Subgroups — C₉×#5590 #13152762

Order 1728.

1414 conjugacy classes of subgroups.

The subgroup lattice has 598 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	2	yes	maximal, complemented
2	C₂×D₃×D₄×C₉	C₂	1	2	yes	maximal, complemented
3	C₃×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	2	yes	maximal, complemented
6	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#884	C₂	1	2	yes	maximal, complemented
8	C₉×#882	C₂	1	2	yes	maximal, complemented
9	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×#5590	C₃	1	1	yes	maximal, characteristic
11	D₄²×C₉	—	3	1	no	maximal
12	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₃×C₉	C₂²	1	2	yes	complemented
15	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
16	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₉×#67	—	2	8	no	—
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	2	yes	complemented
20	C₂×C₉×#67	C₂²	1	2	yes	complemented
21	C₂×C₉×#67	C₂²	1	2	yes	complemented
22	C₂×C₉×#67	C₂²	1	2	yes	complemented
23	C₂²×C₉×Dic₃	C₂²	1	2	yes	complemented
24	D₃×D₄×C₉	—	2	8	no	—
25	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
26	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
28	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₉×#217	C₂²	1	1	yes	characteristic, complemented
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₃×#67	C₂×C₃	1	2	yes	—
36	C₂×C₃×D₃×D₄	C₂×C₃	1	2	yes	—
37	C₃²×#120	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×#937	C₂×C₃	1	1	yes	characteristic
41	C₃×#884	C₂×C₃	1	2	yes	—
42	C₃×#882	C₂×C₃	1	2	yes	—
43	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
44	C₂²×D₄×C₉	—	3	2	no	—
45	C₂²×D₄×C₉	—	3	2	no	—
46	C₉×#127	—	3	1	no	—
47	C₉×#121	—	3	2	no	—
48	C₉×#121	—	3	2	no	—
49	C₉×#120	—	2	1	no	—
50	C₉×#120	—	3	1	no	—
51	C₉×#120	—	3	2	no	—
52	C₉×#120	D₃	1	1	yes	characteristic, complemented
53	C₄×D₄×C₉	—	3	2	no	—
54	C₂³×C₃×C₉	—	2	4	no	—
55	C₂³×C₃×C₉	—	4	1	no	—
56	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
57	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
58	C₂³×C₃×C₉	C₂³	1	2	yes	—
59	C₂²×D₃×C₉	—	2	4	no	—
60	C₂²×D₃×C₉	—	2	4	no	—
61	C₂²×D₃×C₉	—	2	4	no	—
62	C₂²×D₃×C₉	—	4	1	no	—
63	C₂²×D₃×C₉	—	4	2	no	—
64	C₂²×D₃×C₉	C₂³	1	2	yes	—
65	C₂²×D₃×C₉	C₂³	1	2	yes	—
66	C₃×D₄×C₉	—	2	4	no	—
67	C₃×D₄×C₉	—	4	1	no	—
68	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×#67	—	2	4	no	—
71	C₉×#67	—	2	4	no	—
72	C₉×#67	—	2	4	no	—
73	C₉×#67	—	2	4	no	—
74	C₉×#67	D₄	1	8	yes	complemented
75	C₂×C₉×Dic₃	—	2	4	no	—
76	C₂×C₉×Dic₃	C₂³	1	2	yes	—
77	C₂×C₉×Dic₃	C₂³	1	2	yes	—
78	C₉×D₁₂	—	2	4	no	—
79	C₉×D₁₂	—	4	1	no	—
80	C₄×D₃×C₉	—	2	4	no	—
81	C₃×D₄²	—	3	1	no	—
82	#5590	C₉	1	1	yes	characteristic, direct product factor
83	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
85	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×#67	—	2	8	no	—
89	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
