Subgroups — C₃×#37765 #10656372

Order 768.

2000 conjugacy classes of subgroups.

The subgroup lattice has 992 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×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2723	C₂	1	2	yes	maximal
5	C₃×#2721	C₂	1	2	yes	maximal, complemented
6	C₃×#2720	C₂	1	2	yes	maximal, complemented
7	C₃×#2719	C₂	1	2	yes	maximal, complemented
8	C₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2538	C₂	1	1	yes	maximal, characteristic
11	C₃×#2536	C₂	1	1	yes	maximal, characteristic
12	C₃×#2479	C₂	1	2	yes	maximal
13	C₃×#2475	C₂	1	2	yes	maximal, complemented
14	C₃×#2469	C₂	1	2	yes	maximal, complemented
15	C₃×#2462	C₂	1	2	yes	maximal, complemented
16	C₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic
24	#37765	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#541	—	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×#126	C₂²	1	2	yes	—
30	C₂×C₃×#126	C₂²	1	2	yes	—
31	C₂×C₃×#125	C₂²	1	2	yes	—
32	C₂×C₃×#125	C₂²	1	1	yes	characteristic
33	C₂×C₃×#125	C₂²	1	2	yes	—
34	C₂×C₃×#125	C₂²	1	2	yes	—
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
43	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂×C₃×#117	C₂²	1	2	yes	—
50	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
51	C₃×#400	C₂²	1	2	yes	—
52	C₃×#400	C₂²	1	2	yes	—
53	C₃×#400	C₂²	1	2	yes	—
54	C₃×#399	C₂²	1	2	yes	—
55	C₃×#399	C₂²	1	2	yes	—
56	C₃×#399	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×#398	C₂²	1	2	yes	—
61	C₃×#398	C₂²	1	2	yes	—
62	C₃×#397	C₂²	1	2	yes	—
63	C₃×#397	C₂²	1	2	yes	—
64	C₃×#396	C₂²	1	2	yes	—
65	C₃×#396	C₂²	1	2	yes	—
66	C₃×#395	C₂²	1	2	yes	—
67	C₃×#395	C₂²	1	2	yes	—
68	C₃×#395	C₂²	1	2	yes	—
69	C₃×#394	C₂²	1	2	yes	—
70	C₃×#393	C₂²	1	2	yes	—
71	C₃×#391	C₂²	1	1	yes	characteristic
72	C₃×#391	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
77	C₃×#389	C₂²	1	1	yes	characteristic
78	C₃×#389	C₂²	1	2	yes	—
79	C₃×#389	C₂²	1	2	yes	—
80	C₃×#389	C₂²	1	2	yes	—
81	C₃×#389	C₂²	1	2	yes	—
82	C₃×#389	C₂²	1	2	yes	—
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#388	C₂²	1	2	yes	—
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×#388	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	1	yes	characteristic
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	2	yes	—
95	C₃×#387	C₂²	1	1	yes	characteristic
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#387	C₂²	1	2	yes	—
98	C₃×#387	C₂²	1	1	yes	characteristic
99	C₃×#387	C₂²	1	2	yes	—
100	C₃×#387	C₂²	1	2	yes	—
101	C₃×#387	C₂²	1	2	yes	—
102	C₃×#387	C₂²	1	2	yes	—
103	C₃×#386	C₂²	1	1	yes	characteristic
104	C₃×#386	C₂²	1	1	yes	characteristic
105	C₃×#385	C₂²	1	1	yes	characteristic
106	C₃×#385	C₂²	1	2	yes	—
107	C₃×#385	C₂²	1	1	yes	characteristic
108	C₃×#385	C₂²	1	2	yes	—
109	C₃×#384	C₂²	1	1	yes	characteristic
110	C₃×#384	C₂²	1	1	yes	characteristic
111	C₃×#384	C₂²	1	2	yes	—
112	C₃×#382	C₂²	1	1	yes	characteristic
113	C₃×#382	C₂²	1	1	yes	characteristic
114	C₃×#382	C₂²	1	1	yes	characteristic
115	C₃×#382	C₂²	1	2	yes	—
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	1	yes	characteristic
118	C₃×#380	C₂²	1	1	yes	characteristic
119	C₃×#380	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
121	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×#541	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	#2723	C₂×C₃	1	2	yes	—
130	#2721	C₂×C₃	1	2	yes	complemented
131	#2720	C₂×C₃	1	2	yes	complemented
132	#2719	C₂×C₃	1	2	yes	complemented
133	#2660	C₂×C₃	1	1	yes	characteristic, complemented
