Subgroups — C₉×#5619 #13152836

Order 1728.

814 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#939	C₂	1	2	yes	maximal, complemented
4	C₉×#938	C₂	1	2	yes	maximal, complemented
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#886	C₂	1	2	yes	maximal, complemented
11	C₉×#883	C₂	1	2	yes	maximal, complemented
12	C₃×#5619	C₃	1	1	yes	maximal, characteristic
13	C₉×#540	—	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	2	yes	—
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	2	yes	—
20	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
21	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
23	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₉×#217	C₂²	1	1	yes	characteristic
26	C₉×#217	C₂²	1	1	yes	characteristic
27	C₉×#217	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×#121	C₂×C₃	1	1	yes	characteristic
38	C₃×#940	C₂×C₃	1	1	yes	characteristic
39	C₃×#939	C₂×C₃	1	2	yes	—
40	C₃×#938	C₂×C₃	1	2	yes	—
41	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#930	C₂×C₃	1	1	yes	characteristic
43	C₃×#926	C₂×C₃	1	1	yes	characteristic
44	C₃×#893	C₂×C₃	1	1	yes	characteristic
45	C₃×#890	C₂×C₃	1	1	yes	characteristic
46	C₃×#886	C₂×C₃	1	2	yes	—
47	C₃×#883	C₂×C₃	1	2	yes	—
48	C₉×#127	—	3	1	no	—
49	C₉×#125	—	3	1	no	—
50	C₉×#123	—	3	2	no	—
51	C₉×#123	—	3	2	no	—
52	C₉×#121	—	2	1	no	—
53	C₉×#121	—	3	2	no	—
54	C₉×#121	—	3	2	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	C₉×#117	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
62	C₂²×D₃×C₉	C₂³	1	2	yes	—
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	—	4	2	no	—
70	C₉×#67	—	4	2	no	—
71	C₉×#67	—	4	2	no	—
72	C₂×C₉×Dic₃	—	4	2	no	—
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	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₉×D₁₂	—	2	2	no	—
79	C₄×D₃×C₉	—	4	2	no	—
80	C₃×#540	—	3	1	no	—
81	#5619	C₉	1	1	yes	characteristic, direct product factor
82	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
84	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
86	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
87	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
88	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
89	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
91	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×#217	C₂²×C₃	1	2	yes	—
94	C₃×#217	C₂²×C₃	1	1	yes	characteristic
95	C₃×#217	C₂²×C₃	1	1	yes	characteristic
96	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
101	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
103	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
105	C₂×D₄×C₉	—	2	1	no	—
106	C₂×D₄×C₉	—	2	2	no	—
107	C₂×D₄×C₉	—	3	2	no	—
108	C₂×D₄×C₉	—	3	2	no	—
109	C₂×D₄×C₉	—	3	2	no	—
110	C₂×D₄×C₉	—	3	1	no	—
111	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
112	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
113	C₂²×C₄×C₉	—	2	1	no	—
114	C₂²×C₄×C₉	—	3	2	no	—
115	C₂²×C₄×C₉	—	3	2	no	—
116	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
117	C₉×C₄⋊C₄	—	2	1	no	—
118	C₉×C₄⋊C₄	—	3	1	no	—
119	C₉×C₄⋊C₄	—	3	1	no	—
120	C₉×C₄⋊C₄	—	3	1	no	—
121	C₉×C₄⋊C₄	—	3	2	no	—
122	C₉×C₄⋊C₄	—	3	2	no	—
123	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₉×C₂²⋊C₄	—	2	2	no	—
125	C₉×C₂²⋊C₄	—	3	1	no	—
