Subgroups — C₉×#5667 #13153034

Order 1728.

738 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5667	C₃	1	1	yes	maximal, characteristic
17	C₉×#562	—	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	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
29	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×#217	C₂²	1	1	yes	characteristic
36	C₉×#217	C₂²	1	1	yes	characteristic
37	C₉×#217	C₂²	1	1	yes	characteristic
38	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
45	C₉×C₄⋊Dic₃	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	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×#123	C₂×C₃	1	1	yes	characteristic
54	C₃×#939	C₂×C₃	1	1	yes	characteristic
55	C₃×#938	C₂×C₃	1	1	yes	characteristic
56	C₃×#930	C₂×C₃	1	1	yes	characteristic
57	C₃×#924	C₂×C₃	1	1	yes	characteristic
58	C₃×#897	C₂×C₃	1	1	yes	characteristic
59	C₃×#896	C₂×C₃	1	1	yes	characteristic
60	C₃×#894	C₂×C₃	1	1	yes	characteristic
61	C₃×#890	C₂×C₃	1	1	yes	characteristic
62	C₃×#886	C₂×C₃	1	1	yes	characteristic
63	C₃×#885	C₂×C₃	1	1	yes	characteristic
64	C₃×#885	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×#878	C₂×C₃	1	1	yes	characteristic
68	C₉×#125	—	3	1	no	—
69	C₉×#124	—	3	1	no	—
70	C₉×#124	—	3	1	no	—
71	C₉×#123	—	2	1	no	—
72	C₉×#123	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×#123	D₃	1	1	yes	characteristic, complemented
76	C₉×C₂²⋊Q₈	—	3	1	no	—
77	C₉×C₂²⋊Q₈	—	3	1	no	—
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	C₉×#121	—	3	1	no	—
83	C₉×#121	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
86	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
87	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
88	C₃×D₄×C₉	—	4	1	no	—
89	C₂×C₃×C₄×C₉	—	4	1	no	—
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₉×#67	—	4	1	no	—
96	C₉×#67	—	4	1	no	—
97	C₉×#67	—	4	1	no	—
98	C₉×#67	—	4	1	no	—
99	C₂×C₉×Dic₃	—	4	1	no	—
100	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
102	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
103	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
104	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
106	C₉×D₁₂	—	4	1	no	—
107	C₄×D₃×C₉	—	4	1	no	—
108	C₄×D₃×C₉	—	4	1	no	—
109	C₉×Dic₆	—	4	1	no	—
110	C₉×Dic₆	—	4	1	no	—
111	C₃×#562	—	3	1	no	—
112	#5667	C₉	1	1	yes	characteristic, direct product factor
113	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
125	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₃×#217	C₂²×C₃	1	1	yes	characteristic
131	C₃×#217	C₂²×C₃	1	1	yes	characteristic
132	C₃×#217	C₂²×C₃	1	1	yes	characteristic
133	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
140	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
141	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
142	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
143	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
148	C₂×Q₈×C₉	—	3	1	no	—
149	C₂×Q₈×C₉	—	3	1	no	—
150	C₂×D₄×C₉	—	2	1	no	—
151	C₂×D₄×C₉	—	3	1	no	—
