Subgroups — C₃×#35266 #10653873

Order 768.

2018 conjugacy classes of subgroups.

The subgroup lattice has 504 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	4	yes	maximal, complemented
2	C₃×#2644	C₂	1	4	yes	maximal, complemented
3	C₃×#2513	C₂	1	4	yes	maximal, complemented
4	C₃×#2512	C₂	1	4	yes	maximal, complemented
5	C₃×#2480	C₂	1	8	yes	maximal, complemented
6	C₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2309	C₂	1	1	yes	maximal, characteristic
9	C₃×#2309	C₂	1	1	yes	maximal, characteristic
10	C₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#390	C₂	1	1	yes	maximal, characteristic
12	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	#35266	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#126	C₂²	1	8	yes	complemented
16	C₂×C₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₃×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃×#117	C₂²	1	1	yes	characteristic
19	C₂×C₃×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
23	C₃×#397	C₂²	1	8	yes	complemented
24	C₃×#397	C₂²	1	8	yes	complemented
25	C₃×#397	C₂²	1	8	yes	complemented
26	C₃×#396	C₂²	1	8	yes	complemented
27	C₃×#390	C₂²	1	2	yes	—
28	C₃×#390	C₂²	1	4	yes	—
29	C₃×#390	C₂²	1	4	yes	—
30	C₃×#390	C₂²	1	2	yes	—
31	C₃×#390	C₂²	1	4	yes	—
32	C₃×#390	C₂²	1	4	yes	—
33	C₃×#390	C₂²	1	2	yes	—
34	C₃×#390	C₂²	1	2	yes	—
35	C₃×#389	C₂²	1	2	yes	complemented
36	C₃×#389	C₂²	1	4	yes	complemented
37	C₃×#389	C₂²	1	4	yes	complemented
38	C₃×#389	C₂²	1	4	yes	complemented
39	C₃×#389	C₂²	1	2	yes	complemented
40	C₃×#388	C₂²	1	8	yes	complemented
41	C₃×#388	C₂²	1	8	yes	complemented
42	C₃×#388	C₂²	1	8	yes	complemented
43	C₃×#385	C₂²	1	4	yes	—
44	C₃×#385	C₂²	1	4	yes	—
45	C₃×#384	C₂²	1	2	yes	complemented
46	C₃×#382	C₂²	1	2	yes	complemented
47	C₃×#380	C₂²	1	4	yes	—
48	C₃×#379	C₂²	1	4	yes	—
49	C₃×#379	C₂²	1	4	yes	—
50	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
51	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	complemented
52	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
53	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
54	C₃×#376	C₂²	1	2	yes	complemented
55	C₃×C₄³	C₂²	1	2	yes	complemented
56	#2860	C₂×C₃	1	4	yes	complemented
57	#2644	C₂×C₃	1	4	yes	complemented
58	#2513	C₂×C₃	1	4	yes	complemented
59	#2512	C₂×C₃	1	4	yes	complemented
60	#2480	C₂×C₃	1	8	yes	complemented
61	#2317	C₂×C₃	1	1	yes	characteristic, complemented
62	#2316	C₂×C₃	1	1	yes	characteristic, complemented
63	#2309	C₂×C₃	1	1	yes	characteristic
64	#2309	C₂×C₃	1	1	yes	characteristic
65	#2296	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#390	C₂×C₃	1	1	yes	characteristic
67	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂⁵×C₃	C₂³	1	2	yes	—
69	C₂²×C₃×D₄	—	2	4	no	—
70	C₂²×C₃×D₄	—	2	4	no	—
71	C₂²×C₃×D₄	—	2	4	no	—
72	C₂²×C₃×D₄	C₂³	1	2	yes	—
