Subgroups — C₉×#5605 #13152824

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#939	C₂	1	2	yes	maximal, complemented
4	C₉×#937	C₂	1	2	yes	maximal, complemented
5	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#894	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×#5605	C₃	1	1	yes	maximal, characteristic
11	C₉×#534	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂³×D₃×C₉	C₂²	1	2	yes	complemented
14	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	2	yes	complemented
19	C₂×C₉×#67	C₂²	1	2	yes	complemented
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	D₃×D₄×C₉	—	2	8	no	—
22	C₂×C₉×D₁₂	C₂²	1	2	yes	—
23	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₉×#217	C₂²	1	2	yes	complemented
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
32	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
34	C₂×C₃×D₃×D₄	C₂×C₃	1	2	yes	—
35	C₃²×#121	C₂×C₃	1	1	yes	characteristic
36	C₃×#939	C₂×C₃	1	2	yes	—
37	C₃×#937	C₂×C₃	1	2	yes	—
38	C₃×#930	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
40	C₃×#894	C₂×C₃	1	2	yes	—
41	C₃×#883	C₂×C₃	1	2	yes	—
42	C₃×#882	C₂×C₃	1	2	yes	—
43	C₂²×D₄×C₉	—	3	2	no	—
44	C₉×#123	—	3	2	no	—
45	C₉×#123	—	3	2	no	—
46	C₉×#121	—	2	1	no	—
47	C₉×#121	—	3	2	no	—
48	C₉×#121	—	3	1	no	—
49	C₉×#121	D₃	1	1	yes	characteristic, complemented
50	C₉×#120	—	3	2	no	—
51	C₉×#120	—	3	2	no	—
52	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
53	C₂³×C₃×C₉	C₂³	1	2	yes	—
54	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
55	C₂²×D₃×C₉	—	2	4	no	—
56	C₂²×D₃×C₉	—	4	1	no	—
57	C₂²×D₃×C₉	—	4	1	no	—
58	C₂²×D₃×C₉	—	4	2	no	—
59	C₂²×D₃×C₉	—	4	2	no	—
60	C₂²×D₃×C₉	D₄	1	4	yes	complemented
61	C₂²×D₃×C₉	C₂³	1	2	yes	—
62	C₂²×D₃×C₉	C₂³	1	2	yes	—
63	C₃×D₄×C₉	—	2	4	no	—
64	C₃×D₄×C₉	—	4	1	no	—
65	C₂×C₃×C₄×C₉	—	4	1	no	—
66	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₉×#67	—	2	4	no	—
70	C₉×#67	—	2	4	no	—
71	C₉×#67	—	4	2	no	—
72	C₂×C₉×Dic₃	—	4	1	no	—
73	C₂×C₉×Dic₃	C₂³	1	2	yes	—
74	C₂×C₉×Dic₃	C₂³	1	2	yes	—
75	C₉×D₁₂	—	2	4	no	—
76	C₉×D₁₂	—	4	1	no	—
77	C₄×D₃×C₉	—	2	4	no	—
78	C₃×#534	—	3	1	no	—
79	#5605	C₉	1	1	yes	characteristic, direct product factor
80	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
81	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
83	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
86	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
87	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
88	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₃×D₃×D₄	—	2	8	no	—
90	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
91	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
93	C₂⁴×C₉	—	3	1	no	—
94	C₂⁴×C₉	—	3	2	no	—
95	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×#217	C₂²×C₃	1	2	yes	—
98	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
101	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
102	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
103	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×D₄×C₉	—	2	1	no	—
105	C₂×D₄×C₉	—	2	2	no	—
106	C₂×D₄×C₉	—	3	2	no	—
107	C₂×D₄×C₉	—	3	2	no	—
108	C₂×D₄×C₉	—	3	2	no	—
