Subgroups — C₉×#5791 #13153546

Order 1728.

1226 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#953	C₂	1	2	yes	maximal, complemented
4	C₉×#930	C₂	1	2	yes	maximal, complemented
5	C₉×#929	C₂	1	2	yes	maximal, complemented
6	C₄×C₉×#67	C₂	1	4	yes	maximal, complemented
7	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#924	C₂	1	2	yes	maximal, complemented
9	C₃×#5791	C₃	1	1	yes	maximal, characteristic
10	C₉×#525	—	3	1	no	maximal
11	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	—	2	4	no	—
13	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	4	yes	—
19	C₉×#235	—	2	4	no	—
20	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
22	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₉×#217	C₂²	1	4	yes	—
24	C₉×#217	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
26	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
27	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
28	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
29	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
31	C₃×#953	C₂×C₃	1	2	yes	—
32	C₃×#930	C₂×C₃	1	2	yes	—
33	C₃×#929	C₂×C₃	1	2	yes	—
34	C₃×C₄×#67	C₂×C₃	1	4	yes	—
35	C₃×#926	C₂×C₃	1	1	yes	characteristic
36	C₃×#924	C₂×C₃	1	2	yes	—
37	C₂×C₉×#41	—	3	1	no	—
38	C₂³×C₄×C₉	—	2	1	no	—
39	C₂³×C₄×C₉	D₃	1	1	yes	characteristic, complemented
40	C₉×#123	—	3	2	no	—
41	C₉×C₂²⋊Q₈	—	3	2	no	—
42	C₉×#121	—	3	2	no	—
43	C₉×#120	—	3	2	no	—
44	C₄×D₄×C₉	—	3	4	no	—
45	C₉×#117	—	3	1	no	—
46	C₂³×C₃×C₉	—	2	2	no	—
47	C₂³×C₃×C₉	—	2	4	no	—
48	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
49	C₂³×C₃×C₉	C₂³	1	2	yes	—
50	C₂²×D₃×C₉	C₂³	1	2	yes	—
51	C₂×C₃×C₄×C₉	—	2	2	no	—
52	C₂×C₃×C₄×C₉	—	2	4	no	—
53	C₂×C₃×C₄×C₉	—	2	4	no	—
54	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
55	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₉×#67	—	2	4	no	—
59	C₉×#67	—	2	8	no	—
60	C₂×C₉×Dic₃	C₂³	1	2	yes	—
61	C₂×C₉×Dic₃	C₂³	1	4	yes	—
62	C₉×D₁₂	—	2	2	no	—
63	C₄×D₃×C₉	—	2	4	no	—
64	C₉×Dic₆	—	2	2	no	—
65	C₃×#525	—	3	1	no	—
66	#5791	C₉	1	1	yes	characteristic, direct product factor
67	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃²×C₄	—	2	4	no	—
69	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
70	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
71	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
74	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
75	C₃×#235	—	2	4	no	—
76	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
78	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
79	C₂⁴×C₉	—	2	1	no	—
80	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
81	C₃×#217	C₂²×C₃	1	4	yes	—
82	C₃×#217	C₂²×C₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
84	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
85	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
87	C₉×#41	—	6	4	no	—
88	C₂×Q₈×C₉	—	3	1	no	—
89	C₂×D₄×C₉	—	3	4	no	—
90	C₂×D₄×C₉	—	3	2	no	—
91	C₂×D₄×C₉	—	3	1	no	—
92	C₂²×C₄×C₉	—	2	8	no	—
93	C₂²×C₄×C₉	—	2	2	no	—
94	C₂²×C₄×C₉	—	2	2	no	—
95	C₂²×C₄×C₉	—	2	1	no	—
96	C₂²×C₄×C₉	—	2	1	no	—
97	C₂²×C₄×C₉	—	2	4	no	—
