Subgroups — C₃×#10589767 #13153020

Order 1728.

732 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63501	C₂	1	1	yes	maximal, characteristic
3	C₃×D₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63445	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#611⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#63441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#63440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#63440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5665	—	3	1	no	maximal
17	#10589767	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₃×#611	C₂²	1	1	yes	characteristic
21	C₂×C₃×#611	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
26	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×#3676	C₂²	1	1	yes	characteristic
33	C₃×#3676	C₂²	1	1	yes	characteristic
34	C₃×#3676	C₂²	1	1	yes	characteristic
35	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊Dic₉	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×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
44	C₃×C₄⋊Dic₉	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×Dic₉⋊C₄	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×#123	D₃	1	1	yes	characteristic
54	C₃×#939	—	3	1	no	—
55	C₃×D₄×Dic₃	—	3	1	no	—
56	C₃×#929	—	3	1	no	—
57	C₂×C₃×C₄⋊Dic₃	—	3	1	no	—
58	C₃×#898	—	3	1	no	—
59	C₃×#897	—	3	1	no	—
60	C₃×#890	—	3	1	no	—
61	C₃×#889	—	3	1	no	—
62	C₃×#886	—	3	1	no	—
63	C₃×#883	—	3	1	no	—
64	C₃×#67⋊C₄	—	3	1	no	—
65	C₃×#879	—	3	1	no	—
66	C₃×#878	—	3	1	no	—
67	C₃×#878	—	3	1	no	—
68	C₉×#123	—	2	1	no	—
69	C₉×#123	C₂×C₃	1	1	yes	characteristic, complemented
70	#63501	C₂×C₃	1	1	yes	characteristic
71	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
72	#63491	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×C₄⋊Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
74	#63460	C₂×C₃	1	1	yes	characteristic, complemented
75	#63459	C₂×C₃	1	1	yes	characteristic, complemented
76	#63452	C₂×C₃	1	1	yes	characteristic, complemented
77	#63451	C₂×C₃	1	1	yes	characteristic, complemented
78	#63448	C₂×C₃	1	1	yes	characteristic, complemented
79	#63445	C₂×C₃	1	1	yes	characteristic, complemented
80	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
81	#63441	C₂×C₃	1	1	yes	characteristic, complemented
82	#63440	C₂×C₃	1	1	yes	characteristic, complemented
83	#63440	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	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
87	C₃×D₄×C₉	—	2	2	no	—
88	C₂×C₃×C₄×C₉	—	2	2	no	—
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×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₃×#611	—	2	2	no	—
95	C₃×#611	—	4	1	no	—
96	C₂×C₃×Dic₉	—	4	1	no	—
97	C₂×C₃×Dic₉	—	4	1	no	—
98	C₂×C₃×Dic₉	—	4	1	no	—
99	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
101	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
102	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
