Subgroups — C₉×#5586 #13152750

Order 1728.

1120 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#237	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×#939	C₂	1	2	yes	maximal, complemented
6	C₉×#935	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
8	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₉×#878	C₂	1	2	yes	maximal, complemented
11	C₉×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5586	C₃	1	1	yes	maximal, characteristic
13	C₉×#525	—	3	1	no	maximal
14	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	1	yes	characteristic
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₉×Dic₃	—	2	4	no	—
21	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
22	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
24	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₉×#237	—	2	4	no	—
27	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₉×#217	C₂²	1	2	yes	—
32	C₉×#217	C₂²	1	1	yes	characteristic
33	C₉×#217	C₂²	1	2	yes	complemented
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
39	C₂³×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#237	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×#939	C₂×C₃	1	2	yes	—
44	C₃×#935	C₂×C₃	1	1	yes	characteristic
45	C₃×D₄×Dic₃	C₂×C₃	1	2	yes	—
46	C₃×#886	C₂×C₃	1	1	yes	characteristic
47	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
48	C₃×#878	C₂×C₃	1	2	yes	—
49	C₃×#877	C₂×C₃	1	1	yes	characteristic
50	C₂×C₉×#41	—	3	1	no	—
51	C₂³×C₄×C₉	—	3	1	no	—
52	C₉×#123	—	3	1	no	—
53	C₉×#123	—	3	1	no	—
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₉×#121	—	3	2	no	—
56	C₉×#120	—	2	1	no	—
57	C₉×#120	—	3	1	no	—
58	C₉×#120	D₃	1	1	yes	characteristic, complemented
59	C₄×D₄×C₉	—	3	2	no	—
60	C₄×D₄×C₉	—	3	2	no	—
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	—	2	2	no	—
63	C₂³×C₃×C₉	—	2	4	no	—
64	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
65	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
66	C₂³×C₃×C₉	C₂³	1	2	yes	—
67	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
68	C₃×D₄×C₉	—	2	2	no	—
69	C₃×D₄×C₉	—	2	4	no	—
70	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
72	C₉×#67	—	2	2	no	—
73	C₉×#67	—	2	4	no	—
74	C₉×#67	—	2	2	no	—
75	C₂×C₉×Dic₃	—	2	2	no	—
76	C₂×C₉×Dic₃	—	2	2	no	—
77	C₂×C₉×Dic₃	—	2	4	no	—
78	C₂×C₉×Dic₃	—	2	4	no	—
79	C₂×C₉×Dic₃	D₄	1	4	yes	complemented
80	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₉×Dic₃	C₂³	1	2	yes	—
82	C₂×C₉×Dic₃	C₂³	1	2	yes	—
83	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
85	C₄×D₃×C₉	—	2	2	no	—
86	C₉×Dic₆	—	2	2	no	—
87	C₃×#525	—	3	1	no	—
88	#5586	C₉	1	1	yes	characteristic, direct product factor
89	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
93	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₃×Dic₃	—	2	4	no	—
96	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
97	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
98	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×#237	—	2	4	no	—
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
104	C₂⁴×C₉	—	2	1	no	—
105	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₃×#217	C₂²×C₃	1	1	yes	characteristic
