Subgroups — C₃×#10589798 #13153144

Order 1728.

632 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63460	C₂	1	1	yes	maximal, characteristic
3	C₃×#63460	C₂	1	1	yes	maximal, characteristic
4	C₃×#63460	C₂	1	1	yes	maximal, characteristic
5	C₃×#63458	C₂	1	1	yes	maximal, characteristic
6	C₃×#63458	C₂	1	1	yes	maximal, characteristic
7	C₃×#63454	C₂	1	1	yes	maximal, characteristic
8	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#63438	C₂	1	1	yes	maximal, characteristic
15	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5696	—	3	1	no	maximal
17	#10589798	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
38	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
52	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
53	C₃²×#125	D₃	1	1	yes	characteristic
54	C₃×#898	—	3	1	no	—
55	C₃×#898	—	3	1	no	—
56	C₃×#898	—	3	1	no	—
57	C₃×#896	—	3	1	no	—
58	C₃×#896	—	3	1	no	—
59	C₃×#892	—	3	1	no	—
60	C₃×#890	—	3	1	no	—
61	C₃×#889	—	3	1	no	—
62	C₃×#889	—	3	1	no	—
63	C₃×#889	—	3	1	no	—
64	C₃×#888	—	3	1	no	—
65	C₃×#887	—	3	1	no	—
66	C₃×#876	—	3	1	no	—
67	C₃×C₄×Dic₆	—	3	1	no	—
68	C₉×#125	—	2	1	no	—
69	C₉×#125	C₂×C₃	1	1	yes	characteristic, complemented
70	#63460	C₂×C₃	1	1	yes	characteristic
71	#63460	C₂×C₃	1	1	yes	characteristic
72	#63460	C₂×C₃	1	1	yes	characteristic
73	#63458	C₂×C₃	1	1	yes	characteristic
74	#63458	C₂×C₃	1	1	yes	characteristic
75	#63454	C₂×C₃	1	1	yes	characteristic
76	#63452	C₂×C₃	1	1	yes	characteristic, complemented
77	#63451	C₂×C₃	1	1	yes	characteristic, complemented
78	#63451	C₂×C₃	1	1	yes	characteristic, complemented
79	#63451	C₂×C₃	1	1	yes	characteristic, complemented
80	#63450	C₂×C₃	1	1	yes	characteristic, complemented
81	#63449	C₂×C₃	1	1	yes	characteristic, complemented
82	#63438	C₂×C₃	1	1	yes	characteristic
83	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
97	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
98	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
99	C₃×C₄×D₉	—	2	2	no	—
100	C₃×Dic₁₈	—	2	2	no	—
101	C₃×Dic₁₈	—	2	2	no	—
102	C₃×#541	—	9	1	no	—
103	#5696	—	3	1	no	—
104	C₂×C₃×C₄×D₃	—	3	1	no	—
105	C₂×C₃×Dic₆	—	3	1	no	—
106	C₂×C₃×Dic₆	—	3	1	no	—
107	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
108	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
109	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
110	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
112	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
113	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
114	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
115	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
