Subgroups — C₃×#10589581 #13152287

Order 1728.

810 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63492	C₂	1	1	yes	maximal, characteristic
3	C₃×#63491	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×#611	C₂	1	2	yes	maximal, complemented
5	C₃×#63486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63438	C₂	1	2	yes	maximal, complemented
7	C₃×#63437	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63434	C₂	1	2	yes	maximal, complemented
10	C₃×#63432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5479	—	3	1	no	maximal
13	#10589581	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×#611	C₂²	1	2	yes	—
18	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
20	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
23	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₃×#3676	C₂²	1	2	yes	—
26	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
27	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
28	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
29	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
30	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
33	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
34	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
35	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
36	C₃×C₄×Dic₉	C₂²	1	2	yes	—
37	C₂×C₃²×C₄²	D₃	1	1	yes	characteristic
38	C₃×#930	—	3	1	no	—
39	C₃×#929	—	3	2	no	—
40	C₃×C₄×#67	—	3	2	no	—
41	C₃×#924	—	3	1	no	—
42	C₃×#876	—	3	2	no	—
43	C₃×#875	—	3	1	no	—
44	C₃×C₄×D₁₂	—	3	1	no	—
45	C₃×#872	—	3	2	no	—
46	C₃×#870	—	3	1	no	—
47	C₃×C₄×Dic₆	—	3	1	no	—
48	C₂×C₄²×C₉	—	2	1	no	—
49	C₂×C₄²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
50	#63492	C₂×C₃	1	1	yes	characteristic
51	#63491	C₂×C₃	1	2	yes	complemented
52	C₄×#611	C₂×C₃	1	2	yes	complemented
53	#63486	C₂×C₃	1	1	yes	characteristic, complemented
54	#63438	C₂×C₃	1	2	yes	complemented
55	#63437	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
57	#63434	C₂×C₃	1	2	yes	complemented
58	#63432	C₂×C₃	1	1	yes	characteristic, complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₃×D₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	—	2	2	no	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₃×#611	—	2	4	no	—
72	C₂×C₃×Dic₉	C₂³	1	2	yes	—
73	C₂×C₃×Dic₉	C₂³	1	2	yes	—
74	C₂×C₃×Dic₉	C₂³	1	2	yes	—
75	C₃×D₃₆	—	2	2	no	—
76	C₃×C₄×D₉	—	2	4	no	—
77	C₃×Dic₁₈	—	2	2	no	—
78	C₃×#529	—	9	1	no	—
79	#5479	—	3	1	no	—
80	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×#67	—	3	2	no	—
84	C₂×C₃×D₁₂	—	3	1	no	—
85	C₂×C₃×C₄×D₃	—	3	2	no	—
86	C₂×C₃×Dic₆	—	3	1	no	—
87	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
88	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
89	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
91	C₃×#217	—	3	2	no	—
92	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
93	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
94	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
