Subgroups — C₃×#10589703 #13152793

Order 1728.

808 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#611	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×Dic₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63460	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#611⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#63441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#63439	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5601	—	3	1	no	maximal
17	#10589703	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₃×#611	C₂²	1	1	yes	characteristic
23	C₂×C₃×#611	C₂²	1	1	yes	characteristic
24	C₂×C₃×#611	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
27	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
28	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×#3676	C₂²	1	1	yes	characteristic
34	C₃×#3676	C₂²	1	1	yes	characteristic
35	C₃×#3676	C₂²	1	1	yes	characteristic
36	C₃×#3676	C₂²	1	1	yes	characteristic
37	C₃×#3676	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
42	C₃×C₄⋊Dic₉	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×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×Dic₉⋊C₄	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×#121	D₃	1	1	yes	characteristic
54	C₃×#939	—	3	1	no	—
55	C₃×#939	—	3	1	no	—
56	C₃×#939	—	3	1	no	—
57	C₃×#935	—	3	1	no	—
58	C₃×D₄×Dic₃	—	3	1	no	—
59	C₃×D₄×Dic₃	—	3	1	no	—
60	C₃×C₄×#67	—	3	1	no	—
61	C₂×C₃×Dic₃⋊C₄	—	3	1	no	—
62	C₃×#898	—	3	1	no	—
63	C₃×#889	—	3	1	no	—
64	C₃×#883	—	3	1	no	—
65	C₃×#67⋊C₄	—	3	1	no	—
66	C₃×#879	—	3	1	no	—
67	C₃×#877	—	3	1	no	—
68	C₉×#121	—	2	1	no	—
69	C₉×#121	C₂×C₃	1	1	yes	characteristic, complemented
70	#63501	C₂×C₃	1	1	yes	characteristic, complemented
71	#63501	C₂×C₃	1	1	yes	characteristic, complemented
72	#63501	C₂×C₃	1	1	yes	characteristic, complemented
73	#63497	C₂×C₃	1	1	yes	characteristic, complemented
74	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
75	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
76	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×Dic₉⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
78	#63460	C₂×C₃	1	1	yes	characteristic, complemented
79	#63451	C₂×C₃	1	1	yes	characteristic, complemented
80	#63445	C₂×C₃	1	1	yes	characteristic, complemented
81	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
82	#63441	C₂×C₃	1	1	yes	characteristic, complemented
83	#63439	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
86	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
87	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
88	C₃×D₄×C₉	—	2	2	no	—
89	C₃×D₄×C₉	—	2	2	no	—
90	C₃×D₄×C₉	—	4	1	no	—
91	C₂×C₃×C₄×C₉	—	4	1	no	—
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₃×#611	—	2	2	no	—