90	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
91	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
92	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
95	C₃×D₃×D₄	—	2	8	no	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
97	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
99	C₂⁴×C₉	—	2	1	no	—
100	C₂⁴×C₉	—	3	1	no	—
101	C₂⁴×C₉	—	3	2	no	—
102	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic, complemented
103	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₃×#217	C₂²×C₃	1	1	yes	characteristic
106	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
108	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
110	C₂×D₄×C₉	—	2	2	no	—
111	C₂×D₄×C₉	—	2	1	no	—
112	C₂×D₄×C₉	—	3	2	no	—
113	C₂×D₄×C₉	—	3	2	no	—
114	C₂×D₄×C₉	—	3	2	no	—
115	C₂×D₄×C₉	—	3	2	no	—
116	C₂×D₄×C₉	—	3	2	no	—
117	C₂×D₄×C₉	—	3	2	no	—
118	C₂×D₄×C₉	—	3	1	no	—
119	C₂×D₄×C₉	—	6	8	no	—
120	C₂×D₄×C₉	—	6	8	no	—
121	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
122	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
123	C₂²×C₄×C₉	—	3	2	no	—
124	C₂²×C₄×C₉	—	3	2	no	—
125	C₉×C₄⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	—	2	2	no	—
127	C₉×C₂²⋊C₄	—	2	1	no	—
128	C₉×C₂²⋊C₄	—	3	1	no	—
129	C₉×C₂²⋊C₄	—	3	2	no	—
130	C₉×C₂²⋊C₄	—	3	2	no	—
131	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
132	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
133	C₄²×C₉	—	3	1	no	—
134	C₂²×C₃×C₉	—	2	2	no	—
135	C₂²×C₃×C₉	—	2	2	no	—
136	C₂²×C₃×C₉	—	2	2	no	—
137	C₂²×C₃×C₉	—	2	2	no	—
138	C₂²×C₃×C₉	—	2	1	no	—
139	C₂²×C₃×C₉	—	2	1	no	—
140	C₂²×C₃×C₉	—	4	4	no	—
141	C₂²×C₃×C₉	C₂×D₄	1	4	yes	complemented
142	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
143	C₂×D₃×C₉	—	2	2	no	—
144	C₂×D₃×C₉	—	2	2	no	—
145	C₂×D₃×C₉	—	2	2	no	—
146	C₂×D₃×C₉	—	2	2	no	—
147	C₂×D₃×C₉	—	2	2	no	—
148	C₂×D₃×C₉	—	4	4	no	—
149	C₂×D₃×C₉	—	4	8	no	—
150	C₂×D₃×C₉	C₂×D₄	1	4	yes	complemented
151	C₃×C₄×C₉	—	2	2	no	—
152	C₃×C₄×C₉	—	2	1	no	—
153	C₉×Dic₃	—	2	2	no	—
154	C₉×Dic₃	C₂×D₄	1	4	yes	complemented
155	C₂²×C₃×D₄	—	3	2	no	—
156	C₂²×C₃×D₄	—	3	2	no	—
157	C₂²×#67	C₂×C₉	1	2	yes	complemented
158	C₂×D₃×D₄	C₂×C₉	1	2	yes	complemented
159	C₃×#127	—	3	1	no	—
160	C₃×#121	—	3	2	no	—
161	C₃×#121	—	3	2	no	—
162	C₃×#120	—	2	1	no	—
163	C₃×#120	—	3	1	no	—
164	C₃×#120	—	3	2	no	—
165	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
166	C₃×#120	C₃×D₃	1	1	yes	characteristic
167	C₃×C₄×D₄	—	3	2	no	—
168	#940	C₂×C₉	1	1	yes	characteristic, complemented
169	#939	C₂×C₉	1	2	yes	complemented
170	#937	C₂×C₉	1	1	yes	characteristic, complemented
171	#884	C₂×C₉	1	2	yes	complemented
172	#882	C₂×C₉	1	2	yes	complemented
173	#67⋊C₄	C₂×C₉	1	2	yes	complemented
174	C₂³×C₃²	—	2	4	no	—
175	C₂³×C₃²	—	4	1	no	—
176	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
177	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
