Subgroups — C₃×#37691 #10656298

Order 768.

2010 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2732	C₂	1	2	yes	maximal
5	C₃×#2729	C₂	1	2	yes	maximal, complemented
6	C₃×#2720	C₂	1	2	yes	maximal, complemented
7	C₃×#2692	C₂	1	2	yes	maximal
8	C₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2465	C₂	1	2	yes	maximal, complemented
13	C₃×#2462	C₂	1	2	yes	maximal, complemented
14	C₃×#2446	C₂	1	2	yes	maximal, complemented
15	C₃×#2442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2423	C₂	1	2	yes	maximal, complemented
20	C₃×#2354	C₂	1	1	yes	maximal, characteristic
21	C₃×#2352	C₂	1	1	yes	maximal, characteristic
22	C₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic
24	#37691	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#544	—	2	8	no	—
26	C₃×#533	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₃×#125	C₂²	1	1	yes	characteristic
33	C₂×C₃×#125	C₂²	1	1	yes	characteristic
34	C₂×C₃×#125	C₂²	1	1	yes	characteristic
35	C₂×C₃×#125	C₂²	1	2	yes	—
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
41	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
42	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×#117	C₂²	1	1	yes	characteristic
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic
45	C₂×C₃×#117	C₂²	1	1	yes	characteristic
46	C₂×C₃×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
49	C₃×#400	C₂²	1	2	yes	—
50	C₃×#400	C₂²	1	2	yes	—
51	C₃×#399	C₂²	1	2	yes	—
52	C₃×#399	C₂²	1	2	yes	—
53	C₃×#399	C₂²	1	2	yes	—
54	C₃×#398	C₂²	1	2	yes	—
55	C₃×#398	C₂²	1	2	yes	—
56	C₃×#398	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#398	C₂²	1	2	yes	—
60	C₃×#396	C₂²	1	2	yes	—
61	C₃×#396	C₂²	1	2	yes	—
62	C₃×#396	C₂²	1	2	yes	—
63	C₃×#395	C₂²	1	2	yes	—
64	C₃×#395	C₂²	1	2	yes	—
65	C₃×#395	C₂²	1	2	yes	—
66	C₃×#395	C₂²	1	2	yes	—
67	C₃×#393	C₂²	1	2	yes	—
68	C₃×#393	C₂²	1	2	yes	—
69	C₃×#391	C₂²	1	2	yes	—
70	C₃×#391	C₂²	1	2	yes	—
71	C₃×#391	C₂²	1	2	yes	—
72	C₃×#391	C₂²	1	2	yes	—
73	C₃×#390	C₂²	1	2	yes	—
74	C₃×#389	C₂²	1	1	yes	characteristic
75	C₃×#389	C₂²	1	1	yes	characteristic
76	C₃×#389	C₂²	1	2	yes	—
77	C₃×#389	C₂²	1	1	yes	characteristic
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#389	C₂²	1	2	yes	—
80	C₃×#389	C₂²	1	1	yes	characteristic
81	C₃×#389	C₂²	1	1	yes	characteristic
82	C₃×#389	C₂²	1	2	yes	—
83	C₃×#389	C₂²	1	2	yes	—
84	C₃×#388	C₂²	1	1	yes	characteristic
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#388	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
94	C₃×#387	C₂²	1	1	yes	characteristic
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#387	C₂²	1	1	yes	characteristic
97	C₃×#387	C₂²	1	2	yes	—
98	C₃×#387	C₂²	1	2	yes	—
99	C₃×#386	C₂²	1	1	yes	characteristic
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#386	C₂²	1	1	yes	characteristic
102	C₃×#385	C₂²	1	2	yes	—
103	C₃×#385	C₂²	1	2	yes	—
104	C₃×#385	C₂²	1	1	yes	characteristic