97	C₃×#611	—	2	2	no	—
98	C₃×#611	—	4	1	no	—
99	C₂×C₃×Dic₉	—	2	2	no	—
100	C₂×C₃×Dic₉	—	2	2	no	—
101	C₂×C₃×Dic₉	—	4	1	no	—
102	C₂×C₃×Dic₉	—	4	1	no	—
103	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
104	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
105	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
106	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
107	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
108	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
109	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
110	C₃×C₄×D₉	—	4	1	no	—
111	C₃×#553	—	9	1	no	—
112	#5601	—	3	1	no	—
113	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
114	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
115	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
117	C₂×C₃×#67	—	3	1	no	—
118	C₂×C₃×#67	—	3	1	no	—
119	C₂×C₃×#67	—	3	1	no	—
120	C₂²×C₃×Dic₃	—	3	1	no	—
121	C₂²×C₃×Dic₃	—	3	1	no	—
122	C₂²×C₃×Dic₃	—	3	1	no	—
123	C₂²×C₃×Dic₃	—	3	1	no	—
124	C₂×C₃×C₄×D₃	—	3	1	no	—
125	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₃×#217	—	3	1	no	—
129	C₃×#217	—	3	1	no	—
130	C₃×#217	—	3	1	no	—
131	C₃×#217	—	3	1	no	—
132	C₃×#217	—	3	1	no	—
133	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
134	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
135	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
136	C₃×C₄⋊Dic₃	—	3	1	no	—
137	C₃×C₄⋊Dic₃	—	3	1	no	—
138	C₃×Dic₃⋊C₄	—	3	1	no	—
139	C₃×Dic₃⋊C₄	—	3	1	no	—
140	C₃×Dic₃⋊C₄	—	3	1	no	—
141	C₃×Dic₃⋊C₄	—	3	1	no	—
142	C₃×Dic₃⋊C₄	—	3	1	no	—
143	C₃×Dic₃⋊C₄	—	3	1	no	—
144	C₃×Dic₃⋊C₄	—	3	1	no	—
145	C₃×C₄×Dic₃	—	3	1	no	—
146	C₃×C₄×Dic₃	—	3	1	no	—
147	C₃×C₄×Dic₃	—	3	1	no	—
148	C₂×D₄×C₉	—	2	1	no	—
149	C₂×D₄×C₉	—	2	1	no	—
150	C₂×D₄×C₉	—	2	1	no	—
151	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
152	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
153	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₄×C₉	—	2	1	no	—
155	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
156	C₂×#611	C₂²×C₃	1	1	yes	characteristic
157	C₂×#611	C₂²×C₃	1	1	yes	characteristic
158	C₂×#611	C₂²×C₃	1	1	yes	characteristic
159	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
160	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
161	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
162	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
164	C₉×C₄⋊C₄	—	2	1	no	—
165	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₉×C₂²⋊C₄	—	2	1	no	—
167	C₉×C₂²⋊C₄	—	2	1	no	—
168	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	#3676	C₂²×C₃	1	1	yes	characteristic
171	#3676	C₂²×C₃	1	1	yes	characteristic
172	#3676	C₂²×C₃	1	1	yes	characteristic
173	#3676	C₂²×C₃	1	1	yes	characteristic
174	#3676	C₂²×C₃	1	1	yes	characteristic