178	C₂³×C₃²	C₂³×C₃	1	2	yes	—
179	C₂²×C₃×D₃	—	2	4	no	—
180	C₂²×C₃×D₃	—	2	4	no	—
181	C₂²×C₃×D₃	—	2	4	no	—
182	C₂²×C₃×D₃	—	4	1	no	—
183	C₂²×C₃×D₃	—	4	2	no	—
184	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
185	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
186	C₃²×D₄	—	2	4	no	—
187	C₃²×D₄	—	4	1	no	—
188	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
190	C₃×#67	—	2	4	no	—
191	C₃×#67	—	2	4	no	—
192	C₃×#67	—	2	4	no	—
193	C₃×#67	—	2	4	no	—
194	C₃×#67	C₃×D₄	1	8	yes	—
195	C₂×C₃×Dic₃	—	2	4	no	—
196	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
197	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
198	C₃×D₁₂	—	2	4	no	—
199	C₃×D₁₂	—	4	1	no	—
200	C₃×C₄×D₃	—	2	4	no	—
201	C₂³×C₉	—	2	4	no	—
202	C₂³×C₉	—	2	1	no	—
203	C₂³×C₉	—	2	2	no	—
204	C₂³×C₉	—	2	1	no	—
205	C₂³×C₉	—	3	2	no	—
206	C₂³×C₉	—	3	2	no	—
207	C₂³×C₉	—	4	4	no	—
208	C₂³×C₉	—	4	1	no	—
209	C₂³×C₉	—	4	2	no	—
210	C₂³×C₉	—	6	4	no	—
211	C₂³×C₉	—	6	4	no	—
212	C₂³×C₉	—	6	4	no	—
213	C₂³×C₉	—	12	2	no	—
214	C₂³×C₉	—	12	1	no	—
215	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
216	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
217	C₂³×C₉	C₂²×D₃	1	2	yes	—
218	D₄×C₉	—	2	4	no	—
219	D₄×C₉	—	3	8	no	—
220	D₄×C₉	—	4	4	no	—
221	D₄×C₉	—	4	1	no	—
222	D₄×C₉	—	4	2	no	—
223	D₄×C₉	—	6	4	no	—
224	D₄×C₉	—	6	4	no	—
225	D₄×C₉	—	6	4	no	—
226	D₄×C₉	—	6	4	no	—
227	D₄×C₉	—	6	4	no	—
228	D₄×C₉	—	12	1	no	—
229	C₂×C₄×C₉	—	2	1	no	—
230	C₂×C₄×C₉	—	2	2	no	—
231	C₂×C₄×C₉	—	3	2	no	—
232	C₂×C₄×C₉	—	3	2	no	—
233	C₂×C₄×C₉	—	6	4	no	—
234	C₂×C₄×C₉	—	6	4	no	—
235	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
237	D₄²	—	3	1	no	Sylow
238	C₂×C₃×C₉	—	2	4	no	—
239	C₂×C₃×C₉	—	4	1	no	—
240	C₂×C₃×C₉	—	4	1	no	—
241	C₂×C₃×C₉	C₂²×D₄	1	2	yes	—
242	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
243	D₃×C₉	—	2	4	no	—
244	D₃×C₉	—	4	2	no	—
245	C₂⁴×C₃	—	2	1	no	—
246	C₂⁴×C₃	—	3	1	no	—
247	C₂⁴×C₃	—	3	2	no	—
248	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic, complemented
249	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
250	C₂³×D₃	C₂²×C₉	1	2	yes	complemented
251	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
252	C₂×C₃×D₄	—	2	2	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	—	3	2	no	—
255	C₂×C₃×D₄	—	3	2	no	—
256	C₂×C₃×D₄	—	3	2	no	—
257	C₂×C₃×D₄	—	3	2	no	—
258	C₂×C₃×D₄	—	3	2	no	—
259	C₂×C₃×D₄	—	3	2	no	—
260	C₂×C₃×D₄	—	3	1	no	—
261	C₂×C₃×D₄	—	6	8	no	—
262	C₂×C₃×D₄	—	6	8	no	—
263	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
264	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
265	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
266	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
267	C₂²×C₃×C₄	—	3	2	no	—
268	C₂²×C₃×C₄	—	3	2	no	—
269	C₂×#67	—	2	8	no	—
270	C₂×#67	C₂²×C₉	1	2	yes	—
271	C₂×#67	C₂²×C₉	1	2	yes	complemented
272	C₂×#67	C₂²×C₉	1	2	yes	complemented
