Subgroups — C₃×#10589765 #13153000

Order 1728.

798 conjugacy classes of subgroups.

The subgroup lattice has 766 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×#63502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#611	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63457	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63454	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×#63446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#63446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#63445	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#611⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5663	—	3	1	no	maximal
17	#10589765	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	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	C₂×C₃×#611	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
29	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
33	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×#3676	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×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊Dic₉	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×#940	—	3	1	no	—
55	C₃×#939	—	3	1	no	—
56	C₃×#930	—	3	1	no	—
57	C₃×C₄×#67	—	3	1	no	—
58	C₃×#895	—	3	1	no	—
59	C₃×#894	—	3	1	no	—
60	C₃×#892	—	3	1	no	—
61	C₃×#889	—	3	1	no	—
62	C₃×#886	—	3	1	no	—
63	C₃×#884	—	3	1	no	—
64	C₃×#884	—	3	1	no	—
65	C₃×#884	—	3	1	no	—
66	C₃×#883	—	3	1	no	—
67	C₃×#67⋊C₄	—	3	1	no	—
68	C₉×#123	—	2	1	no	—
69	C₉×#123	C₂×C₃	1	1	yes	characteristic, complemented
70	#63502	C₂×C₃	1	1	yes	characteristic, complemented
71	#63501	C₂×C₃	1	1	yes	characteristic, complemented
72	#63492	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
74	#63457	C₂×C₃	1	1	yes	characteristic, complemented
75	#63456	C₂×C₃	1	1	yes	characteristic, complemented
76	#63454	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	#63446	C₂×C₃	1	1	yes	characteristic, complemented
80	#63446	C₂×C₃	1	1	yes	characteristic, complemented
81	#63446	C₂×C₃	1	1	yes	characteristic, complemented
82	#63445	C₂×C₃	1	1	yes	characteristic, complemented
83	#611⋊C₄	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	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
88	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
89	C₃×D₄×C₉	—	4	1	no	—
90	C₂×C₃×C₄×C₉	—	4	1	no	—
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	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	C₃×#611	—	4	1	no	—
100	C₃×#611	—	4	1	no	—
101	C₃×#611	—	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	C₃×D₃₆	—	4	1	no	—
109	C₃×D₃₆	—	4	1	no	—
110	C₃×D₃₆	—	4	1	no	—
111	C₃×C₄×D₉	—	2	2	no	—
112	C₃×C₄×D₉	—	4	1	no	—
