Subgroups — C₉×#5616 #13152804

Order 1728.

802 conjugacy classes of subgroups.

The subgroup lattice has 534 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, complemented
2	C₉×#939	C₂	1	2	yes	maximal, complemented
3	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#936	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	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	2	yes	maximal, complemented
11	C₉×#877	C₂	1	2	yes	maximal, complemented
12	C₃×#5616	C₃	1	1	yes	maximal, characteristic
13	C₉×#555	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	1	yes	characteristic
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
20	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₉×Dic₆	C₂²	1	2	yes	—
22	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₉×#217	C₂²	1	2	yes	—
25	C₉×#217	C₂²	1	1	yes	characteristic
26	C₉×#217	C₂²	1	2	yes	—
27	C₉×#217	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₄×C₉×Dic₃	C₂²	1	2	yes	—
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×#939	C₂×C₃	1	2	yes	—
39	C₃×#938	C₂×C₃	1	1	yes	characteristic
40	C₃×#936	C₂×C₃	1	2	yes	—
41	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
43	C₃×#926	C₂×C₃	1	1	yes	characteristic
44	C₃×#892	C₂×C₃	1	1	yes	characteristic
45	C₃×#888	C₂×C₃	1	1	yes	characteristic
46	C₃×#885	C₂×C₃	1	2	yes	—
47	C₃×#877	C₂×C₃	1	2	yes	—
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#124	—	3	2	no	—
50	C₉×#124	—	3	2	no	—
51	C₉×#121	—	2	1	no	—
52	C₉×#121	—	3	1	no	—
53	C₉×#121	—	3	2	no	—
54	C₉×#121	D₃	1	1	yes	characteristic, complemented
55	C₄×D₄×C₉	—	3	1	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₉×#117	—	3	1	no	—
58	C₉×#117	—	3	1	no	—
59	C₉×#117	—	3	2	no	—
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
62	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
63	C₃×D₄×C₉	—	2	2	no	—
64	C₃×D₄×C₉	—	4	2	no	—
65	C₂×C₃×C₄×C₉	—	2	2	no	—
66	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₉×#67	—	2	2	no	—
70	C₉×#67	—	4	2	no	—
71	C₂×C₉×Dic₃	—	2	4	no	—
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	2	yes	—
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	C₄×D₃×C₉	—	2	2	no	—
78	C₉×Dic₆	—	4	2	no	—
79	C₃×#555	—	3	1	no	—
80	#5616	C₉	1	1	yes	characteristic, direct product factor
81	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
83	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
86	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
89	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×#217	C₂²×C₃	1	2	yes	—
92	C₃×#217	C₂²×C₃	1	2	yes	—
93	C₃×#217	C₂²×C₃	1	2	yes	—
94	C₃×#217	C₂²×C₃	1	1	yes	characteristic
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
101	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
102	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
103	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×Q₈×C₉	—	3	2	no	—
105	C₂×D₄×C₉	—	2	1	no	—
106	C₂×D₄×C₉	—	2	2	no	—
107	C₂×D₄×C₉	—	3	1	no	—
108	C₂×D₄×C₉	—	3	2	no	—
109	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
110	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
111	C₂²×C₄×C₉	—	2	1	no	—
112	C₂²×C₄×C₉	—	3	2	no	—
113	C₂²×C₄×C₉	—	3	1	no	—
114	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
115	C₉×C₄⋊C₄	—	2	1	no	—
116	C₉×C₄⋊C₄	—	3	1	no	—
