Subgroups — C₉×#5589 #13152761

Order 1728.

1168 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#938	C₂	1	2	yes	maximal, complemented
6	C₉×#937	C₂	1	2	yes	maximal, complemented
7	C₉×#935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#884	C₂	1	2	yes	maximal, complemented
10	C₉×#883	C₂	1	2	yes	maximal, complemented
11	D₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5589	C₃	1	1	yes	maximal, characteristic
13	C₉×#534	—	3	1	no	maximal
14	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
19	C₂×C₉×#67	—	2	4	no	—
20	C₂×C₉×#67	C₂²	1	1	yes	characteristic
21	C₂×C₉×#67	C₂²	1	2	yes	—
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×#67	C₂²	1	2	yes	complemented
24	C₂×C₉×#67	C₂²	1	2	yes	complemented
25	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	D₃×D₄×C₉	—	2	4	no	—
27	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₉×#217	C₂²	1	2	yes	complemented
33	C₉×#217	C₂²	1	1	yes	characteristic, complemented
34	C₉×#217	C₂²	1	2	yes	complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
38	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
39	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
41	C₃²×#120	C₂×C₃	1	1	yes	characteristic
42	C₃×#953	C₂×C₃	1	1	yes	characteristic
43	C₃×#938	C₂×C₃	1	2	yes	—
44	C₃×#937	C₂×C₃	1	2	yes	—
45	C₃×#935	C₂×C₃	1	1	yes	characteristic
46	C₃×#886	C₂×C₃	1	1	yes	characteristic
47	C₃×#884	C₂×C₃	1	2	yes	—
48	C₃×#883	C₂×C₃	1	2	yes	—
49	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂²×D₄×C₉	—	3	1	no	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₉×#123	—	3	1	no	—
53	C₉×#123	—	3	2	no	—
54	C₉×#123	—	3	1	no	—
55	C₉×#121	—	3	2	no	—
56	C₉×#121	—	3	2	no	—
57	C₉×#120	—	2	1	no	—
58	C₉×#120	—	3	1	no	—
59	C₉×#120	—	3	2	no	—
60	C₉×#120	D₃	1	1	yes	characteristic, complemented
61	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
62	C₂³×C₃×C₉	—	2	2	no	—
63	C₂³×C₃×C₉	—	4	2	no	—
64	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
65	C₂³×C₃×C₉	C₂³	1	2	yes	—
66	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
67	C₂²×D₃×C₉	—	2	2	no	—
68	C₂²×D₃×C₉	—	4	2	no	—
69	C₂²×D₃×C₉	—	4	2	no	—
70	C₂²×D₃×C₉	D₄	1	4	yes	complemented
71	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
72	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
73	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
74	C₃×D₄×C₉	—	2	2	no	—
75	C₃×D₄×C₉	—	4	2	no	—
76	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
78	C₉×#67	—	2	2	no	—
79	C₉×#67	—	2	2	no	—
80	C₉×#67	—	2	4	no	—
81	C₉×#67	—	2	4	no	—
82	C₉×#67	—	4	2	no	—
83	C₂×C₉×Dic₃	—	2	2	no	—
84	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₉×Dic₃	C₂³	1	2	yes	—
86	C₂×C₉×Dic₃	C₂³	1	2	yes	—
87	C₉×D₁₂	—	2	2	no	—
88	C₄×D₃×C₉	—	2	2	no	—
89	C₄×D₃×C₉	—	4	2	no	—
90	C₃×#534	—	3	1	no	—
91	#5589	C₉	1	1	yes	characteristic, direct product factor
92	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
94	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×#67	—	2	4	no	—
98	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
99	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
