Subgroups — C₉×#5666 #13153033

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 502 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×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#930	C₂	1	2	yes	maximal, complemented
5	C₉×#898	C₂	1	2	yes	maximal, complemented
6	C₉×#895	C₂	1	2	yes	maximal, complemented
7	C₉×#884	C₂	1	2	yes	maximal, complemented
8	C₉×#883	C₂	1	2	yes	maximal, complemented
9	C₉×#882	C₂	1	2	yes	maximal, complemented
10	C₃×#5666	C₃	1	1	yes	maximal, characteristic
11	C₉×#560	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	2	yes	complemented
18	C₂×C₉×D₁₂	C₂²	1	2	yes	—
19	C₂×C₉×D₁₂	C₂²	1	2	yes	—
20	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
22	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₉×#217	C₂²	1	1	yes	characteristic
26	C₉×(C₂×D₃)⋊C₄	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	complemented
30	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
32	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#123	C₂×C₃	1	1	yes	characteristic
34	C₃×#940	C₂×C₃	1	1	yes	characteristic
35	C₃×#937	C₂×C₃	1	1	yes	characteristic
36	C₃×#930	C₂×C₃	1	2	yes	—
37	C₃×#898	C₂×C₃	1	2	yes	—
38	C₃×#895	C₂×C₃	1	2	yes	—
39	C₃×#884	C₂×C₃	1	2	yes	—
40	C₃×#883	C₂×C₃	1	2	yes	—
41	C₃×#882	C₂×C₃	1	2	yes	—
42	C₉×#127	—	3	1	no	—
43	C₉×#126	—	3	2	no	—
44	C₉×#123	—	2	1	no	—
45	C₉×#123	—	3	2	no	—
46	C₉×#123	D₃	1	1	yes	characteristic, complemented
47	C₉×#121	—	3	2	no	—
48	C₉×#121	—	3	2	no	—
49	C₉×#121	—	3	2	no	—
50	C₉×#120	—	3	1	no	—
51	C₉×#120	—	3	2	no	—
52	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
53	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
54	C₂²×D₃×C₉	—	4	1	no	—
55	C₂²×D₃×C₉	—	4	2	no	—
56	C₂²×D₃×C₉	C₂³	1	2	yes	—
57	C₂²×D₃×C₉	C₂³	1	2	yes	—
58	C₃×D₄×C₉	—	4	1	no	—
59	C₂×C₃×C₄×C₉	—	4	1	no	—
60	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₉×#67	—	4	2	no	—
64	C₉×#67	—	4	2	no	—
65	C₉×#67	—	4	2	no	—
66	C₂×C₉×Dic₃	C₂³	1	2	yes	—
67	C₂×C₉×Dic₃	C₂³	1	2	yes	—
68	C₉×D₁₂	—	4	2	no	—
69	C₉×D₁₂	—	4	2	no	—
70	C₉×D₁₂	—	4	1	no	—
71	C₄×D₃×C₉	—	4	2	no	—
72	C₃×#560	—	3	1	no	—
73	#5666	C₉	1	1	yes	characteristic, direct product factor
74	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
78	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
79	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
80	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
81	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
82	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
84	C₂⁴×C₉	—	3	1	no	—
85	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₃×#217	C₂²×C₃	1	1	yes	characteristic
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
96	C₂×D₄×C₉	—	2	1	no	—
97	C₂×D₄×C₉	—	3	2	no	—
98	C₂×D₄×C₉	—	3	2	no	—
99	C₂×D₄×C₉	—	3	2	no	—
100	C₂×D₄×C₉	—	3	2	no	—
101	C₂×D₄×C₉	—	3	2	no	—
102	C₂×D₄×C₉	—	3	1	no	—
103	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	—	3	2	no	—
106	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
107	C₉×C₄⋊C₄	—	2	2	no	—
108	C₉×C₄⋊C₄	—	3	2	no	—
109	C₉×C₄⋊C₄	—	3	2	no	—
110	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