116	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
117	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
118	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
119	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
120	C₃×C₄⋊Dic₃	—	3	1	no	—
121	C₃×C₄⋊Dic₃	—	3	1	no	—
122	C₃×C₄⋊Dic₃	—	3	1	no	—
123	C₃×C₄⋊Dic₃	—	3	1	no	—
124	C₃×Dic₃⋊C₄	—	3	1	no	—
125	C₃×Dic₃⋊C₄	—	3	1	no	—
126	C₃×Dic₃⋊C₄	—	3	1	no	—
127	C₃×Dic₃⋊C₄	—	3	1	no	—
128	C₃×Dic₃⋊C₄	—	3	1	no	—
129	C₃×Dic₃⋊C₄	—	3	1	no	—
130	C₃×Dic₃⋊C₄	—	3	1	no	—
131	C₃×Dic₃⋊C₄	—	3	1	no	—
132	C₃×Dic₃⋊C₄	—	3	1	no	—
133	C₃×Dic₃⋊C₄	—	3	1	no	—
134	C₃×C₄×Dic₃	—	3	1	no	—
135	C₃×C₄×Dic₃	—	3	1	no	—
136	C₃×C₄×Dic₃	—	3	1	no	—
137	C₃×C₄×Dic₃	—	3	1	no	—
138	C₃×C₄×Dic₃	—	3	1	no	—
139	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
140	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
141	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
142	C₉×C₄⋊C₄	—	2	1	no	—
143	C₉×C₄⋊C₄	—	2	1	no	—
144	C₉×C₄⋊C₄	—	2	1	no	—
145	C₉×C₄⋊C₄	—	2	1	no	—
146	C₉×C₄⋊C₄	—	2	1	no	—
147	C₉×C₄⋊C₄	—	2	1	no	—
148	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₄²×C₉	—	2	1	no	—
155	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
156	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
163	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
164	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
165	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
166	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
177	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
178	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
179	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
180	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₃×D₉	—	2	1	no	—
183	C₂×C₃×D₉	—	2	1	no	—
184	C₂×C₃×D₉	—	2	1	no	—
185	C₃×C₄×C₉	—	2	1	no	—
186	C₃×C₄×C₉	—	2	1	no	—
187	C₃×C₄×C₉	—	2	1	no	—
188	C₃×C₄×C₉	—	2	1	no	—
189	C₃×C₄×C₉	—	2	1	no	—
190	C₃×C₄×C₉	—	2	1	no	—
191	C₃×C₄×C₉	—	2	1	no	—
192	C₃×Dic₉	—	2	1	no	—
193	C₃×Dic₉	—	2	1	no	—
194	C₃×Dic₉	—	2	1	no	—
195	C₃×Dic₉	—	2	1	no	—
196	C₃×Dic₉	—	2	1	no	—
197	C₃×Dic₉	—	2	1	no	—
198	C₃×Dic₉	#41	1	2	yes	—
199	C₃×C₄⋊Q₈	—	9	1	no	—
200	C₃×#126	—	9	1	no	—
201	C₃×#126	—	9	1	no	—
202	C₃×#126	—	9	1	no	—
203	C₃×#126	—	9	1	no	—
204	C₃×#125	—	2	1	no	—
205	C₃×#125	—	9	1	no	—
206	C₃×#125	—	9	1	no	—
207	C₃×#125	—	9	1	no	—
208	C₃×#125	—	9	1	no	—
209	C₃×#125	D₉	1	1	yes	characteristic, complemented
210	C₃×#125	C₃×D₃	1	1	yes	characteristic
211	C₃×C₂²⋊Q₈	—	9	1	no	—
212	C₃×C₂²⋊Q₈	—	9	1	no	—
213	C₃×C₄×Q₈	—	9	1	no	—
214	C₃×C₄×Q₈	—	9	1	no	—
215	C₃×#117	—	9	1	no	—
