Subgroups — C₃×#34490 #10653097

Order 768.

1840 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#557	C₂	1	1	yes	maximal, characteristic
2	C₃×#2382	C₂	1	2	yes	maximal
3	C₃×#2381	C₂	1	2	yes	maximal
4	C₃×#2371	C₂	1	2	yes	maximal
5	C₃×#2370	C₂	1	1	yes	maximal, characteristic
6	C₃×#2370	C₂	1	1	yes	maximal, characteristic
7	C₃×#2369	C₂	1	1	yes	maximal, characteristic
8	C₃×#2356	C₂	1	2	yes	maximal
9	C₃×#2356	C₂	1	1	yes	maximal, characteristic
10	C₃×#2356	C₂	1	1	yes	maximal, characteristic
11	C₃×#2355	C₂	1	1	yes	maximal, characteristic
12	C₃×#2355	C₂	1	1	yes	maximal, characteristic
13	C₃×#2336	C₂	1	2	yes	maximal
14	C₃×#2336	C₂	1	2	yes	maximal
15	C₃×#2331	C₂	1	1	yes	maximal, characteristic
16	C₃×#2331	C₂	1	2	yes	maximal
17	C₃×#2330	C₂	1	1	yes	maximal, characteristic
18	C₃×#2320	C₂	1	2	yes	maximal
19	C₃×#2320	C₂	1	1	yes	maximal, characteristic
20	C₃×#2320	C₂	1	1	yes	maximal, characteristic
21	C₃×C₄×#125	C₂	1	1	yes	maximal, characteristic
22	C₃×#2295	C₂	1	1	yes	maximal, characteristic
23	C₃×#2295	C₂	1	1	yes	maximal, characteristic
24	#34490	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#557	C₄	1	16	yes	complemented
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₃×#125	C₂²	1	2	yes	—
31	C₂×C₃×#125	C₂²	1	2	yes	—
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
37	C₃×#391	C₂²	1	2	yes	—
38	C₃×#391	C₂²	1	2	yes	—
39	C₃×#391	C₂²	1	1	yes	characteristic
40	C₃×#391	C₂²	1	2	yes	—
41	C₃×#391	C₂²	1	2	yes	—
42	C₃×#391	C₂²	1	1	yes	characteristic
43	C₃×#391	C₂²	1	1	yes	characteristic
44	C₃×#391	C₂²	1	1	yes	characteristic
45	C₃×#391	C₂²	1	2	yes	—
46	C₃×#391	C₂²	1	1	yes	characteristic
47	C₃×#391	C₂²	1	1	yes	characteristic
48	C₃×#389	C₂²	1	1	yes	characteristic
49	C₃×#389	C₂²	1	1	yes	characteristic
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	1	yes	characteristic
52	C₃×#389	C₂²	1	2	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	1	yes	characteristic
55	C₃×#389	C₂²	1	1	yes	characteristic
56	C₃×#389	C₂²	1	1	yes	characteristic
57	C₃×#389	C₂²	1	1	yes	characteristic
58	C₃×#389	C₂²	1	1	yes	characteristic
59	C₃×#389	C₂²	1	2	yes	—
60	C₃×#389	C₂²	1	2	yes	—
61	C₃×#387	C₂²	1	2	yes	—
62	C₃×#387	C₂²	1	2	yes	—
63	C₃×#387	C₂²	1	2	yes	—
64	C₃×#387	C₂²	1	2	yes	—
65	C₃×#387	C₂²	1	1	yes	characteristic
66	C₃×#387	C₂²	1	2	yes	—
67	C₃×#387	C₂²	1	2	yes	—
68	C₃×#387	C₂²	1	2	yes	—
69	C₃×#387	C₂²	1	2	yes	—
70	C₃×#387	C₂²	1	2	yes	—
71	C₃×#387	C₂²	1	2	yes	—
72	C₃×#387	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	1	yes	characteristic
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	1	yes	characteristic
83	C₃×#387	C₂²	1	1	yes	characteristic
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×#384	C₂²	1	1	yes	characteristic
90	C₃×#383	C₂²	1	2	yes	—
91	C₃×#383	C₂²	1	2	yes	—
92	C₃×#383	C₂²	1	2	yes	—
93	C₃×#383	C₂²	1	2	yes	—
94	C₃×#382	C₂²	1	2	yes	—
95	C₃×#382	C₂²	1	2	yes	—
96	C₃×#382	C₂²	1	1	yes	characteristic
97	C₃×#382	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	1	yes	characteristic
99	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
100	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
119	C₃×#376	C₂²	1	2	yes	—
120	C₃×#376	C₂²	1	2	yes	—
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₃×#376	C₂²	1	1	yes	characteristic
123	C₃×#376	C₂²	1	2	yes	—
124	C₃×C₄³	C₂²	1	1	yes	characteristic
125	C₂×#557	C₂×C₃	1	1	yes	characteristic
126	#2382	C₂×C₃	1	2	yes	—
127	#2381	C₂×C₃	1	2	yes	—
128	#2371	C₂×C₃	1	2	yes	—
129	#2370	C₂×C₃	1	1	yes	characteristic
130	#2370	C₂×C₃	1	1	yes	characteristic
131	#2369	C₂×C₃	1	1	yes	characteristic
132	#2356	C₂×C₃	1	1	yes	characteristic
133	#2356	C₂×C₃	1	2	yes	—
134	#2356	C₂×C₃	1	1	yes	characteristic
135	#2355	C₂×C₃	1	1	yes	characteristic