113	C₃×C₄×D₉	—	4	1	no	—
114	C₃×#540	—	9	1	no	—
115	#5663	—	3	1	no	—
116	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
117	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
118	C₂×C₃×#67	—	3	1	no	—
119	C₂×C₃×#67	—	3	1	no	—
120	C₂×C₃×#67	—	3	1	no	—
121	C₂×C₃×#67	—	3	1	no	—
122	C₂×C₃×#67	—	3	1	no	—
123	C₂×C₃×#67	—	3	1	no	—
124	C₂²×C₃×Dic₃	—	3	1	no	—
125	C₂×C₃×D₁₂	—	3	1	no	—
126	C₂×C₃×D₁₂	—	3	1	no	—
127	C₂×C₃×D₁₂	—	3	1	no	—
128	C₂×C₃×C₄×D₃	—	3	1	no	—
129	C₂×C₃×C₄×D₃	—	3	1	no	—
130	C₂×C₃×C₄×D₃	—	3	1	no	—
131	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
136	C₃×#217	—	3	1	no	—
137	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
138	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
139	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
140	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
141	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
142	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
143	C₃×C₄⋊Dic₃	—	3	1	no	—
144	C₃×C₄⋊Dic₃	—	3	1	no	—
145	C₃×Dic₃⋊C₄	—	3	1	no	—
146	C₃×Dic₃⋊C₄	—	3	1	no	—
147	C₃×Dic₃⋊C₄	—	3	1	no	—
148	C₃×Dic₃⋊C₄	—	3	1	no	—
149	C₃×C₄×Dic₃	—	3	1	no	—
150	C₃×C₄×Dic₃	—	3	1	no	—
151	C₂×D₄×C₉	—	2	1	no	—
152	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₉	—	2	1	no	—
154	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
155	C₂×#611	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	C₂×#611	C₂²×C₃	1	1	yes	characteristic
160	C₂×#611	C₂²×C₃	1	1	yes	characteristic
161	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
162	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
163	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
168	C₉×C₄⋊C₄	—	2	1	no	—
169	C₉×C₄⋊C₄	—	2	1	no	—
170	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	C₉×C₂²⋊C₄	—	2	1	no	—
173	C₉×C₂²⋊C₄	—	2	1	no	—
174	C₉×C₂²⋊C₄	—	2	1	no	—
175	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	#3676	C₂²×C₃	1	1	yes	characteristic
179	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	(C₂×D₉)⋊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	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
189	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
190	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
191	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
192	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
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	—	2	1	no	—
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	C₂×C₃×D₉	—	2	1	no	—
204	C₂×C₃×D₉	—	2	1	no	—
205	C₂×C₃×D₉	—	2	1	no	—
206	C₂×C₃×D₉	—	2	1	no	—
207	C₂×C₃×D₉	—	2	1	no	—
208	C₂×C₃×D₉	—	2	1	no	—
209	C₃×C₄×C₉	—	2	1	no	—
210	C₃×C₄×C₉	—	2	1	no	—
