yes	complemented
224	C₂×C₃×#41	—	3	1	no	—
225	C₂×C₃×#41	—	3	1	no	—
226	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
227	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
228	C₃×C₄⋊Q₈	—	3	1	no	—
229	C₃×#123	—	2	1	no	—
230	C₃×#123	—	3	1	no	—
231	C₃×#123	—	3	1	no	—
232	C₃×#123	—	3	1	no	—
233	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
234	C₃×#123	C₃×D₃	1	1	yes	characteristic
235	C₃×C₂²⋊Q₈	—	3	1	no	—
236	C₃×C₂²⋊Q₈	—	3	1	no	—
237	C₃×#121	—	3	1	no	—
238	C₃×#121	—	3	1	no	—
239	C₃×C₄×D₄	—	3	1	no	—
240	C₃×C₄×D₄	—	3	1	no	—
241	C₂×C₃×C₄⋊C₄	—	3	1	no	—
242	C₂×C₃×C₄⋊C₄	—	3	1	no	—
243	#939	C₂×C₉	1	1	yes	characteristic, complemented
244	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
245	#896	C₂×C₉	1	1	yes	characteristic, complemented
246	#894	C₂×C₉	1	1	yes	characteristic, complemented
247	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
248	#888	C₂×C₉	1	1	yes	characteristic, complemented
249	#886	C₂×C₉	1	1	yes	characteristic, complemented
250	#884	C₂×C₉	1	1	yes	characteristic, complemented
251	#883	C₂×C₉	1	1	yes	characteristic, complemented
252	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
253	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
254	#878	C₂×C₉	1	1	yes	characteristic, complemented
255	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
256	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
259	C₃²×D₄	—	2	2	no	—
260	C₂×C₃²×C₄	—	2	2	no	—
261	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₃×#67	—	2	2	no	—
267	C₃×#67	—	2	2	no	—
268	C₃×#67	—	2	2	no	—
269	C₃×#67	C₃×D₄	1	4	yes	—
270	C₂×C₃×Dic₃	—	2	2	no	—
271	C₂×C₃×Dic₃	—	2	2	no	—
272	C₂×C₃×Dic₃	—	2	2	no	—
273	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
279	C₃×D₁₂	—	2	2	no	—
280	C₃×C₄×D₃	—	2	2	no	—
281	C₃×C₄×D₃	—	2	2	no	—
282	C₃×C₄×D₃	—	2	2	no	—
283	C₃×C₄×D₃	—	2	2	no	—
284	C₃×Dic₆	—	2	2	no	—
285	C₃×Dic₆	—	2	2	no	—
286	C₂³×C₉	—	2	1	no	—
287	C₂³×C₉	—	2	1	no	—
288	C₂³×C₉	—	3	1	no	—
289	C₂³×C₉	—	3	1	no	—
290	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
291	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
292	Q₈×C₉	—	6	2	no	—
293	Q₈×C₉	—	6	2	no	—
294	D₄×C₉	—	2	2	no	—
295	D₄×C₉	—	3	4	no	—
296	D₄×C₉	—	4	2	no	—
297	D₄×C₉	—	6	2	no	—
298	D₄×C₉	—	6	2	no	—
299	D₄×C₉	—	6	2	no	—
300	D₄×C₉	—	6	2	no	—
301	C₂×C₄×C₉	—	2	2	no	—
302	C₂×C₄×C₉	—	2	1	no	—
303	C₂×C₄×C₉	—	2	1	no	—
304	C₂×C₄×C₉	—	2	1	no	—
305	C₂×C₄×C₉	—	2	1	no	—
306	C₂×C₄×C₉	—	2	1	no	—
307	C₂×C₄×C₉	—	3	1	no	—
308	C₂×C₄×C₉	—	3	1	no	—
309	C₂×C₄×C₉	—	3	1	no	—
310	C₂×C₄×C₉	—	3	1	no	—
311	C₂×C₄×C₉	—	3	1	no	—
312	C₂×C₄×C₉	—	3	1	no	—
313	C₂×C₄×C₉	—	4	2	no	—
314	C₂×C₄×C₉	—	6	2	no	—
315	C₂×C₄×C₉	—	6	2	no	—
316	C₂×C₄×C₉	—	6	2	no	—
317	C₂×C₄×C₉	—	6	2	no	—
318	C₂×C₄×C₉	—	6	2	no	—
319	C₂×C₄×C₉	—	6	2	no	—
320	C₂×C₄×C₉	—	6	2	no	—
321	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
322	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