95	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
96	C₃×C₄⋊Dic₃	—	3	1	no	—
97	C₃×C₄⋊Dic₃	—	3	1	no	—
98	C₃×Dic₃⋊C₄	—	3	2	no	—
99	C₃×Dic₃⋊C₄	—	3	2	no	—
100	C₃×Dic₃⋊C₄	—	3	2	no	—
101	C₃×Dic₃⋊C₄	—	3	2	no	—
102	C₃×C₄×Dic₃	—	3	2	no	—
103	C₂²×C₄×C₉	—	2	1	no	—
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
109	C₂×#611	C₂²×C₃	1	2	yes	—
110	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
112	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
113	C₄²×C₉	—	2	1	no	—
114	C₄²×C₉	—	2	1	no	—
115	C₄²×C₉	—	2	1	no	—
116	C₄²×C₉	—	2	1	no	—
117	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
118	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
119	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
120	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
121	#3676	C₂²×C₃	1	2	yes	—
122	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
123	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
124	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
125	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
128	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
129	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
130	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
131	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
132	C₄×Dic₉	C₂²×C₃	1	2	yes	—
133	C₂²×C₃×C₉	—	2	1	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	#41	1	2	yes	—
136	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
137	C₂×C₃×D₉	—	2	2	no	—
138	C₂×C₃×D₉	—	2	2	no	—
139	C₂×C₃×D₉	—	2	2	no	—
140	C₃×C₄×C₉	—	2	1	no	—
141	C₃×C₄×C₉	—	2	1	no	—
142	C₃×C₄×C₉	—	2	1	no	—
143	C₃×C₄×C₉	—	2	1	no	—
144	C₃×C₄×C₉	#41	1	2	yes	—
145	C₃×C₄×C₉	#41	1	2	yes	—
146	C₃×Dic₉	—	2	2	no	—
147	C₃×Dic₉	—	2	2	no	—
148	C₃×Dic₉	—	2	2	no	—
149	C₃×#126	—	9	2	no	—
150	C₃×#125	—	9	1	no	—
151	C₃×#124	—	9	1	no	—
152	C₃×#123	—	9	2	no	—
153	C₃×C₂²⋊Q₈	—	9	1	no	—
154	C₃×#121	—	9	1	no	—
155	C₃×C₄×Q₈	—	9	1	no	—
156	C₃×C₄×D₄	—	9	2	no	—
157	C₃×C₄×D₄	—	9	1	no	—
158	C₃×#117	—	9	2	no	—
159	C₂×C₃×C₄²	—	2	1	no	—
160	C₂×C₃×C₄²	D₉	1	1	yes	characteristic, complemented
161	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
162	#930	—	3	1	no	—
163	#929	—	3	2	no	—
164	C₄×#67	—	3	2	no	—
165	#924	—	3	1	no	—
166	#876	—	3	2	no	—
167	#875	—	3	1	no	—
168	C₄×D₁₂	—	3	1	no	—
169	#872	—	3	2	no	—
170	#870	—	3	1	no	—
171	C₄×Dic₆	—	3	1	no	—
172	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
173	C₂²×C₃×D₃	—	3	2	no	—
174	C₂×C₃²×C₄	—	2	2	no	—
175	C₂×C₃²×C₄	—	2	2	no	—
176	C₂×C₃²×C₄	—	2	2	no	—
177	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
183	C₃×#67	—	6	4	no	—
184	C₂×C₃×Dic₃	—	3	2	no	—
185	C₂×C₃×Dic₃	—	3	2	no	—
186	C₂×C₃×Dic₃	—	3	2	no	—
187	C₃×D₁₂	—	6	2	no	—
188	C₃×C₄×D₃	—	6	4	no	—
189	C₃×Dic₆	—	6	2	no	—
190	C₂³×C₉	—	2	1	no	—
191	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
192	C₂²×D₉	C₂³×C₃	1	2	yes	—
193	C₂×C₄×C₉	—	2	4	no	—
194	C₂×C₄×C₉	—	2	4	no	—
