Subgroups — #11042028

Order 768.

1452 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2722	C₂	1	1	yes	maximal, characteristic
2	#83093	C₂	1	1	yes	maximal, characteristic
3	#83091	C₂	1	1	yes	maximal, characteristic
4	#83075	C₂	1	1	yes	maximal, characteristic
5	Dic₃×#126	C₂	1	1	yes	maximal, characteristic
6	#77917	C₂	1	1	yes	maximal, characteristic, complemented
7	#77916	C₂	1	1	yes	maximal, characteristic, complemented
8	#77836	C₂	1	1	yes	maximal, characteristic, complemented
9	#77814	C₂	1	1	yes	maximal, characteristic, complemented
10	#77778	C₂	1	1	yes	maximal, characteristic, complemented
11	#77777	C₂	1	1	yes	maximal, characteristic, complemented
12	#77774	C₂	1	1	yes	maximal, characteristic, complemented
13	#77751	C₂	1	1	yes	maximal, characteristic, complemented
14	#77557	C₂	1	1	yes	maximal, characteristic
15	#77506	C₂	1	1	yes	maximal, characteristic
16	#77502	C₂	1	1	yes	maximal, characteristic
17	#77496	C₂	1	1	yes	maximal, characteristic
18	#76141	C₂	1	1	yes	maximal, characteristic, complemented
19	#76058	C₂	1	1	yes	maximal, characteristic, complemented
20	#76043	C₂	1	1	yes	maximal, characteristic, complemented
21	#75962	C₂	1	1	yes	maximal, characteristic, complemented
22	#75291	C₂	1	1	yes	maximal, characteristic, complemented
23	#75190	C₂	1	1	yes	maximal, characteristic, complemented
24	#75134	C₂	1	1	yes	maximal, characteristic, complemented
25	#74958	C₂	1	1	yes	maximal, characteristic, complemented
26	#74574	C₂	1	1	yes	maximal, characteristic
27	#74396	C₂	1	1	yes	maximal, characteristic
28	#73931	C₂	1	1	yes	maximal, characteristic
29	#73921	C₂	1	1	yes	maximal, characteristic
30	#73908	C₂	1	1	yes	maximal, characteristic
31	#73867	C₂	1	1	yes	maximal, characteristic
32	#38345	—	3	1	no	maximal, Sylow
33	C₂×C₃×#126	C₂²	1	1	yes	characteristic
34	C₂×C₃×#126	C₂²	1	1	yes	characteristic
35	C₂²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×#889	C₂²	1	1	yes	characteristic
37	C₂×#887	C₂²	1	1	yes	characteristic
38	C₂×#878	C₂²	1	1	yes	characteristic
39	C₃×#398	C₂²	1	1	yes	characteristic
40	C₃×#398	C₂²	1	1	yes	characteristic
41	C₃×#398	C₂²	1	1	yes	characteristic
42	C₃×#398	C₂²	1	1	yes	characteristic
43	C₃×#397	C₂²	1	1	yes	characteristic
44	C₃×#397	C₂²	1	1	yes	characteristic
45	C₃×#389	C₂²	1	1	yes	characteristic
46	C₃×#389	C₂²	1	1	yes	characteristic
47	C₃×#387	C₂²	1	1	yes	characteristic
48	C₃×#387	C₂²	1	1	yes	characteristic
49	C₃×#385	C₂²	1	1	yes	characteristic
50	C₃×#380	C₂²	1	1	yes	characteristic