211	C₃×C₄×C₉	—	2	1	no	—
212	C₃×C₄×C₉	—	2	1	no	—
213	C₃×C₄×C₉	—	2	1	no	—
214	C₃×Dic₉	—	2	1	no	—
215	C₃×Dic₉	—	2	1	no	—
216	C₃×Dic₉	—	2	1	no	—
217	C₃×Dic₉	—	2	1	no	—
218	C₃×Dic₉	#41	1	2	yes	—
219	C₃×#127	—	9	1	no	—
220	C₃×#125	—	9	1	no	—
221	C₃×#123	—	2	1	no	—
222	C₃×#123	—	9	1	no	—
223	C₃×#123	—	9	1	no	—
224	C₃×#123	—	9	1	no	—
225	C₃×#123	D₉	1	1	yes	characteristic, complemented
226	C₃×#123	C₃×D₃	1	1	yes	characteristic
227	C₃×#121	—	9	1	no	—
228	C₃×#121	—	9	1	no	—
229	C₃×#121	—	9	1	no	—
230	C₃×#121	—	9	1	no	—
231	C₃×#121	—	9	1	no	—
232	C₃×#121	—	9	1	no	—
233	C₃×C₄×D₄	—	9	1	no	—
234	C₃×C₄×D₄	—	9	1	no	—
235	C₃×#117	—	9	1	no	—
236	#940	—	3	1	no	—
237	#939	—	3	1	no	—
238	#930	—	3	1	no	—
239	C₄×#67	—	3	1	no	—
240	#895	—	3	1	no	—
241	#894	—	3	1	no	—
242	#892	—	3	1	no	—
243	#889	—	3	1	no	—
244	#886	—	3	1	no	—
245	#884	—	3	1	no	—
246	#884	—	3	1	no	—
247	#884	—	3	1	no	—
248	#883	—	3	1	no	—
249	#67⋊C₄	—	3	1	no	—
250	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
251	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
252	C₂²×C₃×D₃	—	3	1	no	—
253	C₂²×C₃×D₃	—	3	1	no	—
254	C₂²×C₃×D₃	—	3	1	no	—
255	C₃²×D₄	—	4	1	no	—
256	C₂×C₃²×C₄	—	4	1	no	—
257	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
258	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
259	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
260	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
261	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
262	C₃×#67	—	6	2	no	—
263	C₃×#67	—	6	2	no	—
264	C₃×#67	—	12	1	no	—
265	C₃×#67	—	12	1	no	—
266	C₃×#67	—	12	1	no	—
267	C₃×#67	—	12	1	no	—
268	C₂×C₃×Dic₃	—	3	1	no	—
269	C₂×C₃×Dic₃	—	3	1	no	—
270	C₂×C₃×Dic₃	—	3	1	no	—
271	C₂×C₃×Dic₃	—	3	1	no	—
272	C₂×C₃×Dic₃	—	3	1	no	—
273	C₂×C₃×Dic₃	—	12	1	no	—
274	C₃×D₁₂	—	12	1	no	—
275	C₃×D₁₂	—	12	1	no	—
276	C₃×D₁₂	—	12	1	no	—
277	C₃×C₄×D₃	—	6	2	no	—
278	C₃×C₄×D₃	—	12	1	no	—
279	C₃×C₄×D₃	—	12	1	no	—
280	C₂³×C₉	—	2	1	no	—
281	C₂³×C₉	—	2	1	no	—
282	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
283	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
284	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
285	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
286	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
287	D₄×C₉	—	4	1	no	—
288	D₄×C₉	—	4	2	no	—
289	C₂×C₄×C₉	—	2	1	no	—
290	C₂×C₄×C₉	—	2	1	no	—
291	C₂×C₄×C₉	—	2	1	no	—
292	C₂×C₄×C₉	—	2	1	no	—
293	C₂×C₄×C₉	—	2	1	no	—
294	C₂×C₄×C₉	—	4	1	no	—
295	C₂×C₄×C₉	—	4	2	no	—
296	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
301	#611	—	2	2	no	—
302	#611	—	2	2	no	—
303	#611	—	4	1	no	—
304	#611	—	4	1	no	—
305	#611	—	4	1	no	—
306	#611	—	4	1	no	—