117	C₉×C₄⋊C₄	—	3	1	no	—
118	C₉×C₄⋊C₄	—	3	2	no	—
119	C₉×C₄⋊C₄	—	3	1	no	—
120	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
121	C₉×C₂²⋊C₄	—	2	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	1	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	—	3	2	no	—
127	C₉×C₂²⋊C₄	—	3	1	no	—
128	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
129	C₄²×C₉	—	3	2	no	—
130	C₄²×C₉	—	3	2	no	—
131	C₄²×C₉	—	3	1	no	—
132	C₂²×C₃×C₉	—	2	2	no	—
133	C₂²×C₃×C₉	—	2	1	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	—	2	2	no	—
136	C₂²×C₃×C₉	—	2	1	no	—
137	C₂²×C₃×C₉	—	2	2	no	—
138	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
139	C₂×D₃×C₉	—	2	1	no	—
140	C₂×D₃×C₉	—	2	1	no	—
141	C₂×D₃×C₉	—	2	1	no	—
142	C₃×C₄×C₉	—	2	1	no	—
143	C₃×C₄×C₉	—	2	2	no	—
144	C₃×C₄×C₉	#41	1	2	yes	—
145	C₉×Dic₃	—	2	1	no	—
146	C₉×Dic₃	—	2	2	no	—
147	C₉×Dic₃	—	2	1	no	—
148	C₉×Dic₃	—	2	2	no	—
149	C₉×Dic₃	#41	1	2	yes	—
150	C₃×C₄⋊Q₈	—	3	1	no	—
151	C₃×#124	—	3	2	no	—
152	C₃×#124	—	3	2	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	—	3	1	no	—
155	C₃×#121	—	3	2	no	—
156	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
157	C₃×#121	C₃×D₃	1	1	yes	characteristic
158	C₃×C₄×D₄	—	3	1	no	—
159	C₃×C₄×D₄	—	3	1	no	—
160	C₃×#117	—	3	1	no	—
161	C₃×#117	—	3	1	no	—
162	C₃×#117	—	3	2	no	—
163	#939	C₂×C₉	1	2	yes	complemented
164	#938	C₂×C₉	1	1	yes	characteristic, complemented
165	#936	C₂×C₉	1	2	yes	complemented
166	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
167	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
168	#926	C₂×C₉	1	1	yes	characteristic, complemented
169	#892	C₂×C₉	1	1	yes	characteristic, complemented
170	#888	C₂×C₉	1	1	yes	characteristic, complemented
171	#885	C₂×C₉	1	2	yes	complemented
172	#877	C₂×C₉	1	2	yes	complemented
173	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
174	C₂³×C₃²	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
176	C₃²×D₄	—	2	2	no	—
177	C₃²×D₄	—	4	2	no	—
178	C₂×C₃²×C₄	—	2	2	no	—
179	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
181	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₃×#67	—	2	2	no	—
183	C₃×#67	—	4	2	no	—
184	C₂×C₃×Dic₃	—	2	4	no	—
185	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
187	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
188	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
190	C₃×C₄×D₃	—	2	2	no	—
191	C₃×Dic₆	—	4	2	no	—
192	C₂³×C₉	—	2	1	no	—
193	C₂³×C₉	—	2	2	no	—
194	C₂³×C₉	—	3	1	no	—
195	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
196	C₂³×C₉	C₂²×D₃	1	2	yes	—
197	Q₈×C₉	—	12	2	no	—
198	D₄×C₉	—	2	2	no	—
199	D₄×C₉	—	4	2	no	—
200	D₄×C₉	—	4	2	no	—
201	D₄×C₉	—	4	4	no	—
202	D₄×C₉	—	6	2	no	—
203	D₄×C₉	—	12	2	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	2	no	—
208	C₂×C₄×C₉	—	3	1	no	—
209	C₂×C₄×C₉	—	3	1	no	—
210	C₂×C₄×C₉	—	3	2	no	—
211	C₂×C₄×C₉	—	3	1	no	—
212	C₂×C₄×C₉	—	3	2	no	—
213	C₂×C₄×C₉	—	4	2	no	—
214	C₂×C₄×C₉	—	6	4	no	—
215	C₂×C₄×C₉	—	6	2	no	—
216	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
218	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
219	#555	—	3	1	no	Sylow
220	C₂×C₃×C₉	—	4	1	no	—
221	C₂×C₃×C₉	—	4	2	no	—
222	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
223	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
225	D₃×C₉	—	4	1	no	—