51	C₃×#380	C₂²	1	1	yes	characteristic
52	#5212	C₂²	1	1	yes	characteristic
53	#5210	C₂²	1	1	yes	characteristic
54	C₄×#217	C₂²	1	1	yes	characteristic
55	#4986	C₂²	1	1	yes	characteristic
56	#4986	C₂²	1	1	yes	characteristic
57	#4986	C₂²	1	1	yes	characteristic
58	#4986	C₂²	1	1	yes	characteristic
59	#4985	C₂²	1	1	yes	characteristic
60	#4985	C₂²	1	1	yes	characteristic
61	#4985	C₂²	1	1	yes	characteristic
62	#4985	C₂²	1	1	yes	characteristic
63	#4984	C₂²	1	1	yes	characteristic
64	#4984	C₂²	1	1	yes	characteristic
65	#4984	C₂²	1	1	yes	characteristic
66	#4983	C₂²	1	1	yes	characteristic
67	#4982	C₂²	1	1	yes	characteristic
68	#4982	C₂²	1	1	yes	characteristic
69	#4982	C₂²	1	1	yes	characteristic
70	#4981	C₂²	1	1	yes	characteristic
71	#4981	C₂²	1	1	yes	characteristic
72	#4980	C₂²	1	1	yes	characteristic
73	#4980	C₂²	1	1	yes	characteristic
74	#4980	C₂²	1	1	yes	characteristic
75	#4980	C₂²	1	1	yes	characteristic
76	#4980	C₂²	1	1	yes	characteristic
77	#4980	C₂²	1	1	yes	characteristic
78	#4980	C₂²	1	1	yes	characteristic
79	#4980	C₂²	1	1	yes	characteristic
80	#4979	C₂²	1	1	yes	characteristic
81	#4979	C₂²	1	1	yes	characteristic
82	#4978	C₂²	1	1	yes	characteristic
83	#4978	C₂²	1	1	yes	characteristic
84	#4978	C₂²	1	1	yes	characteristic
85	#4978	C₂²	1	1	yes	characteristic
86	#4978	C₂²	1	1	yes	characteristic
87	#4978	C₂²	1	1	yes	characteristic
88	#4978	C₂²	1	1	yes	characteristic
89	#4978	C₂²	1	1	yes	characteristic
90	#4977	C₂²	1	1	yes	characteristic
91	#4977	C₂²	1	1	yes	characteristic
92	#4976	C₂²	1	1	yes	characteristic
93	#4976	C₂²	1	1	yes	characteristic
94	#4976	C₂²	1	1	yes	characteristic
95	#4976	C₂²	1	1	yes	characteristic
96	#4976	C₂²	1	1	yes	characteristic
97	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	#4973	C₂²	1	1	yes	characteristic
105	#4973	C₂²	1	1	yes	characteristic
106	#4972	C₂²	1	1	yes	characteristic
107	#4972	C₂²	1	1	yes	characteristic
108	#4972	C₂²	1	1	yes	characteristic
109	#4952	C₂²	1	1	yes	characteristic
110	#4952	C₂²	1	1	yes	characteristic
111	#4952	C₂²	1	1	yes	characteristic
112	#4952	C₂²	1	1	yes	characteristic
113	#4951	C₂²	1	1	yes	characteristic
114	#4951	C₂²	1	1	yes	characteristic
115	#4951	C₂²	1	1	yes	characteristic
116	#4951	C₂²	1	1	yes	characteristic
117	#4951	C₂²	1	1	yes	characteristic
118	#4951	C₂²	1	1	yes	characteristic
119	#4950	C₂²	1	1	yes	characteristic
120	#4948	C₂²	1	1	yes	characteristic
121	#4947	C₂²	1	1	yes	characteristic
122	#4946	C₂²	1	1	yes	characteristic
123	#4946	C₂²	1	1	yes	characteristic