307	C₂×Dic₉	—	4	1	no	—
308	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
309	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
310	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
311	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
312	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
313	D₃₆	—	4	1	no	—
314	D₃₆	—	4	1	no	—
315	D₃₆	—	4	1	no	—
316	C₄×D₉	—	2	2	no	—
317	C₄×D₉	—	4	1	no	—
318	C₄×D₉	—	4	1	no	—
319	#540	—	9	1	no	Sylow
320	C₂×C₃×C₉	—	4	1	no	—
321	C₂×C₃×C₉	—	4	1	no	—
322	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
323	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
325	C₃×D₉	—	4	1	no	—
326	C₃×D₉	—	4	1	no	—
327	C₃×D₉	—	4	1	no	—
328	C₂×C₃×D₄	—	2	1	no	—
329	C₂×C₃×D₄	—	9	1	no	—
330	C₂×C₃×D₄	—	9	1	no	—
331	C₂×C₃×D₄	—	9	1	no	—
332	C₂×C₃×D₄	—	9	1	no	—
333	C₂×C₃×D₄	—	9	1	no	—
334	C₂×C₃×D₄	—	9	1	no	—
335	C₂×C₃×D₄	—	9	1	no	—
336	C₂×C₃×D₄	—	9	1	no	—
337	C₂×C₃×D₄	—	9	1	no	—
338	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
339	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
340	C₂²×C₃×C₄	—	2	1	no	—
341	C₂²×C₃×C₄	—	9	1	no	—
342	C₂²×C₃×C₄	—	9	1	no	—
343	C₂²×C₃×C₄	—	9	1	no	—
344	C₂²×C₃×C₄	—	9	1	no	—
345	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
347	C₂×#67	—	3	1	no	—
348	C₂×#67	—	3	1	no	—
349	C₂×#67	—	3	1	no	—
350	C₂×#67	—	3	1	no	—
351	C₂×#67	—	3	1	no	—
352	C₂×#67	—	3	1	no	—
353	C₂²×Dic₃	—	3	1	no	—
354	C₂×D₁₂	—	3	1	no	—
355	C₂×D₁₂	—	3	1	no	—
356	C₂×D₁₂	—	3	1	no	—
357	C₂×C₄×D₃	—	3	1	no	—
358	C₂×C₄×D₃	—	3	1	no	—
359	C₂×C₄×D₃	—	3	1	no	—
360	C₃×C₄⋊C₄	—	2	1	no	—
361	C₃×C₄⋊C₄	—	2	1	no	—
362	C₃×C₄⋊C₄	—	9	1	no	—
363	C₃×C₄⋊C₄	—	9	1	no	—
364	C₃×C₄⋊C₄	—	9	1	no	—
365	C₃×C₄⋊C₄	—	9	1	no	—
366	C₃×C₄⋊C₄	—	9	1	no	—
367	C₃×C₄⋊C₄	—	9	1	no	—
368	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
369	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
370	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
371	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
372	C₃×C₂²⋊C₄	—	2	1	no	—
373	C₃×C₂²⋊C₄	—	2	1	no	—
374	C₃×C₂²⋊C₄	—	2	1	no	—
375	C₃×C₂²⋊C₄	—	9	1	no	—
376	C₃×C₂²⋊C₄	—	9	1	no	—
377	C₃×C₂²⋊C₄	—	9	1	no	—
378	C₃×C₂²⋊C₄	—	9	1	no	—
379	C₃×C₂²⋊C₄	—	9	1	no	—
380	C₃×C₂²⋊C₄	—	9	1	no	—
381	C₃×C₂²⋊C₄	—	9	1	no	—
382	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
383	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
384	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
385	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
386	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
387	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
388	C₃×C₄²	—	9	1	no	—
389	C₃×C₄²	—	9	1	no	—
390	#217	—	3	1	no	—