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	C₃×C₄×D₉	—	4	1	no	—
107	C₃×Dic₁₈	—	4	1	no	—
108	C₃×#539	—	9	1	no	—
109	#5665	—	3	1	no	—
110	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
111	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
112	C₂×C₃×#67	—	3	1	no	—
113	C₂×C₃×#67	—	3	1	no	—
114	C₂²×C₃×Dic₃	—	3	1	no	—
115	C₂²×C₃×Dic₃	—	3	1	no	—
116	C₂²×C₃×Dic₃	—	3	1	no	—
117	C₂×C₃×C₄×D₃	—	3	1	no	—
118	C₂×C₃×Dic₆	—	3	1	no	—
119	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
120	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
121	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
122	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
123	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₃×#217	—	3	1	no	—
125	C₃×#217	—	3	1	no	—
126	C₃×#217	—	3	1	no	—
127	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
128	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
129	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
130	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
131	C₃×C₄⋊Dic₃	—	3	1	no	—
132	C₃×C₄⋊Dic₃	—	3	1	no	—
133	C₃×C₄⋊Dic₃	—	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×Dic₃⋊C₄	—	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×C₄×Dic₃	—	3	1	no	—
144	C₃×C₄×Dic₃	—	3	1	no	—
145	C₂×D₄×C₉	—	2	1	no	—
146	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₄×C₉	—	2	1	no	—
148	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
149	C₂×#611	C₂²×C₃	1	1	yes	characteristic
150	C₂×#611	C₂²×C₃	1	1	yes	characteristic
151	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
152	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
153	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
155	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
156	C₉×C₄⋊C₄	—	2	1	no	—
157	C₉×C₄⋊C₄	—	2	1	no	—
158	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₉×C₂²⋊C₄	—	2	1	no	—
161	C₉×C₂²⋊C₄	—	2	1	no	—
162	C₉×C₂²⋊C₄	—	2	1	no	—
163	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	#3676	C₂²×C₃	1	1	yes	characteristic
167	#3676	C₂²×C₃	1	1	yes	characteristic
168	#3676	C₂²×C₃	1	1	yes	characteristic
169	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
174	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
175	C₄⋊Dic₉	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	Dic₉⋊C₄	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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
186	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
187	C₂²×C₃×C₉	—	2	1	no	—
188	C₂²×C₃×C₉	—	2	1	no	—
189	C₂²×C₃×C₉	—	2	1	no	—
190	C₂²×C₃×C₉	—	2	1	no	—
191	C₂²×C₃×C₉	—	2	1	no	—
192	C₂²×C₃×C₉	#41	1	2	yes	—
193	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₃×D₉	—	2	1	no	—
195	C₂×C₃×D₉	—	2	1	no	—
196	C₂×C₃×D₉	—	2	1	no	—
197	C₃×C₄×C₉	—	2	1	no	—
198	C₃×C₄×C₉	—	2	1	no	—
199	C₃×C₄×C₉	—	2	1	no	—
200	C₃×C₄×C₉	—	2	1	no	—
201	C₃×C₄×C₉	—	2	1	no	—
202	C₃×Dic₉	—	2	1	no	—
203	C₃×Dic₉	—	2	1	no	—