109	C₂×D₄×C₉	—	3	2	no	—
110	C₂×D₄×C₉	—	3	1	no	—
111	C₂×D₄×C₉	—	6	8	no	—
112	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
113	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
114	C₂²×C₄×C₉	—	2	1	no	—
115	C₂²×C₄×C₉	—	3	1	no	—
116	C₂²×C₄×C₉	—	3	2	no	—
117	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
118	C₉×C₄⋊C₄	—	2	1	no	—
119	C₉×C₄⋊C₄	—	3	2	no	—
120	C₉×C₄⋊C₄	—	3	1	no	—
121	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
122	C₉×C₂²⋊C₄	—	2	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	—	3	2	no	—
127	C₉×C₂²⋊C₄	—	3	2	no	—
128	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
129	C₂²×C₃×C₉	—	2	1	no	—
130	C₂²×C₃×C₉	—	2	1	no	—
131	C₂²×C₃×C₉	—	2	2	no	—
132	C₂²×C₃×C₉	—	2	2	no	—
133	C₂²×C₃×C₉	—	2	2	no	—
134	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
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	C₂×D₃×C₉	—	2	2	no	—
140	C₂×D₃×C₉	—	2	2	no	—
141	C₂×D₃×C₉	—	4	4	no	—
142	C₂×D₃×C₉	—	4	8	no	—
143	C₂×D₃×C₉	C₂×D₄	1	4	yes	—
144	C₃×C₄×C₉	—	2	2	no	—
145	C₃×C₄×C₉	—	2	1	no	—
146	C₃×C₄×C₉	—	2	1	no	—
147	C₉×Dic₃	—	2	2	no	—
148	C₉×Dic₃	—	2	2	no	—
149	C₂²×C₃×D₄	—	3	2	no	—
150	C₂×D₃×D₄	C₂×C₉	1	2	yes	complemented
151	C₃×#123	—	3	2	no	—
152	C₃×#123	—	3	2	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	—	3	2	no	—
155	C₃×#121	—	3	1	no	—
156	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
157	C₃×#121	C₃×D₃	1	1	yes	characteristic
158	C₃×#120	—	3	2	no	—
159	C₃×#120	—	3	2	no	—
160	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
161	#939	C₂×C₉	1	2	yes	complemented
162	#937	C₂×C₉	1	2	yes	complemented
163	#930	C₂×C₉	1	1	yes	characteristic, complemented
164	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
165	#894	C₂×C₉	1	2	yes	complemented
166	#883	C₂×C₉	1	2	yes	complemented
167	#882	C₂×C₉	1	2	yes	complemented
168	C₂³×C₃²	C₂³×C₃	1	2	yes	—
169	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₃×D₃	—	2	4	no	—
171	C₂²×C₃×D₃	—	4	1	no	—
172	C₂²×C₃×D₃	—	4	1	no	—
173	C₂²×C₃×D₃	—	4	2	no	—
174	C₂²×C₃×D₃	—	4	2	no	—
175	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
176	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
177	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
178	C₃²×D₄	—	2	4	no	—
179	C₃²×D₄	—	4	1	no	—
180	C₂×C₃²×C₄	—	4	1	no	—
181	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
182	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₃×#67	—	2	4	no	—
185	C₃×#67	—	2	4	no	—
186	C₃×#67	—	4	2	no	—
187	C₂×C₃×Dic₃	—	4	1	no	—
188	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
189	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
190	C₃×D₁₂	—	2	4	no	—
191	C₃×D₁₂	—	4	1	no	—
192	C₃×C₄×D₃	—	2	4	no	—
193	C₂³×C₉	—	2	1	no	—
194	C₂³×C₉	—	2	2	no	—
195	C₂³×C₉	—	3	2	no	—
196	C₂³×C₉	—	3	4	no	—
197	C₂³×C₉	—	3	2	no	—
198	C₂³×C₉	—	6	4	no	—
199	C₂³×C₉	—	12	1	no	—
200	C₂³×C₉	—	12	1	no	—
201	C₂³×C₉	—	12	2	no	—
202	C₂³×C₉	—	12	2	no	—
203	C₂³×C₉	C₂²×D₃	1	2	yes	—
204	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
205	D₄×C₉	—	2	4	no	—
206	D₄×C₉	—	4	4	no	—
207	D₄×C₉	—	4	1	no	—
208	D₄×C₉	—	4	2	no	—
209	D₄×C₉	—	6	4	no	—
210	D₄×C₉	—	6	4	no	—
