Subgroups — C₃×#37143 #10655750

Order 768.

1456 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2860	C₂	1	1	yes	maximal, characteristic
2	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2808	C₂	1	1	yes	maximal, characteristic
4	C₃×#2805	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2793	C₂	1	2	yes	maximal, complemented
6	C₃×#2790	C₂	1	2	yes	maximal, complemented
7	C₃×#2788	C₂	1	2	yes	maximal, complemented
8	C₃×#2783	C₂	1	2	yes	maximal, complemented
9	C₃×#2726	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2724	C₂	1	1	yes	maximal, characteristic
11	C₃×#2719	C₂	1	2	yes	maximal, complemented
12	C₃×#2707	C₂	1	2	yes	maximal
13	C₃×#2637	C₂	1	2	yes	maximal, complemented
14	C₃×#2590	C₂	1	2	yes	maximal, complemented
15	C₃×#2558	C₂	1	2	yes	maximal
16	C₃×#2530	C₂	1	2	yes	maximal, complemented
17	C₃×#2529	C₂	1	2	yes	maximal, complemented
18	C₃×#2334	C₂	1	2	yes	maximal, complemented
19	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	#37143	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#126	C₂²	1	2	yes	—
22	C₂×C₃×#125	C₂²	1	2	yes	—
23	C₂×C₃×#125	C₂²	1	2	yes	—
24	C₂×C₃×#123	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
26	C₃×#400	C₂²	1	2	yes	—
27	C₃×#400	C₂²	1	2	yes	—
28	C₃×#400	C₂²	1	2	yes	—
29	C₃×#400	C₂²	1	2	yes	—
30	C₃×#400	C₂²	1	2	yes	—
31	C₃×#398	C₂²	1	2	yes	—
32	C₃×#398	C₂²	1	2	yes	—
33	C₃×#398	C₂²	1	2	yes	—
34	C₃×#398	C₂²	1	2	yes	—
35	C₃×#398	C₂²	1	2	yes	—
36	C₃×#398	C₂²	1	2	yes	—
37	C₃×#398	C₂²	1	2	yes	—
38	C₃×#397	C₂²	1	2	yes	—
39	C₃×#397	C₂²	1	2	yes	—
40	C₃×#397	C₂²	1	2	yes	—
41	C₃×#397	C₂²	1	2	yes	—
42	C₃×#396	C₂²	1	2	yes	—
43	C₃×#396	C₂²	1	2	yes	—
44	C₃×#396	C₂²	1	2	yes	—
45	C₃×#396	C₂²	1	2	yes	—
46	C₃×#396	C₂²	1	2	yes	—
47	C₃×#395	C₂²	1	2	yes	—
48	C₃×#394	C₂²	1	2	yes	—
49	C₃×#393	C₂²	1	2	yes	—
50	C₃×#391	C₂²	1	1	yes	characteristic
51	C₃×#391	C₂²	1	1	yes	characteristic
52	C₃×#390	C₂²	1	1	yes	characteristic
53	C₃×#390	C₂²	1	1	yes	characteristic
54	C₃×#390	C₂²	1	1	yes	characteristic
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	1	yes	characteristic
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	1	yes	characteristic
59	C₃×#389	C₂²	1	1	yes	characteristic
60	C₃×#389	C₂²	1	2	yes	—
61	C₃×#389	C₂²	1	1	yes	characteristic
62	C₃×#389	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	2	yes	—
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	1	yes	characteristic
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#387	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#384	C₂²	1	1	yes	characteristic
98	C₃×#384	C₂²	1	1	yes	characteristic
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
103	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₃×#376	C₂²	1	2	yes	—
107	C₃×C₄³	C₂²	1	1	yes	characteristic
108	#2860	C₂×C₃	1	1	yes	characteristic
109	#2859	C₂×C₃	1	1	yes	characteristic, complemented
110	#2808	C₂×C₃	1	1	yes	characteristic
111	#2805	C₂×C₃	1	1	yes	characteristic, complemented
112	#2793	C₂×C₃	1	2	yes	complemented