152	C₂×D₄×C₉	—	3	1	no	—
153	C₂×D₄×C₉	—	3	1	no	—
154	C₂×D₄×C₉	—	3	1	no	—
155	C₂×D₄×C₉	—	3	1	no	—
156	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
157	C₂²×C₄×C₉	—	2	1	no	—
158	C₂²×C₄×C₉	—	3	1	no	—
159	C₂²×C₄×C₉	—	3	1	no	—
160	C₂²×C₄×C₉	—	3	1	no	—
161	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
162	C₉×C₄⋊C₄	—	2	1	no	—
163	C₉×C₄⋊C₄	—	2	1	no	—
164	C₉×C₄⋊C₄	—	3	1	no	—
165	C₉×C₄⋊C₄	—	3	1	no	—
166	C₉×C₄⋊C₄	—	3	1	no	—
167	C₉×C₄⋊C₄	—	3	1	no	—
168	C₉×C₄⋊C₄	—	3	1	no	—
169	C₉×C₄⋊C₄	—	3	1	no	—
170	C₉×C₄⋊C₄	—	3	1	no	—
171	C₉×C₄⋊C₄	—	3	1	no	—
172	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
173	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₉×C₂²⋊C₄	—	2	1	no	—
175	C₉×C₂²⋊C₄	—	2	1	no	—
176	C₉×C₂²⋊C₄	—	2	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₉×C₂²⋊C₄	—	3	1	no	—
179	C₉×C₂²⋊C₄	—	3	1	no	—
180	C₉×C₂²⋊C₄	—	3	1	no	—
181	C₉×C₂²⋊C₄	—	3	1	no	—
182	C₉×C₂²⋊C₄	—	3	1	no	—
183	C₉×C₂²⋊C₄	—	3	1	no	—
184	C₉×C₂²⋊C₄	—	3	1	no	—
185	C₉×C₂²⋊C₄	—	3	1	no	—
186	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
187	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
188	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
189	C₄²×C₉	—	3	1	no	—
190	C₂²×C₃×C₉	—	2	1	no	—
191	C₂²×C₃×C₉	—	2	1	no	—
192	C₂²×C₃×C₉	—	2	1	no	—
193	C₂²×C₃×C₉	—	2	1	no	—
194	C₂²×C₃×C₉	—	2	1	no	—
195	C₂²×C₃×C₉	—	2	1	no	—
196	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
197	C₂×D₃×C₉	—	2	1	no	—
198	C₂×D₃×C₉	—	2	1	no	—
199	C₂×D₃×C₉	—	2	1	no	—
200	C₂×D₃×C₉	—	2	1	no	—
201	C₂×D₃×C₉	—	2	1	no	—
202	C₂×D₃×C₉	—	2	1	no	—
203	C₃×C₄×C₉	—	2	1	no	—
204	C₃×C₄×C₉	—	2	1	no	—
205	C₃×C₄×C₉	—	2	1	no	—
206	C₃×C₄×C₉	—	2	1	no	—
207	C₃×C₄×C₉	—	2	1	no	—
208	C₉×Dic₃	—	2	1	no	—
209	C₉×Dic₃	—	2	1	no	—
210	C₉×Dic₃	—	2	1	no	—
211	C₉×Dic₃	—	2	1	no	—
212	C₉×Dic₃	—	2	1	no	—
213	C₉×Dic₃	—	2	1	no	—
214	C₃×#125	—	3	1	no	—
215	C₃×#124	—	3	1	no	—
216	C₃×#124	—	3	1	no	—
217	C₃×#123	—	2	1	no	—
218	C₃×#123	—	3	1	no	—
219	C₃×#123	—	3	1	no	—
220	C₃×#123	—	3	1	no	—
221	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
222	C₃×#123	C₃×D₃	1	1	yes	characteristic
223	C₃×C₂²⋊Q₈	—	3	1	no	—
224	C₃×C₂²⋊Q₈	—	3	1	no	—
225	C₃×C₂²⋊Q₈	—	3	1	no	—
226	C₃×C₂²⋊Q₈	—	3	1	no	—
227	C₃×#121	—	3	1	no	—
228	C₃×#121	—	3	1	no	—
229	C₃×#121	—	3	1	no	—
230	C₃×#121	—	3	1	no	—
231	#939	C₂×C₉	1	1	yes	characteristic, complemented
232	#938	C₂×C₉	1	1	yes	characteristic, complemented
233	#930	C₂×C₉	1	1	yes	characteristic, complemented
234	#924	C₂×C₉	1	1	yes	characteristic, complemented
235	#897	C₂×C₉	1	1	yes	characteristic, complemented
236	#896	C₂×C₉	1	1	yes	characteristic, complemented
237	#894	C₂×C₉	1	1	yes	characteristic, complemented
238	#890	C₂×C₉	1	1	yes	characteristic, complemented
239	#886	C₂×C₉	1	1	yes	characteristic, complemented
240	#885	C₂×C₉	1	1	yes	characteristic, complemented
241	#885	C₂×C₉	1	1	yes	characteristic, complemented
242	#884	C₂×C₉	1	1	yes	characteristic, complemented