126	C₉×C₂²⋊C₄	—	3	1	no	—
127	C₉×C₂²⋊C₄	—	3	2	no	—
128	C₉×C₂²⋊C₄	—	3	2	no	—
129	C₉×C₂²⋊C₄	—	3	2	no	—
130	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
131	C₄²×C₉	—	3	1	no	—
132	C₄²×C₉	—	3	1	no	—
133	C₂²×C₃×C₉	—	2	1	no	—
134	C₂²×C₃×C₉	—	2	2	no	—
135	C₂²×C₃×C₉	—	2	1	no	—
136	C₂²×C₃×C₉	—	2	2	no	—
137	C₂²×C₃×C₉	—	2	1	no	—
138	C₂²×C₃×C₉	—	2	2	no	—
139	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
140	C₂×D₃×C₉	—	2	2	no	—
141	C₂×D₃×C₉	—	2	2	no	—
142	C₂×D₃×C₉	—	2	2	no	—
143	C₃×C₄×C₉	—	2	1	no	—
144	C₃×C₄×C₉	—	2	2	no	—
145	C₃×C₄×C₉	#41	1	2	yes	—
146	C₉×Dic₃	—	2	1	no	—
147	C₉×Dic₃	—	2	1	no	—
148	C₉×Dic₃	—	2	2	no	—
149	C₉×Dic₃	—	2	1	no	—
150	C₉×Dic₃	—	2	1	no	—
151	C₃×#127	—	3	1	no	—
152	C₃×#125	—	3	1	no	—
153	C₃×#123	—	3	2	no	—
154	C₃×#123	—	3	2	no	—
155	C₃×#121	—	2	1	no	—
156	C₃×#121	—	3	2	no	—
157	C₃×#121	—	3	2	no	—
158	C₃×#121	—	3	1	no	—
159	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
160	C₃×#121	C₃×D₃	1	1	yes	characteristic
161	C₃×C₄×D₄	—	3	1	no	—
162	C₃×C₄×D₄	—	3	1	no	—
163	C₃×#117	—	3	1	no	—
164	#940	C₂×C₉	1	1	yes	characteristic, complemented
165	#939	C₂×C₉	1	2	yes	complemented
166	#938	C₂×C₉	1	2	yes	complemented
167	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
168	#930	C₂×C₉	1	1	yes	characteristic, complemented
169	#926	C₂×C₉	1	1	yes	characteristic, complemented
170	#893	C₂×C₉	1	1	yes	characteristic, complemented
171	#890	C₂×C₉	1	1	yes	characteristic, complemented
172	#886	C₂×C₉	1	2	yes	complemented
173	#883	C₂×C₉	1	2	yes	complemented
174	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
175	C₂³×C₃²	C₂³×C₃	1	2	yes	—
176	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
177	C₃²×D₄	—	2	2	no	—
178	C₃²×D₄	—	4	2	no	—
179	C₂×C₃²×C₄	—	2	2	no	—
180	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
181	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₃×#67	—	4	2	no	—
184	C₃×#67	—	4	2	no	—
185	C₃×#67	—	4	2	no	—
186	C₂×C₃×Dic₃	—	4	2	no	—
187	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
192	C₃×D₁₂	—	2	2	no	—
193	C₃×C₄×D₃	—	4	2	no	—
194	C₂³×C₉	—	2	1	no	—
195	C₂³×C₉	—	2	2	no	—
196	C₂³×C₉	—	3	2	no	—
197	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
198	C₂³×C₉	C₂²×D₃	1	2	yes	—
199	D₄×C₉	—	2	2	no	—
200	D₄×C₉	—	4	2	no	—
201	D₄×C₉	—	4	2	no	—
202	D₄×C₉	—	4	4	no	—
203	D₄×C₉	—	6	2	no	—
204	D₄×C₉	—	12	2	no	—
205	D₄×C₉	—	12	2	no	—
206	D₄×C₉	—	12	2	no	—
207	C₂×C₄×C₉	—	2	2	no	—
208	C₂×C₄×C₉	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	2	no	—
211	C₂×C₄×C₉	—	3	1	no	—
212	C₂×C₄×C₉	—	3	1	no	—
213	C₂×C₄×C₉	—	3	1	no	—
214	C₂×C₄×C₉	—	3	1	no	—
215	C₂×C₄×C₉	—	3	2	no	—
216	C₂×C₄×C₉	—	4	2	no	—
217	C₂×C₄×C₉	—	12	2	no	—
218	C₂×C₄×C₉	—	12	2	no	—
219	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
220	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
221	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
222	#540	—	3	1	no	Sylow
223	C₂×C₃×C₉	—	4	1	no	—
224	C₂×C₃×C₉	—	4	2	no	—
225	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
226	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
228	D₃×C₉	—	4	2	no	—
229	C₂×C₃×D₄	—	2	1	no	—
230	C₂×C₃×D₄	—	2	2	no	—
231	C₂×C₃×D₄	—	3	2	no	—
232	C₂×C₃×D₄	—	3	2	no	—
233	C₂×C₃×D₄	—	3	2	no	—
234	C₂×C₃×D₄	—	3	1	no	—