105	C₃×#385	C₂²	1	1	yes	characteristic
106	C₃×#385	C₂²	1	2	yes	—
107	C₃×#384	C₂²	1	1	yes	characteristic
108	C₃×#384	C₂²	1	1	yes	characteristic
109	C₃×#384	C₂²	1	2	yes	—
110	C₃×#382	C₂²	1	1	yes	characteristic
111	C₃×#382	C₂²	1	1	yes	characteristic
112	C₃×#382	C₂²	1	1	yes	characteristic
113	C₃×#380	C₂²	1	1	yes	characteristic
114	C₃×#380	C₂²	1	1	yes	characteristic
115	C₃×#380	C₂²	1	2	yes	—
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₃×#376	C₂²	1	1	yes	characteristic
126	C₂×#544	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
128	#2851	C₂×C₃	1	1	yes	characteristic, complemented
129	#2732	C₂×C₃	1	2	yes	—
130	#2729	C₂×C₃	1	2	yes	complemented
131	#2720	C₂×C₃	1	2	yes	complemented
132	#2692	C₂×C₃	1	2	yes	—
133	#2660	C₂×C₃	1	1	yes	characteristic, complemented
134	#2628	C₂×C₃	1	1	yes	characteristic, complemented
135	#2552	C₂×C₃	1	1	yes	characteristic, complemented
136	#2550	C₂×C₃	1	1	yes	characteristic, complemented
137	#2465	C₂×C₃	1	2	yes	complemented
138	#2462	C₂×C₃	1	2	yes	complemented
139	#2446	C₂×C₃	1	2	yes	complemented
140	#2442	C₂×C₃	1	1	yes	characteristic, complemented
141	#2441	C₂×C₃	1	1	yes	characteristic, complemented
142	#2441	C₂×C₃	1	1	yes	characteristic, complemented
143	#2439	C₂×C₃	1	1	yes	characteristic, complemented
144	#2423	C₂×C₃	1	2	yes	complemented
145	#2354	C₂×C₃	1	1	yes	characteristic
146	#2352	C₂×C₃	1	1	yes	characteristic
147	#2331	C₂×C₃	1	1	yes	characteristic, complemented
148	#2290	C₂×C₃	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×Q₈	C₂³	1	2	yes	—
151	C₂²×C₃×Q₈	C₂³	1	2	yes	—
152	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₃×C₄	C₂³	1	2	yes	—
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	—	2	8	no	—
159	C₃×C₄⋊Q₈	—	2	4	no	—
160	C₃×C₄⋊Q₈	—	2	4	no	—
161	C₃×C₄⋊Q₈	D₄	1	8	yes	complemented
162	C₃×#125	—	2	4	no	—
163	C₃×#125	—	2	4	no	—
164	C₃×#125	—	2	8	no	—
165	C₃×#125	—	2	4	no	—
166	C₃×#125	—	2	4	no	—
167	C₃×C₂²⋊Q₈	—	2	8	no	—
168	C₃×C₂²⋊Q₈	—	2	8	no	—
169	C₃×C₂²⋊Q₈	—	2	8	no	—
170	C₃×C₂²⋊Q₈	—	2	8	no	—
171	C₃×C₄×Q₈	—	2	8	no	—
172	C₃×C₄×Q₈	—	2	8	no	—
173	C₃×C₄×D₄	Q₈	1	8	yes	complemented
174	C₃×#117	—	2	4	no	—
175	C₃×#117	—	2	4	no	—
176	C₃×#117	—	2	4	no	—
177	C₃×#117	—	2	4	no	—
178	C₂×C₃×C₄⋊C₄	—	2	4	no	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄²	—	2	4	no	—
230	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂³	1	2	yes	—
234	C₂×C₃×C₄²	C₂³	1	2	yes	—
235	C₂×C₃×C₄²	C₂³	1	2	yes	—
236	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₄²	C₂³	1	2	yes	—
239	C₂×C₃×C₄²	C₂³	1	2	yes	—
240	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	1	yes	characteristic
250	C₃×#95	C₂³	1	1	yes	characteristic
251	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
256	C₃×#95	C₂³	1	1	yes	characteristic
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	2	yes	—
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	#544	—	2	8	no	—