273	C₂×#67	C₂²×C₉	1	2	yes	complemented
274	C₂×#67	C₂²×C₉	1	2	yes	complemented
275	C₂²×Dic₃	C₂²×C₉	1	2	yes	complemented
276	D₃×D₄	—	2	8	no	—
277	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
278	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
279	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
280	C₃×C₄⋊C₄	—	3	2	no	—
281	C₃×C₂²⋊C₄	—	2	2	no	—
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	3	1	no	—
284	C₃×C₂²⋊C₄	—	3	2	no	—
285	C₃×C₂²⋊C₄	—	3	2	no	—
286	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
287	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
288	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
289	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
290	C₃×C₄²	—	3	1	no	—
291	#217	C₂²×C₉	1	1	yes	characteristic, complemented
292	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
293	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
294	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
295	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
296	C₂²×C₃²	—	2	1	no	—
297	C₂²×C₃²	—	2	2	no	—
298	C₂²×C₃²	—	2	2	no	—
299	C₂²×C₃²	—	2	2	no	—
300	C₂²×C₃²	—	2	2	no	—
301	C₂²×C₃²	—	2	1	no	—
302	C₂²×C₃²	—	4	4	no	—
303	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
304	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
305	C₂×C₃×D₃	—	2	2	no	—
306	C₂×C₃×D₃	—	2	2	no	—
307	C₂×C₃×D₃	—	2	2	no	—
308	C₂×C₃×D₃	—	2	2	no	—
309	C₂×C₃×D₃	—	2	2	no	—
310	C₂×C₃×D₃	—	4	4	no	—
311	C₂×C₃×D₃	—	4	8	no	—
312	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
313	C₃²×C₄	—	2	2	no	—
314	C₃²×C₄	—	2	1	no	—
315	C₃×Dic₃	—	2	2	no	—
316	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
317	C₂²×C₉	—	2	2	no	—
318	C₂²×C₉	—	2	2	no	—
319	C₂²×C₉	—	2	2	no	—
320	C₂²×C₉	—	2	2	no	—
321	C₂²×C₉	—	2	2	no	—
322	C₂²×C₉	—	2	1	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	2	1	no	—
325	C₂²×C₉	—	2	4	no	—
326	C₂²×C₉	—	3	4	no	—
327	C₂²×C₉	—	4	2	no	—
328	C₂²×C₉	—	4	2	no	—
329	C₂²×C₉	—	4	2	no	—
330	C₂²×C₉	—	4	2	no	—
331	C₂²×C₉	—	4	1	no	—
332	C₂²×C₉	—	4	4	no	—
333	C₂²×C₉	—	4	8	no	—
334	C₂²×C₉	—	6	2	no	—
335	C₂²×C₉	—	6	2	no	—
336	C₂²×C₉	—	6	2	no	—
337	C₂²×C₉	—	6	2	no	—
338	C₂²×C₉	—	6	2	no	—
339	C₂²×C₉	—	12	8	no	—
340	C₂²×C₉	—	12	4	no	—
341	C₂²×C₉	D₃×D₄	1	4	yes	complemented
342	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
343	C₄×C₉	—	2	2	no	—
344	C₄×C₉	—	2	1	no	—
345	C₄×C₉	—	3	4	no	—
346	C₄×C₉	—	4	2	no	—
347	C₄×C₉	—	4	1	no	—
348	C₄×C₉	—	6	2	no	—
349	C₂²×D₄	—	3	2	no	—
350	C₂²×D₄	—	3	2	no	—
351	#127	—	3	1	no	—
352	#121	—	3	2	no	—
353	#121	—	3	2	no	—
354	#120	—	3	1	no	—
355	#120	—	3	2	no	—
356	#120	D₃×C₉	1	1	yes	characteristic, complemented
357	C₄×D₄	—	3	2	no	—
358	C₃×C₉	D₄²	1	1	yes	characteristic, complemented, Sylow
359	C₂³×C₃	—	2	4	no	—
360	C₂³×C₃	—	2	4	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	2	no	—