226	C₂×C₃×Q₈	—	3	2	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	—	2	2	no	—
229	C₂×C₃×D₄	—	3	1	no	—
230	C₂×C₃×D₄	—	3	2	no	—
231	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
233	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
234	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	3	2	no	—
237	C₂²×C₃×C₄	—	3	1	no	—
238	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₂×#67	C₂²×C₉	1	1	yes	characteristic
241	C₂×#67	C₂²×C₉	1	2	yes	—
242	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
243	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
244	C₂×Dic₆	C₂²×C₉	1	2	yes	—
245	C₃×C₄⋊C₄	—	2	1	no	—
246	C₃×C₄⋊C₄	—	3	1	no	—
247	C₃×C₄⋊C₄	—	3	2	no	—
248	C₃×C₄⋊C₄	—	3	1	no	—
249	C₃×C₄⋊C₄	—	3	1	no	—
250	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	—	3	2	no	—
254	C₃×C₂²⋊C₄	—	3	2	no	—
255	C₃×C₂²⋊C₄	—	3	1	no	—
256	C₃×C₂²⋊C₄	—	3	2	no	—
257	C₃×C₂²⋊C₄	—	3	2	no	—
258	C₃×C₂²⋊C₄	—	3	1	no	—
259	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
260	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
261	C₃×C₄²	—	3	2	no	—
262	C₃×C₄²	—	3	2	no	—
263	C₃×C₄²	—	3	1	no	—
264	#217	C₂²×C₉	1	2	yes	—
265	#217	C₂²×C₉	1	2	yes	—
266	#217	C₂²×C₉	1	2	yes	—
267	#217	C₂²×C₉	1	1	yes	characteristic
268	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
269	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
270	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
271	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
272	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
273	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
274	C₄×Dic₃	C₂²×C₉	1	2	yes	—
275	C₄×Dic₃	C₂²×C₉	1	2	yes	—
276	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
277	C₂²×C₃²	—	2	1	no	—
278	C₂²×C₃²	—	2	2	no	—
279	C₂²×C₃²	—	2	1	no	—
280	C₂²×C₃²	—	2	1	no	—
281	C₂²×C₃²	—	2	2	no	—
282	C₂²×C₃²	—	2	2	no	—
283	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
284	C₂×C₃×D₃	—	2	1	no	—
285	C₂×C₃×D₃	—	2	1	no	—
286	C₂×C₃×D₃	—	2	1	no	—
287	C₃²×C₄	—	2	1	no	—
288	C₃²×C₄	—	2	2	no	—
289	C₃²×C₄	C₃×#41	1	2	yes	—
290	C₃×Dic₃	—	2	1	no	—
291	C₃×Dic₃	—	2	2	no	—
292	C₃×Dic₃	—	2	1	no	—
293	C₃×Dic₃	—	2	2	no	—
294	C₃×Dic₃	C₃×#41	1	2	yes	—
295	C₂²×C₉	—	2	2	no	—
296	C₂²×C₉	—	2	1	no	—
297	C₂²×C₉	—	2	2	no	—
298	C₂²×C₉	—	2	1	no	—
299	C₂²×C₉	—	2	2	no	—
300	C₂²×C₉	—	2	2	no	—
301	C₂²×C₉	—	2	1	no	—
302	C₂²×C₉	—	2	1	no	—
303	C₂²×C₉	—	4	1	no	—
304	C₂²×C₉	—	4	1	no	—
305	C₂²×C₉	—	4	2	no	—
306	C₂²×C₉	—	4	2	no	—
307	C₂²×C₉	—	4	2	no	—
308	C₂²×C₉	—	6	1	no	—
309	C₂²×C₉	—	6	1	no	—
310	C₂²×C₉	—	6	1	no	—
311	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
312	C₄×C₉	—	2	1	no	—
313	C₄×C₉	—	2	2	no	—
314	C₄×C₉	—	2	2	no	—
315	C₄×C₉	—	3	2	no	—
316	C₄×C₉	—	4	1	no	—
317	C₄×C₉	—	4	2	no	—
318	C₄×C₉	—	6	1	no	—
319	C₄×C₉	—	6	2	no	—
320	C₄×C₉	—	6	1	no	—
321	C₄×C₉	—	6	2	no	—
322	C₄×C₉	#237	1	2	yes	—
323	C₄⋊Q₈	—	3	1	no	—
324	#124	—	3	2	no	—
325	#124	—	3	2	no	—
326	#121	—	3	1	no	—
327	#121	—	3	2	no	—
328	#121	D₃×C₉	1	1	yes	characteristic, complemented
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	1	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	2	no	—
334	C₃×C₉	#555	1	1	yes	characteristic, complemented, Sylow
335	C₂³×C₃	—	2	1	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	3	1	no	—