271	#533	—	2	8	no	—
272	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
276	C₂×#125	C₂²×C₃	1	1	yes	characteristic
277	C₂×#125	C₂²×C₃	1	1	yes	characteristic
278	C₂×#125	C₂²×C₃	1	1	yes	characteristic
279	C₂×#125	C₂²×C₃	1	1	yes	characteristic
280	C₂×#125	C₂²×C₃	1	2	yes	—
281	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
282	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
286	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
288	C₂×#117	C₂²×C₃	1	1	yes	characteristic
289	C₂×#117	C₂²×C₃	1	1	yes	characteristic
290	C₂×#117	C₂²×C₃	1	1	yes	characteristic
291	C₂×#117	C₂²×C₃	1	1	yes	characteristic
292	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
293	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
294	#400	C₂²×C₃	1	2	yes	—
295	#400	C₂²×C₃	1	2	yes	—
296	#399	C₂²×C₃	1	2	yes	—
297	#399	C₂²×C₃	1	2	yes	—
298	#399	C₂²×C₃	1	2	yes	—
299	#398	C₂²×C₃	1	2	yes	—
300	#398	C₂²×C₃	1	2	yes	—
301	#398	C₂²×C₃	1	2	yes	—
302	#398	C₂²×C₃	1	2	yes	—
303	#398	C₂²×C₃	1	2	yes	—
304	#398	C₂²×C₃	1	2	yes	—
305	#396	C₂²×C₃	1	2	yes	—
306	#396	C₂²×C₃	1	2	yes	—
307	#396	C₂²×C₃	1	2	yes	—
308	#395	C₂²×C₃	1	2	yes	—
309	#395	C₂²×C₃	1	2	yes	—
310	#395	C₂²×C₃	1	2	yes	—
311	#395	C₂²×C₃	1	2	yes	—
312	#393	C₂²×C₃	1	2	yes	—
313	#393	C₂²×C₃	1	2	yes	—
314	#391	C₂²×C₃	1	2	yes	—
315	#391	C₂²×C₃	1	2	yes	—
316	#391	C₂²×C₃	1	2	yes	—
317	#391	C₂²×C₃	1	2	yes	—
318	#390	C₂²×C₃	1	2	yes	—
319	#389	C₂²×C₃	1	1	yes	characteristic
320	#389	C₂²×C₃	1	1	yes	characteristic
321	#389	C₂²×C₃	1	1	yes	characteristic
322	#389	C₂²×C₃	1	1	yes	characteristic
323	#389	C₂²×C₃	1	1	yes	characteristic
324	#389	C₂²×C₃	1	1	yes	characteristic
325	#389	C₂²×C₃	1	2	yes	—
326	#389	C₂²×C₃	1	2	yes	—
327	#389	C₂²×C₃	1	2	yes	—
328	#389	C₂²×C₃	1	2	yes	—
329	#388	C₂²×C₃	1	2	yes	—
330	#388	C₂²×C₃	1	2	yes	—
331	#388	C₂²×C₃	1	2	yes	—
332	#388	C₂²×C₃	1	1	yes	characteristic
333	#388	C₂²×C₃	1	1	yes	characteristic
334	#387	C₂²×C₃	1	2	yes	—
335	#387	C₂²×C₃	1	2	yes	—
336	#387	C₂²×C₃	1	2	yes	—
337	#387	C₂²×C₃	1	2	yes	—
338	#387	C₂²×C₃	1	2	yes	—
339	#387	C₂²×C₃	1	2	yes	—
340	#387	C₂²×C₃	1	2	yes	—
341	#387	C₂²×C₃	1	2	yes	—
342	#387	C₂²×C₃	1	1	yes	characteristic
343	#387	C₂²×C₃	1	1	yes	characteristic
344	#386	C₂²×C₃	1	2	yes	—
345	#386	C₂²×C₃	1	1	yes	characteristic
346	#386	C₂²×C₃	1	1	yes	characteristic
347	#385	C₂²×C₃	1	2	yes	—
348	#385	C₂²×C₃	1	2	yes	—
349	#385	C₂²×C₃	1	2	yes	—
350	#385	C₂²×C₃	1	1	yes	characteristic
351	#385	C₂²×C₃	1	1	yes	characteristic
352	#384	C₂²×C₃	1	1	yes	characteristic
353	#384	C₂²×C₃	1	1	yes	characteristic
354	#384	C₂²×C₃	1	2	yes	—
355	#382	C₂²×C₃	1	1	yes	characteristic
356	#382	C₂²×C₃	1	1	yes	characteristic
357	#382	C₂²×C₃	1	1	yes	characteristic
358	#380	C₂²×C₃	1	1	yes	characteristic
359	#380	C₂²×C₃	1	1	yes	characteristic
360	#380	C₂²×C₃	1	1	yes	characteristic
361	#380	C₂²×C₃	1	1	yes	characteristic
362	#380	C₂²×C₃	1	2	yes	—