211	D₄×C₉	—	6	4	no	—
212	D₄×C₉	—	12	1	no	—
213	D₄×C₉	—	12	2	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	2	1	no	—
216	C₂×C₄×C₉	—	2	2	no	—
217	C₂×C₄×C₉	—	3	2	no	—
218	C₂×C₄×C₉	—	3	2	no	—
219	C₂×C₄×C₉	—	4	1	no	—
220	C₂×C₄×C₉	—	4	2	no	—
221	C₂×C₄×C₉	—	6	4	no	—
222	C₂×C₄×C₉	—	12	1	no	—
223	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
225	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
226	#534	—	3	1	no	Sylow
227	C₂×C₃×C₉	—	2	2	no	—
228	C₂×C₃×C₉	—	4	2	no	—
229	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
232	D₃×C₉	—	2	4	no	—
233	D₃×C₉	—	4	2	no	—
234	C₂⁴×C₃	—	3	1	no	—
235	C₂⁴×C₃	—	3	2	no	—
236	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
237	C₂³×D₃	C₂²×C₉	1	2	yes	complemented
238	C₂×C₃×D₄	—	2	2	no	—
239	C₂×C₃×D₄	—	2	1	no	—
240	C₂×C₃×D₄	—	3	2	no	—
241	C₂×C₃×D₄	—	3	2	no	—
242	C₂×C₃×D₄	—	3	2	no	—
243	C₂×C₃×D₄	—	3	2	no	—
244	C₂×C₃×D₄	—	3	1	no	—
245	C₂×C₃×D₄	—	6	8	no	—
246	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
247	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
248	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
249	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
250	C₂²×C₃×C₄	—	2	1	no	—
251	C₂²×C₃×C₄	—	3	1	no	—
252	C₂²×C₃×C₄	—	3	2	no	—
253	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
254	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
255	C₂×#67	C₂²×C₉	1	2	yes	—
256	C₂×#67	C₂²×C₉	1	2	yes	complemented
257	C₂×#67	C₂²×C₉	1	2	yes	complemented
258	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
259	D₃×D₄	—	2	8	no	—
260	C₂×D₁₂	C₂²×C₉	1	2	yes	—
261	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
262	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
263	C₃×C₄⋊C₄	—	2	1	no	—
264	C₃×C₄⋊C₄	—	3	2	no	—
265	C₃×C₄⋊C₄	—	3	1	no	—
266	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
267	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
268	C₃×C₂²⋊C₄	—	2	2	no	—
269	C₃×C₂²⋊C₄	—	3	2	no	—
270	C₃×C₂²⋊C₄	—	3	2	no	—
271	C₃×C₂²⋊C₄	—	3	2	no	—
272	C₃×C₂²⋊C₄	—	3	2	no	—
273	C₃×C₂²⋊C₄	—	3	2	no	—
274	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
275	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
276	#217	C₂²×C₉	1	2	yes	complemented
277	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
278	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
279	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
280	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
281	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
282	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
283	C₂²×C₃²	—	2	1	no	—
284	C₂²×C₃²	—	2	1	no	—
285	C₂²×C₃²	—	2	2	no	—
286	C₂²×C₃²	—	2	2	no	—
287	C₂²×C₃²	—	2	2	no	—
288	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
289	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
290	C₂×C₃×D₃	—	2	2	no	—
291	C₂×C₃×D₃	—	2	2	no	—
292	C₂×C₃×D₃	—	2	2	no	—
293	C₂×C₃×D₃	—	2	2	no	—
294	C₂×C₃×D₃	—	2	2	no	—
295	C₂×C₃×D₃	—	4	4	no	—
296	C₂×C₃×D₃	—	4	8	no	—
297	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
298	C₃²×C₄	—	2	1	no	—
299	C₃²×C₄	—	2	2	no	—
300	C₃²×C₄	—	2	1	no	—
301	C₃×Dic₃	—	2	2	no	—