175	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	(C₂×D₉)⋊C₄	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	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
187	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
188	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
189	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
190	C₂²×C₃×C₉	—	2	1	no	—
191	C₂²×C₃×C₉	—	2	1	no	—
192	C₂²×C₃×C₉	—	2	1	no	—
193	C₂²×C₃×C₉	—	2	1	no	—
194	C₂²×C₃×C₉	—	2	1	no	—
195	C₂²×C₃×C₉	—	2	1	no	—
196	C₂²×C₃×C₉	—	2	1	no	—
197	C₂²×C₃×C₉	—	2	1	no	—
198	C₂²×C₃×C₉	#41	1	2	yes	—
199	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
200	C₂×C₃×D₉	—	2	1	no	—
201	C₂×C₃×D₉	—	2	1	no	—
202	C₂×C₃×D₉	—	2	1	no	—
203	C₃×C₄×C₉	—	2	1	no	—
204	C₃×C₄×C₉	—	2	1	no	—
205	C₃×C₄×C₉	—	2	1	no	—
206	C₃×C₄×C₉	—	2	1	no	—
207	C₃×Dic₉	—	2	1	no	—
208	C₃×Dic₉	—	2	1	no	—
209	C₃×Dic₉	—	2	1	no	—
210	C₃×Dic₉	—	2	1	no	—
211	C₃×Dic₉	—	2	1	no	—
212	C₃×Dic₉	—	2	1	no	—
213	C₃×Dic₉	#41	1	2	yes	—
214	C₃×#126	—	9	1	no	—
215	C₃×#126	—	9	1	no	—
216	C₃×#125	—	9	1	no	—
217	C₃×#123	—	9	1	no	—
218	C₃×#123	—	9	1	no	—
219	C₃×#121	—	2	1	no	—
220	C₃×#121	—	9	1	no	—
221	C₃×#121	—	9	1	no	—
222	C₃×#121	—	9	1	no	—
223	C₃×#121	D₉	1	1	yes	characteristic, complemented
224	C₃×#121	C₃×D₃	1	1	yes	characteristic
225	C₃×C₄×D₄	—	9	1	no	—
226	C₃×C₄×D₄	—	9	1	no	—
227	C₃×C₄×D₄	—	9	1	no	—
228	C₃×C₄×D₄	—	9	1	no	—
229	C₃×#117	—	9	1	no	—
230	C₂×C₃×C₄⋊C₄	—	9	1	no	—
231	#939	—	3	1	no	—
232	#939	—	3	1	no	—
233	#939	—	3	1	no	—
234	#935	—	3	1	no	—
235	D₄×Dic₃	—	3	1	no	—
236	D₄×Dic₃	—	3	1	no	—
237	C₄×#67	—	3	1	no	—
238	C₂×Dic₃⋊C₄	—	3	1	no	—
239	#898	—	3	1	no	—
240	#889	—	3	1	no	—
241	#883	—	3	1	no	—
242	#67⋊C₄	—	3	1	no	—
243	#879	—	3	1	no	—
244	#877	—	3	1	no	—
245	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
246	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
247	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
248	C₂²×C₃×D₃	—	3	1	no	—
249	C₃²×D₄	—	2	2	no	—
250	C₃²×D₄	—	2	2	no	—
251	C₃²×D₄	—	4	1	no	—
252	C₂×C₃²×C₄	—	4	1	no	—
253	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
254	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
255	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
257	C₃×#67	—	6	2	no	—
258	C₃×#67	—	6	2	no	—
259	C₃×#67	—	12	1	no	—
260	C₂×C₃×Dic₃	—	3	1	no	—
261	C₂×C₃×Dic₃	—	3	1	no	—
262	C₂×C₃×Dic₃	—	3	1	no	—
263	C₂×C₃×Dic₃	—	3	1	no	—
264	C₂×C₃×Dic₃	—	3	1	no	—
265	C₂×C₃×Dic₃	—	3	1	no	—
266	C₂×C₃×Dic₃	—	3	1	no	—
267	C₂×C₃×Dic₃	—	6	2	no	—
268	C₂×C₃×Dic₃	—	6	2	no	—
269	C₂×C₃×Dic₃	—	12	1	no	—
270	C₂×C₃×Dic₃	—	12	1	no	—
271	C₃×C₄×D₃	—	12	1	no	—
272	C₂³×C₉	—	2	1	no	—
273	C₂³×C₉	—	2	1	no	—
274	C₂³×C₉	—	2	1	no	—
275	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