101	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
103	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₃×D₃×D₄	—	2	4	no	—
105	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
108	C₂⁴×C₉	—	2	1	no	—
109	C₂⁴×C₉	—	3	1	no	—
110	C₂⁴×C₉	—	3	1	no	—
111	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic, complemented
112	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×#217	C₂²×C₃	1	1	yes	characteristic
115	C₃×#217	C₂²×C₃	1	2	yes	—
116	C₃×#217	C₂²×C₃	1	2	yes	—
117	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
118	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
119	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
120	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×D₄×C₉	—	2	1	no	—
122	C₂×D₄×C₉	—	2	2	no	—
123	C₂×D₄×C₉	—	3	2	no	—
124	C₂×D₄×C₉	—	3	1	no	—
125	C₂×D₄×C₉	—	3	1	no	—
126	C₂×D₄×C₉	—	3	2	no	—
127	C₂×D₄×C₉	—	3	2	no	—
128	C₂×D₄×C₉	—	3	1	no	—
129	C₂×D₄×C₉	—	6	4	no	—
130	C₂×D₄×C₉	—	6	4	no	—
131	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
132	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
133	C₂²×C₄×C₉	—	3	1	no	—
134	C₂²×C₄×C₉	—	3	1	no	—
135	C₂²×C₄×C₉	—	3	2	no	—
136	C₉×C₄⋊C₄	—	3	2	no	—
137	C₉×C₄⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	—	2	1	no	—
139	C₉×C₂²⋊C₄	—	2	2	no	—
140	C₉×C₂²⋊C₄	—	3	1	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	—	3	2	no	—
143	C₉×C₂²⋊C₄	—	3	2	no	—
144	C₉×C₂²⋊C₄	—	3	2	no	—
145	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
146	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
147	C₂²×C₃×C₉	—	2	2	no	—
148	C₂²×C₃×C₉	—	2	2	no	—
149	C₂²×C₃×C₉	—	2	1	no	—
150	C₂²×C₃×C₉	—	2	2	no	—
151	C₂²×C₃×C₉	—	2	2	no	—
152	C₂²×C₃×C₉	—	2	2	no	—
153	C₂²×C₃×C₉	—	4	4	no	—
154	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
155	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
156	C₂×D₃×C₉	—	2	2	no	—
157	C₂×D₃×C₉	—	2	2	no	—
158	C₂×D₃×C₉	—	2	1	no	—
159	C₂×D₃×C₉	—	2	2	no	—
160	C₂×D₃×C₉	—	4	4	no	—
161	C₂×D₃×C₉	—	4	4	no	—
162	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
163	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
164	C₃×C₄×C₉	—	2	1	no	—
165	C₃×C₄×C₉	—	2	2	no	—
166	C₉×Dic₃	—	2	1	no	—
167	C₉×Dic₃	—	2	2	no	—
168	C₉×Dic₃	—	2	2	no	—
169	C₂²×C₃×D₄	—	3	1	no	—
170	C₂²×C₃×D₄	—	3	1	no	—
171	C₂²×#67	C₂×C₉	1	1	yes	characteristic, complemented
172	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
173	C₃×#123	—	3	1	no	—
174	C₃×#123	—	3	2	no	—
175	C₃×#123	—	3	1	no	—
176	C₃×#121	—	3	2	no	—
177	C₃×#121	—	3	2	no	—
178	C₃×#120	—	2	1	no	—
179	C₃×#120	—	3	1	no	—
180	C₃×#120	—	3	2	no	—
181	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
182	C₃×#120	C₃×D₃	1	1	yes	characteristic
183	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
184	#953	C₂×C₉	1	1	yes	characteristic, complemented
185	#938	C₂×C₉	1	2	yes	complemented
186	#937	C₂×C₉	1	2	yes	complemented
187	#935	C₂×C₉	1	1	yes	characteristic, complemented
188	#886	C₂×C₉	1	1	yes	characteristic, complemented
189	#884	C₂×C₉	1	2	yes	complemented
190	#883	C₂×C₉	1	2	yes	complemented
