Subgroups — C₃×#37150 #10655757

Order 768.

1880 conjugacy classes of subgroups.

The subgroup lattice has 586 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	2	yes	maximal, complemented
2	C₃×#2808	C₂	1	2	yes	maximal, complemented
3	C₃×#2785	C₂	1	2	yes	maximal, complemented
4	C₃×#2723	C₂	1	4	yes	maximal, complemented
5	C₃×#2685	C₂	1	4	yes	maximal, complemented
6	C₃×#2684	C₂	1	2	yes	maximal, complemented
7	C₃×#2683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2679	C₂	1	1	yes	maximal, characteristic
9	C₃×#2632	C₂	1	2	yes	maximal, complemented
10	C₃×#2518	C₂	1	4	yes	maximal, complemented
11	C₃×#2472	C₂	1	4	yes	maximal, complemented
12	C₃×#2321	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
14	#37150	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×#126	C₂²	1	4	yes	complemented
16	C₂×C₃×#124	C₂²	1	1	yes	characteristic
17	C₂×C₃×#124	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
19	C₂×C₃×#120	C₂²	1	2	yes	—
20	C₂×C₃×#120	C₂²	1	4	yes	—
21	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
24	C₃×#399	C₂²	1	4	yes	complemented
25	C₃×#397	C₂²	1	4	yes	complemented
26	C₃×#397	C₂²	1	4	yes	complemented
27	C₃×#396	C₂²	1	4	yes	complemented
28	C₃×#395	C₂²	1	2	yes	complemented
29	C₃×#395	C₂²	1	2	yes	complemented
30	C₃×#394	C₂²	1	2	yes	—
31	C₃×#394	C₂²	1	2	yes	—
32	C₃×#394	C₂²	1	4	yes	—
33	C₃×#394	C₂²	1	4	yes	—
34	C₃×#394	C₂²	1	4	yes	—
35	C₃×#394	C₂²	1	4	yes	—
36	C₃×#393	C₂²	1	4	yes	complemented
37	C₃×#393	C₂²	1	4	yes	complemented
38	C₃×#391	C₂²	1	1	yes	characteristic, complemented
39	C₃×#390	C₂²	1	1	yes	characteristic
40	C₃×#390	C₂²	1	2	yes	—
41	C₃×#390	C₂²	1	2	yes	—
42	C₃×#390	C₂²	1	4	yes	—
43	C₃×#390	C₂²	1	2	yes	—
44	C₃×#389	C₂²	1	2	yes	complemented
45	C₃×#389	C₂²	1	2	yes	complemented
46	C₃×#389	C₂²	1	2	yes	complemented
47	C₃×#388	C₂²	1	4	yes	complemented
48	C₃×#388	C₂²	1	4	yes	complemented
49	C₃×#388	C₂²	1	4	yes	complemented
50	C₃×#388	C₂²	1	4	yes	complemented
51	C₃×#388	C₂²	1	4	yes	complemented
52	C₃×#388	C₂²	1	4	yes	complemented
53	C₃×#388	C₂²	1	4	yes	complemented
54	C₃×#388	C₂²	1	4	yes	complemented
55	C₃×#387	C₂²	1	4	yes	complemented
56	C₃×#386	C₂²	1	2	yes	—
57	C₃×#386	C₂²	1	4	yes	—
58	C₃×#386	C₂²	1	4	yes	—
59	C₃×#385	C₂²	1	2	yes	complemented
60	C₃×#383	C₂²	1	2	yes	complemented
61	C₃×#382	C₂²	1	4	yes	complemented
62	C₃×#382	C₂²	1	1	yes	characteristic, complemented
63	C₃×#379	C₂²	1	4	yes	complemented
64	C₃×#379	C₂²	1	2	yes	complemented
65	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
66	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
67	C₃×C₄³	C₂²	1	1	yes	characteristic, complemented
68	#2860	C₂×C₃	1	2	yes	complemented