111	C₉×C₂²⋊C₄	—	2	2	no	—
112	C₉×C₂²⋊C₄	—	2	1	no	—
113	C₉×C₂²⋊C₄	—	3	1	no	—
114	C₉×C₂²⋊C₄	—	3	2	no	—
115	C₉×C₂²⋊C₄	—	3	2	no	—
116	C₉×C₂²⋊C₄	—	3	2	no	—
117	C₉×C₂²⋊C₄	—	3	2	no	—
118	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
120	C₄²×C₉	—	3	1	no	—
121	C₂²×C₃×C₉	—	2	1	no	—
122	C₂²×C₃×C₉	—	2	2	no	—
123	C₂²×C₃×C₉	—	2	2	no	—
124	C₂²×C₃×C₉	—	2	1	no	—
125	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
126	C₂×D₃×C₉	—	2	2	no	—
127	C₂×D₃×C₉	—	2	2	no	—
128	C₂×D₃×C₉	—	2	2	no	—
129	C₂×D₃×C₉	—	2	2	no	—
130	C₂×D₃×C₉	—	2	2	no	—
131	C₂×D₃×C₉	—	2	2	no	—
132	C₂×D₃×C₉	—	4	4	no	—
133	C₃×C₄×C₉	—	2	2	no	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	1	no	—
136	C₉×Dic₃	—	2	2	no	—
137	C₉×Dic₃	—	2	2	no	—
138	C₃×#127	—	3	1	no	—
139	C₃×#126	—	3	2	no	—
140	C₃×#123	—	2	1	no	—
141	C₃×#123	—	3	2	no	—
142	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
143	C₃×#123	C₃×D₃	1	1	yes	characteristic
144	C₃×#121	—	3	2	no	—
145	C₃×#121	—	3	2	no	—
146	C₃×#121	—	3	2	no	—
147	C₃×#120	—	3	1	no	—
148	C₃×#120	—	3	2	no	—
149	#940	C₂×C₉	1	1	yes	characteristic, complemented
150	#937	C₂×C₉	1	1	yes	characteristic, complemented
151	#930	C₂×C₉	1	2	yes	complemented
152	#898	C₂×C₉	1	2	yes	complemented
153	#895	C₂×C₉	1	2	yes	complemented
154	#884	C₂×C₉	1	2	yes	complemented
155	#883	C₂×C₉	1	2	yes	complemented
156	#882	C₂×C₉	1	2	yes	complemented
157	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
158	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×D₃	—	4	1	no	—
160	C₂²×C₃×D₃	—	4	2	no	—
161	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
162	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
163	C₃²×D₄	—	4	1	no	—
164	C₂×C₃²×C₄	—	4	1	no	—
165	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
167	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
168	C₃×#67	—	4	2	no	—
169	C₃×#67	—	4	2	no	—
170	C₃×#67	—	4	2	no	—
171	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
172	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
173	C₃×D₁₂	—	4	2	no	—
174	C₃×D₁₂	—	4	2	no	—
175	C₃×D₁₂	—	4	1	no	—
176	C₃×C₄×D₃	—	4	2	no	—
177	C₂³×C₉	—	2	1	no	—
178	C₂³×C₉	—	2	1	no	—
179	C₂³×C₉	—	3	2	no	—
180	C₂³×C₉	—	3	2	no	—
181	C₂³×C₉	—	12	1	no	—
182	C₂³×C₉	—	12	2	no	—
183	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
184	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
185	D₄×C₉	—	4	1	no	—
186	D₄×C₉	—	4	2	no	—
187	D₄×C₉	—	12	2	no	—
188	D₄×C₉	—	12	1	no	—
189	D₄×C₉	—	12	2	no	—
190	D₄×C₉	—	12	2	no	—
191	D₄×C₉	—	12	2	no	—
192	D₄×C₉	—	12	2	no	—
193	C₂×C₄×C₉	—	2	2	no	—
194	C₂×C₄×C₉	—	2	2	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	3	2	no	—
197	C₂×C₄×C₉	—	3	2	no	—
198	C₂×C₄×C₉	—	4	1	no	—
199	C₂×C₄×C₉	—	4	2	no	—
200	C₂×C₄×C₉	—	12	2	no	—
201	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
203	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
204	#560	—	3	1	no	Sylow
205	C₂×C₃×C₉	—	4	1	no	—
206	C₂×C₃×C₉	—	4	1	no	—
207	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
209	D₃×C₉	—	4	2	no	—
210	D₃×C₉	—	4	2	no	—
211	C₂⁴×C₃	—	3	1	no	—
212	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₃×D₄	—	2	1	no	—