391	(C₂×D₃)⋊C₄	—	3	1	no	—
392	(C₂×D₃)⋊C₄	—	3	1	no	—
393	(C₂×D₃)⋊C₄	—	3	1	no	—
394	(C₂×D₃)⋊C₄	—	3	1	no	—
395	(C₂×D₃)⋊C₄	—	3	1	no	—
396	(C₂×D₃)⋊C₄	—	3	1	no	—
397	C₄⋊Dic₃	—	3	1	no	—
398	C₄⋊Dic₃	—	3	1	no	—
399	Dic₃⋊C₄	—	3	1	no	—
400	Dic₃⋊C₄	—	3	1	no	—
401	Dic₃⋊C₄	—	3	1	no	—
402	Dic₃⋊C₄	—	3	1	no	—
403	C₄×Dic₃	—	3	1	no	—
404	C₄×Dic₃	—	3	1	no	—
405	C₂²×C₃²	—	2	1	no	—
406	C₂²×C₃²	—	2	1	no	—
407	C₂²×C₃²	—	2	1	no	—
408	C₂²×C₃²	—	2	1	no	—
409	C₂²×C₃²	—	2	1	no	—
410	C₂²×C₃²	—	2	1	no	—
411	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
412	C₂×C₃×D₃	—	6	1	no	—
413	C₂×C₃×D₃	—	6	1	no	—
414	C₂×C₃×D₃	—	6	1	no	—
415	C₂×C₃×D₃	—	6	1	no	—
416	C₂×C₃×D₃	—	6	1	no	—
417	C₂×C₃×D₃	—	6	1	no	—
418	C₂×C₃×D₃	—	6	1	no	—
419	C₂×C₃×D₃	—	6	1	no	—
420	C₂×C₃×D₃	—	6	1	no	—
421	C₃²×C₄	—	2	1	no	—
422	C₃²×C₄	—	2	1	no	—
423	C₃²×C₄	—	2	1	no	—
424	C₃²×C₄	—	2	1	no	—
425	C₃²×C₄	—	2	1	no	—
426	C₃×Dic₃	—	3	2	no	—
427	C₃×Dic₃	—	6	1	no	—
428	C₃×Dic₃	—	6	1	no	—
429	C₃×Dic₃	—	6	1	no	—
430	C₃×Dic₃	—	6	1	no	—
431	C₂²×C₉	—	2	2	no	—
432	C₂²×C₉	—	2	1	no	—
433	C₂²×C₉	—	2	1	no	—
434	C₂²×C₉	—	2	1	no	—
435	C₂²×C₉	—	2	1	no	—
436	C₂²×C₉	—	2	1	no	—
437	C₂²×C₉	—	2	1	no	—
438	C₂²×C₉	—	2	1	no	—
439	C₂²×C₉	—	4	1	no	—
440	C₂²×C₉	—	4	1	no	—
441	C₂²×C₉	—	4	1	no	—
442	C₂²×C₉	—	4	1	no	—
443	C₂²×C₉	—	4	1	no	—
444	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
445	C₂×D₉	—	2	1	no	—
446	C₂×D₉	—	2	1	no	—
447	C₂×D₉	—	2	1	no	—
448	C₂×D₉	—	2	1	no	—
449	C₂×D₉	—	2	1	no	—
450	C₂×D₉	—	2	1	no	—
451	C₂×D₉	—	2	1	no	—
452	C₂×D₉	—	2	1	no	—
453	C₂×D₉	—	2	1	no	—
454	C₄×C₉	—	2	1	no	—
455	C₄×C₉	—	2	1	no	—
456	C₄×C₉	—	2	1	no	—
457	C₄×C₉	—	2	1	no	—
458	C₄×C₉	—	2	1	no	—
459	C₄×C₉	—	4	1	no	—
460	C₄×C₉	—	4	1	no	—
461	C₄×C₉	—	4	1	no	—
462	C₄×C₉	—	4	1	no	—
463	C₄×C₉	—	4	1	no	—
464	Dic₉	—	2	1	no	—
465	Dic₉	—	2	1	no	—
466	Dic₉	—	2	1	no	—
467	Dic₉	—	2	1	no	—
468	Dic₉	C₃×#41	1	2	yes	—
469	#127	—	9	1	no	—
470	#125	—	9	1	no	—
471	#123	—	9	1	no	—
472	#123	—	9	1	no	—
473	#123	—	9	1	no	—
474	#123	C₃×D₉	1	1	yes	characteristic, complemented
475	#121	—	9	1	no	—
476	#121	—	9	1	no	—
477	#121	—	9	1	no	—
478	#121	—	9	1	no	—
479	#121	—	9	1	no	—
480	#121	—	9	1	no	—
481	C₄×D₄	—	9	1	no	—
482	C₄×D₄	—	9	1	no	—
483	#117	—	9	1	no	—
484	C₃×C₉	#540	1	1	yes	characteristic, complemented, Sylow
485	C₂³×C₃	—	2	1	no	—
486	C₂³×C₃	—	2	1	no	—
487	C₂³×C₃	—	9	1	no	—
488	C₂³×C₃	—	9	1	no	—
489	C₂³×C₃	—	9	1	no	—
490	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
491	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
492	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
493	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
494	C₂²×D₃	—	3	1	no	—
495	C₂²×D₃	—	3	1	no	—
