Subgroups — C₃×#35332 #10653939

Order 768.

2186 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2850	C₂	1	2	yes	maximal, complemented
6	C₃×#2642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2620	C₂	1	2	yes	maximal, complemented
9	C₃×#2559	C₂	1	8	yes	maximal, complemented
10	C₃×#2558	C₂	1	8	yes	maximal, complemented
11	C₃×#2326	C₂	1	2	yes	maximal, complemented
12	C₃×C₄×#124	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	#35332	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃×#541	—	2	8	no	—
16	C₃×#540	—	2	8	no	—
17	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₃×#126	C₂²	1	4	yes	—
20	C₂×C₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₃×#125	C₂²	1	4	yes	—
23	C₂×C₃×#124	C₂²	1	2	yes	—
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#123	C₂²	1	4	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×#121	C₂²	1	2	yes	—
28	C₂×C₃×#121	C₂²	1	4	yes	—
29	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₃×#400	C₂²	1	8	yes	—
35	C₃×#396	C₂²	1	8	yes	—
36	C₃×#394	C₂²	1	8	yes	—
37	C₃×#394	C₂²	1	8	yes	—
38	C₃×#391	C₂²	1	2	yes	—
39	C₃×#391	C₂²	1	2	yes	—
40	C₃×#390	C₂²	1	2	yes	—
41	C₃×#390	C₂²	1	2	yes	—
42	C₃×#390	C₂²	1	8	yes	—
43	C₃×#389	C₂²	1	8	yes	—
44	C₃×#388	C₂²	1	8	yes	—
45	C₃×#388	C₂²	1	8	yes	—
46	C₃×#388	C₂²	1	8	yes	—
47	C₃×#386	C₂²	1	8	yes	—
48	C₃×#385	C₂²	1	8	yes	—
49	C₃×#384	C₂²	1	2	yes	—
50	C₃×#382	C₂²	1	2	yes	—
51	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
52	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₃×C₄×C₂²⋊C₄	C₂²	1	8	yes	—
54	C₃×#376	C₂²	1	1	yes	characteristic
55	C₃×#376	C₂²	1	1	yes	characteristic
56	C₃×C₄³	C₂²	1	1	yes	characteristic
57	C₃×C₄³	C₂²	1	1	yes	characteristic
58	C₂×#541	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#540	C₂×C₃	1	1	yes	characteristic
60	#2859	C₂×C₃	1	1	yes	characteristic, complemented
61	#2858	C₂×C₃	1	1	yes	characteristic, complemented
62	#2850	C₂×C₃	1	2	yes	complemented
63	#2642	C₂×C₃	1	1	yes	characteristic, complemented
64	#2641	C₂×C₃	1	1	yes	characteristic, complemented
65	#2620	C₂×C₃	1	2	yes	complemented
66	#2559	C₂×C₃	1	8	yes	complemented
67	#2558	C₂×C₃	1	8	yes	complemented
68	#2326	C₂×C₃	1	2	yes	complemented
69	C₄×#124	C₂×C₃	1	2	yes	complemented
70	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂²×C₃×Q₈	C₂³	1	2	yes	—
72	C₂²×C₃×D₄	C₂³	1	2	yes	—
73	C₂²×C₃×D₄	C₂³	1	4	yes	—
74	C₂²×C₃×D₄	C₂³	1	4	yes	—
75	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
76	C₂³×C₃×C₄	C₂³	1	4	yes	—
77	C₂³×C₃×C₄	C₂³	1	2	yes	—
78	C₃×C₄⋊Q₈	—	2	4	no	—
79	C₃×#127	—	2	4	no	—
80	C₃×#126	—	2	16	no	—
81	C₃×#125	—	2	16	no	—
82	C₃×#125	—	2	4	no	—
83	C₃×#125	—	2	4	no	—
84	C₃×#124	—	2	8	no	—
85	C₃×#124	—	2	8	no	—
86	C₃×#123	—	2	16	no	—
87	C₃×C₂²⋊Q₈	—	2	8	no	—
88	C₃×#121	—	2	8	no	—
89	C₃×#121	—	2	16	no	—
90	C₃×C₄×Q₈	—	2	8	no	—
91	C₃×C₄×D₄	—	2	8	no	—
92	C₃×#117	—	2	4	no	—
93	C₃×#117	D₄	1	8	yes	—
94	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
103	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₃×C₄²	—	2	4	no	—
114	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