124	#4946	C₂²	1	1	yes	characteristic
125	#4943	C₂²	1	1	yes	characteristic
126	#4943	C₂²	1	1	yes	characteristic
127	Dic₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
128	Dic₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
129	Dic₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
130	Dic₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
131	Dic₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
132	#4937	C₂²	1	1	yes	characteristic
133	C₄×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
134	#4933	C₂²	1	1	yes	characteristic
135	#4933	C₂²	1	1	yes	characteristic
136	#4932	C₂²	1	1	yes	characteristic
137	C₄²×Dic₃	C₂²	1	1	yes	characteristic
138	#4929	C₂²	1	1	yes	characteristic
139	#4928	C₂²	1	1	yes	characteristic
140	C₃⋊#401	C₂²	1	1	yes	characteristic
141	#4661	C₂²	1	1	yes	characteristic
142	#4660	C₂²	1	1	yes	characteristic
143	#4659	C₂²	1	1	yes	characteristic
144	#4659	C₂²	1	1	yes	characteristic
145	#4659	C₂²	1	1	yes	characteristic
146	#4659	C₂²	1	1	yes	characteristic
147	#4658	C₂²	1	1	yes	characteristic
148	#4658	C₂²	1	1	yes	characteristic
149	#4657	C₂²	1	1	yes	characteristic
150	#4657	C₂²	1	1	yes	characteristic
151	#4656	C₂²	1	1	yes	characteristic
152	#4655	C₂²	1	1	yes	characteristic
153	#4655	C₂²	1	1	yes	characteristic
154	#4655	C₂²	1	1	yes	characteristic
155	#4655	C₂²	1	1	yes	characteristic
156	#4655	C₂²	1	1	yes	characteristic
157	#4655	C₂²	1	1	yes	characteristic
158	#4655	C₂²	1	1	yes	characteristic
159	#4655	C₂²	1	1	yes	characteristic
160	#4655	C₂²	1	1	yes	characteristic
161	#4654	C₂²	1	1	yes	characteristic
162	#4653	C₂²	1	1	yes	characteristic
163	#4653	C₂²	1	1	yes	characteristic
164	#4653	C₂²	1	1	yes	characteristic
165	#4653	C₂²	1	1	yes	characteristic
166	#4652	C₂²	1	1	yes	characteristic
167	#4652	C₂²	1	1	yes	characteristic
168	#4652	C₂²	1	1	yes	characteristic
169	#4652	C₂²	1	1	yes	characteristic
170	#4652	C₂²	1	1	yes	characteristic
171	#4652	C₂²	1	1	yes	characteristic
172	#4651	C₂²	1	1	yes	characteristic
173	#4651	C₂²	1	1	yes	characteristic
174	#4651	C₂²	1	1	yes	characteristic
175	#4651	C₂²	1	1	yes	characteristic
176	#4651	C₂²	1	1	yes	characteristic
177	#4650	C₂²	1	1	yes	characteristic
178	#4649	C₂²	1	1	yes	characteristic
179	#4648	C₂²	1	1	yes	characteristic
180	#4648	C₂²	1	1	yes	characteristic
181	#4647	C₂²	1	1	yes	characteristic
182	#4647	C₂²	1	1	yes	characteristic
183	#4646	C₂²	1	1	yes	characteristic
184	#4646	C₂²	1	1	yes	characteristic
185	#4646	C₂²	1	1	yes	characteristic