69	#2808	C₂×C₃	1	2	yes	complemented
70	#2785	C₂×C₃	1	2	yes	complemented
71	#2723	C₂×C₃	1	4	yes	complemented
72	#2685	C₂×C₃	1	4	yes	complemented
73	#2684	C₂×C₃	1	2	yes	complemented
74	#2683	C₂×C₃	1	1	yes	characteristic, complemented
75	#2679	C₂×C₃	1	1	yes	characteristic
76	#2632	C₂×C₃	1	2	yes	complemented
77	#2518	C₂×C₃	1	4	yes	complemented
78	#2472	C₂×C₃	1	4	yes	complemented
79	#2321	C₂×C₃	1	2	yes	complemented
80	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂⁵×C₃	C₂³	1	2	yes	—
82	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
83	C₂²×C₃×Q₈	C₂³	1	2	yes	—
84	C₂²×C₃×D₄	C₂³	1	4	yes	—
85	C₂²×C₃×D₄	C₂³	1	2	yes	—
86	C₂²×C₃×D₄	C₂³	1	2	yes	—
87	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₂³	1	2	yes	—
89	C₂³×C₃×C₄	C₂³	1	2	yes	—
90	C₃×#126	—	4	8	no	—
91	C₃×#124	—	2	4	no	—
92	C₃×#124	—	4	4	no	—
93	C₃×C₂²⋊Q₈	—	4	8	no	—
94	C₃×#120	—	2	8	no	—
95	C₃×#120	—	4	8	no	—
96	C₃×C₄×Q₈	—	4	2	no	—
97	C₃×C₄×D₄	—	4	2	no	—
98	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
109	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂³	1	2	yes	—
129	C₂×C₃×C₄²	C₂³	1	2	yes	—
130	C₂×C₃×C₄²	C₂³	1	2	yes	—
131	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄²	C₂³	1	4	yes	—
133	C₃×#95	C₂³	1	4	yes	—
134	C₃×#95	C₂³	1	4	yes	—
135	C₃×#95	C₂³	1	4	yes	—
136	C₃×#95	C₂³	1	2	yes	—
137	C₃×#95	C₂³	1	4	yes	—
138	C₃×#95	C₂³	1	4	yes	—
139	C₃×#95	C₂³	1	4	yes	—
140	C₃×#95	C₂³	1	2	yes	—
141	C₃×#95	C₂³	1	4	yes	—
142	C₃×#95	C₂³	1	4	yes	—
143	C₂×#126	C₂²×C₃	1	4	yes	complemented
144	C₂×#124	C₂²×C₃	1	1	yes	characteristic
145	C₂×#124	C₂²×C₃	1	2	yes	—
146	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
147	C₂×#120	C₂²×C₃	1	2	yes	—
148	C₂×#120	C₂²×C₃	1	4	yes	—
149	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
151	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
152	#399	C₂²×C₃	1	4	yes	complemented
153	#397	C₂²×C₃	1	4	yes	complemented
154	#397	C₂²×C₃	1	4	yes	complemented
155	#396	C₂²×C₃	1	4	yes	complemented
156	#395	C₂²×C₃	1	2	yes	complemented
157	#395	C₂²×C₃	1	2	yes	complemented
158	#394	C₂²×C₃	1	2	yes	—
159	#394	C₂²×C₃	1	2	yes	—
160	#394	C₂²×C₃	1	4	yes	—
161	#394	C₂²×C₃	1	4	yes	—
162	#394	C₂²×C₃	1	4	yes	—
163	#394	C₂²×C₃	1	4	yes	—
164	#393	C₂²×C₃	1	4	yes	complemented
165	#393	C₂²×C₃	1	4	yes	complemented
166	#391	C₂²×C₃	1	1	yes	characteristic, complemented
167	#390	C₂²×C₃	1	4	yes	—
168	#390	C₂²×C₃	1	2	yes	—
169	#390	C₂²×C₃	1	2	yes	—
170	#390	C₂²×C₃	1	2	yes	—
171	#390	C₂²×C₃	1	1	yes	characteristic
172	#389	C₂²×C₃	1	2	yes	complemented
173	#389	C₂²×C₃	1	2	yes	complemented
174	#389	C₂²×C₃	1	2	yes	complemented
175	#388	C₂²×C₃	1	4	yes	complemented
176	#388	C₂²×C₃	1	4	yes	complemented