113	#2790	C₂×C₃	1	2	yes	complemented
114	#2788	C₂×C₃	1	2	yes	complemented
115	#2783	C₂×C₃	1	2	yes	complemented
116	#2726	C₂×C₃	1	1	yes	characteristic, complemented
117	#2724	C₂×C₃	1	1	yes	characteristic
118	#2719	C₂×C₃	1	2	yes	complemented
119	#2707	C₂×C₃	1	2	yes	—
120	#2637	C₂×C₃	1	2	yes	complemented
121	#2590	C₂×C₃	1	2	yes	complemented
122	#2558	C₂×C₃	1	2	yes	—
123	#2530	C₂×C₃	1	2	yes	complemented
124	#2529	C₂×C₃	1	2	yes	complemented
125	#2334	C₂×C₃	1	2	yes	complemented
126	#2295	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
129	C₂³×C₃×C₄	C₂³	1	2	yes	—
130	C₃×#126	—	2	8	no	—
131	C₃×#125	—	4	4	no	—
132	C₃×#125	—	4	4	no	—
133	C₃×#123	—	4	4	no	—
134	C₃×C₄×Q₈	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂³	1	2	yes	—
183	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	2	yes	—
188	C₂×C₃×C₄²	C₂³	1	2	yes	—
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₃×#95	C₂³	1	2	yes	—
192	C₃×#95	C₂³	1	2	yes	—
193	C₃×#95	C₂³	1	2	yes	—
194	C₃×#95	C₂³	1	2	yes	—
195	C₃×#95	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₂×#126	C₂²×C₃	1	2	yes	—
220	C₂×#125	C₂²×C₃	1	2	yes	—
221	C₂×#125	C₂²×C₃	1	2	yes	—
222	C₂×#123	C₂²×C₃	1	2	yes	—
223	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
224	#400	C₂²×C₃	1	2	yes	—
225	#400	C₂²×C₃	1	2	yes	—
226	#400	C₂²×C₃	1	2	yes	—
227	#400	C₂²×C₃	1	2	yes	—
228	#400	C₂²×C₃	1	2	yes	—
229	#398	C₂²×C₃	1	2	yes	—
230	#398	C₂²×C₃	1	2	yes	—
231	#398	C₂²×C₃	1	2	yes	—
232	#398	C₂²×C₃	1	2	yes	—
233	#398	C₂²×C₃	1	2	yes	—
234	#398	C₂²×C₃	1	2	yes	—
235	#398	C₂²×C₃	1	2	yes	—
236	#397	C₂²×C₃	1	2	yes	—
237	#397	C₂²×C₃	1	2	yes	—
238	#397	C₂²×C₃	1	2	yes	—
239	#397	C₂²×C₃	1	2	yes	—
240	#396	C₂²×C₃	1	2	yes	—
241	#396	C₂²×C₃	1	2	yes	—
242	#396	C₂²×C₃	1	2	yes	—
243	#396	C₂²×C₃	1	2	yes	—
244	#396	C₂²×C₃	1	2	yes	—
245	#395	C₂²×C₃	1	2	yes	—
246	#394	C₂²×C₃	1	2	yes	—
247	#393	C₂²×C₃	1	2	yes	—
248	#391	C₂²×C₃	1	1	yes	characteristic
249	#391	C₂²×C₃	1	1	yes	characteristic
250	#390	C₂²×C₃	1	1	yes	characteristic
251	#390	C₂²×C₃	1	1	yes	characteristic
252	#390	C₂²×C₃	1	1	yes	characteristic
253	#389	C₂²×C₃	1	2	yes	—
254	#389	C₂²×C₃	1	2	yes	—
255	#389	C₂²×C₃	1	1	yes	characteristic
256	#389	C₂²×C₃	1	2	yes	—
257	#389	C₂²×C₃	1	2	yes	—
258	#389	C₂²×C₃	1	1	yes	characteristic
259	#389	C₂²×C₃	1	1	yes	characteristic
260	#389	C₂²×C₃	1	2	yes	—
261	#389	C₂²×C₃	1	1	yes	characteristic
262	#389	C₂²×C₃	1	1	yes	characteristic
263	#389	C₂²×C₃	1	1	yes	characteristic
264	#389	C₂²×C₃	1	1	yes	characteristic
265	#389	C₂²×C₃	1	1	yes	characteristic
266	#389	C₂²×C₃	1	1	yes	characteristic
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#388	C₂²×C₃	1	2	yes	—
272	#388	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	—
274	#388	C₂²×C₃	1	2	yes	—
275	#388	C₂²×C₃	1	2	yes	—
276	#388	C₂²×C₃	1	2	yes	—
277	#388	C₂²×C₃	1	2	yes	—
278	#387	C₂²×C₃	1	2	yes	—
279	#387	C₂²×C₃	1	2	yes	—
280	#387	C₂²×C₃	1	2	yes	—
281	#387	C₂²×C₃	1	2	yes	—
282	#387	C₂²×C₃	1	2	yes	—
283	#387	C₂²×C₃	1	2	yes	—