115	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂³	1	4	yes	—
117	C₂×C₃×C₄²	C₂³	1	2	yes	—
118	C₂×C₃×C₄²	C₂³	1	4	yes	—
119	C₂×C₃×C₄²	C₂³	1	4	yes	—
120	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
124	C₃×#95	C₂³	1	4	yes	—
125	C₃×#95	C₂³	1	4	yes	—
126	C₃×#95	C₂³	1	8	yes	—
127	C₃×#95	C₂³	1	8	yes	—
128	C₃×#95	C₂³	1	8	yes	—
129	#541	—	2	8	no	—
130	#540	—	2	8	no	—
131	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₂×#127	C₂²×C₃	1	1	yes	characteristic
133	C₂×#126	C₂²×C₃	1	4	yes	—
134	C₂×#125	C₂²×C₃	1	1	yes	characteristic
135	C₂×#125	C₂²×C₃	1	1	yes	characteristic
136	C₂×#125	C₂²×C₃	1	4	yes	—
137	C₂×#124	C₂²×C₃	1	2	yes	—
138	C₂×#124	C₂²×C₃	1	2	yes	—
139	C₂×#123	C₂²×C₃	1	4	yes	—
140	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
141	C₂×#121	C₂²×C₃	1	2	yes	—
142	C₂×#121	C₂²×C₃	1	4	yes	—
143	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
144	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
145	C₂×#117	C₂²×C₃	1	1	yes	characteristic
146	C₂×#117	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
148	#400	C₂²×C₃	1	8	yes	—
149	#396	C₂²×C₃	1	8	yes	—
150	#394	C₂²×C₃	1	8	yes	—
151	#394	C₂²×C₃	1	8	yes	—
152	#391	C₂²×C₃	1	2	yes	—
153	#391	C₂²×C₃	1	2	yes	—
154	#390	C₂²×C₃	1	2	yes	—
155	#390	C₂²×C₃	1	8	yes	—
156	#390	C₂²×C₃	1	2	yes	—
157	#389	C₂²×C₃	1	8	yes	—
158	#388	C₂²×C₃	1	8	yes	—
159	#388	C₂²×C₃	1	8	yes	—
160	#388	C₂²×C₃	1	8	yes	—
161	#386	C₂²×C₃	1	8	yes	—
162	#385	C₂²×C₃	1	8	yes	—
163	#384	C₂²×C₃	1	2	yes	—
164	#382	C₂²×C₃	1	2	yes	—
165	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
166	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
167	C₄×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
168	#376	C₂²×C₃	1	1	yes	characteristic
169	#376	C₂²×C₃	1	1	yes	characteristic
170	C₄³	C₂²×C₃	1	1	yes	characteristic
171	C₄³	C₂²×C₃	1	1	yes	characteristic
172	C₂⁴×C₃	C₂⁴	1	4	yes	—
173	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	—	2	4	no	—
176	C₂×C₃×Q₈	—	2	4	no	—
177	C₂×C₃×D₄	—	2	8	no	—
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	2	4	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	4	8	no	—
183	C₂×C₃×D₄	—	4	8	no	—
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	—	2	2	no	—
186	C₂²×C₃×C₄	—	2	4	no	—
187	C₂²×C₃×C₄	—	2	8	no	—
188	C₂²×C₃×C₄	—	4	4	no	—
189	C₂²×C₃×C₄	—	4	8	no	—
190	C₂²×C₃×C₄	C₂×D₄	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	4	yes	—
194	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
195	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
196	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
197	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
198	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
200	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
201	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
202	C₃×C₄⋊C₄	—	2	4	no	—
203	C₃×C₄⋊C₄	—	2	4	no	—
204	C₃×C₄⋊C₄	—	2	8	no	—
205	C₃×C₄⋊C₄	—	2	8	no	—
206	C₃×C₄⋊C₄	—	2	8	no	—
207	C₃×C₄⋊C₄	—	2	8	no	—
208	C₃×C₄⋊C₄	—	2	8	no	—
209	C₃×C₄⋊C₄	—	2	4	no	—
210	C₃×C₄⋊C₄	—	4	8	no	—