302	C₃×Dic₃	—	2	2	no	—
303	C₂²×C₉	—	2	1	no	—
304	C₂²×C₉	—	2	1	no	—
305	C₂²×C₉	—	2	2	no	—
306	C₂²×C₉	—	2	2	no	—
307	C₂²×C₉	—	2	2	no	—
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	—	2	2	no	—
310	C₂²×C₉	—	3	4	no	—
311	C₂²×C₉	—	4	1	no	—
312	C₂²×C₉	—	4	1	no	—
313	C₂²×C₉	—	4	2	no	—
314	C₂²×C₉	—	4	2	no	—
315	C₂²×C₉	—	4	2	no	—
316	C₂²×C₉	—	6	2	no	—
317	C₂²×C₉	—	6	2	no	—
318	C₂²×C₉	—	6	2	no	—
319	C₂²×C₉	—	6	2	no	—
320	C₂²×C₉	—	6	2	no	—
321	C₂²×C₉	—	12	4	no	—
322	C₂²×C₉	—	12	8	no	—
323	C₂²×C₉	D₃×D₄	1	2	yes	—
324	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
325	C₄×C₉	—	2	2	no	—
326	C₄×C₉	—	2	2	no	—
327	C₄×C₉	—	2	1	no	—
328	C₄×C₉	—	2	1	no	—
329	C₄×C₉	—	4	1	no	—
330	C₄×C₉	—	4	2	no	—
331	C₄×C₉	—	6	2	no	—
332	C₄×C₉	—	6	2	no	—
333	C₂²×D₄	—	3	2	no	—
334	#123	—	3	2	no	—
335	#123	—	3	2	no	—
336	#121	—	3	2	no	—
337	#121	—	3	1	no	—
338	#121	D₃×C₉	1	1	yes	characteristic, complemented
339	#120	—	3	2	no	—
340	#120	—	3	2	no	—
341	C₂×C₂²⋊C₄	—	3	1	no	—
342	C₃×C₉	#534	1	1	yes	characteristic, complemented, Sylow
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	2	2	no	—
345	C₂³×C₃	—	3	2	no	—
346	C₂³×C₃	—	3	4	no	—
347	C₂³×C₃	—	3	2	no	—
348	C₂³×C₃	—	6	4	no	—
349	C₂³×C₃	—	12	1	no	—
350	C₂³×C₃	—	12	1	no	—
351	C₂³×C₃	—	12	2	no	—
352	C₂³×C₃	—	12	2	no	—
353	C₂³×C₃	C₂³×C₉	1	2	yes	—
354	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
355	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
356	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂²×D₃	—	2	4	no	—
358	C₂²×D₃	—	4	1	no	—
359	C₂²×D₃	—	4	1	no	—
360	C₂²×D₃	—	4	2	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	D₄×C₉	1	4	yes	complemented
363	C₂²×D₃	C₂³×C₉	1	2	yes	—
364	C₂²×D₃	C₂³×C₉	1	2	yes	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	4	no	—
367	C₃×D₄	—	4	4	no	—
368	C₃×D₄	—	4	1	no	—
369	C₃×D₄	—	4	1	no	—
370	C₃×D₄	—	4	2	no	—
371	C₃×D₄	—	6	4	no	—
372	C₃×D₄	—	6	4	no	—
373	C₃×D₄	—	6	4	no	—
374	C₃×D₄	—	12	1	no	—
375	C₃×D₄	—	12	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	3	2	no	—
380	C₂×C₃×C₄	—	3	2	no	—
381	C₂×C₃×C₄	—	4	1	no	—
382	C₂×C₃×C₄	—	4	1	no	—
383	C₂×C₃×C₄	—	4	2	no	—
384	C₂×C₃×C₄	—	6	4	no	—
385	C₂×C₃×C₄	—	12	1	no	—
386	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
387	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
392	#67	—	2	4	no	—
393	#67	—	2	4	no	—
394	#67	—	4	2	no	—
395	C₂×Dic₃	—	4	1	no	—
396	C₂×Dic₃	C₂³×C₉	1	2	yes	—
397	C₂×Dic₃	C₂³×C₉	1	2	yes	—
398	D₁₂	—	2	4	no	—
399	D₁₂	—	4	1	no	—
400	C₄×D₃	—	2	4	no	—
401	C₂×C₃²	—	2	2	no	—
402	C₂×C₃²	—	4	2	no	—
403	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
404	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
406	C₃×D₃	—	2	4	no	—
407	C₃×D₃	—	4	2	no	—
408	C₂×C₉	—	2	2	no	—
409	C₂×C₉	—	2	1	no	—
410	C₂×C₉	—	2	1	no	—
411	C₂×C₉	—	2	1	no	—
412	C₂×C₉	—	4	2	no	—
413	C₂×C₉	—	4	2	no	—
414	C₂×C₉	—	6	4	no	—
415	C₂×C₉	—	8	2	no	—
416	C₂×C₉	—	12	2	no	—
417	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
418	C₂×C₉	#1004	1	1	yes	characteristic
419	C₂×C₉	#1009	1	1	yes	characteristic
420	C₂⁴	—	3	1	no	—
421	C₂⁴	—	3	2	no	—