284	#387	C₂²×C₃	1	2	yes	—
285	#387	C₂²×C₃	1	2	yes	—
286	#387	C₂²×C₃	1	2	yes	—
287	#387	C₂²×C₃	1	2	yes	—
288	#387	C₂²×C₃	1	2	yes	—
289	#387	C₂²×C₃	1	2	yes	—
290	#387	C₂²×C₃	1	2	yes	—
291	#385	C₂²×C₃	1	2	yes	—
292	#385	C₂²×C₃	1	2	yes	—
293	#385	C₂²×C₃	1	2	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#384	C₂²×C₃	1	1	yes	characteristic
296	#384	C₂²×C₃	1	1	yes	characteristic
297	#382	C₂²×C₃	1	2	yes	—
298	#382	C₂²×C₃	1	2	yes	—
299	#380	C₂²×C₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
301	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
304	#376	C₂²×C₃	1	2	yes	—
305	C₄³	C₂²×C₃	1	1	yes	characteristic
306	C₂⁴×C₃	C₂⁴	1	2	yes	—
307	C₂×C₃×Q₈	—	2	2	no	—
308	C₂×C₃×Q₈	—	4	1	no	—
309	C₂×C₃×Q₈	—	4	1	no	—
310	C₂×C₃×D₄	—	2	2	no	—
311	C₂×C₃×D₄	—	4	1	no	—
312	C₂×C₃×D₄	—	4	1	no	—
313	C₂²×C₃×C₄	—	4	2	no	—
314	C₂²×C₃×C₄	—	4	2	no	—
315	C₂²×C₃×C₄	—	4	2	no	—
316	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
321	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
322	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
323	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
324	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
325	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
326	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
327	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
328	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
334	C₃×C₄⋊C₄	—	2	2	no	—
335	C₃×C₄⋊C₄	—	2	4	no	—
336	C₃×C₄⋊C₄	—	2	4	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	4	no	—
339	C₃×C₄⋊C₄	—	2	4	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	2	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	4	no	—
344	C₃×C₄⋊C₄	—	2	2	no	—
345	C₃×C₄⋊C₄	—	2	2	no	—
346	C₃×C₄⋊C₄	—	4	2	no	—
347	C₃×C₄⋊C₄	—	4	2	no	—
348	C₃×C₄⋊C₄	—	4	1	no	—
349	C₃×C₄⋊C₄	—	4	1	no	—
350	C₃×C₄⋊C₄	—	4	1	no	—
351	C₃×C₄⋊C₄	—	4	1	no	—
352	C₃×C₄⋊C₄	—	4	1	no	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	—	4	2	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	2	no	—
357	C₃×C₄⋊C₄	—	4	2	no	—
358	C₃×C₄⋊C₄	—	4	2	no	—
359	C₃×C₄⋊C₄	—	4	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	2	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₂²⋊C₄	—	2	4	no	—
366	C₃×C₂²⋊C₄	—	2	4	no	—
367	C₃×C₂²⋊C₄	—	2	4	no	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	2	4	no	—
370	C₃×C₂²⋊C₄	—	4	2	no	—
371	C₃×C₂²⋊C₄	—	4	2	no	—
372	C₃×C₂²⋊C₄	—	4	2	no	—
373	C₃×C₂²⋊C₄	—	4	2	no	—
374	C₃×C₂²⋊C₄	—	4	2	no	—
375	C₃×C₂²⋊C₄	—	4	2	no	—
376	C₃×C₂²⋊C₄	—	4	2	no	—
377	C₃×C₂²⋊C₄	—	4	2	no	—
378	C₃×C₄²	—	2	4	no	—
379	C₃×C₄²	—	2	2	no	—
380	C₃×C₄²	—	2	2	no	—
381	C₃×C₄²	—	2	2	no	—
382	C₃×C₄²	—	4	1	no	—
383	C₃×C₄²	—	4	2	no	—
384	C₃×C₄²	—	4	1	no	—
385	C₃×C₄²	—	4	1	no	—
386	C₃×C₄²	—	4	2	no	—
387	C₃×C₄²	—	4	2	no	—
388	C₃×C₄²	—	4	2	no	—
389	C₃×C₄²	#41	1	4	yes	—
390	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
391	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₃	1	2	yes	—
393	#126	—	2	8	no	—