276	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
277	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
278	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
279	D₄×C₉	—	2	2	no	—
280	D₄×C₉	—	2	2	no	—
281	D₄×C₉	—	4	2	no	—
282	D₄×C₉	—	4	2	no	—
283	D₄×C₉	—	4	1	no	—
284	D₄×C₉	—	4	2	no	—
285	C₂×C₄×C₉	—	2	1	no	—
286	C₂×C₄×C₉	—	2	1	no	—
287	C₂×C₄×C₉	—	2	1	no	—
288	C₂×C₄×C₉	—	2	1	no	—
289	C₂×C₄×C₉	—	4	1	no	—
290	C₂×C₄×C₉	—	4	2	no	—
291	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
295	#611	—	2	2	no	—
296	#611	—	2	2	no	—
297	#611	—	4	1	no	—
298	C₂×Dic₉	—	2	2	no	—
299	C₂×Dic₉	—	2	2	no	—
300	C₂×Dic₉	—	4	1	no	—
301	C₂×Dic₉	—	4	1	no	—
302	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
303	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
304	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
305	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
306	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
307	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
308	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
309	C₄×D₉	—	4	1	no	—
310	#553	—	9	1	no	Sylow
311	C₂×C₃×C₉	—	2	2	no	—
312	C₂×C₃×C₉	—	4	1	no	—
313	C₂×C₃×C₉	—	4	1	no	—
314	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
315	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
316	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
317	C₃×D₉	—	4	1	no	—
318	C₂×C₃×D₄	—	2	1	no	—
319	C₂×C₃×D₄	—	2	1	no	—
320	C₂×C₃×D₄	—	2	1	no	—
321	C₂×C₃×D₄	—	9	1	no	—
322	C₂×C₃×D₄	—	9	1	no	—
323	C₂×C₃×D₄	—	9	1	no	—
324	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
325	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
326	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
327	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
328	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
330	C₂²×C₃×C₄	—	2	1	no	—
331	C₂²×C₃×C₄	—	9	1	no	—
332	C₂²×C₃×C₄	—	9	1	no	—
333	C₂²×C₃×C₄	—	9	1	no	—
334	C₂²×C₃×C₄	—	9	1	no	—
335	C₂²×C₃×C₄	—	9	1	no	—
336	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
338	C₂×#67	—	3	1	no	—
339	C₂×#67	—	3	1	no	—
340	C₂×#67	—	3	1	no	—
341	C₂²×Dic₃	—	3	1	no	—
342	C₂²×Dic₃	—	3	1	no	—
343	C₂²×Dic₃	—	3	1	no	—
344	C₂²×Dic₃	—	3	1	no	—
345	C₂×C₄×D₃	—	3	1	no	—
346	C₃×C₄⋊C₄	—	2	1	no	—
347	C₃×C₄⋊C₄	—	9	1	no	—
348	C₃×C₄⋊C₄	—	9	1	no	—
349	C₃×C₄⋊C₄	—	9	1	no	—
350	C₃×C₄⋊C₄	—	9	1	no	—
351	C₃×C₄⋊C₄	—	9	1	no	—
352	C₃×C₄⋊C₄	—	9	1	no	—
353	C₃×C₄⋊C₄	—	9	1	no	—
354	C₃×C₄⋊C₄	—	9	1	no	—
355	C₃×C₄⋊C₄	—	9	1	no	—
356	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
357	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
358	C₃×C₂²⋊C₄	—	2	1	no	—
359	C₃×C₂²⋊C₄	—	2	1	no	—
360	C₃×C₂²⋊C₄	—	9	1	no	—
361	C₃×C₂²⋊C₄	—	9	1	no	—
362	C₃×C₂²⋊C₄	—	9	1	no	—
363	C₃×C₂²⋊C₄	—	9	1	no	—