496	C₂²×D₃	—	3	1	no	—
497	C₃×D₄	—	4	1	no	—
498	C₃×D₄	—	4	1	no	—
499	C₃×D₄	—	4	2	no	—
500	C₃×D₄	—	18	2	no	—
501	C₃×D₄	—	18	2	no	—
502	C₃×D₄	—	36	1	no	—
503	C₃×D₄	—	36	1	no	—
504	C₃×D₄	—	36	1	no	—
505	C₃×D₄	—	36	1	no	—
506	C₃×D₄	—	36	1	no	—
507	C₃×D₄	—	36	1	no	—
508	C₃×D₄	—	36	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	4	1	no	—
515	C₂×C₃×C₄	—	4	1	no	—
516	C₂×C₃×C₄	—	4	2	no	—
517	C₂×C₃×C₄	—	9	1	no	—
518	C₂×C₃×C₄	—	9	1	no	—
519	C₂×C₃×C₄	—	9	1	no	—
520	C₂×C₃×C₄	—	9	1	no	—
521	C₂×C₃×C₄	—	9	1	no	—
522	C₂×C₃×C₄	—	18	2	no	—
523	C₂×C₃×C₄	—	36	1	no	—
524	C₂×C₃×C₄	—	36	1	no	—
525	C₂×C₃×C₄	—	36	1	no	—
526	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
530	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
531	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
532	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
536	#67	—	6	2	no	—
537	#67	—	6	2	no	—
538	#67	—	12	1	no	—
539	#67	—	12	1	no	—
540	#67	—	12	1	no	—
541	#67	—	12	1	no	—
542	C₂×Dic₃	—	3	1	no	—
543	C₂×Dic₃	—	3	1	no	—
544	C₂×Dic₃	—	3	1	no	—
545	C₂×Dic₃	—	3	1	no	—
546	C₂×Dic₃	—	3	1	no	—
547	C₂×Dic₃	—	12	1	no	—
548	D₁₂	—	12	1	no	—
549	D₁₂	—	12	1	no	—
550	D₁₂	—	12	1	no	—
551	C₄×D₃	—	6	2	no	—
552	C₄×D₃	—	12	1	no	—
553	C₄×D₃	—	12	1	no	—
554	C₂×C₃²	—	4	1	no	—
555	C₂×C₃²	—	4	1	no	—
556	C₂×C₃²	#1004	1	1	yes	characteristic
557	C₂×C₃²	D₃×#41	1	1	yes	characteristic
558	C₂×C₃²	#1009	1	1	yes	characteristic
559	C₃×D₃	—	12	1	no	—
560	C₃×D₃	—	12	1	no	—
561	C₃×D₃	—	12	1	no	—
562	C₂×C₉	—	2	1	no	—
563	C₂×C₉	—	2	1	no	—
564	C₂×C₉	—	2	1	no	—
565	C₂×C₉	—	4	2	no	—
566	C₂×C₉	—	4	1	no	—
567	C₂×C₉	—	4	1	no	—
568	C₂×C₉	—	8	1	no	—
569	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
570	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
572	D₉	—	4	1	no	—
573	D₉	—	4	1	no	—
574	D₉	—	4	1	no	—
575	C₂×D₄	—	9	1	no	—
576	C₂×D₄	—	9	1	no	—
577	C₂×D₄	—	9	1	no	—
578	C₂×D₄	—	9	1	no	—
579	C₂×D₄	—	9	1	no	—
580	C₂×D₄	—	9	1	no	—
581	C₂×D₄	—	9	1	no	—
582	C₂×D₄	—	9	1	no	—
583	C₂×D₄	—	9	1	no	—
584	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
585	C₂²×C₄	—	9	1	no	—
586	C₂²×C₄	—	9	1	no	—
587	C₂²×C₄	—	9	1	no	—
588	C₂²×C₄	—	9	1	no	—
589	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
590	C₄⋊C₄	—	9	1	no	—
591	C₄⋊C₄	—	9	1	no	—
592	C₄⋊C₄	—	9	1	no	—
593	C₄⋊C₄	—	9	1	no	—
594	C₄⋊C₄	—	9	1	no	—
595	C₄⋊C₄	—	9	1	no	—
596	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
597	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
598	C₂²⋊C₄	—	9	1	no	—
599	C₂²⋊C₄	—	9	1	no	—
600	C₂²⋊C₄	—	9	1	no	—
601	C₂²⋊C₄	—	9	1	no	—
602	C₂²⋊C₄	—	9	1	no	—
603	C₂²⋊C₄	—	9	1	no	—
604	C₂²⋊C₄	—	9	1	no	—
605	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