109	C₃×#217	C₂²×C₃	1	2	yes	—
110	C₃×#217	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
115	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
116	C₉×#41	—	6	4	no	—
117	C₂×Q₈×C₉	—	3	1	no	—
118	C₂×D₄×C₉	—	2	2	no	—
119	C₂×D₄×C₉	—	2	1	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	—	3	1	no	—
122	C₂×D₄×C₉	—	3	1	no	—
123	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
124	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
125	C₂²×C₄×C₉	—	3	1	no	—
126	C₂²×C₄×C₉	—	3	2	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	—	3	2	no	—
129	C₂²×C₄×C₉	—	3	1	no	—
130	C₂²×C₄×C₉	—	3	1	no	—
131	C₂²×C₄×C₉	—	6	4	no	—
132	C₉×C₄⋊C₄	—	3	2	no	—
133	C₉×C₄⋊C₄	—	3	2	no	—
134	C₉×C₄⋊C₄	—	3	2	no	—
135	C₉×C₂²⋊C₄	—	2	1	no	—
136	C₉×C₂²⋊C₄	—	2	2	no	—
137	C₉×C₂²⋊C₄	—	3	1	no	—
138	C₉×C₂²⋊C₄	—	3	2	no	—
139	C₉×C₂²⋊C₄	—	3	2	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
142	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
143	C₄²×C₉	—	3	2	no	—
144	C₂²×C₃×C₉	—	2	8	no	—
145	C₂²×C₃×C₉	—	2	2	no	—
146	C₂²×C₃×C₉	—	2	2	no	—
147	C₂²×C₃×C₉	—	2	2	no	—
148	C₂²×C₃×C₉	—	2	1	no	—
149	C₂²×C₃×C₉	—	2	2	no	—
150	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
151	C₂²×C₃×C₉	#41	1	4	yes	complemented
152	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
153	C₂×D₃×C₉	—	2	1	no	—
154	C₂×D₃×C₉	—	2	2	no	—
155	C₃×C₄×C₉	—	2	1	no	—
156	C₃×C₄×C₉	—	2	2	no	—
157	C₉×Dic₃	—	2	1	no	—
158	C₉×Dic₃	—	2	2	no	—
159	C₉×Dic₃	—	2	2	no	—
160	C₉×Dic₃	C₂×D₄	1	2	yes	—
161	C₉×Dic₃	C₂×D₄	1	2	yes	—
162	C₂×C₃×#41	—	3	1	no	—
163	C₂³×C₃×C₄	—	3	1	no	—
164	C₂³×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
165	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
166	C₃×#123	—	3	1	no	—
167	C₃×#123	—	3	1	no	—
168	C₃×C₂²⋊Q₈	—	3	2	no	—
169	C₃×#121	—	3	2	no	—
170	C₃×#120	—	2	1	no	—
171	C₃×#120	—	3	1	no	—
172	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
173	C₃×#120	C₃×D₃	1	1	yes	characteristic
174	C₃×C₄×D₄	—	3	2	no	—
175	C₃×C₄×D₄	—	3	2	no	—
176	C₃×#117	—	3	1	no	—
177	#953	C₂×C₉	1	1	yes	characteristic, complemented
178	#939	C₂×C₉	1	2	yes	complemented
179	#935	C₂×C₉	1	1	yes	characteristic, complemented
180	D₄×Dic₃	C₂×C₉	1	2	yes	complemented
181	#886	C₂×C₉	1	1	yes	characteristic, complemented
182	#67⋊C₄	C₂×C₉	1	2	yes	complemented
183	#878	C₂×C₉	1	2	yes	complemented
184	#877	C₂×C₉	1	1	yes	characteristic, complemented
185	C₂³×C₃²	—	2	2	no	—
186	C₂³×C₃²	—	2	4	no	—
187	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
188	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
189	C₂³×C₃²	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
191	C₃²×D₄	—	2	2	no	—
192	C₃²×D₄	—	2	4	no	—
193	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
194	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₃×#67	—	2	2	no	—
196	C₃×#67	—	2	4	no	—
197	C₃×#67	—	2	2	no	—
198	C₂×C₃×Dic₃	—	2	2	no	—
199	C₂×C₃×Dic₃	—	2	2	no	—
200	C₂×C₃×Dic₃	—	2	4	no	—
201	C₂×C₃×Dic₃	—	2	4	no	—
202	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
204	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
208	C₃×C₄×D₃	—	2	2	no	—