364	C₃×C₂²⋊C₄	—	9	1	no	—
365	C₃×C₂²⋊C₄	—	9	1	no	—
366	C₃×C₂²⋊C₄	—	9	1	no	—
367	C₃×C₂²⋊C₄	—	9	1	no	—
368	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
369	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
370	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
371	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
372	C₃×C₄²	—	9	1	no	—
373	C₃×C₄²	—	9	1	no	—
374	C₃×C₄²	—	9	1	no	—
375	#217	—	3	1	no	—
376	#217	—	3	1	no	—
377	#217	—	3	1	no	—
378	#217	—	3	1	no	—
379	#217	—	3	1	no	—
380	(C₂×D₃)⋊C₄	—	3	1	no	—
381	(C₂×D₃)⋊C₄	—	3	1	no	—
382	(C₂×D₃)⋊C₄	—	3	1	no	—
383	C₄⋊Dic₃	—	3	1	no	—
384	C₄⋊Dic₃	—	3	1	no	—
385	Dic₃⋊C₄	—	3	1	no	—
386	Dic₃⋊C₄	—	3	1	no	—
387	Dic₃⋊C₄	—	3	1	no	—
388	Dic₃⋊C₄	—	3	1	no	—
389	Dic₃⋊C₄	—	3	1	no	—
390	Dic₃⋊C₄	—	3	1	no	—
391	Dic₃⋊C₄	—	3	1	no	—
392	C₄×Dic₃	—	3	1	no	—
393	C₄×Dic₃	—	3	1	no	—
394	C₄×Dic₃	—	3	1	no	—
395	C₂²×C₃²	—	2	1	no	—
396	C₂²×C₃²	—	2	1	no	—
397	C₂²×C₃²	—	2	1	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	—	2	1	no	—
400	C₂²×C₃²	—	2	1	no	—
401	C₂²×C₃²	—	2	1	no	—
402	C₂²×C₃²	—	2	1	no	—
403	C₂²×C₃²	#237	1	2	yes	—
404	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
405	C₂×C₃×D₃	—	6	1	no	—
406	C₂×C₃×D₃	—	6	1	no	—
407	C₂×C₃×D₃	—	6	1	no	—
408	C₃²×C₄	—	2	1	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃²×C₄	—	2	1	no	—
412	C₃×Dic₃	—	3	2	no	—
413	C₃×Dic₃	—	6	1	no	—
414	C₃×Dic₃	—	6	1	no	—
415	C₃×Dic₃	—	6	1	no	—
416	C₃×Dic₃	—	6	1	no	—
417	C₃×Dic₃	—	6	1	no	—
418	C₃×Dic₃	—	6	1	no	—
419	C₂²×C₉	—	2	1	no	—
420	C₂²×C₉	—	2	1	no	—
421	C₂²×C₉	—	2	1	no	—
422	C₂²×C₉	—	2	1	no	—
423	C₂²×C₉	—	2	1	no	—
424	C₂²×C₉	—	2	1	no	—
425	C₂²×C₉	—	2	1	no	—
426	C₂²×C₉	—	2	1	no	—
427	C₂²×C₉	—	2	1	no	—
428	C₂²×C₉	—	2	2	no	—
429	C₂²×C₉	—	4	1	no	—
430	C₂²×C₉	—	4	1	no	—
431	C₂²×C₉	—	4	1	no	—
432	C₂²×C₉	—	4	1	no	—
433	C₂²×C₉	—	4	1	no	—
434	C₂²×C₉	—	4	1	no	—
435	C₂²×C₉	—	4	1	no	—
436	C₂²×C₉	—	4	1	no	—
437	C₂²×C₉	C₃×#41	1	2	yes	—
438	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
439	C₂×D₉	—	2	1	no	—
440	C₂×D₉	—	2	1	no	—
441	C₂×D₉	—	2	1	no	—
442	C₄×C₉	—	2	2	no	—
443	C₄×C₉	—	2	1	no	—
444	C₄×C₉	—	2	1	no	—
445	C₄×C₉	—	2	1	no	—
446	C₄×C₉	—	2	1	no	—
447	C₄×C₉	—	4	1	no	—
448	C₄×C₉	—	4	1	no	—
449	C₄×C₉	—	4	1	no	—
450	Dic₉	—	2	1	no	—
451	Dic₉	—	2	1	no	—
452	Dic₉	—	2	1	no	—
453	Dic₉	—	2	1	no	—
454	Dic₉	—	2	1	no	—
455	Dic₉	—	2	1	no	—
456	Dic₉	C₃×#41	1	2	yes	—
457	#126	—	9	1	no	—
458	#126	—	9	1	no	—
459	#125	—	9	1	no	—
460	#123	—	9	1	no	—
461	#123	—	9	1	no	—
462	#121	—	9	1	no	—
463	#121	—	9	1	no	—
464	#121	—	9	1	no	—
465	#121	C₃×D₉	1	1	yes	characteristic, complemented
466	C₄×D₄	—	9	1	no	—
467	C₄×D₄	—	9	1	no	—
468	C₄×D₄	—	9	1	no	—
469	C₄×D₄	—	9	1	no	—
470	#117	—	9	1	no	—
471	C₂×C₄⋊C₄	—	9	1	no	—
472	C₃×C₉	#553	1	1	yes	characteristic, complemented, Sylow