136	#2355	C₂×C₃	1	1	yes	characteristic
137	#2336	C₂×C₃	1	2	yes	—
138	#2336	C₂×C₃	1	2	yes	—
139	#2331	C₂×C₃	1	1	yes	characteristic
140	#2331	C₂×C₃	1	2	yes	—
141	#2330	C₂×C₃	1	1	yes	characteristic
142	#2320	C₂×C₃	1	1	yes	characteristic
143	#2320	C₂×C₃	1	1	yes	characteristic
144	#2320	C₂×C₃	1	2	yes	—
145	C₄×#125	C₂×C₃	1	1	yes	characteristic
146	#2295	C₂×C₃	1	1	yes	characteristic
147	#2295	C₂×C₃	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
152	C₃×C₄⋊Q₈	C₂×C₄	1	16	yes	—
153	C₃×#125	C₂×C₄	1	8	yes	—
154	C₃×#125	C₂×C₄	1	8	yes	—
155	C₃×#125	C₂×C₄	1	16	yes	—
156	C₃×#125	C₂×C₄	1	16	yes	—
157	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
158	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
159	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
160	C₃×C₄×Q₈	C₂×C₄	1	16	yes	—
161	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄²	C₂³	1	2	yes	—
204	C₂×C₃×C₄²	C₂³	1	2	yes	—
205	C₂×C₃×C₄²	C₂³	1	2	yes	—
206	C₂×C₃×C₄²	C₂³	1	2	yes	—
207	C₂×C₃×C₄²	C₂³	1	2	yes	—
208	C₂×C₃×C₄²	C₂³	1	2	yes	—
209	C₂×C₃×C₄²	C₂³	1	2	yes	—
210	C₂×C₃×C₄²	C₂³	1	2	yes	—
211	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄²	C₂³	1	2	yes	—
213	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	2	yes	—
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	1	yes	characteristic
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	1	yes	characteristic
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	1	yes	characteristic
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	1	yes	characteristic
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	1	yes	characteristic
230	C₃×#95	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	1	yes	characteristic
233	C₃×#95	C₂³	1	1	yes	characteristic
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	1	yes	characteristic
236	C₃×#95	C₂³	1	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	1	yes	characteristic
257	C₃×#95	C₂³	1	2	yes	—
258	#557	C₃×C₄	1	16	yes	complemented
259	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
261	C₂×#125	C₂²×C₃	1	1	yes	characteristic
262	C₂×#125	C₂²×C₃	1	1	yes	characteristic
263	C₂×#125	C₂²×C₃	1	2	yes	—
264	C₂×#125	C₂²×C₃	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
267	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
270	#391	C₂²×C₃	1	1	yes	characteristic
271	#391	C₂²×C₃	1	2	yes	—
272	#391	C₂²×C₃	1	1	yes	characteristic
273	#391	C₂²×C₃	1	1	yes	characteristic
274	#391	C₂²×C₃	1	2	yes	—
275	#391	C₂²×C₃	1	1	yes	characteristic
276	#391	C₂²×C₃	1	2	yes	—
277	#391	C₂²×C₃	1	2	yes	—
278	#391	C₂²×C₃	1	2	yes	—
279	#391	C₂²×C₃	1	1	yes	characteristic
280	#391	C₂²×C₃	1	1	yes	characteristic
281	#389	C₂²×C₃	1	1	yes	characteristic
282	#389	C₂²×C₃	1	1	yes	characteristic
283	#389	C₂²×C₃	1	2	yes	—
284	#389	C₂²×C₃	1	1	yes	characteristic
285	#389	C₂²×C₃	1	1	yes	characteristic
286	#389	C₂²×C₃	1	2	yes	—
287	#389	C₂²×C₃	1	2	yes	—
288	#389	C₂²×C₃	1	1	yes	characteristic
289	#389	C₂²×C₃	1	2	yes	—
290	#389	C₂²×C₃	1	1	yes	characteristic
291	#389	C₂²×C₃	1	2	yes	—
292	#389	C₂²×C₃	1	1	yes	characteristic
293	#389	C₂²×C₃	1	1	yes	characteristic
294	#387	C₂²×C₃	1	2	yes	—
295	#387	C₂²×C₃	1	2	yes	—
296	#387	C₂²×C₃	1	1	yes	characteristic
297	#387	C₂²×C₃	1	2	yes	—
298	#387	C₂²×C₃	1	2	yes	—
299	#387	C₂²×C₃	1	2	yes	—
300	#387	C₂²×C₃	1	2	yes	—
301	#387	C₂²×C₃	1	2	yes	—
302	#387	C₂²×C₃	1	2	yes	—
303	#387	C₂²×C₃	1	2	yes	—
304	#387	C₂²×C₃	1	2	yes	—
305	#387	C₂²×C₃	1	2	yes	—
306	#387	C₂²×C₃	1	2	yes	—
307	#387	C₂²×C₃	1	2	yes	—
308	#387	C₂²×C₃	1	2	yes	—
309	#387	C₂²×C₃	1	2	yes	—
310	#387	C₂²×C₃	1	1	yes	characteristic
311	#387	C₂²×C₃	1	2	yes	—
312	#387	C₂²×C₃	1	2	yes	—
313	#387	C₂²×C₃	1	2	yes	—
