Subgroups — C₉×#5534 #13152505

Order 1728.

724 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#930	C₂	1	1	yes	maximal, characteristic
3	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#898	C₂	1	2	yes	maximal, complemented
5	C₉×#896	C₂	1	2	yes	maximal, complemented
6	C₉×#885	C₂	1	2	yes	maximal, complemented
7	C₉×#883	C₂	1	2	yes	maximal, complemented
8	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5534	C₃	1	1	yes	maximal, characteristic
13	C₉×#542	—	3	1	no	maximal
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×Dic₆	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₉×#217	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
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	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×#117	C₂×C₃	1	1	yes	characteristic
38	C₃×#930	C₂×C₃	1	1	yes	characteristic
39	C₃×#924	C₂×C₃	1	1	yes	characteristic
40	C₃×#898	C₂×C₃	1	2	yes	—
41	C₃×#896	C₂×C₃	1	2	yes	—
42	C₃×#885	C₂×C₃	1	2	yes	—
43	C₃×#883	C₂×C₃	1	2	yes	—
44	C₃×#875	C₂×C₃	1	1	yes	characteristic
45	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
46	C₃×#869	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#126	—	3	2	no	—
50	C₉×#124	—	3	2	no	—
51	C₉×#124	—	3	1	no	—
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	1	no	—
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₉×#121	—	3	1	no	—
56	C₄×Q₈×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	1	no	—
58	C₉×#117	—	2	1	no	—
59	C₉×#117	D₃	1	1	yes	characteristic, complemented
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₂×C₉×Dic₃	C₂³	1	2	yes	—
73	C₉×D₁₂	—	2	2	no	—
74	C₄×D₃×C₉	—	4	2	no	—
75	C₉×Dic₆	—	2	2	no	—
76	C₉×Dic₆	—	4	2	no	—
77	C₃×#542	—	3	1	no	—
78	#5534	C₉	1	1	yes	characteristic, direct product factor
79	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
81	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
83	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
90	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
91	C₃×#217	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Dic₃	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	2	yes	—
100	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
101	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
102	C₂×Q₈×C₉	—	3	1	no	—
103	C₂×Q₈×C₉	—	3	2	no	—
104	C₂×D₄×C₉	—	3	2	no	—
105	C₂×D₄×C₉	—	3	1	no	—
106	C₂²×C₄×C₉	—	2	1	no	—
107	C₂²×C₄×C₉	—	3	2	no	—
108	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	3	1	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
117	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₉×C₂²⋊C₄	—	2	1	no	—
119	C₉×C₂²⋊C₄	—	2	1	no	—
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₄²×C₉	—	2	1	no	—
128	C₄²×C₉	—	2	1	no	—
129	C₄²×C₉	—	3	2	no	—
130	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
131	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	—	2	1	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
136	C₂×D₃×C₉	—	2	2	no	—
137	C₂×D₃×C₉	—	2	2	no	—
138	C₂×D₃×C₉	—	2	2	no	—
139	C₃×C₄×C₉	—	2	1	no	—
140	C₃×C₄×C₉	—	2	1	no	—
141	C₃×C₄×C₉	—	2	1	no	—
142	C₃×C₄×C₉	—	2	1	no	—
143	C₃×C₄×C₉	—	2	1	no	—
144	C₃×C₄×C₉	#41	1	2	yes	—
145	C₉×Dic₃	—	2	2	no	—
146	C₉×Dic₃	—	2	2	no	—
147	C₉×Dic₃	—	2	2	no	—
148	C₃×C₄⋊Q₈	—	3	1	no	—
149	C₃×#126	—	3	2	no	—
150	C₃×#124	—	3	2	no	—
151	C₃×#124	—	3	1	no	—
152	C₃×#123	—	3	2	no	—
153	C₃×C₂²⋊Q₈	—	3	1	no	—
154	C₃×C₂²⋊Q₈	—	3	2	no	—
155	C₃×#121	—	3	1	no	—
