Subgroups — C₃×#5655 #10595752

Order 576.

623 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#547	—	3	1	no	maximal
17	#5655	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃²×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×#67	C₂²	1	1	yes	characteristic
21	C₂×C₃×#67	C₂²	1	1	yes	characteristic
22	C₂×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂×C₃×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic
27	C₃×#237	—	2	4	no	—
28	C₃×#235	—	2	4	no	—
29	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
34	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic
35	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic
36	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×#217	C₂²	1	1	yes	characteristic
42	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
47	C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
48	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
54	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
55	C₂×C₃×#41	—	3	1	no	—
56	C₂×C₃×#41	—	3	1	no	—
57	C₂×#237	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#235	C₂×C₃	1	1	yes	characteristic, complemented
59	C₃×C₄⋊Q₈	—	3	1	no	—
60	C₃×#123	—	2	1	no	—
61	C₃×#123	—	3	1	no	—
62	C₃×#123	—	3	1	no	—
63	C₃×#123	—	3	1	no	—
64	C₃×#123	D₃	1	1	yes	characteristic, complemented
65	C₃×#123	C₂×C₃	1	1	yes	characteristic, complemented
66	C₃×C₂²⋊Q₈	—	3	1	no	—
67	C₃×C₂²⋊Q₈	—	3	1	no	—
68	C₃×#121	—	3	1	no	—
69	C₃×#121	—	3	1	no	—
70	C₃×C₄×D₄	—	3	1	no	—
71	C₃×C₄×D₄	—	3	1	no	—
72	C₂×C₃×C₄⋊C₄	—	3	1	no	—
73	C₂×C₃×C₄⋊C₄	—	3	1	no	—
74	#939	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	#896	C₂×C₃	1	1	yes	characteristic, complemented
77	#894	C₂×C₃	1	1	yes	characteristic, complemented
78	D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
79	#888	C₂×C₃	1	1	yes	characteristic, complemented
80	#886	C₂×C₃	1	1	yes	characteristic, complemented
81	#884	C₂×C₃	1	1	yes	characteristic, complemented
82	#883	C₂×C₃	1	1	yes	characteristic, complemented
83	#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
84	#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
85	#878	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×C₃²	C₂³	1	1	yes	characteristic
87	C₂³×C₃²	C₂³	1	1	yes	characteristic
88	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
89	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
90	C₃²×D₄	—	2	2	no	—
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
97	C₃×#67	—	2	2	no	—
98	C₃×#67	—	2	2	no	—
99	C₃×#67	—	2	2	no	—
100	C₃×#67	D₄	1	4	yes	complemented
101	C₂×C₃×Dic₃	—	2	2	no	—
102	C₂×C₃×Dic₃	—	2	2	no	—
103	C₂×C₃×Dic₃	—	2	2	no	—
104	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
109	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
110	C₃×D₁₂	—	2	2	no	—
111	C₃×C₄×D₃	—	2	2	no	—
112	C₃×C₄×D₃	—	2	2	no	—
113	C₃×C₄×D₃	—	2	2	no	—
114	C₃×C₄×D₃	—	2	2	no	—
115	C₃×Dic₆	—	2	2	no	—
116	C₃×Dic₆	—	2	2	no	—
117	#547	—	3	1	no	Sylow
118	C₃×#41	—	6	4	no	—
119	C₃×#41	—	6	4	no	—
120	C₂×C₃×Q₈	—	3	1	no	—
121	C₂×C₃×Q₈	—	3	1	no	—
122	C₂×C₃×D₄	—	2	1	no	—
123	C₂×C₃×D₄	—	3	1	no	—
124	C₂×C₃×D₄	—	3	1	no	—
125	C₂×C₃×D₄	—	3	1	no	—
126	C₂×C₃×D₄	—	3	1	no	—
127	C₂×C₃×D₄	—	3	1	no	—
128	C₂×C₃×D₄	C₂×D₃	1	1	yes	characteristic
129	C₂×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	3	1	no	—
132	C₂²×C₃×C₄	—	3	1	no	—
133	C₂²×C₃×C₄	—	3	1	no	—
134	C₂²×C₃×C₄	—	3	1	no	—
135	C₂²×C₃×C₄	—	3	1	no	—
136	C₂²×C₃×C₄	—	3	1	no	—
137	C₂²×C₃×C₄	—	3	1	no	—
138	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×#67	C₂²×C₃	1	1	yes	characteristic