363	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
364	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
365	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
367	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
368	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
369	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
370	#376	C₂²×C₃	1	1	yes	characteristic
371	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×Q₈	—	2	4	no	—
374	C₂×C₃×Q₈	—	2	4	no	—
375	C₂×C₃×Q₈	—	4	2	no	—
376	C₂×C₃×Q₈	—	4	2	no	—
377	C₂×C₃×Q₈	—	4	2	no	—
378	C₂×C₃×Q₈	—	4	2	no	—
379	C₂×C₃×Q₈	—	4	2	no	—
380	C₂×C₃×Q₈	—	4	2	no	—
381	C₂×C₃×Q₈	C₂×D₄	1	8	yes	—
382	C₂×C₃×D₄	—	4	1	no	—
383	C₂×C₃×D₄	—	4	1	no	—
384	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
385	C₂²×C₃×C₄	—	2	2	no	—
386	C₂²×C₃×C₄	—	2	2	no	—
387	C₂²×C₃×C₄	—	2	2	no	—
388	C₂²×C₃×C₄	—	2	2	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	2	2	no	—
391	C₂²×C₃×C₄	—	2	4	no	—
392	C₂²×C₃×C₄	—	4	1	no	—
393	C₂²×C₃×C₄	—	4	1	no	—
394	C₂²×C₃×C₄	—	4	1	no	—
395	C₂²×C₃×C₄	—	4	1	no	—
396	C₂²×C₃×C₄	—	4	2	no	—
397	C₂²×C₃×C₄	—	4	2	no	—
398	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
399	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
409	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
410	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₃×C₄⋊C₄	—	2	4	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	2	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	2	2	no	—
426	C₃×C₄⋊C₄	—	2	2	no	—
427	C₃×C₄⋊C₄	—	2	2	no	—
428	C₃×C₄⋊C₄	—	2	4	no	—
429	C₃×C₄⋊C₄	—	2	4	no	—
430	C₃×C₄⋊C₄	—	2	4	no	—
431	C₃×C₄⋊C₄	—	2	4	no	—
432	C₃×C₄⋊C₄	—	2	4	no	—
433	C₃×C₄⋊C₄	—	2	4	no	—
434	C₃×C₄⋊C₄	—	2	4	no	—
435	C₃×C₄⋊C₄	—	2	4	no	—
436	C₃×C₄⋊C₄	—	2	4	no	—
437	C₃×C₄⋊C₄	—	2	4	no	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	2	2	no	—
440	C₃×C₄⋊C₄	—	4	1	no	—
441	C₃×C₄⋊C₄	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	1	no	—
443	C₃×C₄⋊C₄	—	4	2	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	2	no	—
446	C₃×C₄⋊C₄	—	4	2	no	—
447	C₃×C₄⋊C₄	—	4	2	no	—
448	C₃×C₄⋊C₄	—	4	2	no	—
449	C₃×C₄⋊C₄	—	4	2	no	—
450	C₃×C₄⋊C₄	—	4	2	no	—
451	C₃×C₄⋊C₄	—	4	2	no	—
452	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
453	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
454	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
455	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
456	C₃×C₂²⋊C₄	—	2	4	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	2	4	no	—
459	C₃×C₂²⋊C₄	—	2	4	no	—
460	C₃×C₂²⋊C₄	—	2	2	no	—
461	C₃×C₂²⋊C₄	—	4	2	no	—
462	C₃×C₂²⋊C₄	—	4	2	no	—
463	C₃×C₂²⋊C₄	—	4	2	no	—
464	C₃×C₂²⋊C₄	—	4	1	no	—
465	C₃×C₂²⋊C₄	—	4	1	no	—
466	C₃×C₂²⋊C₄	—	4	1	no	—
467	C₃×C₂²⋊C₄	—	4	2	no	—
468	C₃×C₂²⋊C₄	—	4	1	no	—
469	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
470	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