211	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
212	C₃×C₂²⋊C₄	—	2	8	no	—
213	C₃×C₂²⋊C₄	—	2	8	no	—
214	C₃×C₂²⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	2	4	no	—
216	C₃×C₂²⋊C₄	—	2	16	no	—
217	C₃×C₂²⋊C₄	—	2	16	no	—
218	C₃×C₂²⋊C₄	—	4	8	no	—
219	C₃×C₂²⋊C₄	—	4	8	no	—
220	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
221	C₃×C₄²	—	2	8	no	—
222	C₃×C₄²	—	2	4	no	—
223	C₃×C₄²	—	2	2	no	—
224	C₃×C₄²	—	2	2	no	—
225	C₃×C₄²	—	4	4	no	—
226	C₃×C₄²	—	4	4	no	—
227	C₃×C₄²	C₂×D₄	1	4	yes	—
228	C₃×C₄²	C₂×D₄	1	4	yes	—
229	C₃×C₄²	#41	1	4	yes	—
230	C₃×C₄²	#41	1	4	yes	—
231	C₂²×Q₈	C₂³×C₃	1	2	yes	—
232	C₂²×D₄	C₂³×C₃	1	2	yes	—
233	C₂²×D₄	C₂³×C₃	1	4	yes	—
234	C₂²×D₄	C₂³×C₃	1	4	yes	—
235	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₃	1	4	yes	—
237	C₂³×C₄	C₂³×C₃	1	2	yes	—
238	C₄⋊Q₈	—	2	4	no	—
239	#127	—	2	4	no	—
240	#126	—	2	16	no	—
241	#125	—	2	16	no	—
242	#125	—	2	4	no	—
243	#125	—	2	4	no	—
244	#124	—	2	8	no	—
245	#124	—	2	8	no	—
246	#123	—	2	16	no	—
247	C₂²⋊Q₈	—	2	8	no	—
248	#121	—	2	8	no	—
249	#121	—	2	16	no	—
250	C₄×Q₈	—	2	8	no	—
251	C₄×D₄	—	2	8	no	—
252	#117	—	2	4	no	—
253	#117	C₃×D₄	1	8	yes	—
254	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃	1	4	yes	—
276	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₃	1	2	yes	—
278	C₂×C₄²	C₂³×C₃	1	4	yes	—
279	C₂×C₄²	C₂³×C₃	1	4	yes	—
280	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
284	#95	C₂³×C₃	1	4	yes	—
285	#95	C₂³×C₃	1	4	yes	—
286	#95	C₂³×C₃	1	8	yes	—
287	#95	C₂³×C₃	1	8	yes	—
288	#95	C₂³×C₃	1	8	yes	—
289	C₂³×C₃	—	2	1	no	—
290	C₂³×C₃	—	2	1	no	—
291	C₂³×C₃	—	2	4	no	—
292	C₂³×C₃	—	2	4	no	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	2	4	no	—
295	C₂³×C₃	—	2	8	no	—
296	C₂³×C₃	—	2	8	no	—
297	C₂³×C₃	C₂²×D₄	1	2	yes	—
298	C₂³×C₃	C₂⁵	1	1	yes	characteristic
299	C₃×Q₈	—	4	8	no	—
300	C₃×D₄	—	4	8	no	—
301	C₃×D₄	—	8	8	no	—
302	C₃×D₄	—	8	8	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	8	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	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	8	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	2	8	no	—
321	C₂×C₃×C₄	—	4	8	no	—
322	C₂×C₃×C₄	—	8	8	no	—
323	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
324	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
325	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
326	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
327	C₂×C₃×C₄	C₂×#41	1	4	yes	—
328	C₂×C₃×C₄	C₂×#41	1	4	yes	—
329	C₂×C₃×C₄	C₂×#41	1	2	yes	—
330	C₂×C₃×C₄	C₂×#41	1	2	yes	—
331	C₂⁴	C₂⁴×C₃	1	4	yes	—
332	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	8	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	8	no	—
349	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	4	8	no	—
370	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
380	C₄²	—	2	8	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	4	no	—
385	C₄²	—	4	4	no	—
386	C₄²	C₂×C₃×D₄	1	4	yes	—
387	C₄²	C₂×C₃×D₄	1	4	yes	—
388	C₄²	C₃×#41	1	4	yes	—
389	C₄²	C₃×#41	1	4	yes	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	—	4	4	no	—