156	C₃×C₄×Q₈	—	3	1	no	—
157	C₃×C₄×D₄	—	3	1	no	—
158	C₃×#117	—	2	1	no	—
159	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
160	C₃×#117	C₃×D₃	1	1	yes	characteristic
161	#930	C₂×C₉	1	1	yes	characteristic
162	#924	C₂×C₉	1	1	yes	characteristic, complemented
163	#898	C₂×C₉	1	2	yes	complemented
164	#896	C₂×C₉	1	2	yes	complemented
165	#885	C₂×C₉	1	2	yes	complemented
166	#883	C₂×C₉	1	2	yes	complemented
167	#875	C₂×C₉	1	1	yes	characteristic, complemented
168	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
169	#869	C₂×C₉	1	1	yes	characteristic, complemented
170	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
171	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
172	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₃×#67	—	4	2	no	—
181	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
182	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
183	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
184	C₃×D₁₂	—	2	2	no	—
185	C₃×C₄×D₃	—	4	2	no	—
186	C₃×Dic₆	—	2	2	no	—
187	C₃×Dic₆	—	4	2	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	3	2	no	—
190	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
191	Q₈×C₉	—	6	2	no	—
192	Q₈×C₉	—	12	2	no	—
193	D₄×C₉	—	6	2	no	—
194	D₄×C₉	—	12	2	no	—
195	C₂×C₄×C₉	—	2	4	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	3	2	no	—
204	C₂×C₄×C₉	—	3	2	no	—
205	C₂×C₄×C₉	—	3	2	no	—
206	C₂×C₄×C₉	—	12	2	no	—
207	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
209	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
210	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
211	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
212	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
213	#542	—	3	1	no	Sylow
214	C₂×C₃×C₉	—	4	1	no	—
215	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
218	D₃×C₉	—	4	2	no	—
219	C₂×C₃×Q₈	—	3	1	no	—
220	C₂×C₃×Q₈	—	3	2	no	—
221	C₂×C₃×D₄	—	3	2	no	—
222	C₂×C₃×D₄	—	3	1	no	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	—	3	2	no	—
225	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
227	C₂×#67	C₂²×C₉	1	2	yes	—
228	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
229	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
230	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
231	C₂×Dic₆	C₂²×C₉	1	2	yes	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	—	3	2	no	—
236	C₃×C₄⋊C₄	—	3	1	no	—
237	C₃×C₄⋊C₄	—	3	1	no	—
238	C₃×C₄⋊C₄	—	3	2	no	—
239	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
241	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
243	C₃×C₂²⋊C₄	—	2	1	no	—
244	C₃×C₂²⋊C₄	—	2	1	no	—
245	C₃×C₂²⋊C₄	—	3	2	no	—
246	C₃×C₂²⋊C₄	—	3	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₂²⋊C₄	—	3	2	no	—
249	C₃×C₂²⋊C₄	—	3	2	no	—
250	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
251	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
252	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
253	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
254	C₃×C₄²	—	2	1	no	—
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	—	3	2	no	—
257	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
258	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
259	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
260	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
261	#217	C₂²×C₉	1	2	yes	—
262	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
263	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