471	C₃×C₄²	—	2	2	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	2	2	no	—
474	C₃×C₄²	—	2	4	no	—
475	C₃×C₄²	—	2	4	no	—
476	C₃×C₄²	—	2	4	no	—
477	C₃×C₄²	—	2	2	no	—
478	C₃×C₄²	—	2	2	no	—
479	C₃×C₄²	—	4	2	no	—
480	C₃×C₄²	—	4	2	no	—
481	C₃×C₄²	C₂×D₄	1	4	yes	—
482	C₃×C₄²	C₂×Q₈	1	4	yes	—
483	C₂²×Q₈	C₂³×C₃	1	2	yes	—
484	C₂²×Q₈	C₂³×C₃	1	2	yes	—
485	C₂²×Q₈	C₂³×C₃	1	2	yes	—
486	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₃	1	2	yes	—
490	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
492	C₄⋊Q₈	—	2	8	no	—
493	C₄⋊Q₈	—	2	4	no	—
494	C₄⋊Q₈	—	2	4	no	—
495	C₄⋊Q₈	C₃×D₄	1	8	yes	complemented
496	#125	—	2	4	no	—
497	#125	—	2	4	no	—
498	#125	—	2	8	no	—
499	#125	—	2	4	no	—
500	#125	—	2	4	no	—
501	C₂²⋊Q₈	—	2	8	no	—
502	C₂²⋊Q₈	—	2	8	no	—
503	C₂²⋊Q₈	—	2	8	no	—
504	C₂²⋊Q₈	—	2	8	no	—
505	C₄×Q₈	—	2	8	no	—
506	C₄×Q₈	—	2	8	no	—
507	C₄×D₄	C₃×Q₈	1	8	yes	complemented
508	#117	—	2	4	no	—
509	#117	—	2	4	no	—
510	#117	—	2	4	no	—
511	#117	—	2	4	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄²	—	2	4	no	—
564	C₂×C₄²	C₂³×C₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
576	#95	C₂³×C₃	1	1	yes	characteristic
577	#95	C₂³×C₃	1	1	yes	characteristic
578	#95	C₂³×C₃	1	1	yes	characteristic
579	#95	C₂³×C₃	1	1	yes	characteristic
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	1	yes	characteristic
583	#95	C₂³×C₃	1	1	yes	characteristic
584	#95	C₂³×C₃	1	1	yes	characteristic
585	#95	C₂³×C₃	1	1	yes	characteristic
586	#95	C₂³×C₃	1	2	yes	—
587	#95	C₂³×C₃	1	2	yes	—
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	1	yes	characteristic
590	#95	C₂³×C₃	1	1	yes	characteristic
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	2	yes	—
595	#95	C₂³×C₃	1	2	yes	—
596	#95	C₂³×C₃	1	2	yes	—
597	#95	C₂³×C₃	1	2	yes	—
598	#95	C₂³×C₃	1	2	yes	—
599	#95	C₂³×C₃	1	2	yes	—
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	2	yes	—
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	C₂³×C₃	—	2	1	no	—
605	C₂³×C₃	—	2	1	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	1	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	C₂²×Q₈	1	2	yes	—
617	C₂³×C₃	C₂²×Q₈	1	2	yes	—
618	C₂³×C₃	C₂⁵	1	1	yes	characteristic
619	C₃×Q₈	—	4	8	no	—
620	C₃×Q₈	—	4	8	no	—
621	C₃×Q₈	—	8	4	no	—
622	C₃×D₄	—	4	4	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	8	no	—
640	C₂×C₃×C₄	—	2	8	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	4	4	no	—
678	C₂×C₃×C₄	—	4	4	no	—
679	C₂×C₃×C₄	—	8	4	no	—
680	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
681	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
682	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
683	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
684	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
685	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
686	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
687	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