141	C₂×#67	C₂²×C₃	1	1	yes	characteristic
142	C₂×#67	C₂²×C₃	1	1	yes	characteristic
143	C₂×#67	C₂²×C₃	1	1	yes	characteristic
144	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic
145	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic
146	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic
147	#237	—	2	4	no	—
148	#235	—	2	4	no	—
149	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
154	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic
155	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	2	1	no	—
157	C₃×C₄⋊C₄	—	2	1	no	—
158	C₃×C₄⋊C₄	—	3	1	no	—
159	C₃×C₄⋊C₄	—	3	1	no	—
160	C₃×C₄⋊C₄	—	3	1	no	—
161	C₃×C₄⋊C₄	—	3	1	no	—
162	C₃×C₄⋊C₄	—	3	1	no	—
163	C₃×C₄⋊C₄	—	3	1	no	—
164	C₃×C₄⋊C₄	—	3	1	no	—
165	C₃×C₄⋊C₄	—	3	1	no	—
166	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
167	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
168	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₂²⋊C₄	—	2	1	no	—
171	C₃×C₂²⋊C₄	—	2	1	no	—
172	C₃×C₂²⋊C₄	—	2	1	no	—
173	C₃×C₂²⋊C₄	—	3	1	no	—
174	C₃×C₂²⋊C₄	—	3	1	no	—
175	C₃×C₂²⋊C₄	—	3	1	no	—
176	C₃×C₂²⋊C₄	—	3	1	no	—
177	C₃×C₂²⋊C₄	—	3	1	no	—
178	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
179	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
180	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
181	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	C₃×C₄²	—	3	1	no	—
185	#217	C₂²×C₃	1	1	yes	characteristic
186	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
187	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
189	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
190	C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
191	C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
192	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
193	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
194	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
195	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
196	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
197	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
198	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
199	C₂²×C₃²	—	2	1	no	—
200	C₂²×C₃²	—	2	1	no	—
201	C₂²×C₃²	—	2	1	no	—
202	C₂²×C₃²	—	2	1	no	—
203	C₂²×C₃²	—	2	1	no	—
204	C₂²×C₃²	C₂×D₄	1	2	yes	—
205	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
206	C₂×C₃×D₃	—	2	1	no	—
207	C₂×C₃×D₃	—	2	1	no	—
208	C₂×C₃×D₃	—	2	1	no	—
209	C₂×C₃×D₃	—	2	1	no	—
210	C₂×C₃×D₃	—	2	1	no	—
211	C₂×C₃×D₃	C₂×D₄	1	2	yes	—
212	C₃²×C₄	—	2	1	no	—
213	C₃²×C₄	—	2	1	no	—
214	C₃²×C₄	—	2	1	no	—
215	C₃²×C₄	—	2	1	no	—
216	C₃²×C₄	—	2	1	no	—
217	C₃×Dic₃	—	2	1	no	—
218	C₃×Dic₃	—	2	1	no	—
219	C₃×Dic₃	—	2	1	no	—
220	C₃×Dic₃	—	2	1	no	—
221	C₃×Dic₃	C₂×D₄	1	2	yes	—
222	C₃×Dic₃	#41	1	2	yes	complemented
223	C₂×#41	—	3	1	no	—
224	C₂×#41	—	3	1	no	—
225	C₄⋊Q₈	—	3	1	no	—
226	#123	—	3	1	no	—
227	#123	—	3	1	no	—
228	#123	—	3	1	no	—
229	#123	C₃×D₃	1	1	yes	characteristic, complemented
230	C₂²⋊Q₈	—	3	1	no	—
231	C₂²⋊Q₈	—	3	1	no	—
232	#121	—	3	1	no	—
233	#121	—	3	1	no	—
234	C₄×D₄	—	3	1	no	—
235	C₄×D₄	—	3	1	no	—
236	C₂×C₄⋊C₄	—	3	1	no	—
237	C₂×C₄⋊C₄	—	3	1	no	—
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	—	3	1	no	—
241	C₂³×C₃	—	3	1	no	—
242	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
243	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
244	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
245	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
246	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
247	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