606	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
607	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
608	C₄²	—	9	1	no	—
609	C₄²	—	9	1	no	—
610	C₂²×C₃	—	2	2	no	—
611	C₂²×C₃	—	2	1	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	2	1	no	—
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	2	1	no	—
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	1	no	—
626	C₂²×C₃	—	4	1	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	4	1	no	—
629	C₂²×C₃	—	18	1	no	—
630	C₂²×C₃	—	18	1	no	—
631	C₂²×C₃	—	18	1	no	—
632	C₂²×C₃	—	18	1	no	—
633	C₂²×C₃	—	18	1	no	—
634	C₂²×C₃	—	18	1	no	—
635	C₂²×C₃	—	18	1	no	—
636	C₂²×C₃	—	18	1	no	—
637	C₂²×C₃	—	18	1	no	—
638	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
639	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
640	C₂×D₃	—	6	1	no	—
641	C₂×D₃	—	6	1	no	—
642	C₂×D₃	—	6	1	no	—
643	C₂×D₃	—	6	1	no	—
644	C₂×D₃	—	6	1	no	—
645	C₂×D₃	—	6	1	no	—
646	C₂×D₃	—	6	1	no	—
647	C₂×D₃	—	6	1	no	—
648	C₂×D₃	—	6	1	no	—
649	C₃×C₄	—	2	1	no	—
650	C₃×C₄	—	2	1	no	—
651	C₃×C₄	—	2	1	no	—
652	C₃×C₄	—	2	1	no	—
653	C₃×C₄	—	2	1	no	—
654	C₃×C₄	—	2	1	no	—
655	C₃×C₄	—	2	1	no	—
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	2	1	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	4	1	no	—
660	C₃×C₄	—	4	1	no	—
661	C₃×C₄	—	4	1	no	—
662	C₃×C₄	—	4	1	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	9	2	no	—
665	C₃×C₄	—	18	1	no	—
666	C₃×C₄	—	18	1	no	—
667	C₃×C₄	—	18	1	no	—
668	C₃×C₄	—	18	1	no	—
669	Dic₃	—	3	2	no	—
670	Dic₃	—	6	1	no	—
671	Dic₃	—	6	1	no	—
672	Dic₃	—	6	1	no	—
673	Dic₃	—	6	1	no	—
674	C₃²	#5663	1	1	yes	characteristic
675	C₉	—	2	1	no	—
676	C₉	C₃×#540	1	1	yes	characteristic, complemented
677	C₂³	—	9	1	no	—
678	C₂³	—	9	1	no	—
679	C₂³	—	9	1	no	—
680	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
681	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
682	D₄	—	4	1	no	—
683	D₄	—	18	2	no	—
684	D₄	—	18	2	no	—
685	D₄	—	36	1	no	—
686	D₄	—	36	1	no	—
687	D₄	—	36	1	no	—
688	D₄	—	36	1	no	—
689	D₄	—	36	1	no	—
690	D₄	—	36	1	no	—
691	D₄	—	36	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	9	1	no	—
694	C₂×C₄	—	9	1	no	—
695	C₂×C₄	—	9	1	no	—
696	C₂×C₄	—	9	1	no	—
697	C₂×C₄	—	9	1	no	—
698	C₂×C₄	—	18	2	no	—
699	C₂×C₄	—	36	1	no	—
700	C₂×C₄	—	36	1	no	—
701	C₂×C₄	—	36	1	no	—
702	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
703	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
704	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
705	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
706	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
707	C₂×C₃	—	2	1	no	—
708	C₂×C₃	—	2	1	no	—
709	C₂×C₃	—	2	1	no	—
710	C₂×C₃	—	4	2	no	—