264	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
265	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
266	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
267	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
268	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
269	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
270	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
271	C₄×Dic₃	C₂²×C₉	1	2	yes	—
272	C₂²×C₃²	—	2	1	no	—
273	C₂²×C₃²	—	2	1	no	—
274	C₂²×C₃²	—	2	1	no	—
275	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
276	C₂×C₃×D₃	—	2	2	no	—
277	C₂×C₃×D₃	—	2	2	no	—
278	C₂×C₃×D₃	—	2	2	no	—
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	—	2	1	no	—
281	C₃²×C₄	—	2	1	no	—
282	C₃²×C₄	—	2	1	no	—
283	C₃²×C₄	—	2	1	no	—
284	C₃²×C₄	C₃×#41	1	2	yes	—
285	C₃×Dic₃	—	2	2	no	—
286	C₃×Dic₃	—	2	2	no	—
287	C₃×Dic₃	—	2	2	no	—
288	C₂²×C₉	—	2	2	no	—
289	C₂²×C₉	—	2	1	no	—
290	C₂²×C₉	—	2	1	no	—
291	C₂²×C₉	—	2	1	no	—
292	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	1	no	—
295	C₂²×C₉	—	6	2	no	—
296	C₂²×C₉	—	6	2	no	—
297	C₂²×C₉	—	6	2	no	—
298	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
299	C₄×C₉	—	2	2	no	—
300	C₄×C₉	—	2	1	no	—
301	C₄×C₉	—	2	1	no	—
302	C₄×C₉	—	2	1	no	—
303	C₄×C₉	—	2	1	no	—
304	C₄×C₉	—	2	1	no	—
305	C₄×C₉	—	2	2	no	—
306	C₄×C₉	—	4	1	no	—
307	C₄×C₉	—	4	1	no	—
308	C₄×C₉	—	4	1	no	—
309	C₄×C₉	—	4	1	no	—
310	C₄×C₉	—	6	2	no	—
311	C₄×C₉	—	6	2	no	—
312	C₄×C₉	—	6	2	no	—
313	C₄×C₉	#235	1	2	yes	—
314	C₄⋊Q₈	—	3	1	no	—
315	#126	—	3	2	no	—
316	#124	—	3	2	no	—
317	#124	—	3	1	no	—
318	#123	—	3	2	no	—
319	C₂²⋊Q₈	—	3	1	no	—
320	C₂²⋊Q₈	—	3	2	no	—
321	#121	—	3	1	no	—
322	C₄×Q₈	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	#117	D₃×C₉	1	1	yes	characteristic, complemented
325	C₃×C₉	#542	1	1	yes	characteristic, complemented, Sylow
326	C₂³×C₃	—	2	1	no	—
327	C₂³×C₃	—	3	2	no	—
328	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
329	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
330	C₂²×D₃	C₂³×C₉	1	2	yes	—
331	C₃×Q₈	—	6	2	no	—
332	C₃×Q₈	—	12	2	no	—
333	C₃×D₄	—	6	2	no	—
334	C₃×D₄	—	12	2	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	3	2	no	—
345	C₂×C₃×C₄	—	3	2	no	—
346	C₂×C₃×C₄	—	3	2	no	—
347	C₂×C₃×C₄	—	12	2	no	—
348	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
360	#67	—	4	2	no	—
361	C₂×Dic₃	C₂³×C₉	1	2	yes	—
362	C₂×Dic₃	C₂³×C₉	1	2	yes	—
363	C₂×Dic₃	C₂³×C₉	1	2	yes	—
364	D₁₂	—	2	2	no	—
365	C₄×D₃	—	4	2	no	—
366	Dic₆	—	2	2	no	—
367	Dic₆	—	4	2	no	—
368	C₂×C₃²	—	4	1	no	—
369	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
370	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
372	C₃×D₃	—	4	2	no	—
373	C₂×C₉	—	2	1	no	—
374	C₂×C₉	—	2	1	no	—
375	C₂×C₉	—	2	1	no	—
376	C₂×C₉	—	4	2	no	—
377	C₂×C₉	—	4	1	no	—
378	C₂×C₉	—	12	2	no	—
379	C₂×C₉	C₂×#235	1	1	yes	characteristic
380	C₂×C₉	#1009	1	1	yes	characteristic
381	C₂×C₉	#1010	1	1	yes	characteristic
382	C₂×Q₈	—	3	1	no	—
383	C₂×Q₈	—	3	2	no	—
384	C₂×D₄	—	3	2	no	—
385	C₂×D₄	—	3	1	no	—
386	C₂²×C₄	—	3	2	no	—
387	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
388	C₄⋊C₄	—	3	1	no	—
389	C₄⋊C₄	—	3	1	no	—
390	C₄⋊C₄	—	3	2	no	—
391	C₄⋊C₄	—	3	2	no	—
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
395	C₂²⋊C₄	—	3	2	no	—
396	C₂²⋊C₄	—	3	2	no	—
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	—	3	2	no	—
400	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