191	D₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
192	C₂³×C₃²	—	2	2	no	—
193	C₂³×C₃²	—	4	2	no	—
194	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
195	C₂³×C₃²	C₂³×C₃	1	2	yes	—
196	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₃×D₃	—	2	2	no	—
198	C₂²×C₃×D₃	—	4	2	no	—
199	C₂²×C₃×D₃	—	4	2	no	—
200	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
201	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
204	C₃²×D₄	—	2	2	no	—
205	C₃²×D₄	—	4	2	no	—
206	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
208	C₃×#67	—	2	2	no	—
209	C₃×#67	—	2	2	no	—
210	C₃×#67	—	2	4	no	—
211	C₃×#67	—	2	4	no	—
212	C₃×#67	—	4	2	no	—
213	C₂×C₃×Dic₃	—	2	2	no	—
214	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
215	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
216	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
217	C₃×D₁₂	—	2	2	no	—
218	C₃×C₄×D₃	—	2	2	no	—
219	C₃×C₄×D₃	—	4	2	no	—
220	C₂³×C₉	—	2	2	no	—
221	C₂³×C₉	—	2	2	no	—
222	C₂³×C₉	—	2	1	no	—
223	C₂³×C₉	—	2	1	no	—
224	C₂³×C₉	—	3	1	no	—
225	C₂³×C₉	—	3	1	no	—
226	C₂³×C₉	—	3	4	no	—
227	C₂³×C₉	—	3	1	no	—
228	C₂³×C₉	—	4	2	no	—
229	C₂³×C₉	—	4	2	no	—
230	C₂³×C₉	—	4	4	no	—
231	C₂³×C₉	—	6	2	no	—
232	C₂³×C₉	—	12	2	no	—
233	C₂³×C₉	—	12	2	no	—
234	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
235	C₂³×C₉	C₂²×D₃	1	2	yes	—
236	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
237	D₄×C₉	—	2	2	no	—
238	D₄×C₉	—	4	2	no	—
239	D₄×C₉	—	4	2	no	—
240	D₄×C₉	—	4	4	no	—
241	D₄×C₉	—	6	2	no	—
242	D₄×C₉	—	6	2	no	—
243	D₄×C₉	—	6	4	no	—
244	D₄×C₉	—	6	4	no	—
245	D₄×C₉	—	6	2	no	—
246	D₄×C₉	—	12	2	no	—
247	C₂×C₄×C₉	—	2	2	no	—
248	C₂×C₄×C₉	—	2	1	no	—
249	C₂×C₄×C₉	—	3	2	no	—
250	C₂×C₄×C₉	—	3	1	no	—
251	C₂×C₄×C₉	—	3	2	no	—
252	C₂×C₄×C₉	—	6	2	no	—
253	C₂×C₄×C₉	—	6	2	no	—
254	C₂×C₄×C₉	—	12	2	no	—
255	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
256	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
257	#534	—	3	1	no	Sylow
258	C₂×C₃×C₉	—	2	2	no	—
259	C₂×C₃×C₉	—	4	2	no	—
260	C₂×C₃×C₉	—	4	1	no	—
261	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
263	D₃×C₉	—	2	2	no	—
264	D₃×C₉	—	2	2	no	—
265	D₃×C₉	—	4	1	no	—
266	C₂⁴×C₃	—	2	1	no	—
267	C₂⁴×C₃	—	3	1	no	—
268	C₂⁴×C₃	—	3	1	no	—
269	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic, complemented
270	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
271	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
272	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
273	C₂×C₃×D₄	—	2	1	no	—
274	C₂×C₃×D₄	—	2	2	no	—
275	C₂×C₃×D₄	—	3	2	no	—
276	C₂×C₃×D₄	—	3	1	no	—
277	C₂×C₃×D₄	—	3	1	no	—
278	C₂×C₃×D₄	—	3	2	no	—
279	C₂×C₃×D₄	—	3	2	no	—
280	C₂×C₃×D₄	—	3	1	no	—
281	C₂×C₃×D₄	—	6	4	no	—
282	C₂×C₃×D₄	—	6	4	no	—
283	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
284	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
285	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
286	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
287	C₂²×C₃×C₄	—	3	1	no	—
288	C₂²×C₃×C₄	—	3	1	no	—
289	C₂²×C₃×C₄	—	3	2	no	—