422	C₂×D₄	—	3	2	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	6	8	no	—
428	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
429	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
433	C₄⋊C₄	—	3	2	no	—
434	C₄⋊C₄	—	3	1	no	—
435	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
436	C₂²⋊C₄	—	3	2	no	—
437	C₂²⋊C₄	—	3	2	no	—
438	C₂²⋊C₄	—	3	2	no	—
439	C₂²⋊C₄	—	3	2	no	—
440	C₂²⋊C₄	—	3	2	no	—
441	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
442	C₂²×C₃	—	2	1	no	—
443	C₂²×C₃	—	2	1	no	—
444	C₂²×C₃	—	2	1	no	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	2	2	no	—
454	C₂²×C₃	—	3	4	no	—
455	C₂²×C₃	—	4	1	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	4	2	no	—
458	C₂²×C₃	—	4	2	no	—
459	C₂²×C₃	—	4	2	no	—
460	C₂²×C₃	—	6	2	no	—
461	C₂²×C₃	—	6	2	no	—
462	C₂²×C₃	—	6	2	no	—
463	C₂²×C₃	—	6	2	no	—
464	C₂²×C₃	—	6	2	no	—
465	C₂²×C₃	—	12	4	no	—
466	C₂²×C₃	—	12	8	no	—
467	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
468	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
469	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
470	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
471	C₂×D₃	—	2	2	no	—
472	C₂×D₃	—	2	2	no	—
473	C₂×D₃	—	2	2	no	—
474	C₂×D₃	—	2	2	no	—
475	C₂×D₃	—	2	2	no	—
476	C₂×D₃	—	4	4	no	—
477	C₂×D₃	—	4	8	no	—
478	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	1	no	—
482	C₃×C₄	—	2	1	no	—
483	C₃×C₄	—	2	2	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	—	4	1	no	—
487	C₃×C₄	—	4	2	no	—
488	C₃×C₄	—	6	2	no	—
489	C₃×C₄	—	6	2	no	—
490	Dic₃	—	2	2	no	—
491	Dic₃	—	2	2	no	—
492	C₃²	C₃×#534	1	1	yes	characteristic
493	C₉	—	2	1	no	—
494	C₉	#5605	1	1	yes	characteristic, direct product factor
495	C₂³	—	3	2	no	—
496	C₂³	—	3	4	no	—
497	C₂³	—	3	2	no	—
498	C₂³	—	6	4	no	—
499	C₂³	—	12	1	no	—
500	C₂³	—	12	1	no	—
501	C₂³	—	12	2	no	—
502	C₂³	—	12	2	no	—
503	C₂³	C₂²×D₃×C₉	1	2	yes	—
504	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
505	D₄	—	2	4	no	—
506	D₄	—	4	1	no	—
507	D₄	—	6	4	no	—
508	D₄	—	6	4	no	—
509	D₄	—	6	4	no	—
510	D₄	—	12	1	no	—
511	D₄	—	12	2	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	6	4	no	—
516	C₂×C₄	—	12	1	no	—
517	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
520	C₂×C₃	—	2	2	no	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	2	1	no	—
523	C₂×C₃	—	2	1	no	—
524	C₂×C₃	—	2	1	no	—
525	C₂×C₃	—	4	2	no	—
526	C₂×C₃	—	4	2	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	—	6	4	no	—
529	C₂×C₃	—	8	2	no	—
530	C₂×C₃	—	12	2	no	—
531	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
532	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
535	C₂×C₃	C₃×#1004	1	1	yes	characteristic
536	C₂×C₃	C₃×#1009	1	1	yes	characteristic
537	D₃	—	2	4	no	—
538	D₃	—	4	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	3	4	no	—
545	C₂²	—	6	2	no	—
546	C₂²	—	6	2	no	—
547	C₂²	—	6	2	no	—
548	C₂²	—	6	2	no	—
549	C₂²	—	6	2	no	—
550	C₂²	—	12	4	no	—
551	C₂²	—	12	8	no	—
552	C₂²	D₃×D₄×C₉	1	2	yes	—
553	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	6	2	no	—
558	C₄	—	6	2	no	—
559	C₃	—	2	1	no	—
560	C₃	C₉×#534	1	1	yes	characteristic, complemented
561	C₃	C₃×#5605	1	1	yes	characteristic