204	C₃×Dic₉	—	2	1	no	—
205	C₃×Dic₉	—	2	1	no	—
206	C₃×Dic₉	—	2	1	no	—
207	C₃×Dic₉	—	2	1	no	—
208	C₃×Dic₉	—	2	1	no	—
209	C₃×#126	—	9	1	no	—
210	C₃×#126	—	9	1	no	—
211	C₃×#125	—	9	1	no	—
212	C₃×#125	—	9	1	no	—
213	C₃×#123	—	2	1	no	—
214	C₃×#123	—	9	1	no	—
215	C₃×#123	—	9	1	no	—
216	C₃×#123	—	9	1	no	—
217	C₃×#123	D₉	1	1	yes	characteristic, complemented
218	C₃×#123	C₃×D₃	1	1	yes	characteristic
219	C₃×C₂²⋊Q₈	—	9	1	no	—
220	C₃×C₂²⋊Q₈	—	9	1	no	—
221	C₃×C₂²⋊Q₈	—	9	1	no	—
222	C₃×#121	—	9	1	no	—
223	C₃×C₄×D₄	—	9	1	no	—
224	C₃×C₄×D₄	—	9	1	no	—
225	C₂×C₃×C₄⋊C₄	—	9	1	no	—
226	#939	—	3	1	no	—
227	D₄×Dic₃	—	3	1	no	—
228	#929	—	3	1	no	—
229	C₂×C₄⋊Dic₃	—	3	1	no	—
230	#898	—	3	1	no	—
231	#897	—	3	1	no	—
232	#890	—	3	1	no	—
233	#889	—	3	1	no	—
234	#886	—	3	1	no	—
235	#883	—	3	1	no	—
236	#67⋊C₄	—	3	1	no	—
237	#879	—	3	1	no	—
238	#878	—	3	1	no	—
239	#878	—	3	1	no	—
240	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
241	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
242	C₂²×C₃×D₃	—	3	1	no	—
243	C₃²×D₄	—	2	2	no	—
244	C₂×C₃²×C₄	—	2	2	no	—
245	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
248	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
249	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
250	C₃×#67	—	6	2	no	—
251	C₃×#67	—	12	1	no	—
252	C₂×C₃×Dic₃	—	3	1	no	—
253	C₂×C₃×Dic₃	—	3	1	no	—
254	C₂×C₃×Dic₃	—	3	1	no	—
255	C₂×C₃×Dic₃	—	3	1	no	—
256	C₂×C₃×Dic₃	—	3	1	no	—
257	C₂×C₃×Dic₃	—	3	1	no	—
258	C₂×C₃×Dic₃	—	3	1	no	—
259	C₂×C₃×Dic₃	—	12	1	no	—
260	C₂×C₃×Dic₃	—	12	1	no	—
261	C₂×C₃×Dic₃	—	12	1	no	—
262	C₃×C₄×D₃	—	12	1	no	—
263	C₃×Dic₆	—	12	1	no	—
264	C₂³×C₉	—	2	1	no	—
265	C₂³×C₉	—	2	1	no	—
266	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
267	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
268	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
269	D₄×C₉	—	2	2	no	—
270	D₄×C₉	—	4	2	no	—
271	C₂×C₄×C₉	—	2	2	no	—
272	C₂×C₄×C₉	—	2	1	no	—
273	C₂×C₄×C₉	—	2	1	no	—
274	C₂×C₄×C₉	—	2	1	no	—
275	C₂×C₄×C₉	—	2	1	no	—
276	C₂×C₄×C₉	—	2	1	no	—
277	C₂×C₄×C₉	—	4	2	no	—
278	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
283	#611	—	2	2	no	—
284	#611	—	4	1	no	—
285	C₂×Dic₉	—	4	1	no	—
286	C₂×Dic₉	—	4	1	no	—
287	C₂×Dic₉	—	4	1	no	—
288	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
289	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
290	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
291	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
292	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
293	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
294	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
295	C₄×D₉	—	4	1	no	—
296	Dic₁₈	—	4	1	no	—
297	#539	—	9	1	no	Sylow
298	C₂×C₃×C₉	—	2	2	no	—
299	C₂×C₃×C₉	—	4	1	no	—
300	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
301	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
303	C₃×D₉	—	4	1	no	—
304	C₂×C₃×Q₈	—	9	1	no	—
305	C₂×C₃×D₄	—	2	1	no	—