323	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
324	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
325	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
326	#547	—	3	1	no	Sylow
327	C₂×C₃×C₉	—	2	2	no	—
328	C₂×C₃×C₉	—	4	1	no	—
329	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
331	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
332	D₃×C₉	—	2	2	no	—
333	D₃×C₉	—	4	1	no	—
334	C₃×#41	—	6	4	no	—
335	C₃×#41	—	6	4	no	—
336	C₂×C₃×Q₈	—	3	1	no	—
337	C₂×C₃×Q₈	—	3	1	no	—
338	C₂×C₃×D₄	—	2	1	no	—
339	C₂×C₃×D₄	—	3	1	no	—
340	C₂×C₃×D₄	—	3	1	no	—
341	C₂×C₃×D₄	—	3	1	no	—
342	C₂×C₃×D₄	—	3	1	no	—
343	C₂×C₃×D₄	—	3	1	no	—
344	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
345	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
346	C₂²×C₃×C₄	—	2	1	no	—
347	C₂²×C₃×C₄	—	3	1	no	—
348	C₂²×C₃×C₄	—	3	1	no	—
349	C₂²×C₃×C₄	—	3	1	no	—
350	C₂²×C₃×C₄	—	3	1	no	—
351	C₂²×C₃×C₄	—	3	1	no	—
352	C₂²×C₃×C₄	—	3	1	no	—
353	C₂²×C₃×C₄	—	3	1	no	—
354	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
356	C₂×#67	C₂²×C₉	1	1	yes	characteristic
357	C₂×#67	C₂²×C₉	1	1	yes	characteristic
358	C₂×#67	C₂²×C₉	1	1	yes	characteristic
359	C₂×#67	C₂²×C₉	1	1	yes	characteristic
360	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
361	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
362	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
363	#237	—	2	4	no	—
364	#235	—	2	4	no	—
365	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
366	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
367	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
368	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
369	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
370	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
371	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
372	C₃×C₄⋊C₄	—	2	1	no	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	3	1	no	—
375	C₃×C₄⋊C₄	—	3	1	no	—
376	C₃×C₄⋊C₄	—	3	1	no	—
377	C₃×C₄⋊C₄	—	3	1	no	—
378	C₃×C₄⋊C₄	—	3	1	no	—
379	C₃×C₄⋊C₄	—	3	1	no	—
380	C₃×C₄⋊C₄	—	3	1	no	—
381	C₃×C₄⋊C₄	—	3	1	no	—
382	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
383	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
384	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
385	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
386	C₃×C₂²⋊C₄	—	2	1	no	—
387	C₃×C₂²⋊C₄	—	2	1	no	—
388	C₃×C₂²⋊C₄	—	2	1	no	—
389	C₃×C₂²⋊C₄	—	3	1	no	—
390	C₃×C₂²⋊C₄	—	3	1	no	—
391	C₃×C₂²⋊C₄	—	3	1	no	—
392	C₃×C₂²⋊C₄	—	3	1	no	—
393	C₃×C₂²⋊C₄	—	3	1	no	—
394	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
395	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
396	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
397	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
398	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