290	C₂×#67	—	2	4	no	—
291	C₂×#67	C₂²×C₉	1	2	yes	—
292	C₂×#67	C₂²×C₉	1	1	yes	characteristic
293	C₂×#67	C₂²×C₉	1	2	yes	complemented
294	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
295	C₂×#67	C₂²×C₉	1	2	yes	complemented
296	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
297	D₃×D₄	—	2	4	no	—
298	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
299	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
300	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
301	C₃×C₄⋊C₄	—	3	2	no	—
302	C₃×C₄⋊C₄	—	3	2	no	—
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₂²⋊C₄	—	2	2	no	—
305	C₃×C₂²⋊C₄	—	3	1	no	—
306	C₃×C₂²⋊C₄	—	3	2	no	—
307	C₃×C₂²⋊C₄	—	3	2	no	—
308	C₃×C₂²⋊C₄	—	3	2	no	—
309	C₃×C₂²⋊C₄	—	3	2	no	—
310	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
311	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
312	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
314	#217	C₂²×C₉	1	1	yes	characteristic, complemented
315	#217	C₂²×C₉	1	2	yes	complemented
316	#217	C₂²×C₉	1	2	yes	complemented
317	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
318	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
319	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
320	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
321	C₂²×C₃²	—	2	2	no	—
322	C₂²×C₃²	—	2	2	no	—
323	C₂²×C₃²	—	2	2	no	—
324	C₂²×C₃²	—	2	1	no	—
325	C₂²×C₃²	—	2	2	no	—
326	C₂²×C₃²	—	2	2	no	—
327	C₂²×C₃²	—	4	4	no	—
328	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
329	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
330	C₂×C₃×D₃	—	2	2	no	—
331	C₂×C₃×D₃	—	2	2	no	—
332	C₂×C₃×D₃	—	2	1	no	—
333	C₂×C₃×D₃	—	2	2	no	—
334	C₂×C₃×D₃	—	4	4	no	—
335	C₂×C₃×D₃	—	4	4	no	—
336	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
337	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
338	C₃²×C₄	—	2	1	no	—
339	C₃²×C₄	—	2	2	no	—
340	C₃×Dic₃	—	2	1	no	—
341	C₃×Dic₃	—	2	2	no	—
342	C₃×Dic₃	—	2	2	no	—
343	C₂²×C₉	—	2	2	no	—
344	C₂²×C₉	—	2	4	no	—
345	C₂²×C₉	—	2	1	no	—
346	C₂²×C₉	—	2	2	no	—
347	C₂²×C₉	—	2	2	no	—
348	C₂²×C₉	—	2	2	no	—
349	C₂²×C₉	—	2	2	no	—
350	C₂²×C₉	—	2	1	no	—
351	C₂²×C₉	—	2	2	no	—
352	C₂²×C₉	—	3	2	no	—
353	C₂²×C₉	—	3	2	no	—
354	C₂²×C₉	—	4	2	no	—
355	C₂²×C₉	—	4	2	no	—
356	C₂²×C₉	—	4	2	no	—
357	C₂²×C₉	—	4	1	no	—
358	C₂²×C₉	—	4	2	no	—
359	C₂²×C₉	—	4	4	no	—
360	C₂²×C₉	—	4	8	no	—
361	C₂²×C₉	—	6	2	no	—
362	C₂²×C₉	—	6	2	no	—
363	C₂²×C₉	—	6	1	no	—
364	C₂²×C₉	—	6	2	no	—
365	C₂²×C₉	—	12	4	no	—
366	C₂²×C₉	—	12	4	no	—
367	C₂²×C₉	D₃×D₄	1	2	yes	—
368	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
369	C₄×C₉	—	2	1	no	—
370	C₄×C₉	—	2	2	no	—
371	C₄×C₉	—	4	1	no	—
372	C₄×C₉	—	4	2	no	—
373	C₄×C₉	—	6	1	no	—
374	C₄×C₉	—	6	2	no	—
375	C₄×C₉	—	6	2	no	—
376	C₂²×D₄	—	3	1	no	—
377	C₂²×D₄	—	3	1	no	—
378	#123	—	3	1	no	—
379	#123	—	3	2	no	—
380	#123	—	3	1	no	—
381	#121	—	3	2	no	—
382	#121	—	3	2	no	—
383	#120	—	3	1	no	—
384	#120	—	3	2	no	—
385	#120	D₃×C₉	1	1	yes	characteristic, complemented
386	C₂×C₂²⋊C₄	—	3	1	no	—
387	C₃×C₉	#534	1	1	yes	characteristic, complemented, Sylow
388	C₂³×C₃	—	2	2	no	—