216	#898	—	3	1	no	—
217	#898	—	3	1	no	—
218	#898	—	3	1	no	—
219	#896	—	3	1	no	—
220	#896	—	3	1	no	—
221	#892	—	3	1	no	—
222	#890	—	3	1	no	—
223	#889	—	3	1	no	—
224	#889	—	3	1	no	—
225	#889	—	3	1	no	—
226	#888	—	3	1	no	—
227	#887	—	3	1	no	—
228	#876	—	3	1	no	—
229	C₄×Dic₆	—	3	1	no	—
230	C₂²×C₃×D₃	—	3	1	no	—
231	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₃×Dic₃	—	3	1	no	—
239	C₂×C₃×Dic₃	—	3	1	no	—
240	C₂×C₃×Dic₃	—	3	1	no	—
241	C₂×C₃×Dic₃	—	3	1	no	—
242	C₂×C₃×Dic₃	—	3	1	no	—
243	C₂×C₃×Dic₃	—	3	1	no	—
244	C₂×C₃×Dic₃	—	3	1	no	—
245	C₃×C₄×D₃	—	6	2	no	—
246	C₃×Dic₆	—	6	2	no	—
247	C₃×Dic₆	—	6	2	no	—
248	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₄×C₉	—	2	1	no	—
250	C₂×C₄×C₉	—	2	1	no	—
251	C₂×C₄×C₉	—	2	1	no	—
252	C₂×C₄×C₉	—	2	1	no	—
253	C₂×C₄×C₉	—	2	1	no	—
254	C₂×C₄×C₉	—	2	1	no	—
255	C₂×C₄×C₉	—	2	1	no	—
256	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
263	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
264	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
265	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
266	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
267	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
268	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
269	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
270	C₄×D₉	—	2	2	no	—
271	Dic₁₈	—	2	2	no	—
272	Dic₁₈	—	2	2	no	—
273	#541	—	9	1	no	Sylow
274	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
276	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
277	C₃×D₉	—	4	1	no	—
278	C₂×C₃×Q₈	—	9	1	no	—
279	C₂×C₃×Q₈	—	9	1	no	—
280	C₂²×C₃×C₄	—	9	1	no	—
281	C₂×C₄×D₃	—	3	1	no	—
282	C₂×Dic₆	—	3	1	no	—
283	C₂×Dic₆	—	3	1	no	—
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	2	1	no	—
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	9	1	no	—
291	C₃×C₄⋊C₄	—	9	1	no	—
292	C₃×C₄⋊C₄	—	9	1	no	—
293	C₃×C₄⋊C₄	—	9	1	no	—
294	C₃×C₄⋊C₄	—	9	1	no	—
295	C₃×C₄⋊C₄	—	9	1	no	—
296	C₃×C₄⋊C₄	—	9	1	no	—
297	C₃×C₄⋊C₄	—	9	1	no	—
298	C₃×C₄⋊C₄	—	9	1	no	—
299	C₃×C₄⋊C₄	—	9	1	no	—
300	C₃×C₄⋊C₄	—	9	1	no	—
301	C₃×C₄⋊C₄	—	9	1	no	—
302	C₃×C₄⋊C₄	—	9	1	no	—
303	C₃×C₄⋊C₄	—	9	1	no	—
304	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
309	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
310	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
311	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
312	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
313	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
314	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
315	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	—	9	1	no	—