235	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
236	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
237	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
238	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
239	C₂²×C₃×C₄	—	2	1	no	—
240	C₂²×C₃×C₄	—	3	2	no	—
241	C₂²×C₃×C₄	—	3	2	no	—
242	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
244	C₂×#67	C₂²×C₉	1	2	yes	—
245	C₂×#67	C₂²×C₉	1	2	yes	—
246	C₂×#67	C₂²×C₉	1	2	yes	—
247	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
248	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
249	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	—	3	2	no	—
252	C₃×C₄⋊C₄	—	3	1	no	—
253	C₃×C₄⋊C₄	—	3	1	no	—
254	C₃×C₄⋊C₄	—	3	1	no	—
255	C₃×C₄⋊C₄	—	3	2	no	—
256	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
257	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	3	1	no	—
260	C₃×C₂²⋊C₄	—	3	1	no	—
261	C₃×C₂²⋊C₄	—	3	2	no	—
262	C₃×C₂²⋊C₄	—	3	2	no	—
263	C₃×C₂²⋊C₄	—	3	2	no	—
264	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
265	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
266	C₃×C₄²	—	3	1	no	—
267	C₃×C₄²	—	3	1	no	—
268	#217	C₂²×C₉	1	2	yes	—
269	#217	C₂²×C₉	1	1	yes	characteristic
270	#217	C₂²×C₉	1	1	yes	characteristic
271	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
272	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
273	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
274	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
275	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
276	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
277	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
278	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
279	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
280	C₂²×C₃²	—	2	1	no	—
281	C₂²×C₃²	—	2	1	no	—
282	C₂²×C₃²	—	2	2	no	—
283	C₂²×C₃²	—	2	2	no	—
284	C₂²×C₃²	—	2	1	no	—
285	C₂²×C₃²	—	2	2	no	—
286	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
287	C₂×C₃×D₃	—	2	2	no	—
288	C₂×C₃×D₃	—	2	2	no	—
289	C₂×C₃×D₃	—	2	2	no	—
290	C₃²×C₄	—	2	1	no	—
291	C₃²×C₄	—	2	2	no	—
292	C₃²×C₄	C₃×#41	1	2	yes	—
293	C₃×Dic₃	—	2	1	no	—
294	C₃×Dic₃	—	2	1	no	—
295	C₃×Dic₃	—	2	2	no	—
296	C₃×Dic₃	—	2	1	no	—
297	C₃×Dic₃	—	2	1	no	—
298	C₂²×C₉	—	2	2	no	—
299	C₂²×C₉	—	2	1	no	—
300	C₂²×C₉	—	2	2	no	—
301	C₂²×C₉	—	2	1	no	—
302	C₂²×C₉	—	2	2	no	—
303	C₂²×C₉	—	2	2	no	—
304	C₂²×C₉	—	2	1	no	—
305	C₂²×C₉	—	2	1	no	—
306	C₂²×C₉	—	4	1	no	—
307	C₂²×C₉	—	4	1	no	—
308	C₂²×C₉	—	4	2	no	—
309	C₂²×C₉	—	4	2	no	—
310	C₂²×C₉	—	4	2	no	—
311	C₂²×C₉	—	6	2	no	—
312	C₂²×C₉	—	6	2	no	—
313	C₂²×C₉	—	6	2	no	—
314	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
315	C₄×C₉	—	2	1	no	—
316	C₄×C₉	—	2	2	no	—
317	C₄×C₉	—	2	2	no	—
318	C₄×C₉	—	4	1	no	—
319	C₄×C₉	—	4	2	no	—
320	C₄×C₉	—	6	1	no	—
321	C₄×C₉	—	6	1	no	—
322	C₄×C₉	—	6	1	no	—
323	C₄×C₉	—	6	2	no	—
324	C₄×C₉	—	6	1	no	—
325	C₄×C₉	#237	1	2	yes	—
326	#127	—	3	1	no	—
327	#125	—	3	1	no	—
328	#123	—	3	2	no	—
329	#123	—	3	2	no	—
330	#121	—	3	2	no	—
331	#121	—	3	2	no	—
332	#121	—	3	1	no	—
333	#121	D₃×C₉	1	1	yes	characteristic, complemented
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	1	no	—
336	#117	—	3	1	no	—
337	C₃×C₉	#540	1	1	yes	characteristic, complemented, Sylow