195	C₂×C₄×C₉	—	2	4	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	2	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
211	#611	—	2	4	no	—
212	C₂×Dic₉	C₂³×C₃	1	2	yes	—
213	C₂×Dic₉	C₂³×C₃	1	2	yes	—
214	C₂×Dic₉	C₂³×C₃	1	2	yes	—
215	D₃₆	—	2	2	no	—
216	C₄×D₉	—	2	4	no	—
217	Dic₁₈	—	2	2	no	—
218	#529	—	9	1	no	Sylow
219	C₂×C₃×C₉	—	2	2	no	—
220	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
223	C₃×D₉	—	4	2	no	—
224	C₂×C₃×Q₈	—	9	1	no	—
225	C₂×C₃×D₄	—	9	2	no	—
226	C₂×C₃×D₄	—	9	1	no	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	—	2	1	no	—
230	C₂²×C₃×C₄	—	9	2	no	—
231	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
237	C₂×#67	—	3	2	no	—
238	C₂×D₁₂	—	3	1	no	—
239	C₂×C₄×D₃	—	3	2	no	—
240	C₂×Dic₆	—	3	1	no	—
241	C₃×C₄⋊C₄	—	9	2	no	—
242	C₃×C₄⋊C₄	—	9	2	no	—
243	C₃×C₄⋊C₄	—	9	2	no	—
244	C₃×C₄⋊C₄	—	9	2	no	—
245	C₃×C₄⋊C₄	—	9	1	no	—
246	C₃×C₄⋊C₄	—	9	1	no	—
247	C₃×C₂²⋊C₄	—	9	2	no	—
248	C₃×C₂²⋊C₄	—	9	2	no	—
249	C₃×C₂²⋊C₄	—	9	2	no	—
250	C₃×C₂²⋊C₄	—	9	2	no	—
251	C₃×C₂²⋊C₄	—	9	2	no	—
252	C₃×C₄²	—	2	1	no	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	—	2	1	no	—
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	—	9	2	no	—
257	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
258	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
259	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
260	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
261	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
262	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
263	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
264	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
265	#217	—	3	2	no	—
266	(C₂×D₃)⋊C₄	—	3	2	no	—
267	(C₂×D₃)⋊C₄	—	3	2	no	—
268	(C₂×D₃)⋊C₄	—	3	2	no	—
269	(C₂×D₃)⋊C₄	—	3	2	no	—
270	C₄⋊Dic₃	—	3	1	no	—
271	C₄⋊Dic₃	—	3	1	no	—
272	Dic₃⋊C₄	—	3	2	no	—
273	Dic₃⋊C₄	—	3	2	no	—
274	Dic₃⋊C₄	—	3	2	no	—
275	Dic₃⋊C₄	—	3	2	no	—
276	C₄×Dic₃	—	3	2	no	—
277	C₂²×C₃²	—	2	1	no	—
278	C₂²×C₃²	—	2	1	no	—
279	C₂²×C₃²	#235	1	2	yes	—
280	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
281	C₂×C₃×D₃	—	6	2	no	—
282	C₂×C₃×D₃	—	6	2	no	—
283	C₂×C₃×D₃	—	6	2	no	—
284	C₃²×C₄	—	2	1	no	—
285	C₃²×C₄	—	2	1	no	—
286	C₃²×C₄	—	2	1	no	—
287	C₃²×C₄	—	2	1	no	—
288	C₃²×C₄	#235	1	2	yes	—
289	C₃²×C₄	#235	1	2	yes	—
290	C₃×Dic₃	—	6	2	no	—
291	C₃×Dic₃	—	6	2	no	—
292	C₃×Dic₃	—	6	2	no	—
293	C₂²×C₉	—	2	2	no	—
294	C₂²×C₉	—	2	2	no	—
295	C₂²×C₉	—	2	1	no	—
296	C₂²×C₉	—	2	1	no	—
297	C₂²×C₉	—	2	1	no	—
298	C₂²×C₉	—	2	2	no	—
299	C₂²×C₉	C₃×#41	1	2	yes	—
300	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
301	C₂×D₉	—	2	2	no	—
302	C₂×D₉	—	2	2	no	—
303	C₂×D₉	—	2	2	no	—
304	C₄×C₉	—	2	2	no	—
305	C₄×C₉	—	2	2	no	—
306	C₄×C₉	—	2	2	no	—
307	C₄×C₉	—	2	2	no	—
308	C₄×C₉	—	2	1	no	—
309	C₄×C₉	—	2	1	no	—
310	C₄×C₉	—	2	1	no	—
311	C₄×C₉	—	2	1	no	—
312	C₄×C₉	—	2	2	no	—
313	C₄×C₉	—	2	2	no	—
314	C₄×C₉	C₃×#41	1	2	yes	—
315	C₄×C₉	C₃×#41	1	2	yes	—
316	Dic₉	—	2	2	no	—