317	C₃×C₂²⋊C₄	—	9	1	no	—
318	C₃×C₂²⋊C₄	—	9	1	no	—
319	C₃×C₂²⋊C₄	—	9	1	no	—
320	C₃×C₂²⋊C₄	—	9	1	no	—
321	C₃×C₂²⋊C₄	—	9	1	no	—
322	C₃×C₄²	—	2	1	no	—
323	C₃×C₄²	—	9	1	no	—
324	C₃×C₄²	—	9	1	no	—
325	C₃×C₄²	—	9	1	no	—
326	C₃×C₄²	—	9	1	no	—
327	C₃×C₄²	—	9	1	no	—
328	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
329	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
330	(C₂×D₃)⋊C₄	—	3	1	no	—
331	(C₂×D₃)⋊C₄	—	3	1	no	—
332	(C₂×D₃)⋊C₄	—	3	1	no	—
333	(C₂×D₃)⋊C₄	—	3	1	no	—
334	(C₂×D₃)⋊C₄	—	3	1	no	—
335	(C₂×D₃)⋊C₄	—	3	1	no	—
336	C₄⋊Dic₃	—	3	1	no	—
337	C₄⋊Dic₃	—	3	1	no	—
338	C₄⋊Dic₃	—	3	1	no	—
339	C₄⋊Dic₃	—	3	1	no	—
340	Dic₃⋊C₄	—	3	1	no	—
341	Dic₃⋊C₄	—	3	1	no	—
342	Dic₃⋊C₄	—	3	1	no	—
343	Dic₃⋊C₄	—	3	1	no	—
344	Dic₃⋊C₄	—	3	1	no	—
345	Dic₃⋊C₄	—	3	1	no	—
346	Dic₃⋊C₄	—	3	1	no	—
347	Dic₃⋊C₄	—	3	1	no	—
348	Dic₃⋊C₄	—	3	1	no	—
349	Dic₃⋊C₄	—	3	1	no	—
350	C₄×Dic₃	—	3	1	no	—
351	C₄×Dic₃	—	3	1	no	—
352	C₄×Dic₃	—	3	1	no	—
353	C₄×Dic₃	—	3	1	no	—
354	C₄×Dic₃	—	3	1	no	—
355	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
356	C₂×C₃×D₃	—	6	1	no	—
357	C₂×C₃×D₃	—	6	1	no	—
358	C₂×C₃×D₃	—	6	1	no	—
359	C₃²×C₄	—	2	1	no	—
360	C₃²×C₄	—	2	1	no	—
361	C₃²×C₄	—	2	1	no	—
362	C₃²×C₄	—	2	1	no	—
363	C₃²×C₄	—	2	1	no	—
364	C₃²×C₄	—	2	1	no	—
365	C₃²×C₄	—	2	1	no	—
366	C₃×Dic₃	—	3	2	no	—
367	C₃×Dic₃	—	6	1	no	—
368	C₃×Dic₃	—	6	1	no	—
369	C₃×Dic₃	—	6	1	no	—
370	C₃×Dic₃	—	6	1	no	—
371	C₃×Dic₃	—	6	1	no	—
372	C₃×Dic₃	—	6	1	no	—
373	C₂²×C₉	—	2	1	no	—
374	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
375	C₂×D₉	—	2	1	no	—
376	C₂×D₉	—	2	1	no	—
377	C₂×D₉	—	2	1	no	—
378	C₄×C₉	—	2	2	no	—
379	C₄×C₉	—	2	1	no	—
380	C₄×C₉	—	2	1	no	—
381	C₄×C₉	—	2	1	no	—
382	C₄×C₉	—	2	1	no	—
383	C₄×C₉	—	2	1	no	—
384	C₄×C₉	—	2	1	no	—
385	C₄×C₉	—	2	1	no	—
386	C₄×C₉	—	4	1	no	—
387	C₄×C₉	—	4	1	no	—
388	C₄×C₉	—	4	1	no	—
389	C₄×C₉	—	4	1	no	—
390	C₄×C₉	—	4	1	no	—
391	C₄×C₉	—	4	1	no	—
392	Dic₉	—	2	1	no	—
393	Dic₉	—	2	1	no	—
394	Dic₉	—	2	1	no	—
395	Dic₉	—	2	1	no	—
396	Dic₉	—	2	1	no	—
397	Dic₉	—	2	1	no	—
398	Dic₉	C₃×#41	1	2	yes	—
399	C₄⋊Q₈	—	9	1	no	—
400	#126	—	9	1	no	—
401	#126	—	9	1	no	—
402	#126	—	9	1	no	—
403	#126	—	9	1	no	—
404	#125	—	9	1	no	—
405	#125	—	9	1	no	—
406	#125	—	9	1	no	—
407	#125	—	9	1	no	—
408	#125	C₃×D₉	1	1	yes	characteristic, complemented
409	C₂²⋊Q₈	—	9	1	no	—
410	C₂²⋊Q₈	—	9	1	no	—
411	C₄×Q₈	—	9	1	no	—
412	C₄×Q₈	—	9	1	no	—
413	#117	—	9	1	no	—
414	C₃×C₉	#541	1	1	yes	characteristic, complemented, Sylow
415	C₂³×C₃	—	9	1	no	—
416	C₂²×D₃	—	3	1	no	—
417	C₃×Q₈	—	18	2	no	—
418	C₃×Q₈	—	18	2	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	9	1	no	—