394	#125	—	4	4	no	—
395	#125	—	4	4	no	—
396	#123	—	4	4	no	—
397	C₄×Q₈	—	2	4	no	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₄²	C₂³×C₃	1	2	yes	—
443	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₃	1	2	yes	—
447	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₃	1	2	yes	—
451	C₂×C₄²	C₂³×C₃	1	2	yes	—
452	C₂×C₄²	C₂³×C₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
454	#95	C₂³×C₃	1	2	yes	—
455	#95	C₂³×C₃	1	2	yes	—
456	#95	C₂³×C₃	1	2	yes	—
457	#95	C₂³×C₃	1	2	yes	—
458	#95	C₂³×C₃	1	2	yes	—
459	#95	C₂³×C₃	1	2	yes	—
460	#95	C₂³×C₃	1	2	yes	—
461	#95	C₂³×C₃	1	2	yes	—
462	#95	C₂³×C₃	1	2	yes	—
463	#95	C₂³×C₃	1	2	yes	—
464	#95	C₂³×C₃	1	2	yes	—
465	#95	C₂³×C₃	1	2	yes	—
466	#95	C₂³×C₃	1	2	yes	—
467	#95	C₂³×C₃	1	2	yes	—
468	#95	C₂³×C₃	1	2	yes	—
469	#95	C₂³×C₃	1	2	yes	—
470	#95	C₂³×C₃	1	2	yes	—
471	#95	C₂³×C₃	1	2	yes	—
472	#95	C₂³×C₃	1	2	yes	—
473	#95	C₂³×C₃	1	2	yes	—
474	#95	C₂³×C₃	1	2	yes	—
475	#95	C₂³×C₃	1	2	yes	—
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	2	yes	—
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	2	yes	—
482	C₂³×C₃	—	2	2	no	—
483	C₂³×C₃	—	2	2	no	—
484	C₂³×C₃	—	2	2	no	—
485	C₂³×C₃	—	2	2	no	—
486	C₂³×C₃	—	2	2	no	—
487	C₂³×C₃	—	2	2	no	—
488	C₂³×C₃	—	2	2	no	—
489	C₂³×C₃	C₂⁵	1	1	yes	characteristic
490	C₃×Q₈	—	4	4	no	—
491	C₃×D₄	—	8	2	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	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	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	8	4	no	—
541	C₂×C₃×C₄	C₂×#41	1	2	yes	—
542	C₂×C₃×C₄	C₂×#41	1	2	yes	—
543	C₂×C₃×C₄	C₂×#41	1	2	yes	—
544	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
545	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
546	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
547	C₂⁴	C₂⁴×C₃	1	2	yes	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	4	1	no	—
550	C₂×Q₈	—	4	1	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	4	1	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	2	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₄⋊C₄	—	4	1	no	—
598	C₄⋊C₄	—	4	1	no	—
599	C₄⋊C₄	—	4	1	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₄⋊C₄	—	4	2	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	2	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	4	2	no	—
624	C₄²	—	4	1	no	—
625	C₄²	—	4	2	no	—
626	C₄²	—	4	1	no	—
627	C₄²	—	4	1	no	—
628	C₄²	—	4	2	no	—
629	C₄²	—	4	2	no	—
630	C₄²	C₃×#41	1	4	yes	—
631	C₂²×C₃	—	4	2	no	—
632	C₂²×C₃	—	4	2	no	—
633	C₂²×C₃	—	4	2	no	—
634	C₂²×C₃	—	4	2	no	—
635	C₂²×C₃	—	4	2	no	—
636	C₂²×C₃	—	4	2	no	—
637	C₂²×C₃	—	4	2	no	—
638	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
639	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
641	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
642	C₂²×C₃	#585	1	1	yes	characteristic
643	C₂²×C₃	#585	1	1	yes	characteristic
644	C₂²×C₃	#585	1	1	yes	characteristic
645	C₃×C₄	—	2	2	no	—
646	C₃×C₄	—	2	2	no	—
647	C₃×C₄	—	2	2	no	—
648	C₃×C₄	—	2	2	no	—
649	C₃×C₄	—	2	2	no	—