338	C₂³×C₃	—	2	1	no	—
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	3	2	no	—
341	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
342	C₂³×C₃	C₂³×C₉	1	2	yes	—
343	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
344	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
345	C₂²×D₃	C₂³×C₉	1	2	yes	—
346	C₃×D₄	—	2	2	no	—
347	C₃×D₄	—	2	2	no	—
348	C₃×D₄	—	4	2	no	—
349	C₃×D₄	—	4	2	no	—
350	C₃×D₄	—	4	2	no	—
351	C₃×D₄	—	4	4	no	—
352	C₃×D₄	—	6	2	no	—
353	C₃×D₄	—	12	2	no	—
354	C₃×D₄	—	12	2	no	—
355	C₃×D₄	—	12	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	3	1	no	—
362	C₂×C₃×C₄	—	3	1	no	—
363	C₂×C₃×C₄	—	3	1	no	—
364	C₂×C₃×C₄	—	3	1	no	—
365	C₂×C₃×C₄	—	3	2	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	—	12	2	no	—
368	C₂×C₃×C₄	—	12	2	no	—
369	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
370	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
374	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
375	#67	—	4	2	no	—
376	#67	—	4	2	no	—
377	#67	—	4	2	no	—
378	C₂×Dic₃	—	4	2	no	—
379	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
380	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
381	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
382	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
383	C₂×Dic₃	C₂³×C₉	1	2	yes	—
384	D₁₂	—	2	2	no	—
385	C₄×D₃	—	4	2	no	—
386	C₂×C₃²	—	4	1	no	—
387	C₂×C₃²	—	4	2	no	—
388	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
389	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
391	C₃×D₃	—	4	2	no	—
392	C₂×C₉	—	2	1	no	—
393	C₂×C₉	—	2	1	no	—
394	C₂×C₉	—	2	1	no	—
395	C₂×C₉	—	4	2	no	—
396	C₂×C₉	—	4	1	no	—
397	C₂×C₉	—	4	2	no	—
398	C₂×C₉	—	8	2	no	—
399	C₂×C₉	—	12	2	no	—
400	C₂×C₉	C₂×#237	1	1	yes	characteristic
401	C₂×C₉	#1004	1	1	yes	characteristic
402	C₂×C₉	#1009	1	1	yes	characteristic
403	C₂×D₄	—	3	2	no	—
404	C₂×D₄	—	3	2	no	—
405	C₂×D₄	—	3	2	no	—
406	C₂×D₄	—	3	1	no	—
407	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
408	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
409	C₂²×C₄	—	3	2	no	—
410	C₂²×C₄	—	3	2	no	—
411	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
412	C₄⋊C₄	—	3	1	no	—
413	C₄⋊C₄	—	3	1	no	—
414	C₄⋊C₄	—	3	1	no	—
415	C₄⋊C₄	—	3	2	no	—
416	C₄⋊C₄	—	3	2	no	—
417	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
418	C₂²⋊C₄	—	3	1	no	—
419	C₂²⋊C₄	—	3	1	no	—
420	C₂²⋊C₄	—	3	2	no	—
421	C₂²⋊C₄	—	3	2	no	—
422	C₂²⋊C₄	—	3	2	no	—
423	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
424	C₄²	—	3	1	no	—
425	C₄²	—	3	1	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	2	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	1	no	—
433	C₂²×C₃	—	2	1	no	—
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	1	no	—
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	1	no	—
439	C₂²×C₃	—	2	1	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	4	1	no	—
442	C₂²×C₃	—	4	2	no	—
443	C₂²×C₃	—	4	2	no	—
444	C₂²×C₃	—	4	2	no	—
445	C₂²×C₃	—	6	2	no	—
446	C₂²×C₃	—	6	2	no	—
447	C₂²×C₃	—	6	2	no	—
448	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
449	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
450	C₂×D₃	—	2	2	no	—
451	C₂×D₃	—	2	2	no	—
452	C₂×D₃	—	2	2	no	—