214	C₂×C₃×D₄	—	3	2	no	—
215	C₂×C₃×D₄	—	3	2	no	—
216	C₂×C₃×D₄	—	3	2	no	—
217	C₂×C₃×D₄	—	3	2	no	—
218	C₂×C₃×D₄	—	3	2	no	—
219	C₂×C₃×D₄	—	3	1	no	—
220	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	—	3	2	no	—
224	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
225	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
226	C₂×#67	C₂²×C₉	1	2	yes	—
227	C₂×#67	C₂²×C₉	1	2	yes	—
228	C₂×#67	C₂²×C₉	1	2	yes	complemented
229	C₂×D₁₂	C₂²×C₉	1	2	yes	—
230	C₂×D₁₂	C₂²×C₉	1	2	yes	—
231	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
232	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
233	C₃×C₄⋊C₄	—	2	2	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	—	3	2	no	—
236	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
237	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
238	C₃×C₂²⋊C₄	—	2	2	no	—
239	C₃×C₂²⋊C₄	—	2	1	no	—
240	C₃×C₂²⋊C₄	—	3	1	no	—
241	C₃×C₂²⋊C₄	—	3	2	no	—
242	C₃×C₂²⋊C₄	—	3	2	no	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
246	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
247	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
248	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
249	C₃×C₄²	—	3	1	no	—
250	#217	C₂²×C₉	1	1	yes	characteristic
251	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
253	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
254	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
255	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
256	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
257	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
258	C₂²×C₃²	—	2	1	no	—
259	C₂²×C₃²	—	2	2	no	—
260	C₂²×C₃²	—	2	2	no	—
261	C₂²×C₃²	—	2	1	no	—
262	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃×D₃	—	2	2	no	—
264	C₂×C₃×D₃	—	2	2	no	—
265	C₂×C₃×D₃	—	2	2	no	—
266	C₂×C₃×D₃	—	2	2	no	—
267	C₂×C₃×D₃	—	2	2	no	—
268	C₂×C₃×D₃	—	2	2	no	—
269	C₂×C₃×D₃	—	4	4	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	—	2	2	no	—
272	C₃²×C₄	—	2	1	no	—
273	C₃×Dic₃	—	2	2	no	—
274	C₃×Dic₃	—	2	2	no	—
275	C₂²×C₉	—	2	2	no	—
276	C₂²×C₉	—	2	1	no	—
277	C₂²×C₉	—	2	1	no	—
278	C₂²×C₉	—	2	2	no	—
279	C₂²×C₉	—	2	2	no	—
280	C₂²×C₉	—	2	1	no	—
281	C₂²×C₉	—	4	2	no	—
282	C₂²×C₉	—	4	1	no	—
283	C₂²×C₉	—	4	2	no	—
284	C₂²×C₉	—	6	2	no	—
285	C₂²×C₉	—	6	2	no	—
286	C₂²×C₉	—	6	2	no	—
287	C₂²×C₉	—	6	2	no	—
288	C₂²×C₉	—	6	2	no	—
289	C₂²×C₉	—	6	2	no	—
290	C₂²×C₉	—	12	4	no	—
291	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
292	C₄×C₉	—	2	2	no	—
293	C₄×C₉	—	2	1	no	—
294	C₄×C₉	—	2	2	no	—
295	C₄×C₉	—	4	2	no	—
296	C₄×C₉	—	4	2	no	—
297	C₄×C₉	—	4	1	no	—
298	C₄×C₉	—	6	2	no	—
299	C₄×C₉	—	6	2	no	—
300	#127	—	3	1	no	—
301	#126	—	3	2	no	—
302	#123	—	3	2	no	—
303	#123	D₃×C₉	1	1	yes	characteristic, complemented
304	#121	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#120	—	3	1	no	—
308	#120	—	3	2	no	—
309	C₃×C₉	#560	1	1	yes	characteristic, complemented, Sylow
310	C₂³×C₃	—	2	1	no	—
311	C₂³×C₃	—	2	1	no	—
312	C₂³×C₃	—	3	2	no	—
313	C₂³×C₃	—	3	2	no	—
314	C₂³×C₃	—	12	1	no	—
315	C₂³×C₃	—	12	2	no	—
316	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