314	#387	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#387	C₂²×C₃	1	2	yes	—
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	1	yes	characteristic
320	#387	C₂²×C₃	1	1	yes	characteristic
321	#387	C₂²×C₃	1	2	yes	—
322	#384	C₂²×C₃	1	1	yes	characteristic
323	#383	C₂²×C₃	1	2	yes	—
324	#383	C₂²×C₃	1	2	yes	—
325	#383	C₂²×C₃	1	2	yes	—
326	#383	C₂²×C₃	1	2	yes	—
327	#382	C₂²×C₃	1	1	yes	characteristic
328	#382	C₂²×C₃	1	2	yes	—
329	#382	C₂²×C₃	1	2	yes	—
330	#382	C₂²×C₃	1	2	yes	—
331	#382	C₂²×C₃	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
333	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
336	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
337	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
344	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
347	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	#376	C₂²×C₃	1	1	yes	characteristic
353	#376	C₂²×C₃	1	1	yes	characteristic
354	#376	C₂²×C₃	1	2	yes	—
355	#376	C₂²×C₃	1	2	yes	—
356	#376	C₂²×C₃	1	2	yes	—
357	C₄³	C₂²×C₃	1	1	yes	characteristic
358	C₂×C₃×Q₈	—	2	2	no	—
359	C₂×C₃×Q₈	—	2	2	no	—
360	C₂×C₃×Q₈	—	4	1	no	—
361	C₂×C₃×Q₈	—	4	2	no	—
362	C₂×C₃×Q₈	—	4	2	no	—
363	C₂×C₃×Q₈	—	4	1	no	—
364	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
365	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
366	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
367	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
390	C₃×C₄⋊C₄	—	2	2	no	—
391	C₃×C₄⋊C₄	—	2	2	no	—
392	C₃×C₄⋊C₄	—	2	2	no	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	—	2	2	no	—
396	C₃×C₄⋊C₄	—	4	1	no	—
397	C₃×C₄⋊C₄	—	4	2	no	—
398	C₃×C₄⋊C₄	—	4	2	no	—
399	C₃×C₄⋊C₄	—	4	1	no	—
400	C₃×C₄⋊C₄	—	4	1	no	—
401	C₃×C₄⋊C₄	—	4	2	no	—
402	C₃×C₄⋊C₄	—	4	2	no	—
403	C₃×C₄⋊C₄	—	4	2	no	—
404	C₃×C₄⋊C₄	—	4	1	no	—
405	C₃×C₄⋊C₄	—	4	2	no	—
406	C₃×C₄⋊C₄	—	4	2	no	—
407	C₃×C₄⋊C₄	—	4	2	no	—
408	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
409	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
410	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
411	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
412	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
413	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
414	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
415	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
416	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
417	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
418	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
419	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
420	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
421	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
422	C₃×C₄²	—	2	2	no	—
423	C₃×C₄²	—	2	4	no	—
424	C₃×C₄²	—	2	2	no	—
425	C₃×C₄²	—	2	2	no	—
426	C₃×C₄²	—	2	2	no	—
427	C₃×C₄²	—	2	2	no	—
428	C₃×C₄²	—	4	2	no	—
429	C₃×C₄²	—	4	1	no	—
430	C₃×C₄²	—	4	2	no	—
431	C₃×C₄²	—	4	1	no	—
432	C₃×C₄²	—	4	2	no	—
433	C₃×C₄²	—	4	2	no	—
434	C₃×C₄²	—	4	2	no	—
435	C₃×C₄²	—	4	2	no	—
436	C₃×C₄²	—	4	2	no	—
437	C₃×C₄²	—	4	2	no	—
438	C₃×C₄²	—	4	1	no	—
439	C₃×C₄²	C₂²×C₄	1	8	yes	—
440	C₃×C₄²	C₂²×C₄	1	8	yes	—
441	C₃×C₄²	C₂²×C₄	1	4	yes	—
442	C₃×C₄²	C₂²×C₄	1	4	yes	—
443	C₃×C₄²	C₂²×C₄	1	8	yes	—
444	C₃×C₄²	C₂²×C₄	1	4	yes	—
445	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₃	1	2	yes	—
447	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
448	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	—
449	C₄⋊Q₈	C₂×C₃×C₄	1	16	yes	—
450	#125	C₂×C₃×C₄	1	8	yes	—
451	#125	C₂×C₃×C₄	1	8	yes	—
452	#125	C₂×C₃×C₄	1	16	yes	—
453	#125	C₂×C₃×C₄	1	16	yes	—
454	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
455	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