427	C₂×C₃×C₄	—	9	1	no	—
428	C₂×C₃×C₄	—	9	1	no	—
429	C₂×C₃×C₄	—	9	1	no	—
430	C₂×C₃×C₄	—	9	1	no	—
431	C₂×C₃×C₄	—	9	1	no	—
432	C₂×C₃×C₄	—	9	1	no	—
433	C₂×C₃×C₄	—	18	2	no	—
434	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
436	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
437	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
442	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
445	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
446	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
447	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
448	C₂×Dic₃	—	3	1	no	—
449	C₂×Dic₃	—	3	1	no	—
450	C₂×Dic₃	—	3	1	no	—
451	C₂×Dic₃	—	3	1	no	—
452	C₂×Dic₃	—	3	1	no	—
453	C₂×Dic₃	—	3	1	no	—
454	C₂×Dic₃	—	3	1	no	—
455	C₄×D₃	—	6	2	no	—
456	Dic₆	—	6	2	no	—
457	Dic₆	—	6	2	no	—
458	C₂×C₃²	#1007	1	1	yes	characteristic
459	C₂×C₃²	D₃×#41	1	1	yes	characteristic
460	C₂×C₃²	#1010	1	1	yes	characteristic
461	C₃×D₃	—	12	1	no	—
462	C₂×C₉	—	2	1	no	—
463	C₂×C₉	—	2	1	no	—
464	C₂×C₉	—	2	1	no	—
465	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
466	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
467	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
468	D₉	—	4	1	no	—
469	C₂×Q₈	—	9	1	no	—
470	C₂×Q₈	—	9	1	no	—
471	C₂²×C₄	—	9	1	no	—
472	C₄⋊C₄	—	9	1	no	—
473	C₄⋊C₄	—	9	1	no	—
474	C₄⋊C₄	—	9	1	no	—
475	C₄⋊C₄	—	9	1	no	—
476	C₄⋊C₄	—	9	1	no	—
477	C₄⋊C₄	—	9	1	no	—
478	C₄⋊C₄	—	9	1	no	—
479	C₄⋊C₄	—	9	1	no	—
480	C₄⋊C₄	—	9	1	no	—
481	C₄⋊C₄	—	9	1	no	—
482	C₄⋊C₄	—	9	1	no	—
483	C₄⋊C₄	—	9	1	no	—
484	C₄⋊C₄	—	9	1	no	—
485	C₄⋊C₄	—	9	1	no	—
486	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
488	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
492	C₂²⋊C₄	—	9	1	no	—
493	C₂²⋊C₄	—	9	1	no	—
494	C₂²⋊C₄	—	9	1	no	—
495	C₂²⋊C₄	—	9	1	no	—
496	C₂²⋊C₄	—	9	1	no	—
497	C₂²⋊C₄	—	9	1	no	—
498	C₄²	—	9	1	no	—
499	C₄²	—	9	1	no	—
500	C₄²	—	9	1	no	—
501	C₄²	—	9	1	no	—
502	C₄²	—	9	1	no	—
503	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	18	1	no	—
506	C₂²×C₃	—	18	1	no	—
507	C₂²×C₃	—	18	1	no	—
508	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
509	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
510	C₂×D₃	—	6	1	no	—
511	C₂×D₃	—	6	1	no	—
512	C₂×D₃	—	6	1	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	2	1	no	—
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	4	1	no	—
529	C₃×C₄	—	4	1	no	—
530	C₃×C₄	—	4	1	no	—
531	C₃×C₄	—	4	1	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	9	2	no	—
535	C₃×C₄	—	18	1	no	—
536	C₃×C₄	—	18	1	no	—
537	C₃×C₄	—	18	1	no	—
538	C₃×C₄	—	18	1	no	—
539	C₃×C₄	—	18	1	no	—