98	C₂²×C₄×C₉	—	3	2	no	—
99	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
100	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
101	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
102	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
103	C₉×C₄⋊C₄	—	3	2	no	—
104	C₉×C₄⋊C₄	—	3	4	no	—
105	C₉×C₂²⋊C₄	—	3	2	no	—
106	C₉×C₂²⋊C₄	—	3	4	no	—
107	C₉×C₂²⋊C₄	—	3	4	no	—
108	C₄²×C₉	—	3	2	no	—
109	C₂²×C₃×C₉	—	2	8	no	—
110	C₂²×C₃×C₉	—	2	2	no	—
111	C₂²×C₃×C₉	—	2	2	no	—
112	C₂²×C₃×C₉	—	2	2	no	—
113	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
114	C₂²×C₃×C₉	#41	1	4	yes	complemented
115	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
116	C₂×D₃×C₉	—	2	2	no	—
117	C₂×D₃×C₉	—	2	4	no	—
118	C₃×C₄×C₉	—	2	2	no	—
119	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
120	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
121	C₉×Dic₃	—	2	2	no	—
122	C₉×Dic₃	—	2	4	no	—
123	C₂×C₃×#41	—	3	1	no	—
124	C₂³×C₃×C₄	—	2	1	no	—
125	C₂³×C₃×C₄	C₂×C₉	1	1	yes	characteristic, complemented
126	C₂³×C₃×C₄	C₃×D₃	1	1	yes	characteristic
127	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
128	C₃×#123	—	3	2	no	—
129	C₃×C₂²⋊Q₈	—	3	2	no	—
130	C₃×#121	—	3	2	no	—
131	C₃×#120	—	3	2	no	—
132	C₃×C₄×D₄	—	3	4	no	—
133	C₃×#117	—	3	1	no	—
134	#953	C₂×C₉	1	2	yes	complemented
135	#930	C₂×C₉	1	2	yes	complemented
136	#929	C₂×C₉	1	2	yes	complemented
137	C₄×#67	C₂×C₉	1	4	yes	complemented
138	#926	C₂×C₉	1	1	yes	characteristic, complemented
139	#924	C₂×C₉	1	2	yes	complemented
140	C₂³×C₃²	—	2	2	no	—
141	C₂³×C₃²	—	2	4	no	—
142	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
143	C₂³×C₃²	C₂³×C₃	1	2	yes	—
144	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
145	C₂×C₃²×C₄	—	2	2	no	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	4	no	—
148	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
152	C₃×#67	—	2	4	no	—
153	C₃×#67	—	2	8	no	—
154	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
155	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
156	C₃×D₁₂	—	2	2	no	—
157	C₃×C₄×D₃	—	2	4	no	—
158	C₃×Dic₆	—	2	2	no	—
159	C₂³×C₉	—	2	4	no	—
160	C₂³×C₉	—	2	8	no	—
161	C₂³×C₉	—	2	4	no	—
162	C₂³×C₉	—	2	2	no	—
163	C₂³×C₉	—	2	2	no	—
164	C₂³×C₉	—	2	1	no	—
165	C₂³×C₉	—	3	2	no	—
166	C₂³×C₉	C₂²×D₃	1	2	yes	—
167	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
168	Q₈×C₉	—	6	2	no	—
169	D₄×C₉	—	6	8	no	—
170	D₄×C₉	—	6	4	no	—
171	D₄×C₉	—	6	2	no	—
172	C₂×C₄×C₉	—	2	4	no	—
173	C₂×C₄×C₉	—	2	8	no	—
174	C₂×C₄×C₉	—	2	8	no	—
175	C₂×C₄×C₉	—	2	2	no	—
176	C₂×C₄×C₉	—	2	4	no	—
177	C₂×C₄×C₉	—	2	4	no	—
178	C₂×C₄×C₉	—	2	4	no	—
179	C₂×C₄×C₉	—	2	2	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	3	4	no	—
183	C₂×C₄×C₉	—	3	2	no	—
184	C₂×C₄×C₉	—	6	4	no	—
185	C₂×C₄×C₉	#67	1	4	yes	complemented
186	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
187	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
188	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
189	#525	—	3	1	no	Sylow
190	C₂×C₃×C₉	—	2	2	no	—
191	C₂×C₃×C₉	—	2	4	no	—
192	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×C₉	C₂×#41	1	2	yes	—