399	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
400	C₃×C₄²	—	3	1	no	—
401	#217	C₂²×C₉	1	1	yes	characteristic
402	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
403	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
404	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
405	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
406	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
407	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
408	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
409	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
410	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
411	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
412	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
413	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
414	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
415	C₂²×C₃²	—	2	1	no	—
416	C₂²×C₃²	—	2	1	no	—
417	C₂²×C₃²	—	2	1	no	—
418	C₂²×C₃²	—	2	1	no	—
419	C₂²×C₃²	—	2	1	no	—
420	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
421	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
422	C₂×C₃×D₃	—	2	1	no	—
423	C₂×C₃×D₃	—	2	1	no	—
424	C₂×C₃×D₃	—	2	1	no	—
425	C₂×C₃×D₃	—	2	1	no	—
426	C₂×C₃×D₃	—	2	1	no	—
427	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
428	C₃²×C₄	—	2	1	no	—
429	C₃²×C₄	—	2	1	no	—
430	C₃²×C₄	—	2	1	no	—
431	C₃²×C₄	—	2	1	no	—
432	C₃²×C₄	—	2	1	no	—
433	C₃×Dic₃	—	2	1	no	—
434	C₃×Dic₃	—	2	1	no	—
435	C₃×Dic₃	—	2	1	no	—
436	C₃×Dic₃	—	2	1	no	—
437	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
438	C₃×Dic₃	C₃×#41	1	2	yes	—
439	C₂²×C₉	—	2	1	no	—
440	C₂²×C₉	—	2	1	no	—
441	C₂²×C₉	—	2	1	no	—
442	C₂²×C₉	—	2	1	no	—
443	C₂²×C₉	—	2	1	no	—
444	C₂²×C₉	—	2	1	no	—
445	C₂²×C₉	—	2	2	no	—
446	C₂²×C₉	—	3	2	no	—
447	C₂²×C₉	—	4	1	no	—
448	C₂²×C₉	—	4	1	no	—
449	C₂²×C₉	—	4	1	no	—
450	C₂²×C₉	—	4	1	no	—
451	C₂²×C₉	—	4	1	no	—
452	C₂²×C₉	—	6	1	no	—
453	C₂²×C₉	—	6	1	no	—
454	C₂²×C₉	—	6	1	no	—
455	C₂²×C₉	—	6	1	no	—
456	C₂²×C₉	—	6	1	no	—
457	C₂²×C₉	D₃×D₄	1	2	yes	—
458	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
459	C₄×C₉	—	2	1	no	—
460	C₄×C₉	—	2	1	no	—
461	C₄×C₉	—	2	1	no	—
462	C₄×C₉	—	2	1	no	—
463	C₄×C₉	—	2	1	no	—
464	C₄×C₉	—	3	2	no	—
465	C₄×C₉	—	3	2	no	—
466	C₄×C₉	—	4	1	no	—
467	C₄×C₉	—	4	1	no	—
468	C₄×C₉	—	4	1	no	—
469	C₄×C₉	—	4	1	no	—
470	C₄×C₉	—	4	1	no	—
471	C₄×C₉	—	6	1	no	—
472	C₄×C₉	—	6	1	no	—
473	C₄×C₉	—	6	1	no	—
474	C₄×C₉	—	6	1	no	—
475	C₂×#41	—	3	1	no	—
476	C₂×#41	—	3	1	no	—
477	C₄⋊Q₈	—	3	1	no	—
478	#123	—	3	1	no	—
479	#123	—	3	1	no	—
480	#123	—	3	1	no	—
481	#123	D₃×C₉	1	1	yes	characteristic, complemented
482	C₂²⋊Q₈	—	3	1	no	—
483	C₂²⋊Q₈	—	3	1	no	—
484	#121	—	3	1	no	—
485	#121	—	3	1	no	—
486	C₄×D₄	—	3	1	no	—
487	C₄×D₄	—	3	1	no	—
488	C₂×C₄⋊C₄	—	3	1	no	—
489	C₂×C₄⋊C₄	—	3	1	no	—
490	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
491	C₂³×C₃	—	2	1	no	—
492	C₂³×C₃	—	2	1	no	—