209	C₃×Dic₆	—	2	2	no	—
210	C₂³×C₉	—	2	2	no	—
211	C₂³×C₉	—	2	4	no	—
212	C₂³×C₉	—	2	1	no	—
213	C₂³×C₉	—	2	2	no	—
214	C₂³×C₉	—	2	1	no	—
215	C₂³×C₉	—	3	1	no	—
216	C₂³×C₉	—	4	2	no	—
217	C₂³×C₉	—	4	4	no	—
218	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
219	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
220	C₂³×C₉	C₂²×D₃	1	2	yes	—
221	Q₈×C₉	—	6	2	no	—
222	D₄×C₉	—	2	2	no	—
223	D₄×C₉	—	2	4	no	—
224	D₄×C₉	—	4	2	no	—
225	D₄×C₉	—	4	4	no	—
226	D₄×C₉	—	6	2	no	—
227	D₄×C₉	—	6	2	no	—
228	D₄×C₉	—	6	4	no	—
229	C₂×C₄×C₉	—	2	2	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	3	4	no	—
232	C₂×C₄×C₉	—	3	1	no	—
233	C₂×C₄×C₉	—	3	1	no	—
234	C₂×C₄×C₉	—	3	2	no	—
235	C₂×C₄×C₉	—	3	2	no	—
236	C₂×C₄×C₉	—	3	1	no	—
237	C₂×C₄×C₉	—	6	2	no	—
238	C₂×C₄×C₉	—	6	4	no	—
239	C₂×C₄×C₉	—	6	4	no	—
240	C₂×C₄×C₉	—	6	2	no	—
241	C₂×C₄×C₉	—	6	2	no	—
242	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
243	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
244	#525	—	3	1	no	Sylow
245	C₂×C₃×C₉	—	2	2	no	—
246	C₂×C₃×C₉	—	2	4	no	—
247	C₂×C₃×C₉	—	4	1	no	—
248	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₃×C₉	C₂×#41	1	2	yes	—
250	D₃×C₉	—	4	1	no	—
251	C₂⁴×C₃	—	2	1	no	—
252	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
253	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
254	C₃×#41	—	6	4	no	—
255	C₂×C₃×Q₈	—	3	1	no	—
256	C₂×C₃×D₄	—	2	2	no	—
257	C₂×C₃×D₄	—	2	1	no	—
258	C₂×C₃×D₄	—	3	2	no	—
259	C₂×C₃×D₄	—	3	1	no	—
260	C₂×C₃×D₄	—	3	1	no	—
261	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
262	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
263	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
264	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
265	C₂²×C₃×C₄	—	3	1	no	—
266	C₂²×C₃×C₄	—	3	2	no	—
267	C₂²×C₃×C₄	—	3	1	no	—
268	C₂²×C₃×C₄	—	3	2	no	—
269	C₂²×C₃×C₄	—	3	1	no	—
270	C₂²×C₃×C₄	—	3	1	no	—
271	C₂²×C₃×C₄	—	6	4	no	—
272	C₂×#67	C₂²×C₉	1	2	yes	—
273	C₂×#67	C₂²×C₉	1	1	yes	characteristic
274	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
275	C₂²×Dic₃	—	2	4	no	—
276	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
277	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
278	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
279	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
280	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
281	#237	—	2	4	no	—
282	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
283	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
284	C₃×C₄⋊C₄	—	3	2	no	—
285	C₃×C₄⋊C₄	—	3	2	no	—
286	C₃×C₄⋊C₄	—	3	2	no	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	—	3	1	no	—
290	C₃×C₂²⋊C₄	—	3	2	no	—
291	C₃×C₂²⋊C₄	—	3	2	no	—
292	C₃×C₂²⋊C₄	—	3	2	no	—
293	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
294	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
295	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
296	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
297	C₃×C₄²	—	3	2	no	—
298	#217	C₂²×C₉	1	1	yes	characteristic
299	#217	C₂²×C₉	1	2	yes	—
300	#217	C₂²×C₉	1	2	yes	complemented
301	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