73	C₂²×C₃×D₄	C₂³	1	2	yes	—
74	C₂³×C₃×C₄	C₂³	1	2	yes	—
75	C₂³×C₃×C₄	C₂³	1	2	yes	—
76	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
77	C₃×#126	—	4	16	no	—
78	C₃×#117	—	2	4	no	—
79	C₃×#117	—	2	4	no	—
80	C₃×#117	—	2	4	no	—
81	C₃×#117	—	2	4	no	—
82	C₂×C₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
94	C₂×C₃×C₂²⋊C₄	—	4	8	no	—
95	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
96	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
97	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
98	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₃×C₄²	—	2	4	no	—
106	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂³	1	2	yes	—
108	C₂×C₃×C₄²	C₂³	1	2	yes	—
109	C₂×C₃×C₄²	C₂³	1	4	yes	—
110	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂³	1	2	yes	—
112	C₂×C₃×C₄²	C₂³	1	2	yes	—
113	C₂×C₃×C₄²	C₂³	1	2	yes	—
114	C₂×C₃×C₄²	C₂³	1	4	yes	—
115	C₃×#95	C₂³	1	4	yes	—
116	C₃×#95	C₂³	1	4	yes	—
117	C₃×#95	C₂³	1	4	yes	—
118	C₃×#95	C₂³	1	4	yes	—
119	C₃×#95	C₂³	1	8	yes	—
120	C₃×#95	C₂³	1	8	yes	—
121	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×#126	C₂²×C₃	1	8	yes	complemented
123	C₂×#117	C₂²×C₃	1	1	yes	characteristic
124	C₂×#117	C₂²×C₃	1	1	yes	characteristic
125	C₂×#117	C₂²×C₃	1	1	yes	characteristic
126	C₂×#117	C₂²×C₃	1	1	yes	characteristic
127	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
129	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
130	#397	C₂²×C₃	1	8	yes	complemented
131	#397	C₂²×C₃	1	8	yes	complemented
132	#397	C₂²×C₃	1	8	yes	complemented
133	#396	C₂²×C₃	1	8	yes	complemented
134	#390	C₂²×C₃	1	4	yes	—
135	#390	C₂²×C₃	1	4	yes	—
136	#390	C₂²×C₃	1	2	yes	—
137	#390	C₂²×C₃	1	4	yes	—
138	#390	C₂²×C₃	1	2	yes	—
139	#390	C₂²×C₃	1	2	yes	—
140	#390	C₂²×C₃	1	2	yes	—
141	#390	C₂²×C₃	1	4	yes	—
142	#389	C₂²×C₃	1	4	yes	complemented
143	#389	C₂²×C₃	1	4	yes	complemented
144	#389	C₂²×C₃	1	4	yes	complemented
145	#389	C₂²×C₃	1	2	yes	complemented
146	#389	C₂²×C₃	1	2	yes	complemented
147	#388	C₂²×C₃	1	8	yes	complemented
148	#388	C₂²×C₃	1	8	yes	complemented
149	#388	C₂²×C₃	1	8	yes	complemented
150	#385	C₂²×C₃	1	4	yes	—
151	#385	C₂²×C₃	1	4	yes	—
152	#384	C₂²×C₃	1	2	yes	complemented
153	#382	C₂²×C₃	1	2	yes	complemented
154	#380	C₂²×C₃	1	4	yes	—
155	#379	C₂²×C₃	1	4	yes	—
156	#379	C₂²×C₃	1	4	yes	—
157	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
158	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
159	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
160	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
161	#376	C₂²×C₃	1	2	yes	complemented
162	C₄³	C₂²×C₃	1	2	yes	complemented
163	C₂⁴×C₃	—	2	4	no	—
164	C₂⁴×C₃	—	2	4	no	—
165	C₂⁴×C₃	—	2	4	no	—
166	C₂⁴×C₃	—	4	4	no	—
167	C₂⁴×C₃	—	4	4	no	—
168	C₂⁴×C₃	C₂⁴	1	4	yes	—
169	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂×C₃×D₄	—	2	4	no	—