456	C₄×Q₈	C₂×C₃×C₄	1	16	yes	—
457	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
458	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₃	1	2	yes	—
501	C₂×C₄²	C₂³×C₃	1	2	yes	—
502	C₂×C₄²	C₂³×C₃	1	2	yes	—
503	C₂×C₄²	C₂³×C₃	1	2	yes	—
504	C₂×C₄²	C₂³×C₃	1	2	yes	—
505	C₂×C₄²	C₂³×C₃	1	2	yes	—
506	C₂×C₄²	C₂³×C₃	1	2	yes	—
507	C₂×C₄²	C₂³×C₃	1	2	yes	—
508	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₃	1	2	yes	—
510	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₃	1	2	yes	—
512	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₃	1	2	yes	—
514	#95	C₂³×C₃	1	1	yes	characteristic
515	#95	C₂³×C₃	1	2	yes	—
516	#95	C₂³×C₃	1	1	yes	characteristic
517	#95	C₂³×C₃	1	2	yes	—
518	#95	C₂³×C₃	1	2	yes	—
519	#95	C₂³×C₃	1	1	yes	characteristic
520	#95	C₂³×C₃	1	2	yes	—
521	#95	C₂³×C₃	1	1	yes	characteristic
522	#95	C₂³×C₃	1	2	yes	—
523	#95	C₂³×C₃	1	2	yes	—
524	#95	C₂³×C₃	1	2	yes	—
525	#95	C₂³×C₃	1	2	yes	—
526	#95	C₂³×C₃	1	1	yes	characteristic
527	#95	C₂³×C₃	1	1	yes	characteristic
528	#95	C₂³×C₃	1	1	yes	characteristic
529	#95	C₂³×C₃	1	1	yes	characteristic
530	#95	C₂³×C₃	1	1	yes	characteristic
531	#95	C₂³×C₃	1	2	yes	—
532	#95	C₂³×C₃	1	1	yes	characteristic
533	#95	C₂³×C₃	1	1	yes	characteristic
534	#95	C₂³×C₃	1	1	yes	characteristic
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	1	yes	characteristic
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	2	yes	—
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	#95	C₂³×C₃	1	1	yes	characteristic
554	#95	C₂³×C₃	1	2	yes	—
555	C₂³×C₃	C₂⁵	1	1	yes	characteristic
556	C₃×Q₈	—	2	8	no	—
557	C₃×Q₈	—	4	4	no	—
558	C₃×Q₈	—	4	8	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	2	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
615	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
616	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
617	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
618	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
619	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
620	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
621	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
622	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
623	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
624	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
625	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
626	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
627	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	—	4	1	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	1	no	—
634	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
635	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
636	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	1	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
679	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
680	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
681	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
682	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
683	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
684	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
685	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
686	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
687	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
688	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
689	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
690	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
691	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	1	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	1	no	—
702	C₄²	—	4	2	no	—
703	C₄²	—	4	2	no	—
704	C₄²	—	4	2	no	—
705	C₄²	—	4	2	no	—