177	#388	C₂²×C₃	1	4	yes	complemented
178	#388	C₂²×C₃	1	4	yes	complemented
179	#388	C₂²×C₃	1	4	yes	complemented
180	#388	C₂²×C₃	1	4	yes	complemented
181	#388	C₂²×C₃	1	4	yes	complemented
182	#388	C₂²×C₃	1	4	yes	complemented
183	#387	C₂²×C₃	1	4	yes	complemented
184	#386	C₂²×C₃	1	2	yes	—
185	#386	C₂²×C₃	1	4	yes	—
186	#386	C₂²×C₃	1	4	yes	—
187	#385	C₂²×C₃	1	2	yes	complemented
188	#383	C₂²×C₃	1	2	yes	complemented
189	#382	C₂²×C₃	1	4	yes	complemented
190	#382	C₂²×C₃	1	1	yes	characteristic, complemented
191	#379	C₂²×C₃	1	2	yes	complemented
192	#379	C₂²×C₃	1	4	yes	complemented
193	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
194	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
195	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂⁴×C₃	—	2	4	no	—
197	C₂⁴×C₃	—	4	2	no	—
198	C₂⁴×C₃	—	4	2	no	—
199	C₂⁴×C₃	—	4	4	no	—
200	C₂⁴×C₃	—	4	4	no	—
201	C₂⁴×C₃	C₂⁴	1	4	yes	—
202	C₂⁴×C₃	C₂⁴	1	2	yes	—
203	C₂×C₃×Q₈	—	2	2	no	—
204	C₂×C₃×Q₈	—	4	1	no	—
205	C₂×C₃×Q₈	—	4	1	no	—
206	C₂×C₃×Q₈	—	4	4	no	—
207	C₂×C₃×Q₈	—	4	2	no	—
208	C₂×C₃×D₄	—	2	8	no	—
209	C₂×C₃×D₄	—	2	4	no	—
210	C₂×C₃×D₄	—	4	1	no	—
211	C₂×C₃×D₄	—	4	1	no	—
212	C₂×C₃×D₄	—	4	4	no	—
213	C₂×C₃×D₄	—	4	4	no	—
214	C₂×C₃×D₄	—	4	2	no	—
215	C₂×C₃×D₄	—	4	2	no	—
216	C₂×C₃×D₄	—	4	2	no	—
217	C₂×C₃×D₄	—	4	4	no	—
218	C₂×C₃×D₄	#41	1	4	yes	—
219	C₂²×C₃×C₄	—	2	4	no	—
220	C₂²×C₃×C₄	—	4	2	no	—
221	C₂²×C₃×C₄	—	4	4	no	—
222	C₂²×C₃×C₄	—	4	4	no	—
223	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
224	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
225	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
226	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
227	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
228	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
229	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
230	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
234	C₃×C₄⋊C₄	—	2	4	no	—
235	C₃×C₄⋊C₄	—	2	8	no	—
236	C₃×C₄⋊C₄	—	4	2	no	—
237	C₃×C₄⋊C₄	—	4	2	no	—
238	C₃×C₄⋊C₄	—	4	1	no	—
239	C₃×C₄⋊C₄	—	4	1	no	—
240	C₃×C₄⋊C₄	—	4	2	no	—
241	C₃×C₄⋊C₄	—	4	4	no	—
242	C₃×C₄⋊C₄	—	4	4	no	—
243	C₃×C₄⋊C₄	—	4	4	no	—
244	C₃×C₂²⋊C₄	—	2	4	no	—
245	C₃×C₂²⋊C₄	—	2	8	no	—
246	C₃×C₂²⋊C₄	—	2	8	no	—
247	C₃×C₂²⋊C₄	—	2	8	no	—
248	C₃×C₂²⋊C₄	—	2	8	no	—
249	C₃×C₂²⋊C₄	—	2	8	no	—
250	C₃×C₂²⋊C₄	—	4	4	no	—
251	C₃×C₂²⋊C₄	—	4	4	no	—
252	C₃×C₂²⋊C₄	—	4	4	no	—
253	C₃×C₂²⋊C₄	—	4	2	no	—
254	C₃×C₂²⋊C₄	—	4	4	no	—
255	C₃×C₂²⋊C₄	—	4	2	no	—
256	C₃×C₂²⋊C₄	—	4	4	no	—
257	C₃×C₂²⋊C₄	—	4	4	no	—
258	C₃×C₂²⋊C₄	—	4	4	no	—
259	C₃×C₂²⋊C₄	—	4	4	no	—
260	C₃×C₂²⋊C₄	—	4	4	no	—
261	C₃×C₄²	—	2	2	no	—
262	C₃×C₄²	—	2	2	no	—
263	C₃×C₄²	—	2	4	no	—
264	C₃×C₄²	—	2	4	no	—