540	C₃×C₄	—	18	1	no	—
541	Dic₃	—	3	2	no	—
542	Dic₃	—	6	1	no	—
543	Dic₃	—	6	1	no	—
544	Dic₃	—	6	1	no	—
545	Dic₃	—	6	1	no	—
546	Dic₃	—	6	1	no	—
547	Dic₃	—	6	1	no	—
548	C₃²	#5696	1	1	yes	characteristic
549	C₉	—	2	1	no	—
550	C₉	C₃×#541	1	1	yes	characteristic, complemented
551	C₂³	—	9	1	no	—
552	Q₈	—	18	2	no	—
553	Q₈	—	18	2	no	—
554	C₂×C₄	—	9	1	no	—
555	C₂×C₄	—	9	1	no	—
556	C₂×C₄	—	9	1	no	—
557	C₂×C₄	—	9	1	no	—
558	C₂×C₄	—	9	1	no	—
559	C₂×C₄	—	9	1	no	—
560	C₂×C₄	—	9	1	no	—
561	C₂×C₄	—	18	2	no	—
562	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
568	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
569	C₂×C₃	—	2	1	no	—
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	2	1	no	—
572	C₂×C₃	—	36	1	no	—
573	C₂×C₃	#63713	1	1	yes	characteristic
574	C₂×C₃	#41×D₉	1	1	yes	characteristic
575	C₂×C₃	#63716	1	1	yes	characteristic
576	C₂×C₃	C₃×#1007	1	1	yes	characteristic
577	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
578	C₂×C₃	C₃×#1010	1	1	yes	characteristic
579	D₃	—	12	1	no	—
580	C₂²	—	18	1	no	—
581	C₂²	—	18	1	no	—
582	C₂²	—	18	1	no	—
583	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	9	2	no	—
592	C₄	—	18	1	no	—
593	C₄	—	18	1	no	—
594	C₄	—	18	1	no	—
595	C₄	—	18	1	no	—
596	C₄	—	18	1	no	—
597	C₄	—	18	1	no	—
598	C₃	—	2	1	no	—
599	C₃	#10589798	1	1	yes	characteristic, direct product factor
600	C₃	C₃×#5696	1	1	yes	characteristic
601	C₂	—	36	1	no	—
602	C₂	C₃×#63713	1	1	yes	characteristic
603	C₂	C₃×#41×D₉	1	1	yes	characteristic
604	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#125	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂²×C₃×D₉	C₂³
hypercenter	C₃×#125	D₉
hypocenter	C₉	C₃×#541
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
8. C₃×#63452	C₂	semidirect
9. C₃×#63451	C₂	semidirect
10. C₃×#63451	C₂	semidirect
11. C₃×#63451	C₂	semidirect
12. C₃×#63450	C₂	semidirect
13. C₃×#63449	C₂	semidirect
15. C₃×C₄×Dic₁₈	C₂	semidirect
17. #10589798	C₃	direct (N × H)
69. C₉×#125	C₂×C₃	semidirect
76. #63452	C₂×C₃	semidirect
77. #63451	C₂×C₃	semidirect
78. #63451	C₂×C₃	semidirect
79. #63451	C₂×C₃	semidirect
80. #63450	C₂×C₃	semidirect
81. #63449	C₂×C₃	semidirect
83. C₄×Dic₁₈	C₂×C₃	semidirect
209. C₃×#125	D₉	semidirect
408. #125	C₃×D₉	semidirect
414. C₃×C₉	#541	semidirect
550. C₉	C₃×#541	semidirect
599. C₃	#10589798	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₉×#125	2
C₃×#63460	2
C₃×#63458	2
C₃×#63454	2
C₃×#63452	2
C₃×#63451	2
C₃×#63450	2
C₃×#63449	2
C₃×#63438	2
C₃×C₄×Dic₁₈	2
C₃×#5696	3
#10589798	3

Subgroups — C3×#10589798 #13153144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589798 #13153144