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	3	2	no	—
365	C₂³×C₃	—	3	2	no	—
366	C₂³×C₃	—	4	4	no	—
367	C₂³×C₃	—	4	1	no	—
368	C₂³×C₃	—	4	1	no	—
369	C₂³×C₃	—	4	2	no	—
370	C₂³×C₃	—	6	4	no	—
371	C₂³×C₃	—	6	4	no	—
372	C₂³×C₃	—	6	4	no	—
373	C₂³×C₃	—	12	2	no	—
374	C₂³×C₃	—	12	1	no	—
375	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
376	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
377	C₂³×C₃	C₂³×C₉	1	2	yes	—
378	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
379	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
380	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
381	C₂²×D₃	—	2	4	no	—
382	C₂²×D₃	—	2	4	no	—
383	C₂²×D₃	—	2	4	no	—
384	C₂²×D₃	—	4	1	no	—
385	C₂²×D₃	—	4	2	no	—
386	C₂²×D₃	C₂³×C₉	1	2	yes	—
387	C₂²×D₃	C₂³×C₉	1	2	yes	—
388	C₃×D₄	—	2	4	no	—
389	C₃×D₄	—	2	4	no	—
390	C₃×D₄	—	3	8	no	—
391	C₃×D₄	—	4	4	no	—
392	C₃×D₄	—	4	1	no	—
393	C₃×D₄	—	4	1	no	—
394	C₃×D₄	—	4	2	no	—
395	C₃×D₄	—	6	4	no	—
396	C₃×D₄	—	6	4	no	—
397	C₃×D₄	—	6	4	no	—
398	C₃×D₄	—	6	4	no	—
399	C₃×D₄	—	6	4	no	—
400	C₃×D₄	—	12	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	3	2	no	—
404	C₂×C₃×C₄	—	3	2	no	—
405	C₂×C₃×C₄	—	6	4	no	—
406	C₂×C₃×C₄	—	6	4	no	—
407	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
409	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
411	#67	—	2	4	no	—
412	#67	—	2	4	no	—
413	#67	—	2	4	no	—
414	#67	—	2	4	no	—
415	#67	D₄×C₉	1	8	yes	complemented
416	C₂×Dic₃	—	2	4	no	—
417	C₂×Dic₃	C₂³×C₉	1	2	yes	—
418	C₂×Dic₃	C₂³×C₉	1	2	yes	—
419	D₁₂	—	2	4	no	—
420	D₁₂	—	4	1	no	—
421	C₄×D₃	—	2	4	no	—
422	C₂×C₃²	—	2	4	no	—
423	C₂×C₃²	—	4	1	no	—
424	C₂×C₃²	—	4	1	no	—
425	C₂×C₃²	C₂²×C₃×D₄	1	2	yes	—
426	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
427	C₃×D₃	—	2	4	no	—
428	C₃×D₃	—	4	2	no	—
429	C₂×C₉	—	2	4	no	—
430	C₂×C₉	—	2	2	no	—
431	C₂×C₉	—	2	1	no	—
432	C₂×C₉	—	4	4	no	—
433	C₂×C₉	—	4	2	no	—
434	C₂×C₉	—	4	1	no	—
435	C₂×C₉	—	4	1	no	—
436	C₂×C₉	—	6	4	no	—
437	C₂×C₉	—	8	1	no	—
438	C₂×C₉	—	12	2	no	—
439	C₂×C₉	C₂×D₃×D₄	1	2	yes	—
440	C₂×C₉	#1004	1	1	yes	characteristic
441	C₂⁴	—	3	1	no	—
442	C₂⁴	—	3	2	no	—
443	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic, complemented
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	2	no	—
448	C₂×D₄	—	3	2	no	—
449	C₂×D₄	—	3	2	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	6	8	no	—
452	C₂×D₄	—	6	8	no	—
453	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
454	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₂²⋊C₄	—	3	1	no	—
459	C₂²⋊C₄	—	3	2	no	—
460	C₂²⋊C₄	—	3	2	no	—
461	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
462	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
463	C₄²	—	3	1	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	4	no	—
479	C₂²×C₃	—	3	4	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	4	2	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	1	no	—
485	C₂²×C₃	—	4	4	no	—