174	C₂×C₃×D₄	—	2	4	no	—
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	4	16	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	—	4	2	no	—
181	C₂²×C₃×C₄	—	4	4	no	—
182	C₂²×C₃×C₄	#41	1	4	yes	—
183	C₂²×C₃×C₄	#41	1	4	yes	—
184	C₂²×C₃×C₄	#41	1	4	yes	—
185	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
186	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
187	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
188	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
189	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
190	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
191	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
192	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
193	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
195	C₃×C₄⋊C₄	—	2	4	no	—
196	C₃×C₄⋊C₄	—	2	4	no	—
197	C₃×C₄⋊C₄	—	2	4	no	—
198	C₃×C₄⋊C₄	—	2	4	no	—
199	C₃×C₄⋊C₄	—	2	4	no	—
200	C₃×C₄⋊C₄	—	2	2	no	—
201	C₃×C₄⋊C₄	—	2	2	no	—
202	C₃×C₄⋊C₄	—	2	8	no	—
203	C₃×C₄⋊C₄	—	4	4	no	—
204	C₃×C₄⋊C₄	—	4	8	no	—
205	C₃×C₄⋊C₄	—	4	8	no	—
206	C₃×C₂²⋊C₄	—	2	4	no	—
207	C₃×C₂²⋊C₄	—	2	4	no	—
208	C₃×C₂²⋊C₄	—	2	4	no	—
209	C₃×C₂²⋊C₄	—	2	4	no	—
210	C₃×C₂²⋊C₄	—	2	16	no	—
211	C₃×C₂²⋊C₄	—	4	8	no	—
212	C₃×C₂²⋊C₄	—	4	8	no	—
213	C₃×C₂²⋊C₄	—	4	8	no	—
214	C₃×C₂²⋊C₄	—	4	8	no	—
215	C₃×C₂²⋊C₄	—	4	8	no	—
216	C₃×C₄²	—	2	2	no	—
217	C₃×C₄²	—	2	4	no	—
218	C₃×C₄²	—	2	2	no	—
219	C₃×C₄²	—	2	4	no	—
220	C₃×C₄²	—	2	4	no	—
221	C₃×C₄²	—	2	4	no	—
222	C₃×C₄²	—	2	4	no	—
223	C₃×C₄²	—	2	8	no	—
224	C₃×C₄²	—	4	4	no	—
225	C₂⁵	C₂³×C₃	1	2	yes	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	—	2	4	no	—
228	C₂²×D₄	—	2	4	no	—
229	C₂²×D₄	C₂³×C₃	1	2	yes	—
230	C₂²×D₄	C₂³×C₃	1	2	yes	—
231	C₂³×C₄	C₂³×C₃	1	2	yes	—
232	C₂³×C₄	C₂³×C₃	1	2	yes	—
233	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
234	#126	—	4	16	no	—
235	#117	—	2	4	no	—
236	#117	—	2	4	no	—
237	#117	—	2	4	no	—
238	#117	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
248	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
249	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
251	C₂×C₂²⋊C₄	—	4	8	no	—
252	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	C₂³×C₃	1	2	yes	—
264	C₂×C₄²	C₂³×C₃	1	2	yes	—
265	C₂×C₄²	C₂³×C₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₃	1	4	yes	—
268	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₃	1	2	yes	—
271	C₂×C₄²	C₂³×C₃	1	4	yes	—
272	#95	C₂³×C₃	1	4	yes	—
273	#95	C₂³×C₃	1	4	yes	—
274	#95	C₂³×C₃	1	4	yes	—
275	#95	C₂³×C₃	1	4	yes	—
276	#95	C₂³×C₃	1	8	yes	—
277	#95	C₂³×C₃	1	8	yes	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	2	4	no	—
282	C₂³×C₃	—	2	4	no	—
283	C₂³×C₃	—	2	8	no	—
284	C₂³×C₃	—	2	8	no	—
285	C₂³×C₃	—	4	16	no	—
286	C₂³×C₃	—	4	8	no	—
287	C₂³×C₃	—	8	8	no	—
288	C₂³×C₃	—	8	4	no	—
289	C₂³×C₃	—	8	4	no	—