302	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
303	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
304	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
305	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
306	C₂²×C₃²	—	2	8	no	—
307	C₂²×C₃²	—	2	2	no	—
308	C₂²×C₃²	—	2	2	no	—
309	C₂²×C₃²	—	2	2	no	—
310	C₂²×C₃²	—	2	1	no	—
311	C₂²×C₃²	—	2	2	no	—
312	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
313	C₂²×C₃²	C₃×#41	1	4	yes	—
314	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
315	C₂×C₃×D₃	—	2	1	no	—
316	C₂×C₃×D₃	—	2	2	no	—
317	C₃²×C₄	—	2	1	no	—
318	C₃²×C₄	—	2	2	no	—
319	C₃×Dic₃	—	2	1	no	—
320	C₃×Dic₃	—	2	2	no	—
321	C₃×Dic₃	—	2	2	no	—
322	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
323	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
324	C₂²×C₉	—	2	8	no	—
325	C₂²×C₉	—	2	2	no	—
326	C₂²×C₉	—	2	2	no	—
327	C₂²×C₉	—	2	2	no	—
328	C₂²×C₉	—	2	1	no	—
329	C₂²×C₉	—	2	2	no	—
330	C₂²×C₉	—	2	1	no	—
331	C₂²×C₉	—	2	2	no	—
332	C₂²×C₉	—	2	4	no	—
333	C₂²×C₉	—	4	2	no	—
334	C₂²×C₉	—	4	2	no	—
335	C₂²×C₉	—	4	2	no	—
336	C₂²×C₉	—	4	1	no	—
337	C₂²×C₉	—	4	2	no	—
338	C₂²×C₉	—	4	8	no	—
339	C₂²×C₉	—	6	1	no	—
340	C₂²×C₉	—	6	2	no	—
341	C₂²×C₉	D₃×D₄	1	2	yes	—
342	C₂²×C₉	#237	1	4	yes	complemented
343	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
344	C₄×C₉	—	2	1	no	—
345	C₄×C₉	—	2	2	no	—
346	C₄×C₉	—	3	2	no	—
347	C₄×C₉	—	3	2	no	—
348	C₄×C₉	—	4	1	no	—
349	C₄×C₉	—	4	2	no	—
350	C₄×C₉	—	6	2	no	—
351	C₄×C₉	—	6	1	no	—
352	C₄×C₉	—	6	2	no	—
353	C₂×#41	—	3	1	no	—
354	C₂³×C₄	—	3	1	no	—
355	#123	—	3	1	no	—
356	#123	—	3	1	no	—
357	C₂²⋊Q₈	—	3	2	no	—
358	#121	—	3	2	no	—
359	#120	—	3	1	no	—
360	#120	D₃×C₉	1	1	yes	characteristic, complemented
361	C₄×D₄	—	3	2	no	—
362	C₄×D₄	—	3	2	no	—
363	#117	—	3	1	no	—
364	C₃×C₉	#525	1	1	yes	characteristic, complemented, Sylow
365	C₂³×C₃	—	2	2	no	—
366	C₂³×C₃	—	2	4	no	—
367	C₂³×C₃	—	2	2	no	—
368	C₂³×C₃	—	2	4	no	—
369	C₂³×C₃	—	2	1	no	—
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	3	1	no	—
373	C₂³×C₃	—	4	2	no	—
374	C₂³×C₃	—	4	4	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	C₂³×C₉	1	1	yes	characteristic
382	C₃×Q₈	—	6	2	no	—
383	C₃×D₄	—	2	2	no	—
384	C₃×D₄	—	2	4	no	—
385	C₃×D₄	—	2	2	no	—
386	C₃×D₄	—	2	4	no	—
387	C₃×D₄	—	4	2	no	—
388	C₃×D₄	—	4	4	no	—
389	C₃×D₄	—	6	2	no	—
390	C₃×D₄	—	6	2	no	—
391	C₃×D₄	—	6	4	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	3	1	no	—
395	C₂×C₃×C₄	—	3	1	no	—
396	C₂×C₃×C₄	—	3	4	no	—
397	C₂×C₃×C₄	—	3	2	no	—
398	C₂×C₃×C₄	—	3	2	no	—
399	C₂×C₃×C₄	—	3	1	no	—
400	C₂×C₃×C₄	—	6	2	no	—
401	C₂×C₃×C₄	—	6	4	no	—
402	C₂×C₃×C₄	—	6	4	no	—
403	C₂×C₃×C₄	—	6	2	no	—
404	C₂×C₃×C₄	—	6	2	no	—
405	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
406	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
408	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
409	#67	—	2	2	no	—
410	#67	—	2	4	no	—
411	#67	—	2	2	no	—
412	C₂×Dic₃	—	2	2	no	—
413	C₂×Dic₃	—	2	2	no	—
414	C₂×Dic₃	—	2	4	no	—
415	C₂×Dic₃	—	2	4	no	—
416	C₂×Dic₃	D₄×C₉	1	4	yes	complemented
417	C₂×Dic₃	C₂³×C₉	1	2	yes	—
418	C₂×Dic₃	C₂³×C₉	1	2	yes	—