317	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
318	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
319	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
320	C₂²×D₃	—	4	1	no	—
321	C₂²×D₃	—	4	2	no	—
322	C₂²×D₃	C₂³×C₉	1	2	yes	—
323	C₂²×D₃	C₂³×C₉	1	2	yes	—
324	C₃×D₄	—	4	1	no	—
325	C₃×D₄	—	4	1	no	—
326	C₃×D₄	—	4	2	no	—
327	C₃×D₄	—	12	2	no	—
328	C₃×D₄	—	12	1	no	—
329	C₃×D₄	—	12	2	no	—
330	C₃×D₄	—	12	2	no	—
331	C₃×D₄	—	12	2	no	—
332	C₃×D₄	—	12	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	3	2	no	—
337	C₂×C₃×C₄	—	3	2	no	—
338	C₂×C₃×C₄	—	4	1	no	—
339	C₂×C₃×C₄	—	4	1	no	—
340	C₂×C₃×C₄	—	4	2	no	—
341	C₂×C₃×C₄	—	12	2	no	—
342	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
344	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
345	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
348	#67	—	4	2	no	—
349	#67	—	4	2	no	—
350	#67	—	4	2	no	—
351	C₂×Dic₃	C₂³×C₉	1	2	yes	—
352	C₂×Dic₃	C₂³×C₉	1	2	yes	—
353	D₁₂	—	4	2	no	—
354	D₁₂	—	4	2	no	—
355	D₁₂	—	4	1	no	—
356	C₄×D₃	—	4	2	no	—
357	C₂×C₃²	—	4	1	no	—
358	C₂×C₃²	—	4	1	no	—
359	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
361	C₃×D₃	—	4	2	no	—
362	C₃×D₃	—	4	2	no	—
363	C₂×C₉	—	2	1	no	—
364	C₂×C₉	—	2	2	no	—
365	C₂×C₉	—	4	2	no	—
366	C₂×C₉	—	4	1	no	—
367	C₂×C₉	—	4	1	no	—
368	C₂×C₉	—	8	1	no	—
369	C₂×C₉	—	12	2	no	—
370	C₂×C₉	—	12	2	no	—
371	C₂×C₉	#1004	1	1	yes	characteristic
372	C₂×C₉	#1009	1	2	yes	—
373	C₂⁴	—	3	1	no	—
374	C₂×D₄	—	3	2	no	—
375	C₂×D₄	—	3	2	no	—
376	C₂×D₄	—	3	2	no	—
377	C₂×D₄	—	3	2	no	—
378	C₂×D₄	—	3	2	no	—
379	C₂×D₄	—	3	1	no	—
380	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
381	C₂²×C₄	—	3	2	no	—
382	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
386	C₂²⋊C₄	—	3	1	no	—
387	C₂²⋊C₄	—	3	2	no	—
388	C₂²⋊C₄	—	3	2	no	—
389	C₂²⋊C₄	—	3	2	no	—
390	C₂²⋊C₄	—	3	2	no	—
391	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
392	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
393	C₄²	—	3	1	no	—
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	4	2	no	—
405	C₂²×C₃	—	4	1	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	6	2	no	—
408	C₂²×C₃	—	6	2	no	—
409	C₂²×C₃	—	6	2	no	—
410	C₂²×C₃	—	6	2	no	—
411	C₂²×C₃	—	6	2	no	—
412	C₂²×C₃	—	6	2	no	—
413	C₂²×C₃	—	12	4	no	—
414	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
415	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
416	C₂×D₃	—	2	2	no	—
417	C₂×D₃	—	2	2	no	—
418	C₂×D₃	—	2	2	no	—
419	C₂×D₃	—	2	2	no	—
420	C₂×D₃	—	2	2	no	—
421	C₂×D₃	—	2	2	no	—
422	C₂×D₃	—	4	4	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	—	4	1	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	—	6	2	no	—
433	C₃×C₄	—	6	2	no	—
434	Dic₃	—	2	2	no	—
435	Dic₃	—	2	2	no	—
436	C₃²	C₃×#560	1	1	yes	characteristic
437	C₉	—	2	1	no	—
438	C₉	#5666	1	1	yes	characteristic, direct product factor
439	C₂³	—	3	2	no	—
440	C₂³	—	3	2	no	—
441	C₂³	—	12	1	no	—
442	C₂³	—	12	2	no	—
443	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
444	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
445	D₄	—	4	1	no	—
446	D₄	—	12	2	no	—
447	D₄	—	12	1	no	—
448	D₄	—	12	2	no	—
449	D₄	—	12	2	no	—
450	D₄	—	12	2	no	—