395	C₂²×C₃	—	4	8	no	—
396	C₂²×C₃	—	4	4	no	—
397	C₂²×C₃	—	4	4	no	—
398	C₂²×C₃	—	4	8	no	—
399	C₂²×C₃	C₂³×D₄	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	#585	1	4	yes	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	4	no	—
405	C₃×C₄	—	2	4	no	—
406	C₃×C₄	—	2	4	no	—
407	C₃×C₄	—	2	4	no	—
408	C₃×C₄	—	4	4	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	4	no	—
411	C₃×C₄	—	4	4	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	#532	1	4	yes	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	8	no	—
422	C₂³	C₂²×C₃×D₄	1	2	yes	—
423	C₂³	C₂⁵×C₃	1	1	yes	characteristic
424	Q₈	—	4	8	no	—
425	D₄	—	4	8	no	—
426	D₄	—	8	8	no	—
427	D₄	—	8	8	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	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	4	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	—	8	8	no	—
448	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
449	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
450	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
451	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
452	C₂×C₄	C₂×C₃×#41	1	4	yes	—
453	C₂×C₄	C₂×C₃×#41	1	4	yes	—
454	C₂×C₄	C₂×C₃×#41	1	2	yes	—
455	C₂×C₄	C₂×C₃×#41	1	2	yes	—
456	C₂×C₃	—	4	2	no	—
457	C₂×C₃	—	8	4	no	—
458	C₂×C₃	C₂×#532	1	1	yes	characteristic
459	C₂×C₃	#3455	1	2	yes	—
460	C₂×C₃	#3500	1	2	yes	—
461	C₂×C₃	#3512	1	2	yes	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	8	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
472	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
473	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
474	C₂²	C₃×#585	1	4	yes	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	C₃×#532	1	4	yes	—
486	C₃	#35332	1	1	yes	characteristic, direct product factor, Sylow
487	C₂	—	4	2	no	—
488	C₂	—	8	4	no	—
489	C₂	C₂×C₃×#532	1	1	yes	characteristic
490	C₂	C₃×#3455	1	2	yes	—
491	C₂	C₃×#3500	1	2	yes	—
492	C₂	C₃×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#540	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. C₂×C₃×#541	C₂	semidirect
3. C₃×#2859	C₂	semidirect
4. C₃×#2858	C₂	semidirect
5. C₃×#2850	C₂	semidirect
6. C₃×#2642	C₂	semidirect
7. C₃×#2641	C₂	semidirect
8. C₃×#2620	C₂	semidirect
9. C₃×#2559	C₂	semidirect
10. C₃×#2558	C₂	semidirect
11. C₃×#2326	C₂	semidirect
12. C₃×C₄×#124	C₂	semidirect
13. C₃×C₄×#117	C₂	semidirect
14. #35332	C₃	direct (N × H)
58. C₂×#541	C₂×C₃	semidirect
60. #2859	C₂×C₃	semidirect
61. #2858	C₂×C₃	semidirect
62. #2850	C₂×C₃	semidirect
63. #2642	C₂×C₃	semidirect
64. #2641	C₂×C₃	semidirect
65. #2620	C₂×C₃	semidirect
66. #2559	C₂×C₃	semidirect
67. #2558	C₂×C₃	semidirect
68. #2326	C₂×C₃	semidirect
69. C₄×#124	C₂×C₃	semidirect
70. C₄×#117	C₂×C₃	semidirect
486. C₃	#35332	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#541	2
C₂×C₃×#540	2
C₃×#2859	2
C₃×#2858	2
C₃×#2850	2
C₃×#2642	2
C₃×#2641	2
C₃×#2620	2
C₃×#2559	2
C₃×#2558	2
C₃×#2326	2
C₃×C₄×#124	2
C₃×C₄×#117	2
#35332	3

Subgroups — C3×#35332 #10653939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35332 #10653939