473	C₂³×C₃	—	2	1	no	—
474	C₂³×C₃	—	2	1	no	—
475	C₂³×C₃	—	2	1	no	—
476	C₂³×C₃	—	9	1	no	—
477	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
478	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
479	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
480	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
481	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
482	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
483	C₂²×D₃	—	3	1	no	—
484	C₃×D₄	—	2	2	no	—
485	C₃×D₄	—	2	2	no	—
486	C₃×D₄	—	2	2	no	—
487	C₃×D₄	—	2	2	no	—
488	C₃×D₄	—	4	2	no	—
489	C₃×D₄	—	4	2	no	—
490	C₃×D₄	—	4	1	no	—
491	C₃×D₄	—	4	1	no	—
492	C₃×D₄	—	4	2	no	—
493	C₃×D₄	—	18	2	no	—
494	C₃×D₄	—	18	2	no	—
495	C₃×D₄	—	36	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	4	1	no	—
501	C₂×C₃×C₄	—	4	1	no	—
502	C₂×C₃×C₄	—	4	2	no	—
503	C₂×C₃×C₄	—	9	1	no	—
504	C₂×C₃×C₄	—	9	1	no	—
505	C₂×C₃×C₄	—	9	1	no	—
506	C₂×C₃×C₄	—	9	1	no	—
507	C₂×C₃×C₄	—	9	1	no	—
508	C₂×C₃×C₄	—	9	1	no	—
509	C₂×C₃×C₄	—	9	1	no	—
510	C₂×C₃×C₄	—	18	2	no	—
511	C₂×C₃×C₄	—	18	2	no	—
512	C₂×C₃×C₄	—	36	1	no	—
513	C₂×C₃×C₄	—	36	1	no	—
514	C₂×C₃×C₄	—	36	1	no	—
515	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
516	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
517	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
518	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
519	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
520	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
523	#67	—	6	2	no	—
524	#67	—	6	2	no	—
525	#67	—	12	1	no	—
526	C₂×Dic₃	—	3	1	no	—
527	C₂×Dic₃	—	3	1	no	—
528	C₂×Dic₃	—	3	1	no	—
529	C₂×Dic₃	—	3	1	no	—
530	C₂×Dic₃	—	3	1	no	—
531	C₂×Dic₃	—	3	1	no	—
532	C₂×Dic₃	—	3	1	no	—
533	C₂×Dic₃	—	6	2	no	—
534	C₂×Dic₃	—	6	2	no	—
535	C₂×Dic₃	—	12	1	no	—
536	C₂×Dic₃	—	12	1	no	—
537	C₄×D₃	—	12	1	no	—
538	C₂×C₃²	—	2	2	no	—
539	C₂×C₃²	—	4	1	no	—
540	C₂×C₃²	—	4	1	no	—
541	C₂×C₃²	C₂×#237	1	1	yes	characteristic
542	C₂×C₃²	#1004	1	1	yes	characteristic
543	C₂×C₃²	D₃×#41	1	1	yes	characteristic
544	C₃×D₃	—	12	1	no	—
545	C₂×C₉	—	2	2	no	—
546	C₂×C₉	—	2	1	no	—
547	C₂×C₉	—	2	1	no	—
548	C₂×C₉	—	2	1	no	—
549	C₂×C₉	—	4	2	no	—
550	C₂×C₉	—	4	1	no	—
551	C₂×C₉	—	4	1	no	—
552	C₂×C₉	—	8	1	no	—
553	C₂×C₉	—	8	1	no	—
554	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
555	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
556	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
557	D₉	—	4	1	no	—
558	C₂×D₄	—	9	1	no	—
559	C₂×D₄	—	9	1	no	—
560	C₂×D₄	—	9	1	no	—
561	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
562	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
563	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
564	C₂²×C₄	—	9	1	no	—
565	C₂²×C₄	—	9	1	no	—
566	C₂²×C₄	—	9	1	no	—