243	#883	C₂×C₉	1	1	yes	characteristic, complemented
244	#878	C₂×C₉	1	1	yes	characteristic, complemented
245	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
246	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
247	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
249	C₃²×D₄	—	4	1	no	—
250	C₂×C₃²×C₄	—	4	1	no	—
251	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
254	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
255	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
256	C₃×#67	—	4	1	no	—
257	C₃×#67	—	4	1	no	—
258	C₃×#67	—	4	1	no	—
259	C₃×#67	—	4	1	no	—
260	C₂×C₃×Dic₃	—	4	1	no	—
261	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
267	C₃×D₁₂	—	4	1	no	—
268	C₃×C₄×D₃	—	4	1	no	—
269	C₃×C₄×D₃	—	4	1	no	—
270	C₃×Dic₆	—	4	1	no	—
271	C₃×Dic₆	—	4	1	no	—
272	C₂³×C₉	—	2	1	no	—
273	C₂³×C₉	—	2	1	no	—
274	C₂³×C₉	—	3	1	no	—
275	C₂³×C₉	—	3	1	no	—
276	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
277	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
278	Q₈×C₉	—	12	1	no	—
279	Q₈×C₉	—	12	1	no	—
280	D₄×C₉	—	4	1	no	—
281	D₄×C₉	—	4	2	no	—
282	D₄×C₉	—	12	1	no	—
283	D₄×C₉	—	12	1	no	—
284	D₄×C₉	—	12	1	no	—
285	D₄×C₉	—	12	1	no	—
286	D₄×C₉	—	12	1	no	—
287	C₂×C₄×C₉	—	2	1	no	—
288	C₂×C₄×C₉	—	2	1	no	—
289	C₂×C₄×C₉	—	2	1	no	—
290	C₂×C₄×C₉	—	2	1	no	—
291	C₂×C₄×C₉	—	2	1	no	—
292	C₂×C₄×C₉	—	3	1	no	—
293	C₂×C₄×C₉	—	3	1	no	—
294	C₂×C₄×C₉	—	3	1	no	—
295	C₂×C₄×C₉	—	3	1	no	—
296	C₂×C₄×C₉	—	3	1	no	—
297	C₂×C₄×C₉	—	3	1	no	—
298	C₂×C₄×C₉	—	4	1	no	—
299	C₂×C₄×C₉	—	4	2	no	—
300	C₂×C₄×C₉	—	12	1	no	—
301	C₂×C₄×C₉	—	12	1	no	—
302	C₂×C₄×C₉	—	12	1	no	—
303	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
307	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
308	#562	—	3	1	no	Sylow
309	C₂×C₃×C₉	—	4	1	no	—
310	C₂×C₃×C₉	—	4	1	no	—
311	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
314	D₃×C₉	—	4	1	no	—
315	D₃×C₉	—	4	1	no	—
316	C₂×C₃×Q₈	—	3	1	no	—
317	C₂×C₃×Q₈	—	3	1	no	—
318	C₂×C₃×D₄	—	2	1	no	—
319	C₂×C₃×D₄	—	3	1	no	—
320	C₂×C₃×D₄	—	3	1	no	—
321	C₂×C₃×D₄	—	3	1	no	—
322	C₂×C₃×D₄	—	3	1	no	—
323	C₂×C₃×D₄	—	3	1	no	—
324	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
325	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
326	C₂²×C₃×C₄	—	2	1	no	—
327	C₂²×C₃×C₄	—	3	1	no	—
328	C₂²×C₃×C₄	—	3	1	no	—
329	C₂²×C₃×C₄	—	3	1	no	—
330	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
332	C₂×#67	C₂²×C₉	1	1	yes	characteristic
333	C₂×#67	C₂²×C₉	1	1	yes	characteristic
334	C₂×#67	C₂²×C₉	1	1	yes	characteristic
335	C₂×#67	C₂²×C₉	1	1	yes	characteristic
336	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
337	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
338	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
339	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
340	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
341	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
342	C₃×C₄⋊C₄	—	2	1	no	—
343	C₃×C₄⋊C₄	—	2	1	no	—
344	C₃×C₄⋊C₄	—	3	1	no	—