248	C₃×Q₈	—	6	2	no	—
249	C₃×Q₈	—	6	2	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	—	2	2	no	—
252	C₃×D₄	—	3	4	no	—
253	C₃×D₄	—	4	2	no	—
254	C₃×D₄	—	6	2	no	—
255	C₃×D₄	—	6	2	no	—
256	C₃×D₄	—	6	2	no	—
257	C₃×D₄	—	6	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	3	1	no	—
266	C₂×C₃×C₄	—	3	1	no	—
267	C₂×C₃×C₄	—	3	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	3	1	no	—
270	C₂×C₃×C₄	—	3	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	6	2	no	—
273	C₂×C₃×C₄	—	6	2	no	—
274	C₂×C₃×C₄	—	6	2	no	—
275	C₂×C₃×C₄	—	6	2	no	—
276	C₂×C₃×C₄	—	6	2	no	—
277	C₂×C₃×C₄	—	6	2	no	—
278	C₂×C₃×C₄	—	6	2	no	—
279	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
289	#67	—	2	2	no	—
290	#67	—	2	2	no	—
291	#67	—	2	2	no	—
292	#67	C₃×D₄	1	4	yes	complemented
293	C₂×Dic₃	—	2	2	no	—
294	C₂×Dic₃	—	2	2	no	—
295	C₂×Dic₃	—	2	2	no	—
296	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
297	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
298	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
299	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
300	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
301	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
302	D₁₂	—	2	2	no	—
303	C₄×D₃	—	2	2	no	—
304	C₄×D₃	—	2	2	no	—
305	C₄×D₃	—	2	2	no	—
306	C₄×D₃	—	2	2	no	—
307	Dic₆	—	2	2	no	—
308	Dic₆	—	2	2	no	—
309	C₂×C₃²	—	2	2	no	—
310	C₂×C₃²	—	4	1	no	—
311	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₃²	C₂×#41	1	1	yes	characteristic
313	C₂×C₃²	2₋¹⁺⁴	1	1	yes	characteristic
314	C₃×D₃	—	2	2	no	—
315	C₃×D₃	—	4	1	no	—
316	#41	—	6	4	no	—
317	#41	—	6	4	no	—
318	C₂×Q₈	—	3	1	no	—
319	C₂×Q₈	—	3	1	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂×D₄	—	3	1	no	—
322	C₂×D₄	—	3	1	no	—
323	C₂×D₄	—	3	1	no	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	C₂×C₃×D₃	1	1	yes	characteristic
326	C₂²×C₄	—	3	1	no	—
327	C₂²×C₄	—	3	1	no	—
328	C₂²×C₄	—	3	1	no	—
329	C₂²×C₄	—	3	1	no	—
330	C₂²×C₄	—	3	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
334	C₄⋊C₄	—	3	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₄⋊C₄	—	3	1	no	—
337	C₄⋊C₄	—	3	1	no	—
338	C₄⋊C₄	—	3	1	no	—
339	C₄⋊C₄	—	3	1	no	—
340	C₄⋊C₄	—	3	1	no	—
341	C₄⋊C₄	—	3	1	no	—
342	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
343	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
344	C₂²⋊C₄	—	3	1	no	—
345	C₂²⋊C₄	—	3	1	no	—
346	C₂²⋊C₄	—	3	1	no	—
347	C₂²⋊C₄	—	3	1	no	—
348	C₂²⋊C₄	—	3	1	no	—
349	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
350	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
351	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
352	C₄²	—	3	1	no	—
353	C₂²×C₃	—	2	1	no	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	3	2	no	—
366	C₂²×C₃	—	4	1	no	—
367	C₂²×C₃	—	4	1	no	—
368	C₂²×C₃	—	4	1	no	—
369	C₂²×C₃	—	4	1	no	—
370	C₂²×C₃	—	4	1	no	—
371	C₂²×C₃	—	6	1	no	—
372	C₂²×C₃	—	6	1	no	—
373	C₂²×C₃	—	6	1	no	—
374	C₂²×C₃	—	6	1	no	—
375	C₂²×C₃	—	6	1	no	—
376	C₂²×C₃	D₃×D₄	1	2	yes	—
377	C₂²×C₃	C₂×C₃×D₄	1	2	yes	—
378	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
379	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
380	C₂×D₃	—	2	1	no	—
381	C₂×D₃	—	2	1	no	—
382	C₂×D₃	—	2	1	no	—
383	C₂×D₃	—	2	1	no	—
384	C₂×D₃	—	2	1	no	—
385	C₂×D₃	C₂×C₃×D₄	1	2	yes	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	3	2	no	—
397	C₃×C₄	—	3	2	no	—
398	C₃×C₄	—	4	1	no	—
399	C₃×C₄	—	4	1	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	—	6	1	no	—
404	C₃×C₄	—	6	1	no	—
405	C₃×C₄	—	6	1	no	—
406	C₃×C₄	—	6	1	no	—
407	Dic₃	—	2	1	no	—
408	Dic₃	—	2	1	no	—
409	Dic₃	—	2	1	no	—