186	#4646	C₂²	1	1	yes	characteristic
187	#4646	C₂²	1	1	yes	characteristic
188	#2863	—	3	1	no	—
189	#2802	—	3	1	no	—
190	#2799	—	3	1	no	—
191	#2788	—	3	1	no	—
192	#2766	—	3	1	no	—
193	#2758	—	3	1	no	—
194	#2722	D₃	1	1	yes	characteristic
195	#2698	—	3	1	no	—
196	#2689	—	3	1	no	—
197	#2655	—	3	1	no	—
198	#2652	—	3	1	no	—
199	#2612	—	3	1	no	—
200	#2606	—	3	1	no	—
201	#2533	—	3	1	no	—
202	#2530	—	3	1	no	—
203	#2527	—	3	1	no	—
204	#2524	—	3	1	no	—
205	#2524	—	3	1	no	—
206	#2523	—	3	1	no	—
207	#2520	—	3	1	no	—
208	#2515	—	3	1	no	—
209	#2509	—	3	1	no	—
210	#2495	—	3	1	no	—
211	#2473	—	3	1	no	—
212	#2462	—	3	1	no	—
213	#2373	—	3	1	no	—
214	#2360	—	3	1	no	—
215	#2336	—	3	1	no	—
216	#2313	—	3	1	no	—
217	C₄×#126	—	3	1	no	—
218	#2295	—	3	1	no	—
219	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
220	C₂³×Dic₃	C₂³	1	1	yes	characteristic
221	C₂³×Dic₃	C₂³	1	1	yes	characteristic
222	C₂²×Dic₆	C₂³	1	1	yes	characteristic
223	C₂²×Dic₆	C₂³	1	1	yes	characteristic
224	C₃×#126	—	2	4	no	—
225	C₃×#126	—	2	4	no	—
226	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×#217	C₂³	1	1	yes	characteristic
249	C₂×#217	C₂³	1	1	yes	characteristic
250	C₂×#217	C₂³	1	1	yes	characteristic
251	C₂×#217	C₂³	1	1	yes	characteristic
252	C₂×#217	C₂³	1	1	yes	characteristic
253	C₂×#217	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
266	C₂×Dic₃⋊C₄	—	2	4	no	—
267	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
305	#889	—	2	4	no	—
306	#887	—	2	4	no	—
307	#878	—	2	4	no	—
308	C₃×#95	C₂³	1	1	yes	characteristic
309	C₃×#95	C₂³	1	1	yes	characteristic
310	C₃×#95	C₂³	1	1	yes	characteristic
311	C₃×#95	C₂³	1	1	yes	characteristic
312	C₃×#95	C₂³	1	1	yes	characteristic
313	C₃×#95	C₂³	1	1	yes	characteristic
314	C₃×#95	C₂³	1	1	yes	characteristic
315	C₃×#95	C₂³	1	1	yes	characteristic
316	C₃×#95	C₂³	1	1	yes	characteristic
317	C₃×#95	C₂³	1	1	yes	characteristic
318	C₃×#95	C₂³	1	1	yes	characteristic
319	C₃×#95	C₂³	1	1	yes	characteristic
320	C₃⋊#95	C₂³	1	1	yes	characteristic
321	C₃⋊#95	C₂³	1	1	yes	characteristic
322	C₃⋊#95	C₂³	1	1	yes	characteristic
323	C₃⋊#95	C₂³	1	1	yes	characteristic
324	C₃⋊#95	C₂³	1	1	yes	characteristic
325	C₃⋊#95	C₂³	1	1	yes	characteristic
326	C₃⋊#95	C₂³	1	1	yes	characteristic
327	C₃⋊#95	C₂³	1	1	yes	characteristic
328	C₃⋊#95	C₂³	1	1	yes	characteristic
329	C₃⋊#95	C₂³	1	1	yes	characteristic
330	C₃⋊#95	C₂³	1	1	yes	characteristic
331	C₃⋊#95	C₂³	1	1	yes	characteristic
332	C₃⋊#95	C₂³	1	1	yes	characteristic
333	C₃⋊#95	C₂³	1	1	yes	characteristic