338	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
339	C₂³×C₃	C₂³×C₉	1	2	yes	—
340	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
341	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
342	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
343	C₃×Q₈	—	12	2	no	—
344	C₃×D₄	—	2	2	no	—
345	C₃×D₄	—	2	2	no	—
346	C₃×D₄	—	4	2	no	—
347	C₃×D₄	—	4	2	no	—
348	C₃×D₄	—	4	2	no	—
349	C₃×D₄	—	4	4	no	—
350	C₃×D₄	—	6	2	no	—
351	C₃×D₄	—	12	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	3	1	no	—
358	C₂×C₃×C₄	—	3	1	no	—
359	C₂×C₃×C₄	—	3	2	no	—
360	C₂×C₃×C₄	—	3	1	no	—
361	C₂×C₃×C₄	—	3	2	no	—
362	C₂×C₃×C₄	—	4	2	no	—
363	C₂×C₃×C₄	—	6	4	no	—
364	C₂×C₃×C₄	—	6	2	no	—
365	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
367	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
370	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
371	#67	—	2	2	no	—
372	#67	—	4	2	no	—
373	C₂×Dic₃	—	2	4	no	—
374	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
375	C₂×Dic₃	C₂³×C₉	1	2	yes	—
376	C₂×Dic₃	C₂³×C₉	1	2	yes	—
377	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
378	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
379	C₄×D₃	—	2	2	no	—
380	Dic₆	—	4	2	no	—
381	C₂×C₃²	—	4	1	no	—
382	C₂×C₃²	—	4	2	no	—
383	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
384	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
385	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
386	C₃×D₃	—	4	1	no	—
387	C₂×C₉	—	2	1	no	—
388	C₂×C₉	—	2	1	no	—
389	C₂×C₉	—	2	1	no	—
390	C₂×C₉	—	4	2	no	—
391	C₂×C₉	—	4	1	no	—
392	C₂×C₉	—	4	2	no	—
393	C₂×C₉	—	8	2	no	—
394	C₂×C₉	—	12	1	no	—
395	C₂×C₉	C₂×#237	1	1	yes	characteristic
396	C₂×C₉	#1004	1	1	yes	characteristic
397	C₂×C₉	D₃×#41	1	1	yes	characteristic
398	C₂×Q₈	—	3	2	no	—
399	C₂×D₄	—	3	1	no	—
400	C₂×D₄	—	3	2	no	—
401	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
402	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
403	C₂²×C₄	—	3	2	no	—
404	C₂²×C₄	—	3	1	no	—
405	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
406	C₄⋊C₄	—	3	1	no	—
407	C₄⋊C₄	—	3	1	no	—
408	C₄⋊C₄	—	3	2	no	—
409	C₄⋊C₄	—	3	1	no	—
410	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
411	C₂²⋊C₄	—	3	2	no	—
412	C₂²⋊C₄	—	3	2	no	—
413	C₂²⋊C₄	—	3	1	no	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	—	3	2	no	—
416	C₂²⋊C₄	—	3	1	no	—
417	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
418	C₄²	—	3	2	no	—
419	C₄²	—	3	2	no	—
420	C₄²	—	3	1	no	—
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	2	1	no	—
423	C₂²×C₃	—	2	2	no	—
424	C₂²×C₃	—	2	1	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	1	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	1	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	1	no	—
434	C₂²×C₃	—	2	1	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	—	4	1	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	2	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	6	1	no	—
441	C₂²×C₃	—	6	1	no	—
442	C₂²×C₃	—	6	1	no	—
443	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
444	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
445	C₂×D₃	—	2	1	no	—
446	C₂×D₃	—	2	1	no	—
447	C₂×D₃	—	2	1	no	—
448	C₃×C₄	—	2	1	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	1	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	3	2	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	—	6	1	no	—