134	#2628	C₂×C₃	1	1	yes	characteristic, complemented
135	#2538	C₂×C₃	1	1	yes	characteristic
136	#2536	C₂×C₃	1	1	yes	characteristic
137	#2479	C₂×C₃	1	2	yes	—
138	#2475	C₂×C₃	1	2	yes	complemented
139	#2469	C₂×C₃	1	2	yes	complemented
140	#2462	C₂×C₃	1	2	yes	complemented
141	#2423	C₂×C₃	1	1	yes	characteristic, complemented
142	#2423	C₂×C₃	1	1	yes	characteristic, complemented
143	#2421	C₂×C₃	1	1	yes	characteristic, complemented
144	#2421	C₂×C₃	1	1	yes	characteristic, complemented
145	#2351	C₂×C₃	1	1	yes	characteristic, complemented
146	Q₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
147	#2327	C₂×C₃	1	1	yes	characteristic, complemented
148	#2290	C₂×C₃	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₃×C₄⋊Q₈	—	2	4	no	—
158	C₃×C₄⋊Q₈	D₄	1	8	yes	complemented
159	C₃×#126	—	2	8	no	—
160	C₃×#126	—	2	8	no	—
161	C₃×#125	—	2	8	no	—
162	C₃×#125	—	2	8	no	—
163	C₃×#125	—	2	8	no	—
164	C₃×#125	—	2	4	no	—
165	C₃×C₂²⋊Q₈	—	2	4	no	—
166	C₃×C₂²⋊Q₈	—	2	4	no	—
167	C₃×C₂²⋊Q₈	—	2	4	no	—
168	C₃×C₂²⋊Q₈	—	2	4	no	—
169	C₃×C₂²⋊Q₈	—	2	8	no	—
170	C₃×C₄×Q₈	—	2	4	no	—
171	C₃×C₄×Q₈	—	2	4	no	—
172	C₃×C₄×Q₈	—	2	4	no	—
173	C₃×C₄×Q₈	—	2	4	no	—
174	C₃×C₄×Q₈	—	2	8	no	—
175	C₃×C₄×Q₈	—	2	4	no	—
176	C₃×C₄×Q₈	—	2	4	no	—
177	C₃×C₄×D₄	—	2	4	no	—
178	C₃×#117	—	2	8	no	—
179	C₃×#117	—	2	4	no	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₄²	—	2	4	no	—
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₄²	C₂³	1	2	yes	—
235	C₂×C₃×C₄²	C₂³	1	2	yes	—
236	C₂×C₃×C₄²	C₂³	1	2	yes	—
237	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	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	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
253	C₃×#95	C₂³	1	1	yes	characteristic
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
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	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	#541	—	2	8	no	—
273	#533	—	2	8	no	—
274	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
276	C₂×#126	C₂²×C₃	1	2	yes	—
277	C₂×#126	C₂²×C₃	1	2	yes	—
278	C₂×#125	C₂²×C₃	1	1	yes	characteristic
279	C₂×#125	C₂²×C₃	1	2	yes	—
280	C₂×#125	C₂²×C₃	1	2	yes	—
281	C₂×#125	C₂²×C₃	1	2	yes	—
282	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
283	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
284	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
285	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
294	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
295	C₂×#117	C₂²×C₃	1	1	yes	characteristic
296	C₂×#117	C₂²×C₃	1	2	yes	—
297	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
298	#400	C₂²×C₃	1	2	yes	—
299	#400	C₂²×C₃	1	2	yes	—
300	#400	C₂²×C₃	1	2	yes	—
301	#399	C₂²×C₃	1	2	yes	—
302	#399	C₂²×C₃	1	2	yes	—
303	#399	C₂²×C₃	1	2	yes	—
304	#398	C₂²×C₃	1	2	yes	—
305	#398	C₂²×C₃	1	2	yes	—
306	#398	C₂²×C₃	1	2	yes	—
307	#398	C₂²×C₃	1	2	yes	—
308	#398	C₂²×C₃	1	2	yes	—
309	#397	C₂²×C₃	1	2	yes	—
310	#397	C₂²×C₃	1	2	yes	—
311	#396	C₂²×C₃	1	2	yes	—
312	#396	C₂²×C₃	1	2	yes	—
313	#395	C₂²×C₃	1	2	yes	—
314	#395	C₂²×C₃	1	2	yes	—
315	#395	C₂²×C₃	1	2	yes	—
316	#394	C₂²×C₃	1	2	yes	—
317	#393	C₂²×C₃	1	2	yes	—
318	#391	C₂²×C₃	1	1	yes	characteristic
319	#391	C₂²×C₃	1	1	yes	characteristic
320	#390	C₂²×C₃	1	2	yes	—
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	2	yes	—
325	#389	C₂²×C₃	1	2	yes	—
326	#389	C₂²×C₃	1	1	yes	characteristic
327	#389	C₂²×C₃	1	2	yes	—
328	#389	C₂²×C₃	1	2	yes	—
329	#389	C₂²×C₃	1	2	yes	—
330	#388	C₂²×C₃	1	2	yes	—
331	#388	C₂²×C₃	1	2	yes	—