419	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
420	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
421	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
422	C₄×D₃	—	2	2	no	—
423	Dic₆	—	2	2	no	—
424	C₂×C₃²	—	2	2	no	—
425	C₂×C₃²	—	2	4	no	—
426	C₂×C₃²	—	4	1	no	—
427	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
428	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
429	C₃×D₃	—	4	1	no	—
430	C₂×C₉	—	2	2	no	—
431	C₂×C₉	—	2	4	no	—
432	C₂×C₉	—	2	1	no	—
433	C₂×C₉	—	2	2	no	—
434	C₂×C₉	—	4	2	no	—
435	C₂×C₉	—	4	4	no	—
436	C₂×C₉	—	4	1	no	—
437	C₂×C₉	—	8	1	no	—
438	C₂×C₉	—	12	1	no	—
439	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
440	C₂×C₉	C₂×#237	1	2	yes	—
441	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
442	#41	—	6	4	no	—
443	C₂×Q₈	—	3	1	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	1	no	—
446	C₂×D₄	—	3	1	no	—
447	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
448	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	6	4	no	—
456	C₄⋊C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₂²⋊C₄	—	3	1	no	—
460	C₂²⋊C₄	—	3	2	no	—
461	C₂²⋊C₄	—	3	2	no	—
462	C₂²⋊C₄	—	3	2	no	—
463	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
464	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
465	C₄²	—	3	2	no	—
466	C₂²×C₃	—	2	8	no	—
467	C₂²×C₃	—	2	8	no	—
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	4	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	2	no	—
486	C₂²×C₃	—	4	8	no	—
487	C₂²×C₃	—	6	1	no	—
488	C₂²×C₃	—	6	2	no	—
489	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
490	C₂²×C₃	C₉×#41	1	4	yes	complemented
491	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
492	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
493	C₂²×C₃	C₃×#237	1	4	yes	—
494	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	—	2	2	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	2	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	2	2	no	—
501	C₃×C₄	—	3	2	no	—
502	C₃×C₄	—	3	2	no	—
503	C₃×C₄	—	4	1	no	—
504	C₃×C₄	—	4	2	no	—
505	C₃×C₄	—	6	2	no	—
506	C₃×C₄	—	6	1	no	—
507	C₃×C₄	—	6	2	no	—
508	Dic₃	—	2	1	no	—
509	Dic₃	—	2	2	no	—
510	Dic₃	—	2	2	no	—
511	Dic₃	C₂×D₄×C₉	1	2	yes	—
512	Dic₃	C₂×D₄×C₉	1	2	yes	—
513	C₃²	C₃×#525	1	1	yes	characteristic
514	C₉	—	2	1	no	—
515	C₉	#5586	1	1	yes	characteristic, direct product factor
516	C₂³	—	2	2	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	3	1	no	—
519	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
520	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
521	C₂³	C₂²×D₃×C₉	1	2	yes	—
522	Q₈	—	6	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	4	no	—
525	D₄	—	6	2	no	—
526	D₄	—	6	2	no	—
527	D₄	—	6	4	no	—
528	C₂×C₄	—	3	1	no	—
529	C₂×C₄	—	3	1	no	—
530	C₂×C₄	—	3	4	no	—
531	C₂×C₄	—	3	2	no	—
532	C₂×C₄	—	3	2	no	—
533	C₂×C₄	—	3	1	no	—
534	C₂×C₄	—	6	2	no	—
535	C₂×C₄	—	6	4	no	—
536	C₂×C₄	—	6	4	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	2	no	—
539	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
540	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
541	C₂×C₃	—	2	2	no	—