486	C₂²×C₃	—	4	4	no	—
487	C₂²×C₃	—	4	8	no	—
488	C₂²×C₃	—	6	2	no	—
489	C₂²×C₃	—	6	2	no	—
490	C₂²×C₃	—	6	2	no	—
491	C₂²×C₃	—	6	2	no	—
492	C₂²×C₃	—	6	2	no	—
493	C₂²×C₃	—	12	8	no	—
494	C₂²×C₃	—	12	4	no	—
495	C₂²×C₃	C₂×D₄×C₉	1	4	yes	complemented
496	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
497	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
498	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
499	C₂×D₃	—	2	2	no	—
500	C₂×D₃	—	2	2	no	—
501	C₂×D₃	—	2	2	no	—
502	C₂×D₃	—	2	2	no	—
503	C₂×D₃	—	2	2	no	—
504	C₂×D₃	—	4	4	no	—
505	C₂×D₃	—	4	8	no	—
506	C₂×D₃	C₂×D₄×C₉	1	4	yes	complemented
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	2	1	no	—
509	C₃×C₄	—	2	2	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	3	4	no	—
512	C₃×C₄	—	4	2	no	—
513	C₃×C₄	—	4	1	no	—
514	C₃×C₄	—	6	2	no	—
515	Dic₃	—	2	2	no	—
516	Dic₃	C₂×D₄×C₉	1	4	yes	complemented
517	C₃²	C₃×D₄²	1	1	yes	characteristic
518	C₉	—	2	1	no	—
519	C₉	#5590	1	1	yes	characteristic, direct product factor
520	C₂³	—	2	4	no	—
521	C₂³	—	3	2	no	—
522	C₂³	—	3	2	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	6	4	no	—
525	C₂³	—	6	4	no	—
526	C₂³	—	6	4	no	—
527	C₂³	—	12	2	no	—
528	C₂³	—	12	1	no	—
529	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
530	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
531	C₂³	C₂²×D₃×C₉	1	2	yes	—
532	D₄	—	2	4	no	—
533	D₄	—	3	8	no	—
534	D₄	—	4	1	no	—
535	D₄	—	6	4	no	—
536	D₄	—	6	4	no	—
537	D₄	—	6	4	no	—
538	D₄	—	6	4	no	—
539	D₄	—	6	4	no	—
540	D₄	—	12	1	no	—
541	C₂×C₄	—	3	2	no	—
542	C₂×C₄	—	3	2	no	—
543	C₂×C₄	—	6	4	no	—
544	C₂×C₄	—	6	4	no	—
545	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
547	C₂×C₃	—	2	4	no	—
548	C₂×C₃	—	2	4	no	—
549	C₂×C₃	—	2	2	no	—
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	4	4	no	—
552	C₂×C₃	—	4	2	no	—
553	C₂×C₃	—	4	1	no	—
554	C₂×C₃	—	4	1	no	—
555	C₂×C₃	—	4	1	no	—
556	C₂×C₃	—	4	1	no	—
557	C₂×C₃	—	6	4	no	—
558	C₂×C₃	—	8	1	no	—
559	C₂×C₃	—	12	2	no	—
560	C₂×C₃	C₂²×D₄×C₉	1	2	yes	—
561	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂×C₃	C₂×C₃×D₃×D₄	1	2	yes	—
563	C₂×C₃	C₃×#1004	1	1	yes	characteristic
564	D₃	—	2	4	no	—
565	D₃	—	4	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	3	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	6	2	no	—
575	C₂²	—	6	2	no	—
576	C₂²	—	6	2	no	—
577	C₂²	—	6	2	no	—
578	C₂²	—	6	2	no	—
579	C₂²	—	12	8	no	—
580	C₂²	—	12	4	no	—
581	C₂²	D₃×D₄×C₉	1	4	yes	complemented
582	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	3	4	no	—
586	C₄	—	6	2	no	—
587	C₃	—	2	1	no	—
588	C₃	D₄²×C₉	1	1	yes	characteristic, complemented
589	C₃	C₃×#5590	1	1	yes	characteristic
590	C₂	—	2	4	no	—
591	C₂	—	4	1	no	—
592	C₂	—	4	1	no	—
593	C₂	—	6	4	no	—
594	C₂	—	12	2	no	—
595	C₂	C₂×D₃×D₄×C₉	1	2	yes	—
596	C₂	C₉×#1004	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×#120	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5590	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	D₄²×C₉