332	#388	C₂²×C₃	1	2	yes	—
333	#388	C₂²×C₃	1	2	yes	—
334	#388	C₂²×C₃	1	2	yes	—
335	#388	C₂²×C₃	1	1	yes	characteristic
336	#388	C₂²×C₃	1	2	yes	—
337	#388	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
343	#387	C₂²×C₃	1	2	yes	—
344	#387	C₂²×C₃	1	2	yes	—
345	#387	C₂²×C₃	1	2	yes	—
346	#387	C₂²×C₃	1	2	yes	—
347	#387	C₂²×C₃	1	2	yes	—
348	#387	C₂²×C₃	1	1	yes	characteristic
349	#387	C₂²×C₃	1	1	yes	characteristic
350	#386	C₂²×C₃	1	1	yes	characteristic
351	#386	C₂²×C₃	1	1	yes	characteristic
352	#385	C₂²×C₃	1	2	yes	—
353	#385	C₂²×C₃	1	2	yes	—
354	#385	C₂²×C₃	1	1	yes	characteristic
355	#385	C₂²×C₃	1	1	yes	characteristic
356	#384	C₂²×C₃	1	1	yes	characteristic
357	#384	C₂²×C₃	1	2	yes	—
358	#384	C₂²×C₃	1	1	yes	characteristic
359	#382	C₂²×C₃	1	1	yes	characteristic
360	#382	C₂²×C₃	1	1	yes	characteristic
361	#382	C₂²×C₃	1	2	yes	—
362	#382	C₂²×C₃	1	1	yes	characteristic
363	#380	C₂²×C₃	1	1	yes	characteristic
364	#380	C₂²×C₃	1	1	yes	characteristic
365	#380	C₂²×C₃	1	1	yes	characteristic
366	#380	C₂²×C₃	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
372	#376	C₂²×C₃	1	1	yes	characteristic
373	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
374	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×Q₈	—	2	4	no	—
376	C₂×C₃×Q₈	—	2	2	no	—
377	C₂×C₃×Q₈	—	2	2	no	—
378	C₂×C₃×Q₈	—	2	2	no	—
379	C₂×C₃×Q₈	—	2	2	no	—
380	C₂×C₃×Q₈	—	4	2	no	—
381	C₂×C₃×Q₈	—	4	2	no	—
382	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
383	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
384	C₂×C₃×D₄	—	2	2	no	—
385	C₂×C₃×D₄	—	2	2	no	—
386	C₂×C₃×D₄	—	4	1	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	2	no	—
392	C₂²×C₃×C₄	—	2	2	no	—
393	C₂²×C₃×C₄	—	2	2	no	—
394	C₂²×C₃×C₄	—	2	2	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	4	1	no	—
398	C₂²×C₃×C₄	—	4	1	no	—
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	4	no	—
423	C₃×C₄⋊C₄	—	2	4	no	—
424	C₃×C₄⋊C₄	—	2	4	no	—
425	C₃×C₄⋊C₄	—	2	4	no	—
426	C₃×C₄⋊C₄	—	2	4	no	—
427	C₃×C₄⋊C₄	—	2	2	no	—
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	2	2	no	—
430	C₃×C₄⋊C₄	—	2	2	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	2	no	—
438	C₃×C₄⋊C₄	—	2	4	no	—
439	C₃×C₄⋊C₄	—	2	4	no	—
440	C₃×C₄⋊C₄	—	2	2	no	—
441	C₃×C₄⋊C₄	—	2	2	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	2	4	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	1	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	8	yes	—
453	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
454	C₃×C₂²⋊C₄	—	2	2	no	—
455	C₃×C₂²⋊C₄	—	2	4	no	—
456	C₃×C₂²⋊C₄	—	2	4	no	—
457	C₃×C₂²⋊C₄	—	2	4	no	—
458	C₃×C₂²⋊C₄	—	2	2	no	—
459	C₃×C₂²⋊C₄	—	2	2	no	—
460	C₃×C₂²⋊C₄	—	2	4	no	—
461	C₃×C₂²⋊C₄	—	2	4	no	—
462	C₃×C₂²⋊C₄	—	2	2	no	—
463	C₃×C₂²⋊C₄	—	2	2	no	—
464	C₃×C₂²⋊C₄	—	2	2	no	—
465	C₃×C₂²⋊C₄	—	4	2	no	—
466	C₃×C₂²⋊C₄	—	4	2	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	C₃×C₂²⋊C₄	—	4	1	no	—
469	C₃×C₂²⋊C₄	—	4	2	no	—
470	C₃×C₄²	—	2	2	no	—
471	C₃×C₄²	—	2	2	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	2	4	no	—
474	C₃×C₄²	—	2	4	no	—
475	C₃×C₄²	—	2	2	no	—
476	C₃×C₄²	—	2	4	no	—
477	C₃×C₄²	—	2	4	no	—
478	C₃×C₄²	—	2	4	no	—
479	C₃×C₄²	—	2	4	no	—
480	C₃×C₄²	—	2	2	no	—
481	C₃×C₄²	C₂×D₄	1	4	yes	—
482	C₃×C₄²	#41	1	4	yes	—
483	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
490	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
491	C₄⋊Q₈	—	2	4	no	—
492	C₄⋊Q₈	C₃×D₄	1	8	yes	complemented
493	#126	—	2	8	no	—
494	#126	—	2	8	no	—
495	#125	—	2	8	no	—
496	#125	—	2	8	no	—
497	#125	—	2	8	no	—