265	C₃×C₄²	—	4	1	no	—
266	C₃×C₄²	—	4	2	no	—
267	C₃×C₄²	—	4	4	no	—
268	C₂⁵	C₂³×C₃	1	2	yes	—
269	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
270	C₂²×Q₈	C₂³×C₃	1	2	yes	—
271	C₂²×D₄	C₂³×C₃	1	4	yes	—
272	C₂²×D₄	C₂³×C₃	1	2	yes	—
273	C₂²×D₄	C₂³×C₃	1	2	yes	—
274	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₃	1	2	yes	—
276	C₂³×C₄	C₂³×C₃	1	2	yes	—
277	#126	—	4	8	no	—
278	#124	—	2	4	no	—
279	#124	—	4	4	no	—
280	C₂²⋊Q₈	—	4	8	no	—
281	#120	—	2	8	no	—
282	#120	—	4	8	no	—
283	C₄×Q₈	—	4	2	no	—
284	C₄×D₄	—	4	2	no	—
285	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
287	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
291	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
295	C₂×C₂²⋊C₄	—	4	4	no	—
296	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
313	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₃	1	2	yes	—
317	C₂×C₄²	C₂³×C₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₃	1	4	yes	—
320	#95	C₂³×C₃	1	4	yes	—
321	#95	C₂³×C₃	1	4	yes	—
322	#95	C₂³×C₃	1	4	yes	—
323	#95	C₂³×C₃	1	2	yes	—
324	#95	C₂³×C₃	1	4	yes	—
325	#95	C₂³×C₃	1	4	yes	—
326	#95	C₂³×C₃	1	4	yes	—
327	#95	C₂³×C₃	1	2	yes	—
328	#95	C₂³×C₃	1	4	yes	—
329	#95	C₂³×C₃	1	4	yes	—
330	C₂³×C₃	—	2	4	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	2	no	—
333	C₂³×C₃	—	2	4	no	—
334	C₂³×C₃	—	2	4	no	—
335	C₂³×C₃	—	2	4	no	—
336	C₂³×C₃	—	2	4	no	—
337	C₂³×C₃	—	2	4	no	—
338	C₂³×C₃	—	2	4	no	—
339	C₂³×C₃	—	2	4	no	—
340	C₂³×C₃	—	2	4	no	—
341	C₂³×C₃	—	4	8	no	—
342	C₂³×C₃	—	8	8	no	—
343	C₂³×C₃	—	8	4	no	—
344	C₂³×C₃	—	8	4	no	—
345	C₂³×C₃	—	8	8	no	—
346	C₂³×C₃	C₂×#41	1	4	yes	—
347	C₂³×C₃	C₂⁵	1	1	yes	characteristic
348	C₃×Q₈	—	4	4	no	—
349	C₃×Q₈	—	8	4	no	—
350	C₃×D₄	—	4	4	no	—
351	C₃×D₄	—	8	4	no	—
352	C₃×D₄	—	8	8	no	—
353	C₃×D₄	—	8	4	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	4	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	4	no	—
368	C₂×C₃×C₄	—	2	4	no	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	4	no	—
376	C₂×C₃×C₄	—	2	4	no	—
377	C₂×C₃×C₄	—	2	4	no	—
378	C₂×C₃×C₄	—	2	4	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	8	4	no	—
381	C₂×C₃×C₄	—	8	4	no	—
382	C₂×C₃×C₄	C₂×#41	1	2	yes	—
383	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	4	2	no	—
387	C₂⁴	—	4	2	no	—
388	C₂⁴	—	4	4	no	—
389	C₂⁴	—	4	4	no	—
390	C₂⁴	C₂⁴×C₃	1	4	yes	—
391	C₂⁴	C₂⁴×C₃	1	2	yes	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	C₃×#41	1	4	yes	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	2	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	—	4	4	no	—
430	C₄⋊C₄	—	4	4	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	4	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	4	1	no	—