493	C₂³×C₃	—	3	1	no	—
494	C₂³×C₃	—	3	1	no	—
495	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
496	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
497	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
498	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
499	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
500	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
501	C₃×Q₈	—	6	2	no	—
502	C₃×Q₈	—	6	2	no	—
503	C₃×D₄	—	2	2	no	—
504	C₃×D₄	—	2	2	no	—
505	C₃×D₄	—	3	4	no	—
506	C₃×D₄	—	4	2	no	—
507	C₃×D₄	—	6	2	no	—
508	C₃×D₄	—	6	2	no	—
509	C₃×D₄	—	6	2	no	—
510	C₃×D₄	—	6	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	3	1	no	—
519	C₂×C₃×C₄	—	3	1	no	—
520	C₂×C₃×C₄	—	3	1	no	—
521	C₂×C₃×C₄	—	3	1	no	—
522	C₂×C₃×C₄	—	3	1	no	—
523	C₂×C₃×C₄	—	3	1	no	—
524	C₂×C₃×C₄	—	4	2	no	—
525	C₂×C₃×C₄	—	6	2	no	—
526	C₂×C₃×C₄	—	6	2	no	—
527	C₂×C₃×C₄	—	6	2	no	—
528	C₂×C₃×C₄	—	6	2	no	—
529	C₂×C₃×C₄	—	6	2	no	—
530	C₂×C₃×C₄	—	6	2	no	—
531	C₂×C₃×C₄	—	6	2	no	—
532	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
537	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
538	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
542	#67	—	2	2	no	—
543	#67	—	2	2	no	—
544	#67	—	2	2	no	—
545	#67	D₄×C₉	1	4	yes	complemented
546	C₂×Dic₃	—	2	2	no	—
547	C₂×Dic₃	—	2	2	no	—
548	C₂×Dic₃	—	2	2	no	—
549	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
550	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
551	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
552	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
553	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
554	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
555	D₁₂	—	2	2	no	—
556	C₄×D₃	—	2	2	no	—
557	C₄×D₃	—	2	2	no	—
558	C₄×D₃	—	2	2	no	—
559	C₄×D₃	—	2	2	no	—
560	Dic₆	—	2	2	no	—
561	Dic₆	—	2	2	no	—
562	C₂×C₃²	—	2	2	no	—
563	C₂×C₃²	—	4	1	no	—
564	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
565	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
566	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
567	C₃×D₃	—	2	2	no	—
568	C₃×D₃	—	4	1	no	—
569	C₂×C₉	—	2	2	no	—
570	C₂×C₉	—	2	1	no	—
571	C₂×C₉	—	2	1	no	—
572	C₂×C₉	—	2	1	no	—
573	C₂×C₉	—	4	2	no	—
574	C₂×C₉	—	4	1	no	—
575	C₂×C₉	—	6	2	no	—
576	C₂×C₉	—	8	1	no	—
577	C₂×C₉	—	12	1	no	—
578	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
579	C₂×C₉	D₃×#41	1	1	yes	characteristic
580	C₂×C₉	#1010	1	1	yes	characteristic
581	#41	—	6	4	no	—
582	#41	—	6	4	no	—
583	C₂×Q₈	—	3	1	no	—
584	C₂×Q₈	—	3	1	no	—
585	C₂×D₄	—	3	1	no	—
586	C₂×D₄	—	3	1	no	—
587	C₂×D₄	—	3	1	no	—
588	C₂×D₄	—	3	1	no	—
589	C₂×D₄	—	3	1	no	—
590	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
591	C₂²×C₄	—	3	1	no	—
592	C₂²×C₄	—	3	1	no	—
593	C₂²×C₄	—	3	1	no	—
594	C₂²×C₄	—	3	1	no	—
595	C₂²×C₄	—	3	1	no	—
596	C₂²×C₄	—	3	1	no	—
597	C₂²×C₄	—	3	1	no	—