306	C₂×C₃×D₄	—	9	1	no	—
307	C₂×C₃×D₄	—	9	1	no	—
308	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
309	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
310	C₂²×C₃×C₄	—	2	1	no	—
311	C₂²×C₃×C₄	—	9	1	no	—
312	C₂²×C₃×C₄	—	9	1	no	—
313	C₂²×C₃×C₄	—	9	1	no	—
314	C₂²×C₃×C₄	—	9	1	no	—
315	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
317	C₂×#67	—	3	1	no	—
318	C₂×#67	—	3	1	no	—
319	C₂²×Dic₃	—	3	1	no	—
320	C₂²×Dic₃	—	3	1	no	—
321	C₂²×Dic₃	—	3	1	no	—
322	C₂×C₄×D₃	—	3	1	no	—
323	C₂×Dic₆	—	3	1	no	—
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	—	2	1	no	—
326	C₃×C₄⋊C₄	—	9	1	no	—
327	C₃×C₄⋊C₄	—	9	1	no	—
328	C₃×C₄⋊C₄	—	9	1	no	—
329	C₃×C₄⋊C₄	—	9	1	no	—
330	C₃×C₄⋊C₄	—	9	1	no	—
331	C₃×C₄⋊C₄	—	9	1	no	—
332	C₃×C₄⋊C₄	—	9	1	no	—
333	C₃×C₄⋊C₄	—	9	1	no	—
334	C₃×C₄⋊C₄	—	9	1	no	—
335	C₃×C₄⋊C₄	—	9	1	no	—
336	C₃×C₄⋊C₄	—	9	1	no	—
337	C₃×C₄⋊C₄	—	9	1	no	—
338	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
339	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
340	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
341	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
342	C₃×C₂²⋊C₄	—	2	1	no	—
343	C₃×C₂²⋊C₄	—	2	1	no	—
344	C₃×C₂²⋊C₄	—	2	1	no	—
345	C₃×C₂²⋊C₄	—	9	1	no	—
346	C₃×C₂²⋊C₄	—	9	1	no	—
347	C₃×C₂²⋊C₄	—	9	1	no	—
348	C₃×C₂²⋊C₄	—	9	1	no	—
349	C₃×C₂²⋊C₄	—	9	1	no	—
350	C₃×C₂²⋊C₄	—	9	1	no	—
351	C₃×C₂²⋊C₄	—	9	1	no	—
352	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
353	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
354	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
355	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
356	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
357	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
358	C₃×C₄²	—	9	1	no	—
359	C₃×C₄²	—	9	1	no	—
360	#217	—	3	1	no	—
361	#217	—	3	1	no	—
362	#217	—	3	1	no	—
363	(C₂×D₃)⋊C₄	—	3	1	no	—
364	(C₂×D₃)⋊C₄	—	3	1	no	—
365	(C₂×D₃)⋊C₄	—	3	1	no	—
366	(C₂×D₃)⋊C₄	—	3	1	no	—
367	C₄⋊Dic₃	—	3	1	no	—
368	C₄⋊Dic₃	—	3	1	no	—
369	C₄⋊Dic₃	—	3	1	no	—
370	C₄⋊Dic₃	—	3	1	no	—
371	C₄⋊Dic₃	—	3	1	no	—
372	C₄⋊Dic₃	—	3	1	no	—
373	Dic₃⋊C₄	—	3	1	no	—
374	Dic₃⋊C₄	—	3	1	no	—
375	Dic₃⋊C₄	—	3	1	no	—
376	Dic₃⋊C₄	—	3	1	no	—
377	Dic₃⋊C₄	—	3	1	no	—
378	Dic₃⋊C₄	—	3	1	no	—
379	C₄×Dic₃	—	3	1	no	—
380	C₄×Dic₃	—	3	1	no	—
381	C₂²×C₃²	—	2	1	no	—
382	C₂²×C₃²	—	2	1	no	—
383	C₂²×C₃²	—	2	1	no	—
384	C₂²×C₃²	—	2	1	no	—
385	C₂²×C₃²	—	2	1	no	—
386	C₂²×C₃²	#237	1	2	yes	—
387	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
388	C₂×C₃×D₃	—	6	1	no	—
389	C₂×C₃×D₃	—	6	1	no	—
390	C₂×C₃×D₃	—	6	1	no	—
391	C₃²×C₄	—	2	1	no	—
392	C₃²×C₄	—	2	1	no	—
393	C₃²×C₄	—	2	1	no	—
394	C₃²×C₄	—	2	1	no	—
395	C₃²×C₄	—	2	1	no	—
396	C₃×Dic₃	—	6	1	no	—
397	C₃×Dic₃	—	6	1	no	—
398	C₃×Dic₃	—	6	1	no	—
399	C₃×Dic₃	—	6	1	no	—
400	C₃×Dic₃	—	6	1	no	—
401	C₃×Dic₃	—	6	1	no	—
402	C₃×Dic₃	—	6	1	no	—
403	C₂²×C₉	—	2	1	no	—
404	C₂²×C₉	—	2	1	no	—
405	C₂²×C₉	—	2	1	no	—
406	C₂²×C₉	—	2	1	no	—