688	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
689	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
690	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
691	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
692	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	C₂×C₃×D₄	1	8	yes	—
702	C₂×D₄	—	4	1	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	—	4	1	no	—
715	C₂²×C₄	—	4	1	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
719	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
773	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
774	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
775	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	1	no	—
785	C₂²⋊C₄	—	4	1	no	—
786	C₂²⋊C₄	—	4	1	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
790	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	4	no	—
795	C₄²	—	2	4	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	C₂×C₃×D₄	1	4	yes	—
802	C₄²	C₂×C₃×Q₈	1	4	yes	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	2	2	no	—
807	C₂²×C₃	—	2	2	no	—
808	C₂²×C₃	—	2	2	no	—
809	C₂²×C₃	—	4	1	no	—
810	C₂²×C₃	—	4	1	no	—
811	C₂²×C₃	—	4	1	no	—
812	C₂²×C₃	—	4	1	no	—
813	C₂²×C₃	—	4	1	no	—
814	C₂²×C₃	—	4	1	no	—
815	C₂²×C₃	—	4	1	no	—
816	C₂²×C₃	—	4	1	no	—
817	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
818	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
819	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
820	C₂²×C₃	#585	1	1	yes	characteristic
821	C₂²×C₃	#585	1	1	yes	characteristic
822	C₂²×C₃	#585	1	1	yes	characteristic
823	C₂²×C₃	#585	1	1	yes	characteristic
824	C₃×C₄	—	2	2	no	—
825	C₃×C₄	—	2	2	no	—
826	C₃×C₄	—	2	2	no	—
827	C₃×C₄	—	2	2	no	—
828	C₃×C₄	—	2	4	no	—
829	C₃×C₄	—	2	4	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	2	2	no	—
832	C₃×C₄	—	4	1	no	—
833	C₃×C₄	—	4	2	no	—
834	C₃×C₄	—	4	1	no	—
835	C₃×C₄	—	4	1	no	—
836	C₃×C₄	—	4	2	no	—
837	C₃×C₄	—	4	1	no	—
838	C₃×C₄	—	4	2	no	—
839	C₃×C₄	—	4	2	no	—
840	C₃×C₄	—	4	1	no	—
841	C₃×C₄	—	4	1	no	—
842	C₃×C₄	—	4	2	no	—
843	C₃×C₄	—	4	2	no	—
844	C₃×C₄	D₄×Q₈	1	4	yes	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	C₂²×C₃×Q₈	1	2	yes	—
858	C₂³	C₂²×C₃×Q₈	1	2	yes	—
859	C₂³	C₂⁵×C₃	1	1	yes	characteristic
860	Q₈	—	4	8	no	—
861	Q₈	—	4	8	no	—
862	Q₈	—	8	4	no	—
863	D₄	—	4	4	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
922	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
923	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
924	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
925	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
926	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
927	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
928	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
929	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
930	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