389	C₂³×C₃	—	2	2	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	1	no	—
392	C₂³×C₃	—	2	1	no	—
393	C₂³×C₃	—	3	1	no	—
394	C₂³×C₃	—	3	1	no	—
395	C₂³×C₃	—	3	4	no	—
396	C₂³×C₃	—	3	1	no	—
397	C₂³×C₃	—	4	2	no	—
398	C₂³×C₃	—	4	2	no	—
399	C₂³×C₃	—	4	2	no	—
400	C₂³×C₃	—	4	4	no	—
401	C₂³×C₃	—	6	2	no	—
402	C₂³×C₃	—	12	2	no	—
403	C₂³×C₃	—	12	2	no	—
404	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
405	C₂³×C₃	C₂³×C₉	1	2	yes	—
406	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
407	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
408	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
409	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
410	C₂²×D₃	—	2	2	no	—
411	C₂²×D₃	—	4	2	no	—
412	C₂²×D₃	—	4	2	no	—
413	C₂²×D₃	D₄×C₉	1	4	yes	complemented
414	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
415	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
416	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
417	C₃×D₄	—	2	2	no	—
418	C₃×D₄	—	2	2	no	—
419	C₃×D₄	—	4	2	no	—
420	C₃×D₄	—	4	2	no	—
421	C₃×D₄	—	4	2	no	—
422	C₃×D₄	—	4	4	no	—
423	C₃×D₄	—	6	2	no	—
424	C₃×D₄	—	6	2	no	—
425	C₃×D₄	—	6	4	no	—
426	C₃×D₄	—	6	4	no	—
427	C₃×D₄	—	6	2	no	—
428	C₃×D₄	—	12	2	no	—
429	C₂×C₃×C₄	—	2	2	no	—
430	C₂×C₃×C₄	—	2	1	no	—
431	C₂×C₃×C₄	—	3	2	no	—
432	C₂×C₃×C₄	—	3	2	no	—
433	C₂×C₃×C₄	—	3	1	no	—
434	C₂×C₃×C₄	—	6	2	no	—
435	C₂×C₃×C₄	—	6	2	no	—
436	C₂×C₃×C₄	—	12	2	no	—
437	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
439	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
440	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
441	#67	—	2	2	no	—
442	#67	—	2	2	no	—
443	#67	—	2	4	no	—
444	#67	—	2	4	no	—
445	#67	—	4	2	no	—
446	C₂×Dic₃	—	2	2	no	—
447	C₂×Dic₃	C₂³×C₉	1	2	yes	—
448	C₂×Dic₃	C₂³×C₉	1	2	yes	—
449	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
450	D₁₂	—	2	2	no	—
451	C₄×D₃	—	2	2	no	—
452	C₄×D₃	—	4	2	no	—
453	C₂×C₃²	—	2	2	no	—
454	C₂×C₃²	—	4	2	no	—
455	C₂×C₃²	—	4	1	no	—
456	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
457	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
458	C₃×D₃	—	2	2	no	—
459	C₃×D₃	—	2	2	no	—
460	C₃×D₃	—	4	1	no	—
461	C₂×C₉	—	2	2	no	—
462	C₂×C₉	—	2	1	no	—
463	C₂×C₉	—	2	2	no	—
464	C₂×C₉	—	4	2	no	—
465	C₂×C₉	—	4	4	no	—
466	C₂×C₉	—	4	2	no	—
467	C₂×C₉	—	4	1	no	—
468	C₂×C₉	—	6	2	no	—
469	C₂×C₉	—	6	2	no	—
470	C₂×C₉	—	8	1	no	—
471	C₂×C₉	—	12	1	no	—
472	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
473	C₂×C₉	#1004	1	2	yes	—
474	C₂⁴	—	3	1	no	—
475	C₂⁴	—	3	1	no	—
476	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic, complemented
477	C₂×D₄	—	3	2	no	—
478	C₂×D₄	—	3	1	no	—
479	C₂×D₄	—	3	1	no	—
480	C₂×D₄	—	3	2	no	—
481	C₂×D₄	—	3	2	no	—
482	C₂×D₄	—	3	1	no	—
483	C₂×D₄	—	6	4	no	—
484	C₂×D₄	—	6	4	no	—
485	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
486	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
487	C₂²×C₄	—	3	1	no	—
488	C₂²×C₄	—	3	1	no	—
489	C₂²×C₄	—	3	2	no	—
490	C₄⋊C₄	—	3	2	no	—
491	C₄⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