407	C₂²×C₉	—	2	1	no	—
408	C₂²×C₉	—	2	1	no	—
409	C₂²×C₉	—	2	2	no	—
410	C₂²×C₉	—	4	1	no	—
411	C₂²×C₉	—	4	1	no	—
412	C₂²×C₉	—	4	1	no	—
413	C₂²×C₉	—	4	1	no	—
414	C₂²×C₉	—	4	1	no	—
415	C₂²×C₉	C₃×#41	1	2	yes	—
416	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
417	C₂×D₉	—	2	1	no	—
418	C₂×D₉	—	2	1	no	—
419	C₂×D₉	—	2	1	no	—
420	C₄×C₉	—	2	1	no	—
421	C₄×C₉	—	2	1	no	—
422	C₄×C₉	—	2	1	no	—
423	C₄×C₉	—	2	1	no	—
424	C₄×C₉	—	2	1	no	—
425	C₄×C₉	—	4	1	no	—
426	C₄×C₉	—	4	1	no	—
427	C₄×C₉	—	4	1	no	—
428	C₄×C₉	—	4	1	no	—
429	C₄×C₉	—	4	1	no	—
430	Dic₉	—	2	1	no	—
431	Dic₉	—	2	1	no	—
432	Dic₉	—	2	1	no	—
433	Dic₉	—	2	1	no	—
434	Dic₉	—	2	1	no	—
435	Dic₉	—	2	1	no	—
436	Dic₉	—	2	1	no	—
437	#126	—	9	1	no	—
438	#126	—	9	1	no	—
439	#125	—	9	1	no	—
440	#125	—	9	1	no	—
441	#123	—	9	1	no	—
442	#123	—	9	1	no	—
443	#123	—	9	1	no	—
444	#123	C₃×D₉	1	1	yes	characteristic, complemented
445	C₂²⋊Q₈	—	9	1	no	—
446	C₂²⋊Q₈	—	9	1	no	—
447	C₂²⋊Q₈	—	9	1	no	—
448	#121	—	9	1	no	—
449	C₄×D₄	—	9	1	no	—
450	C₄×D₄	—	9	1	no	—
451	C₂×C₄⋊C₄	—	9	1	no	—
452	C₃×C₉	#539	1	1	yes	characteristic, complemented, Sylow
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	—	2	1	no	—
455	C₂³×C₃	—	9	1	no	—
456	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
457	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
458	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
459	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
460	C₂²×D₃	—	3	1	no	—
461	C₃×Q₈	—	36	1	no	—
462	C₃×D₄	—	2	2	no	—
463	C₃×D₄	—	2	2	no	—
464	C₃×D₄	—	4	2	no	—
465	C₃×D₄	—	18	2	no	—
466	C₃×D₄	—	36	1	no	—
467	C₂×C₃×C₄	—	2	2	no	—
468	C₂×C₃×C₄	—	2	2	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	4	2	no	—
475	C₂×C₃×C₄	—	9	1	no	—
476	C₂×C₃×C₄	—	9	1	no	—
477	C₂×C₃×C₄	—	9	1	no	—
478	C₂×C₃×C₄	—	9	1	no	—
479	C₂×C₃×C₄	—	9	1	no	—
480	C₂×C₃×C₄	—	9	1	no	—
481	C₂×C₃×C₄	—	9	1	no	—
482	C₂×C₃×C₄	—	36	1	no	—
483	C₂×C₃×C₄	—	36	1	no	—
484	C₂×C₃×C₄	—	36	1	no	—
485	C₂×C₃×C₄	—	36	1	no	—
486	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
492	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
496	#67	—	6	2	no	—
497	#67	—	12	1	no	—
498	C₂×Dic₃	—	3	1	no	—
499	C₂×Dic₃	—	3	1	no	—
500	C₂×Dic₃	—	3	1	no	—
501	C₂×Dic₃	—	3	1	no	—
502	C₂×Dic₃	—	3	1	no	—
503	C₂×Dic₃	—	3	1	no	—
504	C₂×Dic₃	—	3	1	no	—
505	C₂×Dic₃	—	12	1	no	—
506	C₂×Dic₃	—	12	1	no	—
507	C₂×Dic₃	—	12	1	no	—
508	C₄×D₃	—	12	1	no	—
509	Dic₆	—	12	1	no	—
510	C₂×C₃²	—	2	2	no	—
511	C₂×C₃²	—	4	1	no	—
512	C₂×C₃²	C₂×#237	1	1	yes	characteristic
513	C₂×C₃²	#1009	1	1	yes	characteristic
514	C₂×C₃²	#1010	1	1	yes	characteristic
515	C₃×D₃	—	12	1	no	—
516	C₂×C₉	—	2	2	no	—
517	C₂×C₉	—	2	1	no	—
518	C₂×C₉	—	2	1	no	—
519	C₂×C₉	—	2	1	no	—
520	C₂×C₉	—	4	2	no	—
521	C₂×C₉	—	4	1	no	—
522	C₂×C₉	—	8	1	no	—
523	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
524	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
526	D₉	—	4	1	no	—
527	C₂×Q₈	—	9	1	no	—
528	C₂×D₄	—	9	1	no	—