498	#125	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	8	no	—
504	C₄×Q₈	—	2	4	no	—
505	C₄×Q₈	—	2	4	no	—
506	C₄×Q₈	—	2	4	no	—
507	C₄×Q₈	—	2	4	no	—
508	C₄×Q₈	—	2	8	no	—
509	C₄×Q₈	—	2	4	no	—
510	C₄×Q₈	—	2	4	no	—
511	C₄×D₄	—	2	4	no	—
512	#117	—	2	8	no	—
513	#117	—	2	4	no	—
514	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄²	—	2	4	no	—
565	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	2	yes	—
571	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₄²	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	1	yes	characteristic
581	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
587	#95	C₂³×C₃	1	1	yes	characteristic
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	2	yes	—
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	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	2	yes	—
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	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
620	C₂³×C₃	C₂⁵	1	1	yes	characteristic
621	C₃×Q₈	—	2	8	no	—
622	C₃×Q₈	—	2	8	no	—
623	C₃×Q₈	—	4	8	no	—
624	C₃×D₄	—	4	4	no	—
625	C₂×C₃×C₄	—	2	8	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	2	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	1	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	2	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	2	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	1	no	—
668	C₂×C₃×C₄	—	2	2	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	4	4	no	—
680	C₂×C₃×C₄	—	4	4	no	—
681	C₂×C₃×C₄	—	4	4	no	—
682	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
683	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
684	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
685	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
686	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
687	C₂×C₃×C₄	C₂×#41	1	2	yes	—
688	C₂×C₃×C₄	C₂×#41	1	2	yes	—
689	C₂×C₃×C₄	C₂×#41	1	2	yes	—
690	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
691	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
692	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
693	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
702	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	4	1	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	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	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	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	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	C₂×C₃×D₄	1	8	yes	—
772	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	1	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	4	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	4	no	—
799	C₄²	—	2	2	no	—
800	C₄²	C₂×C₃×D₄	1	4	yes	—
801	C₄²	C₃×#41	1	4	yes	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	4	1	no	—
806	C₂²×C₃	—	4	1	no	—
807	C₂²×C₃	—	4	1	no	—
808	C₂²×C₃	—	4	1	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	C₂³×D₄	1	1	yes	characteristic
817	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
818	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
819	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
820	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
821	C₂²×C₃	#585	1	1	yes	characteristic
822	C₂²×C₃	#585	1	1	yes	characteristic
823	C₃×C₄	—	2	2	no	—
824	C₃×C₄	—	2	4	no	—
825	C₃×C₄	—	2	4	no	—
826	C₃×C₄	—	2	2	no	—
827	C₃×C₄	—	2	2	no	—
828	C₃×C₄	—	2	2	no	—
829	C₃×C₄	—	2	2	no	—
830	C₃×C₄	—	4	2	no	—
831	C₃×C₄	—	4	1	no	—
832	C₃×C₄	—	4	1	no	—