334	C₃⋊#95	C₂³	1	1	yes	characteristic
335	C₃⋊#95	C₂³	1	1	yes	characteristic
336	C₃⋊#95	C₂³	1	1	yes	characteristic
337	C₃⋊#95	C₂³	1	1	yes	characteristic
338	C₃⋊#95	C₂³	1	1	yes	characteristic
339	C₃⋊#95	C₂³	1	1	yes	characteristic
340	C₃⋊#95	C₂³	1	1	yes	characteristic
341	C₃⋊#95	C₂³	1	1	yes	characteristic
342	C₃⋊#95	C₂³	1	1	yes	characteristic
343	C₃⋊#95	C₂³	1	1	yes	characteristic
344	C₃⋊#95	C₂³	1	1	yes	characteristic
345	C₃⋊#95	C₂³	1	1	yes	characteristic
346	C₃⋊#95	C₂³	1	1	yes	characteristic
347	C₃⋊#95	C₂³	1	1	yes	characteristic
348	C₃⋊#95	C₂³	1	1	yes	characteristic
349	C₃⋊#95	C₂³	1	1	yes	characteristic
350	C₃⋊#95	C₂³	1	1	yes	characteristic
351	C₃⋊#95	C₂³	1	1	yes	characteristic
352	C₃⋊#95	C₂³	1	1	yes	characteristic
353	C₃⋊#95	C₂³	1	1	yes	characteristic
354	C₃⋊#95	C₂³	1	1	yes	characteristic
355	C₃⋊#95	C₂³	1	1	yes	characteristic
356	C₃⋊#95	C₂³	1	1	yes	characteristic
357	C₃⋊#95	C₂³	1	1	yes	characteristic
358	C₃⋊#95	C₂³	1	1	yes	characteristic
359	C₃⋊#95	C₂³	1	1	yes	characteristic
360	C₃⋊#95	C₂³	1	1	yes	characteristic
361	C₃⋊#95	C₂³	1	1	yes	characteristic
362	C₃⋊#95	C₂³	1	1	yes	characteristic
363	C₃⋊#95	C₂³	1	1	yes	characteristic
364	C₃⋊#95	C₂³	1	1	yes	characteristic
365	C₃⋊#95	C₂³	1	1	yes	characteristic
366	C₃⋊#95	C₂³	1	1	yes	characteristic
367	C₃⋊#95	C₂³	1	1	yes	characteristic
368	C₃⋊#95	C₂³	1	1	yes	characteristic
369	C₃⋊#95	C₂³	1	1	yes	characteristic
370	C₃⋊#95	C₂³	1	1	yes	characteristic
371	C₃⋊#95	C₂³	1	1	yes	characteristic
372	C₃⋊#95	C₂³	1	1	yes	characteristic
373	C₃⋊#95	C₂³	1	1	yes	characteristic
374	C₃⋊#95	C₂³	1	1	yes	characteristic
375	C₃⋊#95	C₂³	1	1	yes	characteristic
376	C₃⋊#95	C₂³	1	1	yes	characteristic
377	C₃⋊#95	C₂³	1	1	yes	characteristic
378	C₃⋊#95	C₂³	1	1	yes	characteristic
379	C₃⋊#95	C₂³	1	1	yes	characteristic
380	C₂×#126	C₂×D₃	1	1	yes	characteristic
381	C₂×#126	C₂×D₃	1	1	yes	characteristic
382	C₂×#125	—	3	1	no	—
383	C₂×C₂²⋊Q₈	—	3	1	no	—
384	C₂×C₄×Q₈	—	3	1	no	—
385	C₂²×C₄⋊C₄	—	3	1	no	—
386	#401	—	3	1	no	—
387	#400	—	3	1	no	—
388	#400	—	3	1	no	—
389	#400	—	3	1	no	—
390	#400	—	3	1	no	—
391	#400	—	3	1	no	—
392	#400	—	3	1	no	—
393	#400	—	3	1	no	—
394	#400	—	3	1	no	—
395	#400	—	3	1	no	—
396	#400	—	3	1	no	—
397	#400	—	3	1	no	—
398	#400	—	3	1	no	—
399	#400	—	3	1	no	—
400	#400	—	3	1	no	—
401	#400	—	3	1	no	—
402	#398	—	3	1	no	—
403	#398	—	3	1	no	—
404	#398	—	3	1	no	—
405	#398	—	3	1	no	—
406	#398	—	3	1	no	—
407	#398	—	3	1	no	—
408	#398	—	3	1	no	—
409	#398	—	3	1	no	—
410	#398	—	3	1	no	—