529	C₂×D₄	—	9	1	no	—
530	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
531	C₂²×C₄	—	9	1	no	—
532	C₂²×C₄	—	9	1	no	—
533	C₂²×C₄	—	9	1	no	—
534	C₂²×C₄	—	9	1	no	—
535	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
536	C₄⋊C₄	—	9	1	no	—
537	C₄⋊C₄	—	9	1	no	—
538	C₄⋊C₄	—	9	1	no	—
539	C₄⋊C₄	—	9	1	no	—
540	C₄⋊C₄	—	9	1	no	—
541	C₄⋊C₄	—	9	1	no	—
542	C₄⋊C₄	—	9	1	no	—
543	C₄⋊C₄	—	9	1	no	—
544	C₄⋊C₄	—	9	1	no	—
545	C₄⋊C₄	—	9	1	no	—
546	C₄⋊C₄	—	9	1	no	—
547	C₄⋊C₄	—	9	1	no	—
548	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
550	C₂²⋊C₄	—	9	1	no	—
551	C₂²⋊C₄	—	9	1	no	—
552	C₂²⋊C₄	—	9	1	no	—
553	C₂²⋊C₄	—	9	1	no	—
554	C₂²⋊C₄	—	9	1	no	—
555	C₂²⋊C₄	—	9	1	no	—
556	C₂²⋊C₄	—	9	1	no	—
557	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
558	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
559	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
560	C₄²	—	9	1	no	—
561	C₄²	—	9	1	no	—
562	C₂²×C₃	—	2	1	no	—
563	C₂²×C₃	—	2	1	no	—
564	C₂²×C₃	—	2	1	no	—
565	C₂²×C₃	—	2	1	no	—
566	C₂²×C₃	—	2	1	no	—
567	C₂²×C₃	—	2	1	no	—
568	C₂²×C₃	—	2	1	no	—
569	C₂²×C₃	—	2	1	no	—
570	C₂²×C₃	—	2	1	no	—
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	1	no	—
573	C₂²×C₃	—	2	2	no	—
574	C₂²×C₃	—	4	1	no	—
575	C₂²×C₃	—	4	1	no	—
576	C₂²×C₃	—	4	1	no	—
577	C₂²×C₃	—	4	1	no	—
578	C₂²×C₃	—	4	1	no	—
579	C₂²×C₃	—	18	1	no	—
580	C₂²×C₃	—	18	1	no	—
581	C₂²×C₃	—	18	1	no	—
582	C₂²×C₃	#3699	1	2	yes	—
583	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
584	C₂²×C₃	C₃×#237	1	2	yes	—
585	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
586	C₂×D₃	—	6	1	no	—
587	C₂×D₃	—	6	1	no	—
588	C₂×D₃	—	6	1	no	—
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	1	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	2	1	no	—
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	—	2	1	no	—
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	2	1	no	—
599	C₃×C₄	—	4	1	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	—	4	1	no	—
602	C₃×C₄	—	4	1	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	18	1	no	—
605	C₃×C₄	—	18	1	no	—
606	C₃×C₄	—	18	1	no	—
607	C₃×C₄	—	18	1	no	—
608	C₃×C₄	—	18	1	no	—
609	C₃×C₄	—	18	1	no	—
610	C₃×C₄	—	18	1	no	—
611	Dic₃	—	6	1	no	—
612	Dic₃	—	6	1	no	—
613	Dic₃	—	6	1	no	—
614	Dic₃	—	6	1	no	—
615	Dic₃	—	6	1	no	—
616	Dic₃	—	6	1	no	—
617	Dic₃	—	6	1	no	—
618	C₃²	#5665	1	1	yes	characteristic
619	C₉	—	2	1	no	—
620	C₉	C₃×#539	1	1	yes	characteristic, complemented
621	C₂³	—	9	1	no	—
622	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
623	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
624	Q₈	—	36	1	no	—
625	D₄	—	2	2	no	—
626	D₄	—	18	2	no	—
627	D₄	—	36	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	9	1	no	—
630	C₂×C₄	—	9	1	no	—
631	C₂×C₄	—	9	1	no	—
632	C₂×C₄	—	9	1	no	—
633	C₂×C₄	—	9	1	no	—
634	C₂×C₄	—	9	1	no	—
635	C₂×C₄	—	9	1	no	—
636	C₂×C₄	—	36	1	no	—
637	C₂×C₄	—	36	1	no	—
638	C₂×C₄	—	36	1	no	—
639	C₂×C₄	—	36	1	no	—