498	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	2	4	no	—
502	C₂²×C₃	—	2	1	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	2	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	3	2	no	—
515	C₂²×C₃	—	3	2	no	—
516	C₂²×C₃	—	4	2	no	—
517	C₂²×C₃	—	4	2	no	—
518	C₂²×C₃	—	4	2	no	—
519	C₂²×C₃	—	4	1	no	—
520	C₂²×C₃	—	4	2	no	—
521	C₂²×C₃	—	4	4	no	—
522	C₂²×C₃	—	4	4	no	—
523	C₂²×C₃	—	4	8	no	—
524	C₂²×C₃	—	6	2	no	—
525	C₂²×C₃	—	6	2	no	—
526	C₂²×C₃	—	6	1	no	—
527	C₂²×C₃	—	6	2	no	—
528	C₂²×C₃	—	12	4	no	—
529	C₂²×C₃	—	12	4	no	—
530	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
531	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
532	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
533	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	4	4	no	—
539	C₂×D₃	—	4	4	no	—
540	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
541	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	2	no	—
548	C₃×C₄	—	6	1	no	—
549	C₃×C₄	—	6	2	no	—
550	C₃×C₄	—	6	2	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	2	no	—
553	Dic₃	—	2	2	no	—
554	C₃²	C₃×#534	1	1	yes	characteristic
555	C₉	—	2	1	no	—
556	C₉	#5589	1	1	yes	characteristic, direct product factor
557	C₂³	—	2	2	no	—
558	C₂³	—	3	1	no	—
559	C₂³	—	3	1	no	—
560	C₂³	—	3	4	no	—
561	C₂³	—	3	1	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	6	2	no	—
564	C₂³	—	12	2	no	—
565	C₂³	—	12	2	no	—
566	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
567	C₂³	C₂²×D₃×C₉	1	2	yes	—
568	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
569	D₄	—	2	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	6	2	no	—
572	D₄	—	6	2	no	—
573	D₄	—	6	4	no	—
574	D₄	—	6	4	no	—
575	D₄	—	6	2	no	—
576	D₄	—	12	2	no	—
577	C₂×C₄	—	3	2	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	2	no	—
580	C₂×C₄	—	6	2	no	—
581	C₂×C₄	—	6	2	no	—
582	C₂×C₄	—	12	2	no	—
583	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
584	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
585	C₂×C₃	—	2	2	no	—
586	C₂×C₃	—	2	2	no	—
587	C₂×C₃	—	2	1	no	—
588	C₂×C₃	—	2	2	no	—
589	C₂×C₃	—	4	2	no	—
590	C₂×C₃	—	4	4	no	—
591	C₂×C₃	—	4	1	no	—
592	C₂×C₃	—	4	2	no	—
593	C₂×C₃	—	4	2	no	—
594	C₂×C₃	—	4	1	no	—
595	C₂×C₃	—	6	2	no	—
596	C₂×C₃	—	6	2	no	—
597	C₂×C₃	—	8	1	no	—
598	C₂×C₃	—	12	1	no	—
599	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
600	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
601	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
602	C₂×C₃	C₃×#1004	1	2	yes	—
603	D₃	—	2	2	no	—
604	D₃	—	2	2	no	—
605	D₃	—	4	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	3	2	no	—
613	C₂²	—	3	2	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	6	2	no	—
616	C₂²	—	6	2	no	—
617	C₂²	—	6	1	no	—
618	C₂²	—	6	2	no	—
619	C₂²	—	12	4	no	—
620	C₂²	—	12	4	no	—
621	C₂²	D₃×D₄×C₉	1	2	yes	—
622	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	6	1	no	—
626	C₄	—	6	2	no	—
627	C₄	—	6	2	no	—
628	C₃	—	2	1	no	—
629	C₃	C₉×#534	1	1	yes	characteristic, complemented
630	C₃	C₃×#5589	1	1	yes	characteristic
631	C₂	—	2	2	no	—
632	C₂	—	4	2	no	—
633	C₂	—	4	1	no	—