562	C₂	—	2	2	no	—
563	C₂	—	4	2	no	—
564	C₂	—	6	4	no	—
565	C₂	—	12	2	no	—
566	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
567	C₂	C₉×#1004	1	1	yes	characteristic
568	C₂	C₉×#1009	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×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5605	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₃×C₉×#121	C₂	semidirect
3. C₉×#939	C₂	semidirect
4. C₉×#937	C₂	semidirect
5. C₉×#930	C₂	semidirect
6. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#883	C₂	semidirect
9. C₉×#882	C₂	semidirect
13. C₂³×D₃×C₉	C₂²	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
15. C₂×C₃×D₄×C₉	C₂²	semidirect
16. C₂²×C₃×C₄×C₉	C₂²	semidirect
18. C₂×C₉×#67	C₂²	semidirect
19. C₂×C₉×#67	C₂²	semidirect
20. C₂²×C₉×Dic₃	C₂²	semidirect
23. C₂×C₉×D₁₂	C₂²	semidirect
24. C₂×C₄×D₃×C₉	C₂²	semidirect
25. C₃×C₉×C₄⋊C₄	C₂²	semidirect
26. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
27. C₉×#217	C₂²	semidirect
28. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
29. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
30. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
31. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₉×C₄⋊Dic₃	C₂²	semidirect
33. C₉×Dic₃⋊C₄	C₂²	semidirect
49. C₉×#121	D₃	semidirect
60. C₂²×D₃×C₉	D₄	semidirect
79. #5605	C₉	direct (N × H)
112. C₂×D₄×C₉	C₂×D₃	semidirect
113. C₂×D₄×C₉	C₂×D₃	semidirect
117. C₂²×C₄×C₉	C₂×D₃	semidirect
121. C₉×C₄⋊C₄	C₂×D₃	semidirect
128. C₉×C₂²⋊C₄	C₂×D₃	semidirect
150. C₂×D₃×D₄	C₂×C₉	semidirect
156. C₃×#121	C₂×C₉	semidirect
161. #939	C₂×C₉	semidirect
162. #937	C₂×C₉	semidirect
163. #930	C₂×C₉	semidirect
164. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
165. #894	C₂×C₉	semidirect
166. #883	C₂×C₉	semidirect
167. #882	C₂×C₉	semidirect
237. C₂³×D₃	C₂²×C₉	semidirect
246. C₂×C₃×D₄	C₂²×C₉	semidirect
247. C₂×C₃×D₄	C₂²×C₉	semidirect
253. C₂²×C₃×C₄	C₂²×C₉	semidirect
256. C₂×#67	C₂²×C₉	semidirect
257. C₂×#67	C₂²×C₉	semidirect
258. C₂²×Dic₃	C₂²×C₉	semidirect
261. C₂×D₁₂	C₂²×C₉	semidirect
262. C₂×C₄×D₃	C₂²×C₉	semidirect
266. C₃×C₄⋊C₄	C₂²×C₉	semidirect
274. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
276. #217	C₂²×C₉	semidirect
277. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
278. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
279. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
280. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
281. C₄⋊Dic₃	C₂²×C₉	semidirect
282. Dic₃⋊C₄	C₂²×C₉	semidirect
338. #121	D₃×C₉	semidirect
342. C₃×C₉	#534	semidirect
362. C₂²×D₃	D₄×C₉	semidirect
428. C₂×D₄	C₂×D₃×C₉	semidirect
429. C₂×D₄	C₂×D₃×C₉	semidirect
432. C₂²×C₄	C₂×D₃×C₉	semidirect
435. C₄⋊C₄	C₂×D₃×C₉	semidirect
441. C₂²⋊C₄	C₂×D₃×C₉	semidirect
494. C₉	#5605	direct (N × H)
560. 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
C₂×D₃×D₄×C₉	2
C₃×C₉×#121	2
C₉×#939	2
C₉×#937	2
C₉×#930	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#894	2
C₉×#883	2
C₉×#882	2
C₃×#5605	3
C₉×#534	3

Subgroups — C9×#5605 #13152824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5605 #13152824