711	C₂×C₃	—	4	1	no	—
712	C₂×C₃	—	4	1	no	—
713	C₂×C₃	—	4	1	no	—
714	C₂×C₃	—	4	1	no	—
715	C₂×C₃	—	8	1	no	—
716	C₂×C₃	—	36	1	no	—
717	C₂×C₃	—	36	1	no	—
718	C₂×C₃	—	36	1	no	—
719	C₂×C₃	#63710	1	1	yes	characteristic
720	C₂×C₃	#41×D₉	1	1	yes	characteristic
721	C₂×C₃	#63715	1	1	yes	characteristic
722	C₂×C₃	C₃×#1004	1	1	yes	characteristic
723	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
724	C₂×C₃	C₃×#1009	1	1	yes	characteristic
725	D₃	—	12	1	no	—
726	D₃	—	12	1	no	—
727	D₃	—	12	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	18	1	no	—
735	C₂²	—	18	1	no	—
736	C₂²	—	18	1	no	—
737	C₂²	—	18	1	no	—
738	C₂²	—	18	1	no	—
739	C₂²	—	18	1	no	—
740	C₂²	—	18	1	no	—
741	C₂²	—	18	1	no	—
742	C₂²	—	18	1	no	—
743	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	9	2	no	—
750	C₄	—	18	1	no	—
751	C₄	—	18	1	no	—
752	C₄	—	18	1	no	—
753	C₄	—	18	1	no	—
754	C₃	—	2	1	no	—
755	C₃	#10589765	1	1	yes	characteristic, direct product factor
756	C₃	C₃×#5663	1	1	yes	characteristic
757	C₂	—	4	1	no	—
758	C₂	—	4	1	no	—
759	C₂	—	36	1	no	—
760	C₂	—	36	1	no	—
761	C₂	—	36	1	no	—
762	C₂	C₃×#63710	1	1	yes	characteristic
763	C₂	C₃×#41×D₉	1	1	yes	characteristic
764	C₂	C₃×#63715	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
hypercenter	C₃×#123	D₉
hypocenter	C₉	C₃×#540
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
2. C₃×#63502	C₂	semidirect
3. C₃×#63501	C₂	semidirect
4. C₃×#63492	C₂	semidirect
5. C₃×C₄×#611	C₂	semidirect
6. C₃×#63457	C₂	semidirect
7. C₃×#63456	C₂	semidirect
8. C₃×#63454	C₂	semidirect
9. C₃×#63451	C₂	semidirect
10. C₃×#63448	C₂	semidirect
11. C₃×#63446	C₂	semidirect
12. C₃×#63446	C₂	semidirect
13. C₃×#63446	C₂	semidirect
14. C₃×#63445	C₂	semidirect
15. C₃×#611⋊C₄	C₂	semidirect
17. #10589765	C₃	direct (N × H)
69. C₉×#123	C₂×C₃	semidirect
70. #63502	C₂×C₃	semidirect
71. #63501	C₂×C₃	semidirect
72. #63492	C₂×C₃	semidirect
73. C₄×#611	C₂×C₃	semidirect
74. #63457	C₂×C₃	semidirect
75. #63456	C₂×C₃	semidirect
76. #63454	C₂×C₃	semidirect
77. #63451	C₂×C₃	semidirect
78. #63448	C₂×C₃	semidirect
79. #63446	C₂×C₃	semidirect
80. #63446	C₂×C₃	semidirect
81. #63446	C₂×C₃	semidirect
82. #63445	C₂×C₃	semidirect
83. #611⋊C₄	C₂×C₃	semidirect
225. C₃×#123	D₉	semidirect
474. #123	C₃×D₉	semidirect
484. C₃×C₉	#540	semidirect
676. C₉	C₃×#540	semidirect
755. C₃	#10589765	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×#63502	2
C₃×#63501	2
C₃×#63492	2
C₃×C₄×#611	2
C₃×#63457	2
C₃×#63456	2
C₃×#63454	2
C₃×#63451	2
C₃×#63448	2
C₃×#63446	2
C₃×#63445	2
C₃×#611⋊C₄	2
C₃×#5663	3
#10589765	3

Subgroups — C3×#10589765 #13153000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589765 #13153000