598	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
599	C₄⋊C₄	—	3	1	no	—
600	C₄⋊C₄	—	3	1	no	—
601	C₄⋊C₄	—	3	1	no	—
602	C₄⋊C₄	—	3	1	no	—
603	C₄⋊C₄	—	3	1	no	—
604	C₄⋊C₄	—	3	1	no	—
605	C₄⋊C₄	—	3	1	no	—
606	C₄⋊C₄	—	3	1	no	—
607	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
608	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
609	C₂²⋊C₄	—	3	1	no	—
610	C₂²⋊C₄	—	3	1	no	—
611	C₂²⋊C₄	—	3	1	no	—
612	C₂²⋊C₄	—	3	1	no	—
613	C₂²⋊C₄	—	3	1	no	—
614	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
615	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
616	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
617	C₄²	—	3	1	no	—
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	2	1	no	—
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	1	no	—
625	C₂²×C₃	—	2	1	no	—
626	C₂²×C₃	—	2	1	no	—
627	C₂²×C₃	—	2	1	no	—
628	C₂²×C₃	—	2	1	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	3	2	no	—
631	C₂²×C₃	—	4	1	no	—
632	C₂²×C₃	—	4	1	no	—
633	C₂²×C₃	—	4	1	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	4	1	no	—
636	C₂²×C₃	—	6	1	no	—
637	C₂²×C₃	—	6	1	no	—
638	C₂²×C₃	—	6	1	no	—
639	C₂²×C₃	—	6	1	no	—
640	C₂²×C₃	—	6	1	no	—
641	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
642	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
643	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
644	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
645	C₂×D₃	—	2	1	no	—
646	C₂×D₃	—	2	1	no	—
647	C₂×D₃	—	2	1	no	—
648	C₂×D₃	—	2	1	no	—
649	C₂×D₃	—	2	1	no	—
650	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
651	C₃×C₄	—	2	1	no	—
652	C₃×C₄	—	2	1	no	—
653	C₃×C₄	—	2	1	no	—
654	C₃×C₄	—	2	1	no	—
655	C₃×C₄	—	2	1	no	—
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	2	1	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	3	2	no	—
662	C₃×C₄	—	3	2	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	1	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	—	4	1	no	—
668	C₃×C₄	—	6	1	no	—
669	C₃×C₄	—	6	1	no	—
670	C₃×C₄	—	6	1	no	—
671	C₃×C₄	—	6	1	no	—
672	Dic₃	—	2	1	no	—
673	Dic₃	—	2	1	no	—
674	Dic₃	—	2	1	no	—
675	Dic₃	—	2	1	no	—
676	Dic₃	C₂×D₄×C₉	1	2	yes	—
677	Dic₃	C₉×#41	1	2	yes	complemented
678	C₃²	C₃×#547	1	1	yes	characteristic
679	C₉	—	2	1	no	—
680	C₉	#5655	1	1	yes	characteristic, direct product factor
681	C₂³	—	3	1	no	—
682	C₂³	—	3	1	no	—
683	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
684	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
685	Q₈	—	6	2	no	—
686	Q₈	—	6	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	3	4	no	—
689	D₄	—	6	2	no	—
690	D₄	—	6	2	no	—
691	D₄	—	6	2	no	—
692	D₄	—	6	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	3	1	no	—
695	C₂×C₄	—	3	1	no	—
696	C₂×C₄	—	3	1	no	—
697	C₂×C₄	—	3	1	no	—
698	C₂×C₄	—	3	1	no	—
699	C₂×C₄	—	3	1	no	—
700	C₂×C₄	—	6	2	no	—
701	C₂×C₄	—	6	2	no	—
702	C₂×C₄	—	6	2	no	—
703	C₂×C₄	—	6	2	no	—
704	C₂×C₄	—	6	2	no	—