317	Dic₉	—	2	2	no	—
318	Dic₉	—	2	2	no	—
319	#126	—	9	2	no	—
320	#125	—	9	1	no	—
321	#124	—	9	1	no	—
322	#123	—	9	2	no	—
323	C₂²⋊Q₈	—	9	1	no	—
324	#121	—	9	1	no	—
325	C₄×Q₈	—	9	1	no	—
326	C₄×D₄	—	9	2	no	—
327	C₄×D₄	—	9	1	no	—
328	#117	—	9	2	no	—
329	C₂×C₄²	C₃×D₉	1	1	yes	characteristic, complemented
330	C₃×C₉	#529	1	1	yes	characteristic, complemented, Sylow
331	C₂³×C₃	—	2	1	no	—
332	C₂³×C₃	—	9	2	no	—
333	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
334	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂²×D₃	—	3	2	no	—
336	C₃×Q₈	—	18	2	no	—
337	C₃×D₄	—	18	4	no	—
338	C₃×D₄	—	18	2	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	4	no	—
341	C₂×C₃×C₄	—	2	4	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	9	2	no	—
355	C₂×C₃×C₄	—	9	2	no	—
356	C₂×C₃×C₄	—	9	2	no	—
357	C₂×C₃×C₄	—	18	4	no	—
358	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
361	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
370	#67	—	6	4	no	—
371	C₂×Dic₃	—	3	2	no	—
372	C₂×Dic₃	—	3	2	no	—
373	C₂×Dic₃	—	3	2	no	—
374	D₁₂	—	6	2	no	—
375	C₄×D₃	—	6	4	no	—
376	Dic₆	—	6	2	no	—
377	C₂×C₃²	—	2	2	no	—
378	C₂×C₃²	C₂×#235	1	1	yes	characteristic
379	C₂×C₃²	C₂×#235	1	1	yes	characteristic
380	C₂×C₃²	C₂×#235	1	1	yes	characteristic
381	C₃×D₃	—	12	2	no	—
382	C₂×C₉	—	2	4	no	—
383	C₂×C₉	—	2	2	no	—
384	C₂×C₉	—	2	1	no	—
385	C₂×C₉	—	2	1	no	—
386	C₂×C₉	—	2	1	no	—
387	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
388	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
389	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
390	D₉	—	4	2	no	—
391	C₂×Q₈	—	9	1	no	—
392	C₂×D₄	—	9	2	no	—
393	C₂×D₄	—	9	1	no	—
394	C₂²×C₄	—	9	2	no	—
395	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
398	C₄⋊C₄	—	9	2	no	—
399	C₄⋊C₄	—	9	2	no	—
400	C₄⋊C₄	—	9	1	no	—
401	C₄⋊C₄	—	9	2	no	—
402	C₄⋊C₄	—	9	1	no	—
403	C₄⋊C₄	—	9	2	no	—
404	C₂²⋊C₄	—	9	2	no	—
405	C₂²⋊C₄	—	9	2	no	—
406	C₂²⋊C₄	—	9	2	no	—
407	C₂²⋊C₄	—	9	2	no	—
408	C₂²⋊C₄	—	9	2	no	—
409	C₄²	—	9	2	no	—
410	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
411	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
412	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
413	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	2	1	no	—
418	C₂²×C₃	—	2	1	no	—
419	C₂²×C₃	—	2	1	no	—
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	18	2	no	—
423	C₂²×C₃	—	18	2	no	—
424	C₂²×C₃	—	18	2	no	—
425	C₂²×C₃	#3697	1	2	yes	—
426	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
427	C₂²×C₃	C₃×#235	1	2	yes	—
428	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
429	C₂×D₃	—	6	2	no	—
430	C₂×D₃	—	6	2	no	—
431	C₂×D₃	—	6	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	2	1	no	—
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	2	1	no	—
440	C₃×C₄	—	2	1	no	—
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	2	1	no	—
444	C₃×C₄	—	2	2	no	—
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	18	2	no	—
447	C₃×C₄	—	18	2	no	—
