Subgroups — C₃×#10589636 #13152492

Order 1728.

724 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63492	C₂	1	1	yes	maximal, characteristic
3	C₃×#63486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63460	C₂	1	2	yes	maximal, complemented
5	C₃×#63458	C₂	1	2	yes	maximal, complemented
6	C₃×#63447	C₂	1	2	yes	maximal, complemented
7	C₃×#63445	C₂	1	2	yes	maximal, complemented
8	C₃×#63437	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63431	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5534	—	3	1	no	maximal
13	#10589636	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×#611	C₂²	1	2	yes	—
16	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₃×#3676	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×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
31	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
32	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
33	C₃×C₄⋊Dic₉	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	C₃²×#117	D₃	1	1	yes	characteristic
38	C₃×#930	—	3	1	no	—
39	C₃×#924	—	3	1	no	—
40	C₃×#898	—	3	2	no	—
41	C₃×#896	—	3	2	no	—
42	C₃×#885	—	3	2	no	—
43	C₃×#883	—	3	2	no	—
44	C₃×#875	—	3	1	no	—
45	C₃×C₄×D₁₂	—	3	1	no	—
46	C₃×#869	—	3	1	no	—
47	C₃×C₄×Dic₆	—	3	1	no	—
48	C₉×#117	—	2	1	no	—
49	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
50	#63492	C₂×C₃	1	1	yes	characteristic
51	#63486	C₂×C₃	1	1	yes	characteristic, complemented
52	#63460	C₂×C₃	1	2	yes	complemented
53	#63458	C₂×C₃	1	2	yes	complemented
54	#63447	C₂×C₃	1	2	yes	complemented
55	#63445	C₂×C₃	1	2	yes	complemented
56	#63437	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
58	#63431	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	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₃×#611	—	4	2	no	—
70	C₂×C₃×Dic₉	C₂³	1	2	yes	—
71	C₂×C₃×Dic₉	C₂³	1	2	yes	—
72	C₂×C₃×Dic₉	C₂³	1	2	yes	—
73	C₃×D₃₆	—	2	2	no	—
74	C₃×C₄×D₉	—	4	2	no	—
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×Dic₁₈	—	4	2	no	—
77	C₃×#542	—	9	1	no	—
78	#5534	—	3	1	no	—
79	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×#67	—	3	2	no	—
81	C₂×C₃×D₁₂	—	3	1	no	—
82	C₂×C₃×C₄×D₃	—	3	2	no	—
83	C₂×C₃×Dic₆	—	3	1	no	—
84	C₂×C₃×Dic₆	—	3	2	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₃²×C₂²⋊C₄	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	2	no	—
97	C₃×C₄⋊Dic₃	—	3	1	no	—
98	C₃×C₄⋊Dic₃	—	3	1	no	—
99	C₃×Dic₃⋊C₄	—	3	2	no	—
100	C₃×Dic₃⋊C₄	—	3	2	no	—
101	C₃×C₄×Dic₃	—	3	2	no	—
102	C₂²×C₄×C₉	—	2	1	no	—
103	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
104	C₂×#611	C₂²×C₃	1	2	yes	—
105	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
107	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
108	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₉×C₂²⋊C₄	—	2	1	no	—
114	C₉×C₂²⋊C₄	—	2	1	no	—
115	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₄²×C₉	—	2	1	no	—
118	C₄²×C₉	—	2	1	no	—
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	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
129	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
130	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