455	C₄²	—	4	2	no	—
456	C₄²	—	4	4	no	—
457	C₂²×C₃	—	2	4	no	—
458	C₂²×C₃	—	2	8	no	—
459	C₂²×C₃	—	4	2	no	—
460	C₂²×C₃	—	4	2	no	—
461	C₂²×C₃	—	4	4	no	—
462	C₂²×C₃	—	4	4	no	—
463	C₂²×C₃	—	4	4	no	—
464	C₂²×C₃	—	4	4	no	—
465	C₂²×C₃	—	4	4	no	—
466	C₂²×C₃	—	4	4	no	—
467	C₂²×C₃	—	4	4	no	—
468	C₂²×C₃	—	4	4	no	—
469	C₂²×C₃	—	8	16	no	—
470	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
473	C₂²×C₃	#585	1	1	yes	characteristic
474	C₂²×C₃	#585	1	2	yes	—
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	2	4	no	—
478	C₃×C₄	—	4	2	no	—
479	C₃×C₄	—	4	2	no	—
480	C₃×C₄	—	4	4	no	—
481	C₃×C₄	—	4	2	no	—
482	C₃×C₄	—	4	1	no	—
483	C₃×C₄	—	4	4	no	—
484	C₃×C₄	—	4	2	no	—
485	C₃×C₄	—	4	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	8	no	—
498	C₂³	—	8	8	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	—	8	8	no	—
502	C₂³	C₂×C₃×#41	1	4	yes	—
503	C₂³	C₂⁵×C₃	1	1	yes	characteristic
504	Q₈	—	4	4	no	—
505	Q₈	—	8	4	no	—
506	D₄	—	4	4	no	—
507	D₄	—	8	4	no	—
508	D₄	—	8	8	no	—
509	D₄	—	8	4	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	8	4	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	C₂×C₃×#41	1	2	yes	—
539	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
540	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
541	C₂×C₃	—	4	4	no	—
542	C₂×C₃	—	8	4	no	—
543	C₂×C₃	#3459	1	1	yes	characteristic
544	C₂×C₃	#3514	1	2	yes	—
545	C₂×C₃	#3545	1	1	yes	characteristic
546	C₂×C₃	#3549	1	1	yes	characteristic
547	C₂×C₃	#3560	1	2	yes	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	8	16	no	—
561	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
562	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
564	C₂²	C₃×#585	1	1	yes	characteristic
565	C₂²	C₃×#585	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	4	no	—
577	C₃	#37150	1	1	yes	characteristic, direct product factor, Sylow
578	C₂	—	4	4	no	—
579	C₂	—	8	4	no	—
580	C₂	C₃×#3459	1	1	yes	characteristic
581	C₂	C₃×#3514	1	2	yes	—
582	C₂	C₃×#3545	1	1	yes	characteristic
583	C₂	C₃×#3549	1	1	yes	characteristic
584	C₂	C₃×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2679	C₂
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
1. C₃×#2860	C₂	semidirect
2. C₃×#2808	C₂	semidirect
3. C₃×#2785	C₂	semidirect
4. C₃×#2723	C₂	semidirect
5. C₃×#2685	C₂	semidirect
6. C₃×#2684	C₂	semidirect
7. C₃×#2683	C₂	semidirect
9. C₃×#2632	C₂	semidirect
10. C₃×#2518	C₂	semidirect
11. C₃×#2472	C₂	semidirect
12. C₃×#2321	C₂	semidirect
13. C₃×C₄×#124	C₂	semidirect
14. #37150	C₃	direct (N × H)
15. C₂×C₃×#126	C₂²	semidirect
18. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
21. C₂×C₃×C₄×Q₈	C₂²	semidirect
23. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