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×#940	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. C₉×#884	C₂	semidirect
8. C₉×#882	C₂	semidirect
9. C₉×#67⋊C₄	C₂	semidirect
12. C₂⁴×C₃×C₉	C₂²	semidirect
13. C₂³×D₃×C₉	C₂²	semidirect
14. C₂³×D₃×C₉	C₂²	semidirect
15. C₂×C₃×D₄×C₉	C₂²	semidirect
16. C₂×C₃×D₄×C₉	C₂²	semidirect
19. C₂×C₉×#67	C₂²	semidirect
20. C₂×C₉×#67	C₂²	semidirect
21. C₂×C₉×#67	C₂²	semidirect
22. C₂×C₉×#67	C₂²	semidirect
23. C₂²×C₉×Dic₃	C₂²	semidirect
25. C₂×C₉×D₁₂	C₂²	semidirect
26. C₂×C₉×D₁₂	C₂²	semidirect
27. C₂×C₄×D₃×C₉	C₂²	semidirect
28. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
30. C₉×#217	C₂²	semidirect
31. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₉×Dic₃⋊C₄	C₂²	semidirect
34. C₄×C₉×Dic₃	C₂²	semidirect
52. C₉×#120	D₃	semidirect
74. C₉×#67	D₄	semidirect
82. #5590	C₉	direct (N × H)
102. C₂⁴×C₉	C₂×D₃	semidirect
121. C₂×D₄×C₉	C₂×D₃	semidirect
122. C₂×D₄×C₉	C₂×D₃	semidirect
131. C₉×C₂²⋊C₄	C₂×D₃	semidirect
132. C₉×C₂²⋊C₄	C₂×D₃	semidirect
141. C₂²×C₃×C₉	C₂×D₄	semidirect
150. C₂×D₃×C₉	C₂×D₄	semidirect
154. C₉×Dic₃	C₂×D₄	semidirect
157. C₂²×#67	C₂×C₉	semidirect
158. C₂×D₃×D₄	C₂×C₉	semidirect
165. C₃×#120	C₂×C₉	semidirect
168. #940	C₂×C₉	semidirect
169. #939	C₂×C₉	semidirect
170. #937	C₂×C₉	semidirect
171. #884	C₂×C₉	semidirect
172. #882	C₂×C₉	semidirect
173. #67⋊C₄	C₂×C₉	semidirect
248. C₂⁴×C₃	C₂²×C₉	semidirect
250. C₂³×D₃	C₂²×C₉	semidirect
251. C₂³×D₃	C₂²×C₉	semidirect
263. C₂×C₃×D₄	C₂²×C₉	semidirect
264. C₂×C₃×D₄	C₂²×C₉	semidirect
271. C₂×#67	C₂²×C₉	semidirect
272. C₂×#67	C₂²×C₉	semidirect
273. C₂×#67	C₂²×C₉	semidirect
274. C₂×#67	C₂²×C₉	semidirect
275. C₂²×Dic₃	C₂²×C₉	semidirect
277. C₂×D₁₂	C₂²×C₉	semidirect
278. C₂×D₁₂	C₂²×C₉	semidirect
279. C₂×C₄×D₃	C₂²×C₉	semidirect
286. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
287. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
291. #217	C₂²×C₉	semidirect
292. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
293. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
294. Dic₃⋊C₄	C₂²×C₉	semidirect
295. C₄×Dic₃	C₂²×C₉	semidirect
341. C₂²×C₉	D₃×D₄	semidirect
356. #120	D₃×C₉	semidirect
358. C₃×C₉	D₄²	semidirect
415. #67	D₄×C₉	semidirect
443. C₂⁴	C₂×D₃×C₉	semidirect
453. C₂×D₄	C₂×D₃×C₉	semidirect
454. C₂×D₄	C₂×D₃×C₉	semidirect
461. C₂²⋊C₄	C₂×D₃×C₉	semidirect
462. C₂²⋊C₄	C₂×D₃×C₉	semidirect
495. C₂²×C₃	C₂×D₄×C₉	semidirect
506. C₂×D₃	C₂×D₄×C₉	semidirect
516. Dic₃	C₂×D₄×C₉	semidirect
519. C₉	#5590	direct (N × H)
581. C₂²	D₃×D₄×C₉	semidirect
588. C₃	D₄²×C₉	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×#940	2
C₉×#939	2
C₉×#937	2
C₉×#884	2
C₉×#882	2
C₉×#67⋊C₄	2
C₃×#5590	3
D₄²×C₉	3

Subgroups — C9×#5590 #13152762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5590 #13152762