131	C₄×Dic₉	C₂²×C₃	1	2	yes	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	—	2	1	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×D₉	—	2	2	no	—
137	C₂×C₃×D₉	—	2	2	no	—
138	C₂×C₃×D₉	—	2	2	no	—
139	C₃×C₄×C₉	—	2	1	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×Dic₉	—	2	2	no	—
146	C₃×Dic₉	—	2	2	no	—
147	C₃×Dic₉	—	2	2	no	—
148	C₃×C₄⋊Q₈	—	9	1	no	—
149	C₃×#126	—	9	2	no	—
150	C₃×#124	—	9	2	no	—
151	C₃×#124	—	9	1	no	—
152	C₃×#123	—	9	2	no	—
153	C₃×C₂²⋊Q₈	—	9	1	no	—
154	C₃×C₂²⋊Q₈	—	9	2	no	—
155	C₃×#121	—	9	1	no	—
156	C₃×C₄×Q₈	—	9	1	no	—
157	C₃×C₄×D₄	—	9	1	no	—
158	C₃×#117	—	2	1	no	—
159	C₃×#117	D₉	1	1	yes	characteristic, complemented
160	C₃×#117	C₃×D₃	1	1	yes	characteristic
161	#930	—	3	1	no	—
162	#924	—	3	1	no	—
163	#898	—	3	2	no	—
164	#896	—	3	2	no	—
165	#885	—	3	2	no	—
166	#883	—	3	2	no	—
167	#875	—	3	1	no	—
168	C₄×D₁₂	—	3	1	no	—
169	#869	—	3	1	no	—
170	C₄×Dic₆	—	3	1	no	—
171	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
172	C₂²×C₃×D₃	—	3	2	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
175	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
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	C₃×#67	—	12	2	no	—
181	C₂×C₃×Dic₃	—	3	2	no	—
182	C₂×C₃×Dic₃	—	3	2	no	—
183	C₂×C₃×Dic₃	—	3	2	no	—
184	C₃×D₁₂	—	6	2	no	—
185	C₃×C₄×D₃	—	12	2	no	—
186	C₃×Dic₆	—	6	2	no	—
187	C₃×Dic₆	—	12	2	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
190	C₂²×D₉	C₂³×C₃	1	2	yes	—
191	C₂×C₄×C₉	—	2	4	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
205	#611	—	4	2	no	—
206	C₂×Dic₉	C₂³×C₃	1	2	yes	—
207	C₂×Dic₉	C₂³×C₃	1	2	yes	—
208	C₂×Dic₉	C₂³×C₃	1	2	yes	—
209	D₃₆	—	2	2	no	—
210	C₄×D₉	—	4	2	no	—
211	Dic₁₈	—	2	2	no	—
212	Dic₁₈	—	4	2	no	—
213	#542	—	9	1	no	Sylow
214	C₂×C₃×C₉	—	4	1	no	—
215	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
218	C₃×D₉	—	4	2	no	—
219	C₂×C₃×Q₈	—	9	1	no	—
220	C₂×C₃×Q₈	—	9	2	no	—
221	C₂×C₃×D₄	—	9	2	no	—
222	C₂×C₃×D₄	—	9	1	no	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	—	9	2	no	—
225	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
227	C₂×#67	—	3	2	no	—
228	C₂×D₁₂	—	3	1	no	—
229	C₂×C₄×D₃	—	3	2	no	—
230	C₂×Dic₆	—	3	1	no	—
231	C₂×Dic₆	—	3	2	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	—	9	2	no	—
235	C₃×C₄⋊C₄	—	9	2	no	—
236	C₃×C₄⋊C₄	—	9	1	no	—
237	C₃×C₄⋊C₄	—	9	1	no	—
238	C₃×C₄⋊C₄	—	9	2	no	—
239	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
241	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
243	C₃×C₂²⋊C₄	—	2	1	no	—
244	C₃×C₂²⋊C₄	—	2	1	no	—
245	C₃×C₂²⋊C₄	—	9	2	no	—
246	C₃×C₂²⋊C₄	—	9	2	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	C₂×D₉	1	1	yes	characteristic
251	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
252	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
253	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
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×C₃×D₃	1	1	yes	characteristic
260	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
261	#217	—	3	2	no	—
262	(C₂×D₃)⋊C₄	—	3	2	no	—
263	(C₂×D₃)⋊C₄	—	3	2	no	—
264	(C₂×D₃)⋊C₄	—	3	2	no	—
265	(C₂×D₃)⋊C₄	—	3	2	no	—
266	C₄⋊Dic₃	—	3	1	no	—
267	C₄⋊Dic₃	—	3	1	no	—
268	C₄⋊Dic₃	—	3	2	no	—
269	Dic₃⋊C₄	—	3	2	no	—
270	Dic₃⋊C₄	—	3	2	no	—
271	C₄×Dic₃	—	3	2	no	—
272	C₂²×C₃²	—	2	1	no	—
273	C₂²×C₃²	—	2	1	no	—