24. C₃×#399	C₂²	semidirect
25. C₃×#397	C₂²	semidirect
26. C₃×#397	C₂²	semidirect
27. C₃×#396	C₂²	semidirect
28. C₃×#395	C₂²	semidirect
29. C₃×#395	C₂²	semidirect
36. C₃×#393	C₂²	semidirect
37. C₃×#393	C₂²	semidirect
38. C₃×#391	C₂²	semidirect
44. C₃×#389	C₂²	semidirect
45. C₃×#389	C₂²	semidirect
46. C₃×#389	C₂²	semidirect
47. C₃×#388	C₂²	semidirect
48. C₃×#388	C₂²	semidirect
49. C₃×#388	C₂²	semidirect
50. C₃×#388	C₂²	semidirect
51. C₃×#388	C₂²	semidirect
52. C₃×#388	C₂²	semidirect
53. C₃×#388	C₂²	semidirect
54. C₃×#388	C₂²	semidirect
55. C₃×#387	C₂²	semidirect
59. C₃×#385	C₂²	semidirect
60. C₃×#383	C₂²	semidirect
61. C₃×#382	C₂²	semidirect
62. C₃×#382	C₂²	semidirect
63. C₃×#379	C₂²	semidirect
64. C₃×#379	C₂²	semidirect
65. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
66. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
67. C₃×C₄³	C₂²	semidirect
68. #2860	C₂×C₃	semidirect
69. #2808	C₂×C₃	semidirect
70. #2785	C₂×C₃	semidirect
71. #2723	C₂×C₃	semidirect
72. #2685	C₂×C₃	semidirect
73. #2684	C₂×C₃	semidirect
74. #2683	C₂×C₃	semidirect
76. #2632	C₂×C₃	semidirect
77. #2518	C₂×C₃	semidirect
78. #2472	C₂×C₃	semidirect
79. #2321	C₂×C₃	semidirect
80. C₄×#124	C₂×C₃	semidirect
143. C₂×#126	C₂²×C₃	semidirect
146. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
149. C₂×C₄×Q₈	C₂²×C₃	semidirect
151. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
152. #399	C₂²×C₃	semidirect
153. #397	C₂²×C₃	semidirect
154. #397	C₂²×C₃	semidirect
155. #396	C₂²×C₃	semidirect
156. #395	C₂²×C₃	semidirect
157. #395	C₂²×C₃	semidirect
164. #393	C₂²×C₃	semidirect
165. #393	C₂²×C₃	semidirect
166. #391	C₂²×C₃	semidirect
172. #389	C₂²×C₃	semidirect
173. #389	C₂²×C₃	semidirect
174. #389	C₂²×C₃	semidirect
175. #388	C₂²×C₃	semidirect
176. #388	C₂²×C₃	semidirect
177. #388	C₂²×C₃	semidirect
178. #388	C₂²×C₃	semidirect
179. #388	C₂²×C₃	semidirect
180. #388	C₂²×C₃	semidirect
181. #388	C₂²×C₃	semidirect
182. #388	C₂²×C₃	semidirect
183. #387	C₂²×C₃	semidirect
187. #385	C₂²×C₃	semidirect
188. #383	C₂²×C₃	semidirect
189. #382	C₂²×C₃	semidirect
190. #382	C₂²×C₃	semidirect
191. #379	C₂²×C₃	semidirect
192. #379	C₂²×C₃	semidirect
193. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
194. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
195. C₄³	C₂²×C₃	semidirect
577. C₃	#37150	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×#2808	2
C₃×#2785	2
C₃×#2723	2
C₃×#2685	2
C₃×#2684	2
C₃×#2683	2
C₃×#2679	2
C₃×#2632	2
C₃×#2518	2
C₃×#2472	2
C₃×#2321	2
C₃×C₄×#124	2
#37150	3

Subgroups — C3×#37150 #10655757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37150 #10655757