542	C₂×C₃	—	2	4	no	—
543	C₂×C₃	—	2	2	no	—
544	C₂×C₃	—	2	4	no	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	2	2	no	—
547	C₂×C₃	—	4	2	no	—
548	C₂×C₃	—	4	4	no	—
549	C₂×C₃	—	4	1	no	—
550	C₂×C₃	—	4	1	no	—
551	C₂×C₃	—	8	1	no	—
552	C₂×C₃	—	12	1	no	—
553	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
554	C₂×C₃	C₂×C₉×#41	1	2	yes	—
555	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
556	C₂×C₃	C₂×C₃×#237	1	2	yes	—
557	D₃	—	4	1	no	—
558	C₂²	—	2	8	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	6	1	no	—
565	C₂²	—	6	2	no	—
566	C₂²	D₃×D₄×C₉	1	2	yes	—
567	C₂²	C₉×#237	1	4	yes	complemented
568	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	3	2	no	—
572	C₄	—	3	2	no	—
573	C₄	—	6	2	no	—
574	C₄	—	6	1	no	—
575	C₄	—	6	2	no	—
576	C₃	—	2	1	no	—
577	C₃	C₉×#525	1	1	yes	characteristic, complemented
578	C₃	C₃×#5586	1	1	yes	characteristic
579	C₂	—	2	2	no	—
580	C₂	—	2	4	no	—
581	C₂	—	4	1	no	—
582	C₂	—	12	1	no	—
583	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
584	C₂	C₂×C₉×#237	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×#5586	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	C₉×#525
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. C₂³×C₉×Dic₃	C₂	semidirect
2. C₂×C₉×#237	C₂	semidirect
3. C₃×C₉×#120	C₂	semidirect
4. C₉×#953	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#935	C₂	semidirect
7. D₄×C₉×Dic₃	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#67⋊C₄	C₂	semidirect
10. C₉×#878	C₂	semidirect
11. C₉×#877	C₂	semidirect
19. C₂×C₉×#67	C₂²	semidirect
25. C₂²×C₉×Dic₃	C₂²	semidirect
27. C₂×C₄×D₃×C₉	C₂²	semidirect
28. C₂×C₉×Dic₆	C₂²	semidirect
33. C₉×#217	C₂²	semidirect
34. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₉×C₄⋊Dic₃	C₂²	semidirect
36. C₉×Dic₃⋊C₄	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
58. C₉×#120	D₃	semidirect
79. C₂×C₉×Dic₃	D₄	semidirect
88. #5586	C₉	direct (N × H)
151. C₂²×C₃×C₉	#41	semidirect
164. C₂³×Dic₃	C₂×C₉	semidirect
165. C₂×#237	C₂×C₉	semidirect
172. C₃×#120	C₂×C₉	semidirect
177. #953	C₂×C₉	semidirect
178. #939	C₂×C₉	semidirect
179. #935	C₂×C₉	semidirect
180. D₄×Dic₃	C₂×C₉	semidirect
181. #886	C₂×C₉	semidirect
182. #67⋊C₄	C₂×C₉	semidirect
183. #878	C₂×C₉	semidirect
184. #877	C₂×C₉	semidirect
274. C₂×#67	C₂²×C₉	semidirect
280. C₂²×Dic₃	C₂²×C₉	semidirect
282. C₂×C₄×D₃	C₂²×C₉	semidirect
283. C₂×Dic₆	C₂²×C₉	semidirect
300. #217	C₂²×C₉	semidirect
301. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
302. C₄⋊Dic₃	C₂²×C₉	semidirect
303. Dic₃⋊C₄	C₂²×C₉	semidirect
304. Dic₃⋊C₄	C₂²×C₉	semidirect
305. C₄×Dic₃	C₂²×C₉	semidirect
342. C₂²×C₉	#237	semidirect
360. #120	D₃×C₉	semidirect
364. C₃×C₉	#525	semidirect
416. C₂×Dic₃	D₄×C₉	semidirect
490. C₂²×C₃	C₉×#41	semidirect
515. C₉	#5586	direct (N × H)
567. C₂²	C₉×#237	semidirect
577. 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×C₉×Dic₃	2
C₂×C₉×#237	2
C₃×C₉×#120	2
C₉×#953	2
C₉×#939	2
C₉×#935	2
D₄×C₉×Dic₃	2
C₉×#886	2
C₉×#67⋊C₄	2
C₉×#878	2
C₉×#877	2
C₃×#5586	3
C₉×#525	3

Subgroups — C9×#5586 #13152750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5586 #13152750