274	C₂²×C₃²	—	2	1	no	—
275	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
276	C₂×C₃×D₃	—	6	2	no	—
277	C₂×C₃×D₃	—	6	2	no	—
278	C₂×C₃×D₃	—	6	2	no	—
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	—	2	1	no	—
281	C₃²×C₄	—	2	1	no	—
282	C₃²×C₄	—	2	1	no	—
283	C₃²×C₄	—	2	1	no	—
284	C₃²×C₄	#235	1	2	yes	—
285	C₃×Dic₃	—	6	2	no	—
286	C₃×Dic₃	—	6	2	no	—
287	C₃×Dic₃	—	6	2	no	—
288	C₂²×C₉	—	2	2	no	—
289	C₂²×C₉	—	2	1	no	—
290	C₂²×C₉	—	2	1	no	—
291	C₂²×C₉	—	2	1	no	—
292	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	1	no	—
295	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
296	C₂×D₉	—	2	2	no	—
297	C₂×D₉	—	2	2	no	—
298	C₂×D₉	—	2	2	no	—
299	C₄×C₉	—	2	2	no	—
300	C₄×C₉	—	2	1	no	—
301	C₄×C₉	—	2	1	no	—
302	C₄×C₉	—	2	1	no	—
303	C₄×C₉	—	2	1	no	—
304	C₄×C₉	—	2	1	no	—
305	C₄×C₉	—	2	2	no	—
306	C₄×C₉	—	4	1	no	—
307	C₄×C₉	—	4	1	no	—
308	C₄×C₉	—	4	1	no	—
309	C₄×C₉	—	4	1	no	—
310	C₄×C₉	C₃×#41	1	2	yes	—
311	Dic₉	—	2	2	no	—
312	Dic₉	—	2	2	no	—
313	Dic₉	—	2	2	no	—
314	C₄⋊Q₈	—	9	1	no	—
315	#126	—	9	2	no	—
316	#124	—	9	2	no	—
317	#124	—	9	1	no	—
318	#123	—	9	2	no	—
319	C₂²⋊Q₈	—	9	1	no	—
320	C₂²⋊Q₈	—	9	2	no	—
321	#121	—	9	1	no	—
322	C₄×Q₈	—	9	1	no	—
323	C₄×D₄	—	9	1	no	—
324	#117	C₃×D₉	1	1	yes	characteristic, complemented
325	C₃×C₉	#542	1	1	yes	characteristic, complemented, Sylow
326	C₂³×C₃	—	2	1	no	—
327	C₂³×C₃	—	9	2	no	—
328	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
329	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
330	C₂²×D₃	—	3	2	no	—
331	C₃×Q₈	—	18	2	no	—
332	C₃×Q₈	—	36	2	no	—
333	C₃×D₄	—	18	2	no	—
334	C₃×D₄	—	36	2	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	9	2	no	—
345	C₂×C₃×C₄	—	9	2	no	—
346	C₂×C₃×C₄	—	9	2	no	—
347	C₂×C₃×C₄	—	36	2	no	—
348	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
360	#67	—	12	2	no	—
361	C₂×Dic₃	—	3	2	no	—
362	C₂×Dic₃	—	3	2	no	—
363	C₂×Dic₃	—	3	2	no	—
364	D₁₂	—	6	2	no	—
365	C₄×D₃	—	12	2	no	—
366	Dic₆	—	6	2	no	—
367	Dic₆	—	12	2	no	—
368	C₂×C₃²	—	4	1	no	—
369	C₂×C₃²	C₂×#235	1	1	yes	characteristic
370	C₂×C₃²	#1009	1	1	yes	characteristic
371	C₂×C₃²	#1010	1	1	yes	characteristic
372	C₃×D₃	—	12	2	no	—
373	C₂×C₉	—	2	1	no	—
374	C₂×C₉	—	2	1	no	—
375	C₂×C₉	—	2	1	no	—
376	C₂×C₉	—	4	2	no	—
377	C₂×C₉	—	4	1	no	—
378	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
379	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
381	D₉	—	4	2	no	—
382	C₂×Q₈	—	9	1	no	—
383	C₂×Q₈	—	9	2	no	—
384	C₂×D₄	—	9	2	no	—
385	C₂×D₄	—	9	1	no	—
386	C₂²×C₄	—	9	2	no	—
387	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
388	C₄⋊C₄	—	9	1	no	—
389	C₄⋊C₄	—	9	1	no	—
390	C₄⋊C₄	—	9	2	no	—
391	C₄⋊C₄	—	9	2	no	—
392	C₄⋊C₄	—	9	2	no	—
393	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
394	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
395	C₂²⋊C₄	—	9	2	no	—
396	C₂²⋊C₄	—	9	2	no	—
397	C₂²⋊C₄	—	9	2	no	—
398	C₂²⋊C₄	—	9	2	no	—
399	C₂²⋊C₄	—	9	2	no	—
400	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
401	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
402	C₄²	—	9	2	no	—
403	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
404	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	2	1	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	—	4	1	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	—	18	2	no	—