931	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
932	C₂×C₃	—	4	2	no	—
933	C₂×C₃	—	4	2	no	—
934	C₂×C₃	#3458	1	1	yes	characteristic
935	C₂×C₃	C₂×D₄×Q₈	1	1	yes	characteristic
936	C₂×C₃	#3485	1	1	yes	characteristic
937	C₂×C₃	#3487	1	1	yes	characteristic
938	C₂×C₃	#3504	1	1	yes	characteristic
939	C₂×C₃	#3565	1	1	yes	characteristic
940	C₂×C₃	#3565	1	1	yes	characteristic
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
956	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
957	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
958	C₂²	C₃×#585	1	1	yes	characteristic
959	C₂²	C₃×#585	1	1	yes	characteristic
960	C₂²	C₃×#585	1	1	yes	characteristic
961	C₂²	C₃×#585	1	1	yes	characteristic
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	4	no	—
967	C₄	—	2	4	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	C₃×D₄×Q₈	1	4	yes	—
983	C₃	#37691	1	1	yes	characteristic, direct product factor, Sylow
984	C₂	—	4	2	no	—
985	C₂	—	4	2	no	—
986	C₂	C₃×#3458	1	1	yes	characteristic
987	C₂	C₂×C₃×D₄×Q₈	1	1	yes	characteristic
988	C₂	C₃×#3485	1	1	yes	characteristic
989	C₂	C₃×#3487	1	1	yes	characteristic
990	C₂	C₃×#3504	1	1	yes	characteristic
991	C₂	C₃×#3565	1	1	yes	characteristic
992	C₂	C₃×#3565	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
1. C₂×C₃×#544	C₂	semidirect
2. C₂×C₃×#533	C₂	semidirect
3. C₃×#2851	C₂	semidirect
5. C₃×#2729	C₂	semidirect
6. C₃×#2720	C₂	semidirect
8. C₃×#2660	C₂	semidirect
9. C₃×#2628	C₂	semidirect
10. C₃×#2552	C₂	semidirect
11. C₃×#2550	C₂	semidirect
12. C₃×#2465	C₂	semidirect
13. C₃×#2462	C₂	semidirect
14. C₃×#2446	C₂	semidirect
15. C₃×#2442	C₂	semidirect
16. C₃×#2441	C₂	semidirect
17. C₃×#2441	C₂	semidirect
18. C₃×#2439	C₂	semidirect
19. C₃×#2423	C₂	semidirect
22. C₃×#2331	C₂	semidirect
24. #37691	C₃	direct (N × H)
126. C₂×#544	C₂×C₃	semidirect
127. C₂×#533	C₂×C₃	semidirect
128. #2851	C₂×C₃	semidirect
130. #2729	C₂×C₃	semidirect
131. #2720	C₂×C₃	semidirect
133. #2660	C₂×C₃	semidirect
134. #2628	C₂×C₃	semidirect
135. #2552	C₂×C₃	semidirect
136. #2550	C₂×C₃	semidirect
137. #2465	C₂×C₃	semidirect
138. #2462	C₂×C₃	semidirect
139. #2446	C₂×C₃	semidirect
140. #2442	C₂×C₃	semidirect
141. #2441	C₂×C₃	semidirect
142. #2441	C₂×C₃	semidirect
143. #2439	C₂×C₃	semidirect
144. #2423	C₂×C₃	semidirect
147. #2331	C₂×C₃	semidirect
161. C₃×C₄⋊Q₈	D₄	semidirect
173. C₃×C₄×D₄	Q₈	semidirect
495. C₄⋊Q₈	C₃×D₄	semidirect
507. C₄×D₄	C₃×Q₈	semidirect
983. C₃	#37691	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×#544	2
C₂×C₃×#533	2
C₃×#2851	2
C₃×#2732	2
C₃×#2729	2
C₃×#2720	2
C₃×#2692	2
C₃×#2660	2
C₃×#2628	2
C₃×#2552	2
C₃×#2550	2
C₃×#2465	2
C₃×#2462	2
C₃×#2446	2
C₃×#2442	2
C₃×#2441	2
C₃×#2439	2
C₃×#2423	2
C₃×#2354	2
C₃×#2352	2
C₃×#2331	2
C₃×#2290	2
#37691	3

Subgroups — C3×#37691 #10656298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37691 #10656298