345	C₃×C₄⋊C₄	—	3	1	no	—
346	C₃×C₄⋊C₄	—	3	1	no	—
347	C₃×C₄⋊C₄	—	3	1	no	—
348	C₃×C₄⋊C₄	—	3	1	no	—
349	C₃×C₄⋊C₄	—	3	1	no	—
350	C₃×C₄⋊C₄	—	3	1	no	—
351	C₃×C₄⋊C₄	—	3	1	no	—
352	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
353	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
354	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
355	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
356	C₃×C₂²⋊C₄	—	2	1	no	—
357	C₃×C₂²⋊C₄	—	2	1	no	—
358	C₃×C₂²⋊C₄	—	2	1	no	—
359	C₃×C₂²⋊C₄	—	3	1	no	—
360	C₃×C₂²⋊C₄	—	3	1	no	—
361	C₃×C₂²⋊C₄	—	3	1	no	—
362	C₃×C₂²⋊C₄	—	3	1	no	—
363	C₃×C₂²⋊C₄	—	3	1	no	—
364	C₃×C₂²⋊C₄	—	3	1	no	—
365	C₃×C₂²⋊C₄	—	3	1	no	—
366	C₃×C₂²⋊C₄	—	3	1	no	—
367	C₃×C₂²⋊C₄	—	3	1	no	—
368	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
369	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
370	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
371	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
372	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
373	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
374	C₃×C₄²	—	3	1	no	—
375	#217	C₂²×C₉	1	1	yes	characteristic
376	#217	C₂²×C₉	1	1	yes	characteristic
377	#217	C₂²×C₉	1	1	yes	characteristic
378	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
379	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
380	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
381	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
382	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
383	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
384	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
385	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
386	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
387	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
388	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
389	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
390	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
391	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
392	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
393	C₂²×C₃²	—	2	1	no	—
394	C₂²×C₃²	—	2	1	no	—
395	C₂²×C₃²	—	2	1	no	—
396	C₂²×C₃²	—	2	1	no	—
397	C₂²×C₃²	—	2	1	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
400	C₂×C₃×D₃	—	2	1	no	—
401	C₂×C₃×D₃	—	2	1	no	—
402	C₂×C₃×D₃	—	2	1	no	—
403	C₂×C₃×D₃	—	2	1	no	—
404	C₂×C₃×D₃	—	2	1	no	—
405	C₂×C₃×D₃	—	2	1	no	—
406	C₃²×C₄	—	2	1	no	—
407	C₃²×C₄	—	2	1	no	—
408	C₃²×C₄	—	2	1	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃×Dic₃	—	2	1	no	—
412	C₃×Dic₃	—	2	1	no	—
413	C₃×Dic₃	—	2	1	no	—
414	C₃×Dic₃	—	2	1	no	—
415	C₃×Dic₃	—	2	1	no	—
416	C₃×Dic₃	—	2	1	no	—
417	C₂²×C₉	—	2	2	no	—
418	C₂²×C₉	—	2	1	no	—
419	C₂²×C₉	—	2	1	no	—
420	C₂²×C₉	—	2	1	no	—
421	C₂²×C₉	—	2	1	no	—
422	C₂²×C₉	—	2	1	no	—
423	C₂²×C₉	—	2	1	no	—
424	C₂²×C₉	—	2	1	no	—
425	C₂²×C₉	—	4	1	no	—
426	C₂²×C₉	—	4	1	no	—
427	C₂²×C₉	—	4	1	no	—
428	C₂²×C₉	—	4	1	no	—
429	C₂²×C₉	—	4	1	no	—