401	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
402	C₄²	—	3	2	no	—
403	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
404	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	2	1	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	—	4	1	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	—	6	2	no	—
416	C₂²×C₃	—	6	2	no	—
417	C₂²×C₃	—	6	2	no	—
418	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
419	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
420	C₂×D₃	—	2	2	no	—
421	C₂×D₃	—	2	2	no	—
422	C₂×D₃	—	2	2	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	1	no	—
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	1	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	6	2	no	—
440	C₃×C₄	—	6	2	no	—
441	C₃×C₄	—	6	2	no	—
442	C₃×C₄	C₉×#41	1	2	yes	—
443	C₃×C₄	C₃×#235	1	2	yes	—
444	Dic₃	—	2	2	no	—
445	Dic₃	—	2	2	no	—
446	Dic₃	—	2	2	no	—
447	C₃²	C₃×#542	1	1	yes	characteristic
448	C₉	—	2	1	no	—
449	C₉	#5534	1	1	yes	characteristic, direct product factor
450	C₂³	—	3	2	no	—
451	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
452	Q₈	—	6	2	no	—
453	Q₈	—	12	2	no	—
454	D₄	—	6	2	no	—
455	D₄	—	12	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	3	2	no	—
458	C₂×C₄	—	3	2	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	12	2	no	—
461	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	4	2	no	—
471	C₂×C₃	—	4	1	no	—
472	C₂×C₃	—	4	1	no	—
473	C₂×C₃	—	12	2	no	—
474	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
475	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
477	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
478	C₂×C₃	C₃×#1009	1	1	yes	characteristic
479	C₂×C₃	C₃×#1010	1	1	yes	characteristic
480	D₃	—	4	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	6	2	no	—
485	C₂²	—	6	2	no	—
486	C₂²	—	6	2	no	—
487	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	6	2	no	—
494	C₄	—	6	2	no	—
495	C₄	—	6	2	no	—
496	C₄	C₉×#235	1	2	yes	—
497	C₃	—	2	1	no	—
498	C₃	C₉×#542	1	1	yes	characteristic, complemented
499	C₃	C₃×#5534	1	1	yes	characteristic
500	C₂	—	4	1	no	—
501	C₂	—	12	2	no	—
502	C₂	C₂×C₉×#235	1	1	yes	characteristic
503	C₂	C₉×#1009	1	1	yes	characteristic
504	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×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#930	C₂×C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₉×#542
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#117	C₂	semidirect
3. C₉×#924	C₂	semidirect
4. C₉×#898	C₂	semidirect
5. C₉×#896	C₂	semidirect
6. C₉×#885	C₂	semidirect
7. C₉×#883	C₂	semidirect
8. C₉×#875	C₂	semidirect
9. C₄×C₉×D₁₂	C₂	semidirect
10. C₉×#869	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
59. C₉×#117	D₃	semidirect
78. #5534	C₉	direct (N × H)
159. C₃×#117	C₂×C₉	semidirect
162. #924	C₂×C₉	semidirect
163. #898	C₂×C₉	semidirect
164. #896	C₂×C₉	semidirect
165. #885	C₂×C₉	semidirect
166. #883	C₂×C₉	semidirect
167. #875	C₂×C₉	semidirect
168. C₄×D₁₂	C₂×C₉	semidirect
169. #869	C₂×C₉	semidirect
170. C₄×Dic₆	C₂×C₉	semidirect
324. #117	D₃×C₉	semidirect
325. C₃×C₉	#542	semidirect
449. C₉	#5534	direct (N × H)
498. C₃	C₉×#542	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#117	2
C₉×#930	2
C₉×#924	2
C₉×#898	2
C₉×#896	2
C₉×#885	2
C₉×#883	2
C₉×#875	2
C₄×C₉×D₁₂	2
C₉×#869	2
C₄×C₉×Dic₆	2
C₃×#5534	3
C₉×#542	3

Subgroups — C9×#5534 #13152505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5534 #13152505