194	D₃×C₉	—	4	2	no	—
195	C₂⁴×C₃	—	2	1	no	—
196	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
197	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
198	C₃×#41	—	6	4	no	—
199	C₂×C₃×Q₈	—	3	1	no	—
200	C₂×C₃×D₄	—	3	4	no	—
201	C₂×C₃×D₄	—	3	2	no	—
202	C₂×C₃×D₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	2	8	no	—
204	C₂²×C₃×C₄	—	2	4	no	—
205	C₂²×C₃×C₄	—	2	4	no	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	3	2	no	—
211	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
212	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
213	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
216	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
217	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
219	C₂×#67	C₂²×C₉	1	4	yes	—
220	C₂×#67	C₂²×C₉	1	2	yes	—
221	#235	—	2	4	no	—
222	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
223	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
224	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
225	C₃×C₄⋊C₄	—	3	4	no	—
226	C₃×C₄⋊C₄	—	3	2	no	—
227	C₃×C₂²⋊C₄	—	3	2	no	—
228	C₃×C₂²⋊C₄	—	3	4	no	—
229	C₃×C₂²⋊C₄	—	3	4	no	—
230	C₃×C₄²	—	3	2	no	—
231	#217	C₂²×C₉	1	4	yes	—
232	#217	C₂²×C₉	1	2	yes	—
233	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
234	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
235	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
236	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
237	C₂²×C₃²	—	2	8	no	—
238	C₂²×C₃²	—	2	2	no	—
239	C₂²×C₃²	—	2	2	no	—
240	C₂²×C₃²	—	2	2	no	—
241	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
242	C₂²×C₃²	C₃×#41	1	4	yes	—
243	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
244	C₂×C₃×D₃	—	2	2	no	—
245	C₂×C₃×D₃	—	2	4	no	—
246	C₃²×C₄	—	2	2	no	—
247	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
248	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
249	C₃×Dic₃	—	2	2	no	—
250	C₃×Dic₃	—	2	4	no	—
251	C₂²×C₉	—	2	4	no	—
252	C₂²×C₉	—	2	16	no	—
253	C₂²×C₉	—	2	8	no	—
254	C₂²×C₉	—	2	4	no	—
255	C₂²×C₉	—	2	4	no	—
256	C₂²×C₉	—	2	2	no	—
257	C₂²×C₉	—	2	2	no	—
258	C₂²×C₉	—	2	2	no	—
259	C₂²×C₉	—	2	1	no	—
260	C₂²×C₉	—	2	4	no	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	6	4	no	—
263	C₂²×C₉	—	6	2	no	—
264	C₂²×C₉	#235	1	4	yes	complemented
265	C₂²×C₉	C₂×#67	1	2	yes	—
266	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
267	C₄×C₉	—	2	4	no	—
268	C₄×C₉	—	2	2	no	—
269	C₄×C₉	—	2	2	no	—
270	C₄×C₉	—	2	2	no	—
271	C₄×C₉	—	6	4	no	—
272	C₄×C₉	—	6	2	no	—
273	C₄×C₉	C₂×#67	1	2	yes	—
274	C₄×C₉	C₂×#67	1	2	yes	—
275	C₂×#41	—	3	1	no	—
276	C₂³×C₄	D₃×C₉	1	1	yes	characteristic, complemented
277	#123	—	3	2	no	—
278	C₂²⋊Q₈	—	3	2	no	—
279	#121	—	3	2	no	—
280	#120	—	3	2	no	—
281	C₄×D₄	—	3	4	no	—
282	#117	—	3	1	no	—
283	C₃×C₉	#525	1	1	yes	characteristic, complemented, Sylow
284	C₂³×C₃	—	2	4	no	—
285	C₂³×C₃	—	2	8	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	4	no	—
288	C₂³×C₃	—	2	4	no	—
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	2	no	—
291	C₂³×C₃	—	2	1	no	—
292	C₂³×C₃	—	3	2	no	—
293	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