290	C₂³×C₃	C₂×#41	1	2	yes	—
291	C₂³×C₃	C₂×#41	1	2	yes	—
292	C₂³×C₃	C₂×#41	1	2	yes	—
293	C₂³×C₃	C₂⁵	1	1	yes	characteristic
294	C₃×D₄	—	4	8	no	—
295	C₃×D₄	—	4	8	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	4	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	8	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	4	8	no	—
317	C₂×C₃×C₄	—	8	4	no	—
318	C₂×C₃×C₄	#126	1	16	yes	complemented
319	C₂×C₃×C₄	C₂×#41	1	2	yes	—
320	C₂×C₃×C₄	C₂×#41	1	2	yes	—
321	C₂×C₃×C₄	C₂×#41	1	2	yes	—
322	C₂×C₃×C₄	C₂×#41	1	2	yes	—
323	C₂×C₃×C₄	C₂×#41	1	2	yes	—
324	C₂×C₃×C₄	C₂×#41	1	2	yes	—
325	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	4	4	no	—
330	C₂⁴	—	4	4	no	—
331	C₂⁴	C₂⁴×C₃	1	4	yes	—
332	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	4	16	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	C₃×#41	1	4	yes	—
346	C₂²×C₄	C₃×#41	1	4	yes	—
347	C₂²×C₄	C₃×#41	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	4	8	no	—
367	C₄⋊C₄	—	4	8	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	16	no	—
374	C₂²⋊C₄	—	4	8	no	—
375	C₂²⋊C₄	—	4	8	no	—
376	C₂²⋊C₄	—	4	8	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	8	no	—
387	C₄²	—	4	4	no	—
388	C₂²×C₃	—	2	4	no	—
389	C₂²×C₃	—	2	4	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	4	4	no	—
393	C₂²×C₃	—	4	8	no	—
394	C₂²×C₃	—	4	8	no	—
395	C₂²×C₃	—	4	4	no	—
396	C₂²×C₃	—	4	4	no	—
397	C₂²×C₃	—	8	16	no	—
398	C₂²×C₃	C₂×#126	1	4	yes	—
399	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
401	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
402	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
403	C₂²×C₃	#585	1	2	yes	—
404	C₃×C₄	—	2	4	no	—
405	C₃×C₄	—	4	4	no	—
406	C₃×C₄	—	4	4	no	—
407	C₃×C₄	—	4	4	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	4	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	C₂×#126	1	4	yes	—
413	C₃×C₄	C₂×#126	1	4	yes	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	4	16	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	8	8	no	—
424	C₂³	—	8	4	no	—
425	C₂³	—	8	4	no	—
426	C₂³	C₂×C₃×#41	1	2	yes	—
427	C₂³	C₂×C₃×#41	1	2	yes	—
428	C₂³	C₂×C₃×#41	1	2	yes	—
429	C₂³	C₂⁵×C₃	1	1	yes	characteristic
430	D₄	—	4	8	no	—
431	D₄	—	4	8	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	8	4	no	—
454	C₂×C₄	C₃×#126	1	16	yes	complemented
455	C₂×C₄	C₂×C₃×#41	1	2	yes	—
456	C₂×C₄	C₂×C₃×#41	1	2	yes	—
457	C₂×C₄	C₂×C₃×#41	1	2	yes	—
458	C₂×C₄	C₂×C₃×#41	1	2	yes	—
459	C₂×C₄	C₂×C₃×#41	1	2	yes	—
460	C₂×C₄	C₂×C₃×#41	1	2	yes	—
461	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
462	C₂×C₃	—	2	4	no	—
463	C₂×C₃	—	8	4	no	—
464	C₂×C₃	C₂²×#126	1	1	yes	characteristic
465	C₂×C₃	#3460	1	2	yes	—
466	C₂×C₃	#3494	1	2	yes	—
467	C₂×C₃	#3508	1	1	yes	characteristic
468	C₂×C₃	#3510	1	1	yes	characteristic
469	C₂²	—	2	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	8	16	no	—