430	C₂²×C₉	—	6	1	no	—
431	C₂²×C₉	—	6	1	no	—
432	C₂²×C₉	—	6	1	no	—
433	C₂²×C₉	—	6	1	no	—
434	C₂²×C₉	—	6	1	no	—
435	C₂²×C₉	—	6	1	no	—
436	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
437	C₄×C₉	—	2	1	no	—
438	C₄×C₉	—	2	1	no	—
439	C₄×C₉	—	2	1	no	—
440	C₄×C₉	—	2	1	no	—
441	C₄×C₉	—	2	1	no	—
442	C₄×C₉	—	4	1	no	—
443	C₄×C₉	—	4	1	no	—
444	C₄×C₉	—	4	1	no	—
445	C₄×C₉	—	4	1	no	—
446	C₄×C₉	—	4	1	no	—
447	C₄×C₉	—	6	1	no	—
448	C₄×C₉	—	6	1	no	—
449	C₄×C₉	—	6	1	no	—
450	C₄×C₉	—	6	1	no	—
451	C₄×C₉	—	6	1	no	—
452	C₄×C₉	—	6	1	no	—
453	#125	—	3	1	no	—
454	#124	—	3	1	no	—
455	#124	—	3	1	no	—
456	#123	—	3	1	no	—
457	#123	—	3	1	no	—
458	#123	—	3	1	no	—
459	#123	D₃×C₉	1	1	yes	characteristic, complemented
460	C₂²⋊Q₈	—	3	1	no	—
461	C₂²⋊Q₈	—	3	1	no	—
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	#121	—	3	1	no	—
465	#121	—	3	1	no	—
466	#121	—	3	1	no	—
467	#121	—	3	1	no	—
468	C₃×C₉	#562	1	1	yes	characteristic, complemented, Sylow
469	C₂³×C₃	—	2	1	no	—
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	3	1	no	—
472	C₂³×C₃	—	3	1	no	—
473	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
474	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
475	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
476	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
477	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
478	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
479	C₃×Q₈	—	12	1	no	—
480	C₃×Q₈	—	12	1	no	—
481	C₃×D₄	—	4	1	no	—
482	C₃×D₄	—	4	1	no	—
483	C₃×D₄	—	4	2	no	—
484	C₃×D₄	—	12	1	no	—
485	C₃×D₄	—	12	1	no	—
486	C₃×D₄	—	12	1	no	—
487	C₃×D₄	—	12	1	no	—
488	C₃×D₄	—	12	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	3	1	no	—
495	C₂×C₃×C₄	—	3	1	no	—
496	C₂×C₃×C₄	—	3	1	no	—
497	C₂×C₃×C₄	—	3	1	no	—
498	C₂×C₃×C₄	—	3	1	no	—
499	C₂×C₃×C₄	—	3	1	no	—
500	C₂×C₃×C₄	—	4	1	no	—
501	C₂×C₃×C₄	—	4	1	no	—
502	C₂×C₃×C₄	—	4	2	no	—
503	C₂×C₃×C₄	—	12	1	no	—
504	C₂×C₃×C₄	—	12	1	no	—
505	C₂×C₃×C₄	—	12	1	no	—
506	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
509	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
510	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
511	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
515	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
516	#67	—	4	1	no	—
517	#67	—	4	1	no	—
518	#67	—	4	1	no	—
519	#67	—	4	1	no	—
520	C₂×Dic₃	—	4	1	no	—
521	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
522	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
523	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
524	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
525	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
526	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
527	D₁₂	—	4	1	no	—
528	C₄×D₃	—	4	1	no	—
529	C₄×D₃	—	4	1	no	—
530	Dic₆	—	4	1	no	—
531	Dic₆	—	4	1	no	—
532	C₂×C₃²	—	4	1	no	—
533	C₂×C₃²	—	4	1	no	—
534	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
537	C₃×D₃	—	4	1	no	—