706	C₄²	—	4	2	no	—
707	C₄²	—	4	2	no	—
708	C₄²	—	4	1	no	—
709	C₄²	C₂²×C₃×C₄	1	8	yes	—
710	C₄²	C₂²×C₃×C₄	1	8	yes	—
711	C₄²	C₂²×C₃×C₄	1	4	yes	—
712	C₄²	C₂²×C₃×C₄	1	4	yes	—
713	C₄²	C₂²×C₃×C₄	1	8	yes	—
714	C₄²	C₂²×C₃×C₄	1	4	yes	—
715	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
716	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
717	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
718	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
719	C₂²×C₃	#585	1	1	yes	characteristic
720	C₂²×C₃	#585	1	1	yes	characteristic
721	C₂²×C₃	#585	1	1	yes	characteristic
722	C₃×C₄	—	2	4	no	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	2	4	no	—
725	C₃×C₄	—	2	4	no	—
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	2	2	no	—
728	C₃×C₄	—	2	2	no	—
729	C₃×C₄	—	2	4	no	—
730	C₃×C₄	—	2	2	no	—
731	C₃×C₄	—	2	2	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	4	1	no	—
734	C₃×C₄	—	4	2	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	2	no	—
737	C₃×C₄	—	4	2	no	—
738	C₃×C₄	—	4	1	no	—
739	C₃×C₄	—	4	1	no	—
740	C₃×C₄	—	4	1	no	—
741	C₃×C₄	—	4	1	no	—
742	C₃×C₄	—	4	1	no	—
743	C₃×C₄	—	4	2	no	—
744	C₃×C₄	#519	1	4	yes	—
745	C₂³	C₂⁵×C₃	1	1	yes	characteristic
746	Q₈	—	2	8	no	—
747	Q₈	—	4	4	no	—
748	Q₈	—	4	8	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
805	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
806	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
807	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
808	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
809	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
810	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
811	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
812	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
813	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
814	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
815	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
816	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
817	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
818	C₂×C₃	C₂×#519	1	1	yes	characteristic
819	C₂×C₃	#3428	1	1	yes	characteristic
820	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
821	C₂×C₃	#3555	1	1	yes	characteristic
822	C₂×C₃	#3557	1	1	yes	characteristic
823	C₂×C₃	#3563	1	1	yes	characteristic
824	C₂×C₃	#3565	1	1	yes	characteristic
825	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
826	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
827	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
828	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
829	C₂²	C₃×#585	1	1	yes	characteristic
830	C₂²	C₃×#585	1	1	yes	characteristic
831	C₂²	C₃×#585	1	1	yes	characteristic
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	4	no	—
836	C₄	—	2	4	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	2	no	—
854	C₄	C₃×#519	1	4	yes	—
855	C₃	#34490	1	1	yes	characteristic, direct product factor, Sylow
856	C₂	C₂×C₃×#519	1	1	yes	characteristic
857	C₂	C₃×#3428	1	1	yes	characteristic
858	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂	C₃×#3555	1	1	yes	characteristic
860	C₂	C₃×#3557	1	1	yes	characteristic
861	C₂	C₃×#3563	1	1	yes	characteristic
862	C₂	C₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
24. #34490	C₃	direct (N × H)
25. C₃×#557	C₄	semidirect
258. #557	C₃×C₄	semidirect
855. C₃	#34490	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×#557	2
C₃×#2382	2
C₃×#2381	2
C₃×#2371	2
C₃×#2370	2
C₃×#2369	2
C₃×#2356	2
C₃×#2355	2
C₃×#2336	2
C₃×#2331	2
C₃×#2330	2
C₃×#2320	2
C₃×C₄×#125	2
C₃×#2295	2
#34490	3

Subgroups — C3×#34490 #10653097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34490 #10653097