640	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
641	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
642	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
643	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
644	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
645	C₂×C₃	—	2	2	no	—
646	C₂×C₃	—	2	2	no	—
647	C₂×C₃	—	2	1	no	—
648	C₂×C₃	—	2	1	no	—
649	C₂×C₃	—	2	1	no	—
650	C₂×C₃	—	4	2	no	—
651	C₂×C₃	—	4	1	no	—
652	C₂×C₃	—	4	1	no	—
653	C₂×C₃	—	8	1	no	—
654	C₂×C₃	—	36	1	no	—
655	C₂×C₃	C₂×#3699	1	1	yes	characteristic
656	C₂×C₃	#63715	1	1	yes	characteristic
657	C₂×C₃	#63716	1	1	yes	characteristic
658	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
659	C₂×C₃	C₃×#1009	1	1	yes	characteristic
660	C₂×C₃	C₃×#1010	1	1	yes	characteristic
661	D₃	—	12	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	18	1	no	—
668	C₂²	—	18	1	no	—
669	C₂²	—	18	1	no	—
670	C₂²	C₃×#3699	1	2	yes	—
671	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	18	1	no	—
678	C₄	—	18	1	no	—
679	C₄	—	18	1	no	—
680	C₄	—	18	1	no	—
681	C₄	—	18	1	no	—
682	C₄	—	18	1	no	—
683	C₄	—	18	1	no	—
684	C₃	—	2	1	no	—
685	C₃	#10589767	1	1	yes	characteristic, direct product factor
686	C₃	C₃×#5665	1	1	yes	characteristic
687	C₂	—	2	2	no	—
688	C₂	—	4	1	no	—
689	C₂	—	36	1	no	—
690	C₂	C₂×C₃×#3699	1	1	yes	characteristic
691	C₂	C₃×#63715	1	1	yes	characteristic
692	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×#123	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₃×#63501	C₂
hypercenter	C₃×#123	D₉
hypocenter	C₉	C₃×#539
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#123	C₂	semidirect
3. C₃×D₄×Dic₉	C₂	semidirect
4. C₃×#63491	C₂	semidirect
5. C₂×C₃×C₄⋊Dic₉	C₂	semidirect
6. C₃×#63460	C₂	semidirect
7. C₃×#63459	C₂	semidirect
8. C₃×#63452	C₂	semidirect
9. C₃×#63451	C₂	semidirect
10. C₃×#63448	C₂	semidirect
11. C₃×#63445	C₂	semidirect
12. C₃×#611⋊C₄	C₂	semidirect
13. C₃×#63441	C₂	semidirect
14. C₃×#63440	C₂	semidirect
15. C₃×#63440	C₂	semidirect
17. #10589767	C₃	direct (N × H)
69. C₉×#123	C₂×C₃	semidirect
71. D₄×Dic₉	C₂×C₃	semidirect
72. #63491	C₂×C₃	semidirect
73. C₂×C₄⋊Dic₉	C₂×C₃	semidirect
74. #63460	C₂×C₃	semidirect
75. #63459	C₂×C₃	semidirect
76. #63452	C₂×C₃	semidirect
77. #63451	C₂×C₃	semidirect
78. #63448	C₂×C₃	semidirect
79. #63445	C₂×C₃	semidirect
80. #611⋊C₄	C₂×C₃	semidirect
81. #63441	C₂×C₃	semidirect
82. #63440	C₂×C₃	semidirect
83. #63440	C₂×C₃	semidirect
217. C₃×#123	D₉	semidirect
444. #123	C₃×D₉	semidirect
452. C₃×C₉	#539	semidirect
620. C₉	C₃×#539	semidirect
685. C₃	#10589767	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×#123	2
C₃×#63501	2
C₃×D₄×Dic₉	2
C₃×#63491	2
C₂×C₃×C₄⋊Dic₉	2
C₃×#63460	2
C₃×#63459	2
C₃×#63452	2
C₃×#63451	2
C₃×#63448	2
C₃×#63445	2
C₃×#611⋊C₄	2
C₃×#63441	2
C₃×#63440	2
C₃×#5665	3
#10589767	3

Subgroups — C3×#10589767 #13153020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589767 #13153020