538	C₃×D₃	—	4	1	no	—
539	C₂×C₉	—	2	1	no	—
540	C₂×C₉	—	2	1	no	—
541	C₂×C₉	—	2	1	no	—
542	C₂×C₉	—	4	2	no	—
543	C₂×C₉	—	4	1	no	—
544	C₂×C₉	—	4	1	no	—
545	C₂×C₉	—	8	1	no	—
546	C₂×C₉	—	12	1	no	—
547	C₂×C₉	—	12	1	no	—
548	C₂×C₉	#1004	1	1	yes	characteristic
549	C₂×C₉	#1009	1	1	yes	characteristic
550	C₂×C₉	#1010	1	1	yes	characteristic
551	C₂×Q₈	—	3	1	no	—
552	C₂×Q₈	—	3	1	no	—
553	C₂×D₄	—	3	1	no	—
554	C₂×D₄	—	3	1	no	—
555	C₂×D₄	—	3	1	no	—
556	C₂×D₄	—	3	1	no	—
557	C₂×D₄	—	3	1	no	—
558	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
559	C₂²×C₄	—	3	1	no	—
560	C₂²×C₄	—	3	1	no	—
561	C₂²×C₄	—	3	1	no	—
562	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	3	1	no	—
566	C₄⋊C₄	—	3	1	no	—
567	C₄⋊C₄	—	3	1	no	—
568	C₄⋊C₄	—	3	1	no	—
569	C₄⋊C₄	—	3	1	no	—
570	C₄⋊C₄	—	3	1	no	—
571	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
572	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
573	C₂²⋊C₄	—	3	1	no	—
574	C₂²⋊C₄	—	3	1	no	—
575	C₂²⋊C₄	—	3	1	no	—
576	C₂²⋊C₄	—	3	1	no	—
577	C₂²⋊C₄	—	3	1	no	—
578	C₂²⋊C₄	—	3	1	no	—
579	C₂²⋊C₄	—	3	1	no	—
580	C₂²⋊C₄	—	3	1	no	—
581	C₂²⋊C₄	—	3	1	no	—
582	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
583	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
584	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
585	C₄²	—	3	1	no	—
586	C₂²×C₃	—	2	2	no	—
587	C₂²×C₃	—	2	1	no	—
588	C₂²×C₃	—	2	1	no	—
589	C₂²×C₃	—	2	1	no	—
590	C₂²×C₃	—	2	1	no	—
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	1	no	—
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	4	1	no	—
601	C₂²×C₃	—	4	1	no	—
602	C₂²×C₃	—	4	1	no	—
603	C₂²×C₃	—	4	1	no	—
604	C₂²×C₃	—	4	1	no	—
605	C₂²×C₃	—	6	1	no	—
606	C₂²×C₃	—	6	1	no	—
607	C₂²×C₃	—	6	1	no	—
608	C₂²×C₃	—	6	1	no	—
609	C₂²×C₃	—	6	1	no	—
610	C₂²×C₃	—	6	1	no	—
611	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
612	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
613	C₂×D₃	—	2	1	no	—
614	C₂×D₃	—	2	1	no	—
615	C₂×D₃	—	2	1	no	—
616	C₂×D₃	—	2	1	no	—
617	C₂×D₃	—	2	1	no	—
618	C₂×D₃	—	2	1	no	—
619	C₃×C₄	—	2	1	no	—
620	C₃×C₄	—	2	1	no	—
621	C₃×C₄	—	2	1	no	—
622	C₃×C₄	—	2	1	no	—
623	C₃×C₄	—	2	1	no	—
624	C₃×C₄	—	2	1	no	—
625	C₃×C₄	—	2	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	—	4	1	no	—
631	C₃×C₄	—	4	1	no	—
632	C₃×C₄	—	4	1	no	—
633	C₃×C₄	—	4	1	no	—
634	C₃×C₄	—	6	1	no	—
635	C₃×C₄	—	6	1	no	—
636	C₃×C₄	—	6	1	no	—
637	C₃×C₄	—	6	1	no	—
638	C₃×C₄	—	6	1	no	—
639	C₃×C₄	—	6	1	no	—
640	Dic₃	—	2	1	no	—
641	Dic₃	—	2	1	no	—
642	Dic₃	—	2	1	no	—
643	Dic₃	—	2	1	no	—
644	Dic₃	—	2	1	no	—
645	Dic₃	—	2	1	no	—
646	C₃²	C₃×#562	1	1	yes	characteristic
647	C₉	—	2	1	no	—
648	C₉	#5667	1	1	yes	characteristic, direct product factor
649	C₂³	—	3	1	no	—
650	C₂³	—	3	1	no	—
651	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
652	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
653	Q₈	—	12	1	no	—
654	Q₈	—	12	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	12	1	no	—
657	D₄	—	12	1	no	—
658	D₄	—	12	1	no	—