457	C₃×C₄	—	6	2	no	—
458	C₃×C₄	—	6	1	no	—
459	C₃×C₄	—	6	2	no	—
460	C₃×C₄	C₉×#41	1	2	yes	—
461	C₃×C₄	C₃×#237	1	2	yes	—
462	Dic₃	—	2	1	no	—
463	Dic₃	—	2	2	no	—
464	Dic₃	—	2	1	no	—
465	Dic₃	—	2	2	no	—
466	Dic₃	C₉×#41	1	2	yes	—
467	C₃²	C₃×#555	1	1	yes	characteristic
468	C₉	—	2	1	no	—
469	C₉	#5616	1	1	yes	characteristic, direct product factor
470	C₂³	—	3	1	no	—
471	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
472	C₂³	C₂²×D₃×C₉	1	2	yes	—
473	Q₈	—	12	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	6	2	no	—
477	D₄	—	12	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	3	1	no	—
480	C₂×C₄	—	3	1	no	—
481	C₂×C₄	—	3	2	no	—
482	C₂×C₄	—	3	1	no	—
483	C₂×C₄	—	3	2	no	—
484	C₂×C₄	—	6	4	no	—
485	C₂×C₄	—	6	2	no	—
486	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
488	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
489	C₂×C₃	—	2	1	no	—
490	C₂×C₃	—	2	1	no	—
491	C₂×C₃	—	2	1	no	—
492	C₂×C₃	—	4	2	no	—
493	C₂×C₃	—	4	1	no	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	—	4	1	no	—
496	C₂×C₃	—	4	2	no	—
497	C₂×C₃	—	8	2	no	—
498	C₂×C₃	—	12	1	no	—
499	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
500	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
501	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
503	C₂×C₃	C₃×#1004	1	1	yes	characteristic
504	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
505	D₃	—	4	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	6	1	no	—
513	C₂²	—	6	1	no	—
514	C₂²	—	6	1	no	—
515	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
516	C₄	—	2	1	no	—
517	C₄	—	2	2	no	—
518	C₄	—	3	2	no	—
519	C₄	—	6	1	no	—
520	C₄	—	6	2	no	—
521	C₄	—	6	1	no	—
522	C₄	—	6	2	no	—
523	C₄	C₉×#237	1	2	yes	—
524	C₃	—	2	1	no	—
525	C₃	C₉×#555	1	1	yes	characteristic, complemented
526	C₃	C₃×#5616	1	1	yes	characteristic
527	C₂	—	4	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	12	1	no	—
530	C₂	C₂×C₉×#237	1	1	yes	characteristic
531	C₂	C₉×#1004	1	1	yes	characteristic
532	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	C₃×#5616	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#555
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. C₃×C₉×#121	C₂	semidirect
2. C₉×#939	C₂	semidirect
3. C₉×#938	C₂	semidirect
4. C₉×#936	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₄×C₉×#67	C₂	semidirect
7. C₉×#926	C₂	semidirect
8. C₉×#892	C₂	semidirect
9. C₉×#888	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#877	C₂	semidirect
54. C₉×#121	D₃	semidirect
80. #5616	C₉	direct (N × H)
156. C₃×#121	C₂×C₉	semidirect
163. #939	C₂×C₉	semidirect
164. #938	C₂×C₉	semidirect
165. #936	C₂×C₉	semidirect
166. D₄×Dic₃	C₂×C₉	semidirect
167. C₄×#67	C₂×C₉	semidirect
168. #926	C₂×C₉	semidirect
169. #892	C₂×C₉	semidirect
170. #888	C₂×C₉	semidirect
171. #885	C₂×C₉	semidirect
172. #877	C₂×C₉	semidirect
328. #121	D₃×C₉	semidirect
334. C₃×C₉	#555	semidirect
469. C₉	#5616	direct (N × H)
525. C₃	C₉×#555	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×#939	2
C₉×#938	2
C₉×#936	2
D₄×C₉×Dic₃	2
C₄×C₉×#67	2
C₉×#926	2
C₉×#892	2
C₉×#888	2
C₉×#885	2
C₉×#877	2
C₃×#5616	3
C₉×#555	3

Subgroups — C9×#5616 #13152804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5616 #13152804