411	#398	C₂×D₃	1	1	yes	characteristic
412	#398	C₂×D₃	1	1	yes	characteristic
413	#398	C₂×D₃	1	1	yes	characteristic
414	#398	C₂×D₃	1	1	yes	characteristic
415	#397	—	3	1	no	—
416	#397	—	3	1	no	—
417	#397	—	3	1	no	—
418	#397	—	3	1	no	—
419	#397	C₂×D₃	1	1	yes	characteristic
420	#397	C₂×D₃	1	1	yes	characteristic
421	#396	—	3	1	no	—
422	#395	—	3	1	no	—
423	#395	—	3	1	no	—
424	#395	—	3	1	no	—
425	#393	—	3	1	no	—
426	#391	—	3	1	no	—
427	#391	—	3	1	no	—
428	#391	—	3	1	no	—
429	#391	—	3	1	no	—
430	#391	—	3	1	no	—
431	#391	—	3	1	no	—
432	#391	—	3	1	no	—
433	#391	—	3	1	no	—
434	#389	—	3	1	no	—
435	#389	—	3	1	no	—
436	#389	—	3	1	no	—
437	#389	—	3	1	no	—
438	#389	—	3	1	no	—
439	#389	—	3	1	no	—
440	#389	—	3	1	no	—
441	#389	—	3	1	no	—
442	#389	—	3	1	no	—
443	#389	—	3	1	no	—
444	#389	—	3	1	no	—
445	#389	—	3	1	no	—
446	#389	—	3	1	no	—
447	#389	—	3	1	no	—
448	#389	C₂×D₃	1	1	yes	characteristic
449	#389	C₂×D₃	1	1	yes	characteristic
450	#388	—	3	1	no	—
451	#388	—	3	1	no	—
452	#388	—	3	1	no	—
453	#388	—	3	1	no	—
454	#388	—	3	1	no	—
455	#388	—	3	1	no	—
456	#387	—	3	1	no	—
457	#387	—	3	1	no	—
458	#387	—	3	1	no	—
459	#387	—	3	1	no	—
460	#387	—	3	1	no	—
461	#387	—	3	1	no	—
462	#387	—	3	1	no	—
463	#387	—	3	1	no	—
464	#387	—	3	1	no	—
465	#387	—	3	1	no	—
466	#387	—	3	1	no	—
467	#387	—	3	1	no	—
468	#387	—	3	1	no	—
469	#387	—	3	1	no	—
470	#387	—	3	1	no	—
471	#387	—	3	1	no	—
472	#387	—	3	1	no	—
473	#387	—	3	1	no	—
474	#387	—	3	1	no	—
475	#387	—	3	1	no	—
476	#387	—	3	1	no	—
477	#387	—	3	1	no	—
478	#387	—	3	1	no	—
479	#387	—	3	1	no	—
480	#387	—	3	1	no	—
481	#387	—	3	1	no	—
482	#387	—	3	1	no	—
483	#387	—	3	1	no	—
484	#387	—	3	1	no	—
485	#387	—	3	1	no	—
486	#387	—	3	1	no	—
487	#387	—	3	1	no	—
488	#387	—	3	1	no	—
489	#387	—	3	1	no	—
490	#387	—	3	1	no	—
491	#387	—	3	1	no	—
492	#387	—	3	1	no	—
493	#387	—	3	1	no	—
494	#387	C₂×D₃	1	1	yes	characteristic
495	#387	C₂×D₃	1	1	yes	characteristic
496	#385	—	3	1	no	—
497	#385	—	3	1	no	—
498	#385	—	3	1	no	—
499	#385	—	3	1	no	—
500	#385	—	3	1	no	—
501	#385	C₂×D₃	1	1	yes	characteristic
502	#383	—	3	1	no	—
503	#383	—	3	1	no	—
504	#383	—	3	1	no	—
505	#383	—	3	1	no	—
506	#383	—	3	1	no	—
507	#383	—	3	1	no	—
508	#382	—	3	1	no	—
509	#382	—	3	1	no	—
510	#382	—	3	1	no	—
511	#381	—	3	1	no	—
512	#381	—	3	1	no	—
513	#380	—	3	1	no	—
514	#380	C₂×D₃	1	1	yes	characteristic
515	#380	C₂×D₃	1	1	yes	characteristic
516	C₄×C₄⋊C₄	—	3	1	no	—
517	C₄×C₄⋊C₄	—	3	1	no	—
518	C₄×C₄⋊C₄	—	3	1	no	—
519	C₄×C₄⋊C₄	—	3	1	no	—
520	C₄×C₄⋊C₄	—	3	1	no	—