659	D₄	—	12	1	no	—
660	D₄	—	12	1	no	—
661	C₂×C₄	—	3	1	no	—
662	C₂×C₄	—	3	1	no	—
663	C₂×C₄	—	3	1	no	—
664	C₂×C₄	—	3	1	no	—
665	C₂×C₄	—	3	1	no	—
666	C₂×C₄	—	3	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	12	1	no	—
669	C₂×C₄	—	12	1	no	—
670	C₂×C₄	—	12	1	no	—
671	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
675	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
676	C₂×C₃	—	2	1	no	—
677	C₂×C₃	—	2	1	no	—
678	C₂×C₃	—	2	1	no	—
679	C₂×C₃	—	4	2	no	—
680	C₂×C₃	—	4	1	no	—
681	C₂×C₃	—	4	1	no	—
682	C₂×C₃	—	4	1	no	—
683	C₂×C₃	—	4	1	no	—
684	C₂×C₃	—	8	1	no	—
685	C₂×C₃	—	12	1	no	—
686	C₂×C₃	—	12	1	no	—
687	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
688	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂×C₃	C₃×#1004	1	1	yes	characteristic
691	C₂×C₃	C₃×#1009	1	1	yes	characteristic
692	C₂×C₃	C₃×#1010	1	1	yes	characteristic
693	D₃	—	4	1	no	—
694	D₃	—	4	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	6	1	no	—
702	C₂²	—	6	1	no	—
703	C₂²	—	6	1	no	—
704	C₂²	—	6	1	no	—
705	C₂²	—	6	1	no	—
706	C₂²	—	6	1	no	—
707	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	6	1	no	—
714	C₄	—	6	1	no	—
715	C₄	—	6	1	no	—
716	C₄	—	6	1	no	—
717	C₄	—	6	1	no	—
718	C₄	—	6	1	no	—
719	C₃	—	2	1	no	—
720	C₃	C₉×#562	1	1	yes	characteristic, complemented
721	C₃	C₃×#5667	1	1	yes	characteristic
722	C₂	—	4	1	no	—
723	C₂	—	4	1	no	—
724	C₂	—	12	1	no	—
725	C₂	—	12	1	no	—
726	C₂	C₉×#1004	1	1	yes	characteristic
727	C₂	C₉×#1009	1	1	yes	characteristic
728	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×#5667	C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#562
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. C₃×C₉×#123	C₂	semidirect
2. C₉×#939	C₂	semidirect
3. C₉×#938	C₂	semidirect
4. C₉×#930	C₂	semidirect
5. C₉×#924	C₂	semidirect
6. C₉×#897	C₂	semidirect
7. C₉×#896	C₂	semidirect
8. C₉×#894	C₂	semidirect
9. C₉×#890	C₂	semidirect
10. C₉×#886	C₂	semidirect
11. C₉×#885	C₂	semidirect
12. C₉×#885	C₂	semidirect
13. C₉×#884	C₂	semidirect
14. C₉×#883	C₂	semidirect
15. C₉×#878	C₂	semidirect
75. C₉×#123	D₃	semidirect
112. #5667	C₉	direct (N × H)
221. C₃×#123	C₂×C₉	semidirect
231. #939	C₂×C₉	semidirect
232. #938	C₂×C₉	semidirect
233. #930	C₂×C₉	semidirect
234. #924	C₂×C₉	semidirect
235. #897	C₂×C₉	semidirect
236. #896	C₂×C₉	semidirect
237. #894	C₂×C₉	semidirect
238. #890	C₂×C₉	semidirect
239. #886	C₂×C₉	semidirect
240. #885	C₂×C₉	semidirect
241. #885	C₂×C₉	semidirect
242. #884	C₂×C₉	semidirect
243. #883	C₂×C₉	semidirect
244. #878	C₂×C₉	semidirect
459. #123	D₃×C₉	semidirect
468. C₃×C₉	#562	semidirect
648. C₉	#5667	direct (N × H)
720. C₃	C₉×#562	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#123	2
C₉×#939	2
C₉×#938	2
C₉×#930	2
C₉×#924	2
C₉×#897	2
C₉×#896	2
C₉×#894	2
C₉×#890	2
C₉×#886	2
C₉×#885	2
C₉×#884	2
C₉×#883	2
C₉×#878	2
C₃×#5667	3
C₉×#562	3

Subgroups — C9×#5667 #13153034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5667 #13153034