567	C₂²×C₄	—	9	1	no	—
568	C₂²×C₄	—	9	1	no	—
569	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
570	C₄⋊C₄	—	9	1	no	—
571	C₄⋊C₄	—	9	1	no	—
572	C₄⋊C₄	—	9	1	no	—
573	C₄⋊C₄	—	9	1	no	—
574	C₄⋊C₄	—	9	1	no	—
575	C₄⋊C₄	—	9	1	no	—
576	C₄⋊C₄	—	9	1	no	—
577	C₄⋊C₄	—	9	1	no	—
578	C₄⋊C₄	—	9	1	no	—
579	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
580	C₂²⋊C₄	—	9	1	no	—
581	C₂²⋊C₄	—	9	1	no	—
582	C₂²⋊C₄	—	9	1	no	—
583	C₂²⋊C₄	—	9	1	no	—
584	C₂²⋊C₄	—	9	1	no	—
585	C₂²⋊C₄	—	9	1	no	—
586	C₂²⋊C₄	—	9	1	no	—
587	C₂²⋊C₄	—	9	1	no	—
588	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
589	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
590	C₄²	—	9	1	no	—
591	C₄²	—	9	1	no	—
592	C₄²	—	9	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	1	no	—
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	2	1	no	—
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	2	1	no	—
610	C₂²×C₃	—	2	2	no	—
611	C₂²×C₃	—	4	1	no	—
612	C₂²×C₃	—	4	1	no	—
613	C₂²×C₃	—	4	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	18	1	no	—
620	C₂²×C₃	—	18	1	no	—
621	C₂²×C₃	—	18	1	no	—
622	C₂²×C₃	#3699	1	2	yes	—
623	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
624	C₂²×C₃	C₃×#237	1	2	yes	—
625	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
626	C₂×D₃	—	6	1	no	—
627	C₂×D₃	—	6	1	no	—
628	C₂×D₃	—	6	1	no	—
629	C₃×C₄	—	2	2	no	—
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	2	1	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	2	1	no	—
637	C₃×C₄	—	2	1	no	—
638	C₃×C₄	—	4	1	no	—
639	C₃×C₄	—	4	1	no	—
640	C₃×C₄	—	4	1	no	—
641	C₃×C₄	—	9	2	no	—
642	C₃×C₄	—	18	1	no	—
643	C₃×C₄	—	18	1	no	—
644	C₃×C₄	—	18	1	no	—
645	C₃×C₄	—	18	1	no	—
646	C₃×C₄	—	18	1	no	—
647	C₃×C₄	—	18	1	no	—
648	Dic₃	—	3	2	no	—
649	Dic₃	—	6	1	no	—
650	Dic₃	—	6	1	no	—
651	Dic₃	—	6	1	no	—
652	Dic₃	—	6	1	no	—
653	Dic₃	—	6	1	no	—
654	Dic₃	—	6	1	no	—
655	C₃²	#5601	1	1	yes	characteristic
656	C₉	—	2	1	no	—
657	C₉	C₃×#553	1	1	yes	characteristic, complemented
658	C₂³	—	9	1	no	—
659	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
660	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
661	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
662	D₄	—	2	2	no	—
663	D₄	—	2	2	no	—
664	D₄	—	4	1	no	—
665	D₄	—	18	2	no	—
666	D₄	—	18	2	no	—
667	D₄	—	36	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	9	1	no	—
670	C₂×C₄	—	9	1	no	—
671	C₂×C₄	—	9	1	no	—
672	C₂×C₄	—	9	1	no	—
673	C₂×C₄	—	9	1	no	—
674	C₂×C₄	—	9	1	no	—
675	C₂×C₄	—	9	1	no	—
676	C₂×C₄	—	18	2	no	—
677	C₂×C₄	—	18	2	no	—
678	C₂×C₄	—	36	1	no	—
679	C₂×C₄	—	36	1	no	—
680	C₂×C₄	—	36	1	no	—
681	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
682	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
683	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