479	C₂²	C₂×C₃×#126	1	4	yes	—
480	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
481	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
482	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
483	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
484	C₂²	C₃×#585	1	2	yes	—
485	C₄	—	2	4	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	C₂×C₃×#126	1	4	yes	—
494	C₄	C₂×C₃×#126	1	4	yes	—
495	C₃	#35266	1	1	yes	characteristic, direct product factor, Sylow
496	C₂	—	2	4	no	—
497	C₂	—	8	4	no	—
498	C₂	C₂²×C₃×#126	1	1	yes	characteristic
499	C₂	C₃×#3460	1	2	yes	—
500	C₂	C₃×#3494	1	2	yes	—
501	C₂	C₃×#3508	1	1	yes	characteristic
502	C₂	C₃×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
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×#2644	C₂	semidirect
3. C₃×#2513	C₂	semidirect
4. C₃×#2512	C₂	semidirect
5. C₃×#2480	C₂	semidirect
6. C₃×#2317	C₂	semidirect
7. C₃×#2316	C₂	semidirect
10. C₃×#2296	C₂	semidirect
12. C₃×C₄×#117	C₂	semidirect
13. #35266	C₃	direct (N × H)
15. C₂×C₃×#126	C₂²	semidirect
23. C₃×#397	C₂²	semidirect
24. C₃×#397	C₂²	semidirect
25. C₃×#397	C₂²	semidirect
26. C₃×#396	C₂²	semidirect
35. C₃×#389	C₂²	semidirect
36. C₃×#389	C₂²	semidirect
37. C₃×#389	C₂²	semidirect
38. C₃×#389	C₂²	semidirect
39. C₃×#389	C₂²	semidirect
40. C₃×#388	C₂²	semidirect
41. C₃×#388	C₂²	semidirect
42. C₃×#388	C₂²	semidirect
45. C₃×#384	C₂²	semidirect
46. C₃×#382	C₂²	semidirect
50. C₃×C₄×C₄⋊C₄	C₂²	semidirect
51. C₃×C₄×C₄⋊C₄	C₂²	semidirect
52. C₃×C₄×C₄⋊C₄	C₂²	semidirect
54. C₃×#376	C₂²	semidirect
55. C₃×C₄³	C₂²	semidirect
56. #2860	C₂×C₃	semidirect
57. #2644	C₂×C₃	semidirect
58. #2513	C₂×C₃	semidirect
59. #2512	C₂×C₃	semidirect
60. #2480	C₂×C₃	semidirect
61. #2317	C₂×C₃	semidirect
62. #2316	C₂×C₃	semidirect
65. #2296	C₂×C₃	semidirect
67. C₄×#117	C₂×C₃	semidirect
122. C₂×#126	C₂²×C₃	semidirect
130. #397	C₂²×C₃	semidirect
131. #397	C₂²×C₃	semidirect
132. #397	C₂²×C₃	semidirect
133. #396	C₂²×C₃	semidirect
142. #389	C₂²×C₃	semidirect
143. #389	C₂²×C₃	semidirect
144. #389	C₂²×C₃	semidirect
145. #389	C₂²×C₃	semidirect
146. #389	C₂²×C₃	semidirect
147. #388	C₂²×C₃	semidirect
148. #388	C₂²×C₃	semidirect
149. #388	C₂²×C₃	semidirect
152. #384	C₂²×C₃	semidirect
153. #382	C₂²×C₃	semidirect
157. C₄×C₄⋊C₄	C₂²×C₃	semidirect
158. C₄×C₄⋊C₄	C₂²×C₃	semidirect
159. C₄×C₄⋊C₄	C₂²×C₃	semidirect
161. #376	C₂²×C₃	semidirect
162. C₄³	C₂²×C₃	semidirect
318. C₂×C₃×C₄	#126	semidirect
454. C₂×C₄	C₃×#126	semidirect
495. C₃	#35266	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×#2644	2
C₃×#2513	2
C₃×#2512	2
C₃×#2480	2
C₃×#2317	2
C₃×#2316	2
C₃×#2309	2
C₃×#2296	2
C₂×C₃×#390	2
C₃×C₄×#117	2
#35266	3

Subgroups — C3×#35266 #10653873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35266 #10653873