416	C₂²×C₃	—	18	2	no	—
417	C₂²×C₃	—	18	2	no	—
418	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
419	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
420	C₂×D₃	—	6	2	no	—
421	C₂×D₃	—	6	2	no	—
422	C₂×D₃	—	6	2	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	1	no	—
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	1	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	18	2	no	—
440	C₃×C₄	—	18	2	no	—
441	C₃×C₄	—	18	2	no	—
442	C₃×C₄	#3697	1	2	yes	—
443	C₃×C₄	C₃×#235	1	2	yes	—
444	Dic₃	—	6	2	no	—
445	Dic₃	—	6	2	no	—
446	Dic₃	—	6	2	no	—
447	C₃²	#5534	1	1	yes	characteristic
448	C₉	—	2	1	no	—
449	C₉	C₃×#542	1	1	yes	characteristic, complemented
450	C₂³	—	9	2	no	—
451	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
452	Q₈	—	18	2	no	—
453	Q₈	—	36	2	no	—
454	D₄	—	18	2	no	—
455	D₄	—	36	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	9	2	no	—
458	C₂×C₄	—	9	2	no	—
459	C₂×C₄	—	9	2	no	—
460	C₂×C₄	—	36	2	no	—
461	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	4	2	no	—
471	C₂×C₃	—	4	1	no	—
472	C₂×C₃	—	4	1	no	—
473	C₂×C₃	—	36	2	no	—
474	C₂×C₃	C₂×#3697	1	1	yes	characteristic
475	C₂×C₃	#63715	1	1	yes	characteristic
476	C₂×C₃	#63716	1	1	yes	characteristic
477	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
478	C₂×C₃	C₃×#1009	1	1	yes	characteristic
479	C₂×C₃	C₃×#1010	1	1	yes	characteristic
480	D₃	—	12	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	18	2	no	—
485	C₂²	—	18	2	no	—
486	C₂²	—	18	2	no	—
487	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	18	2	no	—
494	C₄	—	18	2	no	—
495	C₄	—	18	2	no	—
496	C₄	C₃×#3697	1	2	yes	—
497	C₃	—	2	1	no	—
498	C₃	#10589636	1	1	yes	characteristic, direct product factor
499	C₃	C₃×#5534	1	1	yes	characteristic
500	C₂	—	4	1	no	—
501	C₂	—	36	2	no	—
502	C₂	C₂×C₃×#3697	1	1	yes	characteristic
503	C₂	C₃×#63715	1	1	yes	characteristic
504	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×#117	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₃×#63492	C₂
hypercenter	C₃×#117	D₉
hypocenter	C₉	C₃×#542
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#117	C₂	semidirect
3. C₃×#63486	C₂	semidirect
4. C₃×#63460	C₂	semidirect
5. C₃×#63458	C₂	semidirect
6. C₃×#63447	C₂	semidirect
7. C₃×#63445	C₂	semidirect
8. C₃×#63437	C₂	semidirect
9. C₃×C₄×D₃₆	C₂	semidirect
10. C₃×#63431	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589636	C₃	direct (N × H)
49. C₉×#117	C₂×C₃	semidirect
51. #63486	C₂×C₃	semidirect
52. #63460	C₂×C₃	semidirect
53. #63458	C₂×C₃	semidirect
54. #63447	C₂×C₃	semidirect
55. #63445	C₂×C₃	semidirect
56. #63437	C₂×C₃	semidirect
57. C₄×D₃₆	C₂×C₃	semidirect
58. #63431	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
159. C₃×#117	D₉	semidirect
324. #117	C₃×D₉	semidirect
325. C₃×C₉	#542	semidirect
449. C₉	C₃×#542	semidirect
498. C₃	#10589636	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×#117	2
C₃×#63492	2
C₃×#63486	2
C₃×#63460	2
C₃×#63458	2
C₃×#63447	2
C₃×#63445	2
C₃×#63437	2
C₃×C₄×D₃₆	2
C₃×#63431	2
C₃×C₄×Dic₁₈	2
C₃×#5534	3
#10589636	3

Subgroups — C3×#10589636 #13152492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589636 #13152492