294	C₂³×C₃	C₂³×C₉	1	2	yes	—
295	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
296	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
297	C₂²×D₃	C₂³×C₉	1	2	yes	—
298	C₃×Q₈	—	6	2	no	—
299	C₃×D₄	—	6	8	no	—
300	C₃×D₄	—	6	4	no	—
301	C₃×D₄	—	6	2	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	2	8	no	—
304	C₂×C₃×C₄	—	2	8	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	3	4	no	—
316	C₂×C₃×C₄	—	3	2	no	—
317	C₂×C₃×C₄	—	6	4	no	—
318	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
319	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
320	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
322	C₂×C₃×C₄	C₃×#67	1	4	yes	—
323	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
324	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
326	#67	—	2	4	no	—
327	#67	—	2	8	no	—
328	C₂×Dic₃	C₂³×C₉	1	4	yes	—
329	C₂×Dic₃	C₂³×C₉	1	2	yes	—
330	D₁₂	—	2	2	no	—
331	C₄×D₃	—	2	4	no	—
332	Dic₆	—	2	2	no	—
333	C₂×C₃²	—	2	2	no	—
334	C₂×C₃²	—	2	4	no	—
335	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
336	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
337	C₃×D₃	—	4	2	no	—
338	C₂×C₉	—	2	8	no	—
339	C₂×C₉	—	2	4	no	—
340	C₂×C₉	—	2	4	no	—
341	C₂×C₉	—	2	2	no	—
342	C₂×C₉	—	2	2	no	—
343	C₂×C₉	—	2	1	no	—
344	C₂×C₉	—	12	2	no	—
345	C₂×C₉	C₂×#235	1	2	yes	—
346	C₂×C₉	C₂²×#67	1	1	yes	characteristic
347	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
348	#41	—	6	4	no	—
349	C₂×Q₈	—	3	1	no	—
350	C₂×D₄	—	3	4	no	—
351	C₂×D₄	—	3	2	no	—
352	C₂×D₄	—	3	1	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	3	2	no	—
355	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
356	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
357	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
359	C₄⋊C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	4	no	—
361	C₂²⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	3	4	no	—
363	C₂²⋊C₄	—	3	4	no	—
364	C₄²	—	3	2	no	—
365	C₂²×C₃	—	2	4	no	—
366	C₂²×C₃	—	2	8	no	—
367	C₂²×C₃	—	2	16	no	—
368	C₂²×C₃	—	2	8	no	—
369	C₂²×C₃	—	2	4	no	—
370	C₂²×C₃	—	2	4	no	—
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	6	4	no	—
381	C₂²×C₃	—	6	2	no	—
382	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
383	C₂²×C₃	C₉×#41	1	4	yes	complemented
384	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
385	C₂²×C₃	C₃×#235	1	4	yes	—
386	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
387	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	—	2	4	no	—
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	6	4	no	—
396	C₃×C₄	—	6	2	no	—
397	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
398	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
399	C₃×C₄	C₂×C₃×#67	1	2	yes	—
400	C₃×C₄	C₂×C₃×#67	1	2	yes	—
401	Dic₃	—	2	2	no	—
402	Dic₃	—	2	4	no	—
403	C₃²	C₃×#525	1	1	yes	characteristic
404	C₉	—	2	1	no	—
405	C₉	#5791	1	1	yes	characteristic, direct product factor
406	C₂³	—	2	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	3	2	no	—
409	C₂³	C₂²×D₃×C₉	1	2	yes	—
410	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
411	Q₈	—	6	2	no	—