634	C₂	—	6	2	no	—
635	C₂	—	6	2	no	—
636	C₂	—	12	1	no	—
637	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
638	C₂	C₉×#1004	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×#120	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5589	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	C₉×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×#67	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₃×C₉×#120	C₂	semidirect
4. C₉×#953	C₂	semidirect
5. C₉×#938	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. C₉×#935	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#884	C₂	semidirect
10. C₉×#883	C₂	semidirect
11. D₃×C₉×C₂²⋊C₄	C₂	semidirect
14. C₂⁴×C₃×C₉	C₂²	semidirect
16. C₂³×D₃×C₉	C₂²	semidirect
18. C₂×C₃×D₄×C₉	C₂²	semidirect
22. C₂×C₉×#67	C₂²	semidirect
23. C₂×C₉×#67	C₂²	semidirect
24. C₂×C₉×#67	C₂²	semidirect
25. C₂²×C₉×Dic₃	C₂²	semidirect
27. C₂×C₉×D₁₂	C₂²	semidirect
28. C₂×C₄×D₃×C₉	C₂²	semidirect
29. C₂×C₄×D₃×C₉	C₂²	semidirect
30. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
31. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
32. C₉×#217	C₂²	semidirect
33. C₉×#217	C₂²	semidirect
34. C₉×#217	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×C₄⋊Dic₃	C₂²	semidirect
38. C₉×Dic₃⋊C₄	C₂²	semidirect
60. C₉×#120	D₃	semidirect
70. C₂²×D₃×C₉	D₄	semidirect
91. #5589	C₉	direct (N × H)
111. C₂⁴×C₉	C₂×D₃	semidirect
132. C₂×D₄×C₉	C₂×D₃	semidirect
145. C₉×C₂²⋊C₄	C₂×D₃	semidirect
146. C₉×C₂²⋊C₄	C₂×D₃	semidirect
171. C₂²×#67	C₂×C₉	semidirect
172. C₂×D₃×D₄	C₂×C₉	semidirect
181. C₃×#120	C₂×C₉	semidirect
184. #953	C₂×C₉	semidirect
185. #938	C₂×C₉	semidirect
186. #937	C₂×C₉	semidirect
187. #935	C₂×C₉	semidirect
188. #886	C₂×C₉	semidirect
189. #884	C₂×C₉	semidirect
190. #883	C₂×C₉	semidirect
191. D₃×C₂²⋊C₄	C₂×C₉	semidirect
269. C₂⁴×C₃	C₂²×C₉	semidirect
272. C₂³×D₃	C₂²×C₉	semidirect
284. C₂×C₃×D₄	C₂²×C₉	semidirect
293. C₂×#67	C₂²×C₉	semidirect
294. C₂×#67	C₂²×C₉	semidirect
295. C₂×#67	C₂²×C₉	semidirect
296. C₂²×Dic₃	C₂²×C₉	semidirect
298. C₂×D₁₂	C₂²×C₉	semidirect
299. C₂×C₄×D₃	C₂²×C₉	semidirect
300. C₂×C₄×D₃	C₂²×C₉	semidirect
310. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
311. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
314. #217	C₂²×C₉	semidirect
315. #217	C₂²×C₉	semidirect
316. #217	C₂²×C₉	semidirect
317. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
318. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
319. C₄⋊Dic₃	C₂²×C₉	semidirect
320. Dic₃⋊C₄	C₂²×C₉	semidirect
385. #120	D₃×C₉	semidirect
387. C₃×C₉	#534	semidirect
413. C₂²×D₃	D₄×C₉	semidirect
476. C₂⁴	C₂×D₃×C₉	semidirect
486. C₂×D₄	C₂×D₃×C₉	semidirect
497. C₂²⋊C₄	C₂×D₃×C₉	semidirect
498. C₂²⋊C₄	C₂×D₃×C₉	semidirect
556. C₉	#5589	direct (N × H)
629. C₃	C₉×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×#67	2
C₂×D₃×D₄×C₉	2
C₃×C₉×#120	2
C₉×#953	2
C₉×#938	2
C₉×#937	2
C₉×#935	2
C₉×#886	2
C₉×#884	2
C₉×#883	2
D₃×C₉×C₂²⋊C₄	2
C₃×#5589	3
C₉×#534	3

Subgroups — C9×#5589 #13152761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5589 #13152761