451	D₄	—	12	2	no	—
452	C₂×C₄	—	3	2	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	12	2	no	—
456	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
458	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
459	C₂×C₃	—	2	1	no	—
460	C₂×C₃	—	2	2	no	—
461	C₂×C₃	—	4	2	no	—
462	C₂×C₃	—	4	1	no	—
463	C₂×C₃	—	4	1	no	—
464	C₂×C₃	—	4	1	no	—
465	C₂×C₃	—	4	1	no	—
466	C₂×C₃	—	8	1	no	—
467	C₂×C₃	—	12	2	no	—
468	C₂×C₃	—	12	2	no	—
469	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
471	C₂×C₃	C₃×#1004	1	1	yes	characteristic
472	C₂×C₃	C₃×#1009	1	2	yes	—
473	D₃	—	4	2	no	—
474	D₃	—	4	2	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	6	2	no	—
480	C₂²	—	6	2	no	—
481	C₂²	—	6	2	no	—
482	C₂²	—	6	2	no	—
483	C₂²	—	6	2	no	—
484	C₂²	—	6	2	no	—
485	C₂²	—	12	4	no	—
486	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	6	2	no	—
491	C₄	—	6	2	no	—
492	C₃	—	2	1	no	—
493	C₃	C₉×#560	1	1	yes	characteristic, complemented
494	C₃	C₃×#5666	1	1	yes	characteristic
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	12	2	no	—
498	C₂	—	12	2	no	—
499	C₂	C₉×#1004	1	1	yes	characteristic
500	C₂	C₉×#1009	1	2	yes	—

	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×#5666	C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#560
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×#940	C₂	semidirect
3. C₉×#937	C₂	semidirect
4. C₉×#930	C₂	semidirect
5. C₉×#898	C₂	semidirect
6. C₉×#895	C₂	semidirect
7. C₉×#884	C₂	semidirect
8. C₉×#883	C₂	semidirect
9. C₉×#882	C₂	semidirect
14. C₂²×C₃×C₄×C₉	C₂²	semidirect
17. C₂×C₉×#67	C₂²	semidirect
20. C₂×C₉×D₁₂	C₂²	semidirect
21. C₂×C₄×D₃×C₉	C₂²	semidirect
22. C₃×C₉×C₄⋊C₄	C₂²	semidirect
24. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
29. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
30. C₉×C₄⋊Dic₃	C₂²	semidirect
31. C₉×Dic₃⋊C₄	C₂²	semidirect
32. C₄×C₉×Dic₃	C₂²	semidirect
46. C₉×#123	D₃	semidirect
73. #5666	C₉	direct (N × H)
106. C₂²×C₄×C₉	C₂×D₃	semidirect
110. C₉×C₄⋊C₄	C₂×D₃	semidirect
119. C₉×C₂²⋊C₄	C₂×D₃	semidirect
142. C₃×#123	C₂×C₉	semidirect
149. #940	C₂×C₉	semidirect
150. #937	C₂×C₉	semidirect
151. #930	C₂×C₉	semidirect
152. #898	C₂×C₉	semidirect
153. #895	C₂×C₉	semidirect
154. #884	C₂×C₉	semidirect
155. #883	C₂×C₉	semidirect
156. #882	C₂×C₉	semidirect
224. C₂²×C₃×C₄	C₂²×C₉	semidirect
228. C₂×#67	C₂²×C₉	semidirect
231. C₂×D₁₂	C₂²×C₉	semidirect
232. C₂×C₄×D₃	C₂²×C₉	semidirect
236. C₃×C₄⋊C₄	C₂²×C₉	semidirect
246. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
254. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
255. C₄⋊Dic₃	C₂²×C₉	semidirect
256. Dic₃⋊C₄	C₂²×C₉	semidirect
257. C₄×Dic₃	C₂²×C₉	semidirect
303. #123	D₃×C₉	semidirect
309. C₃×C₉	#560	semidirect
382. C₂²×C₄	C₂×D₃×C₉	semidirect
385. C₄⋊C₄	C₂×D₃×C₉	semidirect
392. C₂²⋊C₄	C₂×D₃×C₉	semidirect
438. C₉	#5666	direct (N × H)
493. C₃	C₉×#560	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×#940	2
C₉×#937	2
C₉×#930	2
C₉×#898	2
C₉×#895	2
C₉×#884	2
C₉×#883	2
C₉×#882	2
C₃×#5666	3
C₉×#560	3

Subgroups — C9×#5666 #13153033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5666 #13153033