412	D₄	—	6	8	no	—
413	D₄	—	6	4	no	—
414	D₄	—	6	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	3	4	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	6	4	no	—
421	C₂×C₄	C₉×#67	1	4	yes	complemented
422	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
423	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
425	C₂×C₃	—	2	8	no	—
426	C₂×C₃	—	2	4	no	—
427	C₂×C₃	—	2	2	no	—
428	C₂×C₃	—	2	4	no	—
429	C₂×C₃	—	2	4	no	—
430	C₂×C₃	—	2	2	no	—
431	C₂×C₃	—	2	2	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	12	2	no	—
434	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
435	C₂×C₃	C₂×C₉×#41	1	2	yes	—
436	C₂×C₃	C₂×C₃×#235	1	2	yes	—
437	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
438	D₃	—	4	2	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	6	4	no	—
444	C₂²	—	6	2	no	—
445	C₂²	C₉×#235	1	4	yes	complemented
446	C₂²	C₂×C₉×#67	1	2	yes	—
447	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	6	4	no	—
450	C₄	—	6	2	no	—
451	C₄	C₂×C₉×#67	1	2	yes	—
452	C₄	C₂×C₉×#67	1	2	yes	—
453	C₃	—	2	1	no	—
454	C₃	C₉×#525	1	1	yes	characteristic, complemented
455	C₃	C₃×#5791	1	1	yes	characteristic
456	C₂	—	2	4	no	—
457	C₂	—	2	2	no	—
458	C₂	—	12	2	no	—
459	C₂	C₂×C₉×#235	1	2	yes	—
460	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂³×C₃×C₄×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5791	C₃
hypercenter	C₂³×C₄×C₉	D₃
hypocenter	C₃	C₉×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂³×C₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₄×C₉	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₉×#953	C₂	semidirect
4. C₉×#930	C₂	semidirect
5. C₉×#929	C₂	semidirect
6. C₄×C₉×#67	C₂	semidirect
7. C₉×#926	C₂	semidirect
8. C₉×#924	C₂	semidirect
20. C₂×C₉×D₁₂	C₂²	semidirect
21. C₂×C₄×D₃×C₉	C₂²	semidirect
22. C₂×C₉×Dic₆	C₂²	semidirect
25. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₉×C₄⋊Dic₃	C₂²	semidirect
27. C₉×Dic₃⋊C₄	C₂²	semidirect
28. C₄×C₉×Dic₃	C₂²	semidirect
39. C₂³×C₄×C₉	D₃	semidirect
54. C₂×C₃×C₄×C₉	D₄	semidirect
66. #5791	C₉	direct (N × H)
114. C₂²×C₃×C₉	#41	semidirect
125. C₂³×C₃×C₄	C₂×C₉	semidirect
127. C₂×#235	C₂×C₉	semidirect
134. #953	C₂×C₉	semidirect
135. #930	C₂×C₉	semidirect
136. #929	C₂×C₉	semidirect
137. C₄×#67	C₂×C₉	semidirect
138. #926	C₂×C₉	semidirect
139. #924	C₂×C₉	semidirect
185. C₂×C₄×C₉	#67	semidirect
222. C₂×D₁₂	C₂²×C₉	semidirect
223. C₂×C₄×D₃	C₂²×C₉	semidirect
224. C₂×Dic₆	C₂²×C₉	semidirect
233. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
234. C₄⋊Dic₃	C₂²×C₉	semidirect
235. Dic₃⋊C₄	C₂²×C₉	semidirect
236. C₄×Dic₃	C₂²×C₉	semidirect
264. C₂²×C₉	#235	semidirect
276. C₂³×C₄	D₃×C₉	semidirect
283. C₃×C₉	#525	semidirect
318. C₂×C₃×C₄	D₄×C₉	semidirect
383. C₂²×C₃	C₉×#41	semidirect
405. C₉	#5791	direct (N × H)
421. C₂×C₄	C₉×#67	semidirect
445. C₂²	C₉×#235	semidirect
454. C₃	C₉×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×C₉	2
C₂×C₉×#235	2
C₉×#953	2
C₉×#930	2
C₉×#929	2
C₄×C₉×#67	2
C₉×#926	2
C₉×#924	2
C₃×#5791	3
C₉×#525	3

Subgroups — C9×#5791 #13153546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5791 #13153546