521	C₄×C₄⋊C₄	—	3	1	no	—
522	C₄×C₄⋊C₄	—	3	1	no	—
523	C₄×C₄⋊C₄	—	3	1	no	—
524	C₄×C₄⋊C₄	—	3	1	no	—
525	C₄×C₂²⋊C₄	—	3	1	no	—
526	C₄×C₂²⋊C₄	—	3	1	no	—
527	C₄×C₂²⋊C₄	—	3	1	no	—
528	C₄×C₂²⋊C₄	—	3	1	no	—
529	C₄×C₂²⋊C₄	—	3	1	no	—
530	C₄×C₂²⋊C₄	—	3	1	no	—
531	#376	—	3	1	no	—
532	#376	—	3	1	no	—
533	#376	—	3	1	no	—
534	C₄³	—	3	1	no	—
535	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
536	C₂²×C₃×C₄	—	2	2	no	—
537	C₂²×C₃×C₄	—	4	1	no	—
538	C₂²×C₃×C₄	—	4	1	no	—
539	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
540	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
541	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
542	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
543	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
544	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
545	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
546	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
547	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
548	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
549	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
550	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
551	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
552	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
553	C₂²×Dic₃	—	2	2	no	—
554	C₂²×Dic₃	—	2	2	no	—
555	C₂²×Dic₃	—	2	2	no	—
556	C₂²×Dic₃	—	4	1	no	—
557	C₂²×Dic₃	—	4	1	no	—
558	C₂²×Dic₃	—	4	1	no	—
559	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
560	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
561	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
562	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
563	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
564	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
565	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
566	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
567	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
568	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
569	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
570	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
571	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
572	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
573	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
574	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
575	C₂×Dic₆	—	2	2	no	—
576	C₂×Dic₆	—	2	2	no	—
577	C₂×Dic₆	—	2	2	no	—
578	C₂×Dic₆	—	4	1	no	—