685	C₂×C₃	—	2	2	no	—
686	C₂×C₃	—	2	2	no	—
687	C₂×C₃	—	2	1	no	—
688	C₂×C₃	—	2	1	no	—
689	C₂×C₃	—	2	1	no	—
690	C₂×C₃	—	4	2	no	—
691	C₂×C₃	—	4	1	no	—
692	C₂×C₃	—	4	1	no	—
693	C₂×C₃	—	4	1	no	—
694	C₂×C₃	—	4	1	no	—
695	C₂×C₃	—	8	1	no	—
696	C₂×C₃	—	8	1	no	—
697	C₂×C₃	—	36	1	no	—
698	C₂×C₃	C₂×#3699	1	1	yes	characteristic
699	C₂×C₃	#63710	1	1	yes	characteristic
700	C₂×C₃	#41×D₉	1	1	yes	characteristic
701	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
702	C₂×C₃	C₃×#1004	1	1	yes	characteristic
703	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
704	D₃	—	12	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	18	1	no	—
714	C₂²	—	18	1	no	—
715	C₂²	—	18	1	no	—
716	C₂²	C₃×#3699	1	2	yes	—
717	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	9	2	no	—
723	C₄	—	18	1	no	—
724	C₄	—	18	1	no	—
725	C₄	—	18	1	no	—
726	C₄	—	18	1	no	—
727	C₄	—	18	1	no	—
728	C₄	—	18	1	no	—
729	C₃	—	2	1	no	—
730	C₃	#10589703	1	1	yes	characteristic, direct product factor
731	C₃	C₃×#5601	1	1	yes	characteristic
732	C₂	—	2	2	no	—
733	C₂	—	4	1	no	—
734	C₂	—	4	1	no	—
735	C₂	—	36	1	no	—
736	C₂	C₂×C₃×#3699	1	1	yes	characteristic
737	C₂	C₃×#63710	1	1	yes	characteristic
738	C₂	C₃×#41×D₉	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×#121	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×#121	D₉
hypocenter	C₉	C₃×#553
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#121	C₂	semidirect
2. C₃×#63501	C₂	semidirect
3. C₃×#63501	C₂	semidirect
4. C₃×#63501	C₂	semidirect
5. C₃×#63497	C₂	semidirect
6. C₃×D₄×Dic₉	C₂	semidirect
7. C₃×D₄×Dic₉	C₂	semidirect
8. C₃×C₄×#611	C₂	semidirect
9. C₂×C₃×Dic₉⋊C₄	C₂	semidirect
10. C₃×#63460	C₂	semidirect
11. C₃×#63451	C₂	semidirect
12. C₃×#63445	C₂	semidirect
13. C₃×#611⋊C₄	C₂	semidirect
14. C₃×#63441	C₂	semidirect
15. C₃×#63439	C₂	semidirect
17. #10589703	C₃	direct (N × H)
69. C₉×#121	C₂×C₃	semidirect
70. #63501	C₂×C₃	semidirect
71. #63501	C₂×C₃	semidirect
72. #63501	C₂×C₃	semidirect
73. #63497	C₂×C₃	semidirect
74. D₄×Dic₉	C₂×C₃	semidirect
75. D₄×Dic₉	C₂×C₃	semidirect
76. C₄×#611	C₂×C₃	semidirect
77. C₂×Dic₉⋊C₄	C₂×C₃	semidirect
78. #63460	C₂×C₃	semidirect
79. #63451	C₂×C₃	semidirect
80. #63445	C₂×C₃	semidirect
81. #611⋊C₄	C₂×C₃	semidirect
82. #63441	C₂×C₃	semidirect
83. #63439	C₂×C₃	semidirect
223. C₃×#121	D₉	semidirect
465. #121	C₃×D₉	semidirect
472. C₃×C₉	#553	semidirect
657. C₉	C₃×#553	semidirect
730. C₃	#10589703	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×#121	2
C₃×#63501	2
C₃×#63497	2
C₃×D₄×Dic₉	2
C₃×C₄×#611	2
C₂×C₃×Dic₉⋊C₄	2
C₃×#63460	2
C₃×#63451	2
C₃×#63445	2
C₃×#611⋊C₄	2
C₃×#63441	2
C₃×#63439	2
C₃×#5601	3
#10589703	3

Subgroups — C3×#10589703 #13152793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589703 #13152793