705	C₂×C₄	—	6	2	no	—
706	C₂×C₄	—	6	2	no	—
707	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
712	C₂×C₃	—	2	2	no	—
713	C₂×C₃	—	2	2	no	—
714	C₂×C₃	—	2	1	no	—
715	C₂×C₃	—	2	1	no	—
716	C₂×C₃	—	2	1	no	—
717	C₂×C₃	—	4	2	no	—
718	C₂×C₃	—	4	1	no	—
719	C₂×C₃	—	4	1	no	—
720	C₂×C₃	—	6	2	no	—
721	C₂×C₃	—	8	1	no	—
722	C₂×C₃	—	12	1	no	—
723	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
724	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
725	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
726	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
727	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
728	C₂×C₃	C₃×#1010	1	1	yes	characteristic
729	D₃	—	2	2	no	—
730	D₃	—	4	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	3	2	no	—
737	C₂²	—	6	1	no	—
738	C₂²	—	6	1	no	—
739	C₂²	—	6	1	no	—
740	C₂²	—	6	1	no	—
741	C₂²	—	6	1	no	—
742	C₂²	D₃×D₄×C₉	1	2	yes	—
743	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	3	2	no	—
750	C₄	—	3	2	no	—
751	C₄	—	6	1	no	—
752	C₄	—	6	1	no	—
753	C₄	—	6	1	no	—
754	C₄	—	6	1	no	—
755	C₃	—	2	1	no	—
756	C₃	C₉×#547	1	1	yes	characteristic, complemented
757	C₃	C₃×#5655	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	4	1	no	—
760	C₂	—	6	2	no	—
761	C₂	—	12	1	no	—
762	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
763	C₂	D₃×C₉×#41	1	1	yes	characteristic
764	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×#123	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5655	C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#237	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. D₃×C₉×C₄⋊C₄	C₂	semidirect
9. C₉×#888	C₂	semidirect
10. C₉×#886	C₂	semidirect
11. C₉×#884	C₂	semidirect
12. C₉×#883	C₂	semidirect
13. C₉×#67⋊C₄	C₂	semidirect
14. C₉×#67⋊C₄	C₂	semidirect
15. C₉×#878	C₂	semidirect
77. C₉×#123	D₃	semidirect
100. C₉×#67	D₄	semidirect
118. #5655	C₉	direct (N × H)
223. C₉×Dic₃	#41	semidirect
226. C₂×#237	C₂×C₉	semidirect
227. C₂×#235	C₂×C₉	semidirect
233. C₃×#123	C₂×C₉	semidirect
243. #939	C₂×C₉	semidirect
244. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
245. #896	C₂×C₉	semidirect
246. #894	C₂×C₉	semidirect
247. D₃×C₄⋊C₄	C₂×C₉	semidirect
248. #888	C₂×C₉	semidirect
249. #886	C₂×C₉	semidirect
250. #884	C₂×C₉	semidirect
251. #883	C₂×C₉	semidirect
252. #67⋊C₄	C₂×C₉	semidirect
253. #67⋊C₄	C₂×C₉	semidirect
254. #878	C₂×C₉	semidirect
481. #123	D₃×C₉	semidirect
490. C₃×C₉	#547	semidirect
545. #67	D₄×C₉	semidirect
677. Dic₃	C₉×#41	semidirect
680. C₉	#5655	direct (N × H)
756. 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
C₂×C₉×#235	2
C₃×C₉×#123	2
C₉×#939	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#896	2
C₉×#894	2
D₃×C₉×C₄⋊C₄	2
C₉×#888	2
C₉×#886	2
C₉×#884	2
C₉×#883	2
C₉×#67⋊C₄	2
C₉×#878	2
C₃×#5655	3
C₉×#547	3

Subgroups — C9×#5655 #13153026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5655 #13153026