448	C₃×C₄	—	18	2	no	—
449	C₃×C₄	#3697	1	2	yes	—
450	C₃×C₄	#3697	1	2	yes	—
451	C₃×C₄	C₃×#235	1	2	yes	—
452	C₃×C₄	C₃×#235	1	2	yes	—
453	Dic₃	—	6	2	no	—
454	Dic₃	—	6	2	no	—
455	Dic₃	—	6	2	no	—
456	C₃²	#5479	1	1	yes	characteristic
457	C₉	—	2	1	no	—
458	C₉	C₃×#529	1	1	yes	characteristic, complemented
459	C₂³	—	9	2	no	—
460	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
461	Q₈	—	18	2	no	—
462	D₄	—	18	4	no	—
463	D₄	—	18	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	9	2	no	—
468	C₂×C₄	—	9	2	no	—
469	C₂×C₄	—	9	2	no	—
470	C₂×C₄	—	18	4	no	—
471	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
477	C₂×C₃	—	2	4	no	—
478	C₂×C₃	—	2	2	no	—
479	C₂×C₃	—	2	2	no	—
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	2	1	no	—
483	C₂×C₃	—	36	2	no	—
484	C₂×C₃	C₂×#3697	1	1	yes	characteristic
485	C₂×C₃	C₂×#3697	1	1	yes	characteristic
486	C₂×C₃	C₂×#3697	1	1	yes	characteristic
487	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
488	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
489	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
490	D₃	—	12	2	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	18	2	no	—
494	C₂²	—	18	2	no	—
495	C₂²	—	18	2	no	—
496	C₂²	C₃×#3697	1	2	yes	—
497	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	18	2	no	—
503	C₄	—	18	2	no	—
504	C₄	—	18	2	no	—
505	C₄	C₃×#3697	1	2	yes	—
506	C₄	C₃×#3697	1	2	yes	—
507	C₃	—	2	1	no	—
508	C₃	#10589581	1	1	yes	characteristic, direct product factor
509	C₃	C₃×#5479	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	36	2	no	—
512	C₂	C₂×C₃×#3697	1	1	yes	characteristic
513	C₂	C₂×C₃×#3697	1	1	yes	characteristic
514	C₂	C₂×C₃×#3697	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₄²×C₉	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₃×#63492	C₂
hypercenter	C₂×C₃×C₄²	D₉
hypocenter	C₉	C₃×#529
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄²×C₉	C₂	semidirect
3. C₃×#63491	C₂	semidirect
4. C₃×C₄×#611	C₂	semidirect
5. C₃×#63486	C₂	semidirect
6. C₃×#63438	C₂	semidirect
7. C₃×#63437	C₂	semidirect
8. C₃×C₄×D₃₆	C₂	semidirect
9. C₃×#63434	C₂	semidirect
10. C₃×#63432	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589581	C₃	direct (N × H)
49. C₂×C₄²×C₉	C₂×C₃	semidirect
51. #63491	C₂×C₃	semidirect
52. C₄×#611	C₂×C₃	semidirect
53. #63486	C₂×C₃	semidirect
54. #63438	C₂×C₃	semidirect
55. #63437	C₂×C₃	semidirect
56. C₄×D₃₆	C₂×C₃	semidirect
57. #63434	C₂×C₃	semidirect
58. #63432	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
160. C₂×C₃×C₄²	D₉	semidirect
329. C₂×C₄²	C₃×D₉	semidirect
330. C₃×C₉	#529	semidirect
458. C₉	C₃×#529	semidirect
508. C₃	#10589581	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₉	2
C₃×#63492	2
C₃×#63491	2
C₃×C₄×#611	2
C₃×#63486	2
C₃×#63438	2
C₃×#63437	2
C₃×C₄×D₃₆	2
C₃×#63434	2
C₃×#63432	2
C₃×C₄×Dic₁₈	2
C₃×#5479	3
#10589581	3

Subgroups — C3×#10589581 #13152287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589581 #13152287