410	Dic₃	—	2	1	no	—
411	Dic₃	C₂×C₃×D₄	1	2	yes	—
412	Dic₃	C₃×#41	1	2	yes	complemented
413	C₃²	#547	1	1	yes	characteristic, complemented, Sylow
414	C₂³	—	3	1	no	—
415	C₂³	—	3	1	no	—
416	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
417	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
418	Q₈	—	6	2	no	—
419	Q₈	—	6	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	3	4	no	—
422	D₄	—	6	2	no	—
423	D₄	—	6	2	no	—
424	D₄	—	6	2	no	—
425	D₄	—	6	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	3	1	no	—
431	C₂×C₄	—	3	1	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	6	2	no	—
437	C₂×C₄	—	6	2	no	—
438	C₂×C₄	—	6	2	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
445	C₂×C₃	—	2	2	no	—
446	C₂×C₃	—	2	2	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	2	1	no	—
450	C₂×C₃	—	4	2	no	—
451	C₂×C₃	—	4	1	no	—
452	C₂×C₃	—	4	1	no	—
453	C₂×C₃	—	6	2	no	—
454	C₂×C₃	—	8	1	no	—
455	C₂×C₃	—	12	1	no	—
456	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
457	C₂×C₃	D₃×#41	1	1	yes	characteristic
458	C₂×C₃	#1010	1	1	yes	characteristic
459	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
460	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
461	C₂×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
462	D₃	—	2	2	no	—
463	D₃	—	4	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	3	2	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	6	1	no	—
472	C₂²	—	6	1	no	—
473	C₂²	—	6	1	no	—
474	C₂²	—	6	1	no	—
475	C₂²	C₃×D₃×D₄	1	2	yes	—
476	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	3	2	no	—
483	C₄	—	3	2	no	—
484	C₄	—	6	1	no	—
485	C₄	—	6	1	no	—
486	C₄	—	6	1	no	—
487	C₄	—	6	1	no	—
488	C₃	—	2	1	no	—
489	C₃	#5655	1	1	yes	characteristic, direct product factor
490	C₃	C₃×#547	1	1	yes	characteristic, complemented
491	C₂	—	2	2	no	—
492	C₂	—	4	1	no	—
493	C₂	—	6	2	no	—
494	C₂	—	12	1	no	—
495	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
496	C₂	C₃×D₃×#41	1	1	yes	characteristic
497	C₂	C₃×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×#123	C₂
socle	C₂²×C₃²	C₂⁴
hypercenter	C₃×#123	D₃
hypocenter	C₃	C₃×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#237	C₂	semidirect
2. C₂×C₃×#235	C₂	semidirect
3. C₃²×#123	C₂	semidirect
4. C₃×#939	C₂	semidirect
5. C₂×C₃×Dic₃⋊C₄	C₂	semidirect
6. C₃×#896	C₂	semidirect
7. C₃×#894	C₂	semidirect
8. C₃×D₃×C₄⋊C₄	C₂	semidirect
9. C₃×#888	C₂	semidirect
10. C₃×#886	C₂	semidirect
11. C₃×#884	C₂	semidirect
12. C₃×#883	C₂	semidirect
13. C₃×#67⋊C₄	C₂	semidirect
14. C₃×#67⋊C₄	C₂	semidirect
15. C₃×#878	C₂	semidirect
17. #5655	C₃	direct (N × H)
57. C₂×#237	C₂×C₃	semidirect
58. C₂×#235	C₂×C₃	semidirect
64. C₃×#123	D₃	semidirect
65. C₃×#123	C₂×C₃	semidirect
74. #939	C₂×C₃	semidirect
75. C₂×Dic₃⋊C₄	C₂×C₃	semidirect
76. #896	C₂×C₃	semidirect
77. #894	C₂×C₃	semidirect
78. D₃×C₄⋊C₄	C₂×C₃	semidirect
79. #888	C₂×C₃	semidirect
80. #886	C₂×C₃	semidirect
81. #884	C₂×C₃	semidirect
82. #883	C₂×C₃	semidirect
83. #67⋊C₄	C₂×C₃	semidirect
84. #67⋊C₄	C₂×C₃	semidirect
85. #878	C₂×C₃	semidirect
100. C₃×#67	D₄	semidirect
222. C₃×Dic₃	#41	semidirect
229. #123	C₃×D₃	semidirect
292. #67	C₃×D₄	semidirect
412. Dic₃	C₃×#41	semidirect
413. C₃²	#547	semidirect
489. C₃	#5655	direct (N × H)
490. C₃	C₃×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#237	2
C₂×C₃×#235	2
C₃²×#123	2
C₃×#939	2
C₂×C₃×Dic₃⋊C₄	2
C₃×#896	2
C₃×#894	2
C₃×D₃×C₄⋊C₄	2
C₃×#888	2
C₃×#886	2
C₃×#884	2
C₃×#883	2
C₃×#67⋊C₄	2
C₃×#878	2
C₃×#547	3
#5655	3

Subgroups — C3×#5655 #10595752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5655 #10595752