833	C₃×C₄	—	4	1	no	—
834	C₃×C₄	—	4	2	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	2	no	—
841	C₃×C₄	—	4	1	no	—
842	C₃×C₄	—	4	1	no	—
843	C₃×C₄	#547	1	4	yes	—
844	C₂³	—	2	1	no	—
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	C₃×2₋¹⁺⁴	1	2	yes	—
858	C₂³	C₂⁵×C₃	1	1	yes	characteristic
859	Q₈	—	2	8	no	—
860	Q₈	—	2	8	no	—
861	Q₈	—	4	8	no	—
862	D₄	—	4	4	no	—
863	C₂×C₄	—	2	8	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	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	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
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	2	yes	—
925	C₂×C₄	C₂×C₃×#41	1	2	yes	—
926	C₂×C₄	C₂×C₃×#41	1	2	yes	—
927	C₂×C₄	C₂×C₃×#41	1	2	yes	—
928	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
929	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
930	C₂×C₃	—	4	2	no	—
931	C₂×C₃	—	8	1	no	—
932	C₂×C₃	#3461	1	1	yes	characteristic
933	C₂×C₃	C₂×#547	1	1	yes	characteristic
934	C₂×C₃	#3486	1	1	yes	characteristic
935	C₂×C₃	#3487	1	1	yes	characteristic
936	C₂×C₃	#3495	1	1	yes	characteristic
937	C₂×C₃	#3555	1	1	yes	characteristic
938	C₂×C₃	#3563	1	1	yes	characteristic
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	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	C₂³×C₃×D₄	1	1	yes	characteristic
954	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
955	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
956	C₂²	C₂×C₃×2₋¹⁺⁴	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	C₄	—	2	2	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	C₃×#547	1	4	yes	—
981	C₃	#37765	1	1	yes	characteristic, direct product factor, Sylow
982	C₂	—	4	2	no	—
983	C₂	—	8	1	no	—
984	C₂	C₃×#3461	1	1	yes	characteristic
985	C₂	C₂×C₃×#547	1	1	yes	characteristic
986	C₂	C₃×#3486	1	1	yes	characteristic
987	C₂	C₃×#3487	1	1	yes	characteristic
988	C₂	C₃×#3495	1	1	yes	characteristic
989	C₂	C₃×#3555	1	1	yes	characteristic
990	C₂	C₃×#3563	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×#541	C₂	semidirect
2. C₂×C₃×#533	C₂	semidirect
3. C₃×#2851	C₂	semidirect
5. C₃×#2721	C₂	semidirect
6. C₃×#2720	C₂	semidirect
7. C₃×#2719	C₂	semidirect
8. C₃×#2660	C₂	semidirect
9. C₃×#2628	C₂	semidirect
13. C₃×#2475	C₂	semidirect
14. C₃×#2469	C₂	semidirect
15. C₃×#2462	C₂	semidirect
16. C₃×#2423	C₂	semidirect
17. C₃×#2423	C₂	semidirect
18. C₃×#2421	C₂	semidirect
19. C₃×#2421	C₂	semidirect
20. C₃×#2351	C₂	semidirect
21. C₃×Q₈×C₄⋊C₄	C₂	semidirect
22. C₃×#2327	C₂	semidirect
24. #37765	C₃	direct (N × H)
126. C₂×#541	C₂×C₃	semidirect
127. C₂×#533	C₂×C₃	semidirect
128. #2851	C₂×C₃	semidirect
130. #2721	C₂×C₃	semidirect
131. #2720	C₂×C₃	semidirect
132. #2719	C₂×C₃	semidirect
133. #2660	C₂×C₃	semidirect
134. #2628	C₂×C₃	semidirect
138. #2475	C₂×C₃	semidirect
139. #2469	C₂×C₃	semidirect
140. #2462	C₂×C₃	semidirect
141. #2423	C₂×C₃	semidirect
142. #2423	C₂×C₃	semidirect
143. #2421	C₂×C₃	semidirect
144. #2421	C₂×C₃	semidirect
145. #2351	C₂×C₃	semidirect
146. Q₈×C₄⋊C₄	C₂×C₃	semidirect
147. #2327	C₂×C₃	semidirect
158. C₃×C₄⋊Q₈	D₄	semidirect
492. C₄⋊Q₈	C₃×D₄	semidirect
981. C₃	#37765	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×#533	2
C₃×#2851	2
C₃×#2723	2
C₃×#2721	2
C₃×#2720	2
C₃×#2719	2
C₃×#2660	2
C₃×#2628	2
C₃×#2538	2
C₃×#2536	2
C₃×#2479	2
C₃×#2475	2
C₃×#2469	2
C₃×#2462	2
C₃×#2423	2
C₃×#2421	2
C₃×#2351	2
C₃×Q₈×C₄⋊C₄	2
C₃×#2327	2
C₃×#2290	2
#37765	3

Subgroups — C3×#37765 #10656372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37765 #10656372