453	C₃×C₄	—	2	1	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	2	1	no	—
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	2	2	no	—
458	C₃×C₄	—	4	1	no	—
459	C₃×C₄	—	4	2	no	—
460	C₃×C₄	—	6	1	no	—
461	C₃×C₄	—	6	1	no	—
462	C₃×C₄	—	6	1	no	—
463	C₃×C₄	—	6	2	no	—
464	C₃×C₄	—	6	1	no	—
465	C₃×C₄	C₉×#41	1	2	yes	—
466	C₃×C₄	C₃×#237	1	2	yes	—
467	Dic₃	—	2	1	no	—
468	Dic₃	—	2	1	no	—
469	Dic₃	—	2	2	no	—
470	Dic₃	—	2	1	no	—
471	Dic₃	—	2	1	no	—
472	C₃²	C₃×#540	1	1	yes	characteristic
473	C₉	—	2	1	no	—
474	C₉	#5619	1	1	yes	characteristic, direct product factor
475	C₂³	—	3	2	no	—
476	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
477	C₂³	C₂²×D₃×C₉	1	2	yes	—
478	D₄	—	2	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	6	2	no	—
481	D₄	—	12	2	no	—
482	D₄	—	12	2	no	—
483	D₄	—	12	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	3	1	no	—
486	C₂×C₄	—	3	1	no	—
487	C₂×C₄	—	3	1	no	—
488	C₂×C₄	—	3	1	no	—
489	C₂×C₄	—	3	2	no	—
490	C₂×C₄	—	12	2	no	—
491	C₂×C₄	—	12	2	no	—
492	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
494	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	2	1	no	—
497	C₂×C₃	—	2	1	no	—
498	C₂×C₃	—	4	2	no	—
499	C₂×C₃	—	4	1	no	—
500	C₂×C₃	—	4	2	no	—
501	C₂×C₃	—	4	1	no	—
502	C₂×C₃	—	4	2	no	—
503	C₂×C₃	—	8	2	no	—
504	C₂×C₃	—	12	2	no	—
505	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
506	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
509	C₂×C₃	C₃×#1004	1	1	yes	characteristic
510	C₂×C₃	C₃×#1009	1	1	yes	characteristic
511	D₃	—	4	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	6	2	no	—
519	C₂²	—	6	2	no	—
520	C₂²	—	6	2	no	—
521	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	2	no	—
524	C₄	—	6	1	no	—
525	C₄	—	6	1	no	—
526	C₄	—	6	1	no	—
527	C₄	—	6	2	no	—
528	C₄	—	6	1	no	—
529	C₄	C₉×#237	1	2	yes	—
530	C₃	—	2	1	no	—
531	C₃	C₉×#540	1	1	yes	characteristic, complemented
532	C₃	C₃×#5619	1	1	yes	characteristic
533	C₂	—	4	1	no	—
534	C₂	—	4	2	no	—
535	C₂	—	12	2	no	—
536	C₂	C₂×C₉×#237	1	1	yes	characteristic
537	C₂	C₉×#1004	1	1	yes	characteristic
538	C₂	C₉×#1009	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×#5619	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#540
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×#940	C₂	semidirect
3. C₉×#939	C₂	semidirect
4. C₉×#938	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₉×#930	C₂	semidirect
7. C₉×#926	C₂	semidirect
8. C₉×#893	C₂	semidirect
9. C₉×#890	C₂	semidirect
10. C₉×#886	C₂	semidirect
11. C₉×#883	C₂	semidirect
56. C₉×#121	D₃	semidirect
81. #5619	C₉	direct (N × H)
159. C₃×#121	C₂×C₉	semidirect
164. #940	C₂×C₉	semidirect
165. #939	C₂×C₉	semidirect
166. #938	C₂×C₉	semidirect
167. D₄×Dic₃	C₂×C₉	semidirect
168. #930	C₂×C₉	semidirect
169. #926	C₂×C₉	semidirect
170. #893	C₂×C₉	semidirect
171. #890	C₂×C₉	semidirect
172. #886	C₂×C₉	semidirect
173. #883	C₂×C₉	semidirect
333. #121	D₃×C₉	semidirect
337. C₃×C₉	#540	semidirect
474. C₉	#5619	direct (N × H)
531. C₃	C₉×#540	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×#940	2
C₉×#939	2
C₉×#938	2
D₄×C₉×Dic₃	2
C₉×#930	2
C₉×#926	2
C₉×#893	2
C₉×#890	2
C₉×#886	2
C₉×#883	2
C₃×#5619	3
C₉×#540	3

Subgroups — C9×#5619 #13152836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5619 #13152836