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	4	2	no	—
652	C₃×C₄	—	4	2	no	—
653	C₃×C₄	—	4	2	no	—
654	C₃×C₄	—	4	2	no	—
655	C₃×C₄	—	4	2	no	—
656	C₃×C₄	—	4	1	no	—
657	C₃×C₄	—	4	2	no	—
658	C₃×C₄	—	4	2	no	—
659	C₃×C₄	—	4	2	no	—
660	C₃×C₄	—	4	2	no	—
661	C₃×C₄	—	4	2	no	—
662	C₃×C₄	—	4	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	C₂⁵×C₃	1	1	yes	characteristic
671	Q₈	—	4	4	no	—
672	D₄	—	8	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂×C₃×#41	1	2	yes	—
723	C₂×C₄	C₂×C₃×#41	1	2	yes	—
724	C₂×C₄	C₂×C₃×#41	1	2	yes	—
725	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
726	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
727	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
728	C₂×C₃	—	8	2	no	—
729	C₂×C₃	#3455	1	1	yes	characteristic
730	C₂×C₃	#3507	1	1	yes	characteristic
731	C₂×C₃	#3511	1	1	yes	characteristic
732	C₂×C₃	#3547	1	1	yes	characteristic
733	C₂×C₃	#3553	1	1	yes	characteristic
734	C₂×C₃	#3560	1	1	yes	characteristic
735	C₂×C₃	#3563	1	1	yes	characteristic
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
744	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
745	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
746	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
747	C₂²	C₃×#585	1	1	yes	characteristic
748	C₂²	C₃×#585	1	1	yes	characteristic
749	C₂²	C₃×#585	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₃	#37143	1	1	yes	characteristic, direct product factor, Sylow
769	C₂	—	8	2	no	—
770	C₂	C₃×#3455	1	1	yes	characteristic
771	C₂	C₃×#3507	1	1	yes	characteristic
772	C₂	C₃×#3511	1	1	yes	characteristic
773	C₂	C₃×#3547	1	1	yes	characteristic
774	C₂	C₃×#3553	1	1	yes	characteristic
775	C₂	C₃×#3560	1	1	yes	characteristic
776	C₂	C₃×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2859	C₂	semidirect
4. C₃×#2805	C₂	semidirect
5. C₃×#2793	C₂	semidirect
6. C₃×#2790	C₂	semidirect
7. C₃×#2788	C₂	semidirect
8. C₃×#2783	C₂	semidirect
9. C₃×#2726	C₂	semidirect
11. C₃×#2719	C₂	semidirect
13. C₃×#2637	C₂	semidirect
14. C₃×#2590	C₂	semidirect
16. C₃×#2530	C₂	semidirect
17. C₃×#2529	C₂	semidirect
18. C₃×#2334	C₂	semidirect
19. C₃×#2295	C₂	semidirect
20. #37143	C₃	direct (N × H)
109. #2859	C₂×C₃	semidirect
111. #2805	C₂×C₃	semidirect
112. #2793	C₂×C₃	semidirect
113. #2790	C₂×C₃	semidirect
114. #2788	C₂×C₃	semidirect
115. #2783	C₂×C₃	semidirect
116. #2726	C₂×C₃	semidirect
118. #2719	C₂×C₃	semidirect
120. #2637	C₂×C₃	semidirect
121. #2590	C₂×C₃	semidirect
123. #2530	C₂×C₃	semidirect
124. #2529	C₂×C₃	semidirect
125. #2334	C₂×C₃	semidirect
126. #2295	C₂×C₃	semidirect
768. C₃	#37143	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×#2860	2
C₃×#2859	2
C₃×#2808	2
C₃×#2805	2
C₃×#2793	2
C₃×#2790	2
C₃×#2788	2
C₃×#2783	2
C₃×#2726	2
C₃×#2724	2
C₃×#2719	2
C₃×#2707	2
C₃×#2637	2
C₃×#2590	2
C₃×#2558	2
C₃×#2530	2
C₃×#2529	2
C₃×#2334	2
C₃×#2295	2
#37143	3

Subgroups — C3×#37143 #10655750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37143 #10655750