579	C₂×Dic₆	—	4	1	no	—
580	C₂×Dic₆	—	4	1	no	—
581	C₃×C₄⋊C₄	—	2	2	no	—
582	C₃×C₄⋊C₄	—	2	2	no	—
583	C₃×C₄⋊C₄	—	2	2	no	—
584	C₃×C₄⋊C₄	—	2	2	no	—
585	C₃×C₄⋊C₄	—	2	2	no	—
586	C₃×C₄⋊C₄	—	2	2	no	—
587	C₃×C₄⋊C₄	—	2	2	no	—
588	C₃×C₄⋊C₄	—	2	2	no	—
589	C₃×C₄⋊C₄	—	4	1	no	—
590	C₃×C₄⋊C₄	—	4	1	no	—
591	C₃×C₄⋊C₄	—	4	1	no	—
592	C₃×C₄⋊C₄	—	4	1	no	—
593	C₃×C₄⋊C₄	—	4	1	no	—
594	C₃×C₄⋊C₄	—	4	1	no	—
595	C₃×C₂²⋊C₄	—	2	2	no	—
596	C₃×C₂²⋊C₄	—	2	2	no	—
597	C₃×C₂²⋊C₄	—	2	2	no	—
598	C₃×C₂²⋊C₄	—	2	2	no	—
599	C₃×C₂²⋊C₄	—	4	1	no	—
600	C₃×C₂²⋊C₄	#41	1	4	yes	—
601	C₃×C₄²	—	2	2	no	—
602	C₃×C₄²	—	2	2	no	—
603	#217	—	2	2	no	—
604	#217	—	2	2	no	—
605	#217	—	2	2	no	—
606	#217	—	4	1	no	—
607	#217	—	4	1	no	—
608	#217	—	4	1	no	—
609	C₄⋊Dic₃	—	2	2	no	—
610	C₄⋊Dic₃	—	2	2	no	—
611	C₄⋊Dic₃	—	2	2	no	—
612	C₄⋊Dic₃	—	2	2	no	—
613	C₄⋊Dic₃	—	4	1	no	—
614	C₄⋊Dic₃	—	4	1	no	—
615	C₄⋊Dic₃	—	4	1	no	—
616	C₄⋊Dic₃	—	4	1	no	—
617	C₄⋊Dic₃	—	4	1	no	—
618	C₄⋊Dic₃	—	4	1	no	—
619	C₄⋊Dic₃	—	4	1	no	—
620	C₄⋊Dic₃	—	4	1	no	—
621	Dic₃⋊C₄	—	2	2	no	—
622	Dic₃⋊C₄	—	2	2	no	—
623	Dic₃⋊C₄	—	2	2	no	—
624	Dic₃⋊C₄	—	2	2	no	—
625	Dic₃⋊C₄	—	2	2	no	—
626	Dic₃⋊C₄	—	2	2	no	—
627	Dic₃⋊C₄	—	2	2	no	—
628	Dic₃⋊C₄	—	2	2	no	—
629	Dic₃⋊C₄	—	2	2	no	—
630	Dic₃⋊C₄	—	2	2	no	—
631	Dic₃⋊C₄	—	4	1	no	—
632	Dic₃⋊C₄	—	4	1	no	—
633	Dic₃⋊C₄	—	4	1	no	—
634	Dic₃⋊C₄	—	4	1	no	—
635	Dic₃⋊C₄	—	4	1	no	—
636	Dic₃⋊C₄	—	4	1	no	—
637	Dic₃⋊C₄	—	4	1	no	—
638	Dic₃⋊C₄	—	4	1	no	—
639	Dic₃⋊C₄	—	4	1	no	—
640	Dic₃⋊C₄	#41	1	4	yes	—
641	C₄×Dic₃	—	2	2	no	—
642	C₄×Dic₃	—	2	2	no	—
643	C₄×Dic₃	—	2	2	no	—
644	C₄×Dic₃	—	2	2	no	—
645	C₄×Dic₃	—	2	2	no	—
646	C₄×Dic₃	—	2	2	no	—
647	C₄×Dic₃	—	2	2	no	—
648	C₄×Dic₃	—	2	2	no	—
649	C₄×Dic₃	—	4	1	no	—
650	C₄×Dic₃	—	4	1	no	—
651	C₄×Dic₃	—	4	1	no	—
652	C₄×Dic₃	—	4	1	no	—
653	C₄×Dic₃	—	4	1	no	—
654	C₄×Dic₃	—	4	1	no	—
655	C₄×Dic₃	—	4	1	no	—
656	C₄×Dic₃	—	4	1	no	—
657	C₄×Dic₃	—	4	1	no	—
658	C₄×Dic₃	—	4	1	no	—
659	C₂²×Q₈	—	3	1	no	—
660	C₂²×Q₈	—	3	1	no	—
661	C₂³×C₄	—	3	1	no	—
662	C₂³×C₄	—	3	1	no	—
663	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
664	#126	—	2	4	no	—
665	#126	—	2	4	no	—
666	#125	—	6	4	no	—
667	C₂²⋊Q₈	—	6	4	no	—
668	C₄×Q₈	—	6	4	no	—
669	C₂×C₄⋊C₄	—	3	1	no	—
670	C₂×C₄⋊C₄	—	3	1	no	—
671	C₂×C₄⋊C₄	—	3	1	no	—
672	C₂×C₄⋊C₄	—	3	1	no	—
673	C₂×C₄⋊C₄	—	3	1	no	—
674	C₂×C₄⋊C₄	—	3	1	no	—
675	C₂×C₄⋊C₄	—	3	1	no	—
676	C₂×C₄⋊C₄	—	3	1	no	—
677	C₂×C₄⋊C₄	—	3	1	no	—
678	C₂×C₄⋊C₄	—	3	1	no	—
679	C₂×C₄⋊C₄	—	3	1	no	—
680	C₂×C₄⋊C₄	—	3	1	no	—
681	C₂×C₄⋊C₄	—	3	1	no	—
682	C₂×C₄⋊C₄	—	3	1	no	—
683	C₂×C₄⋊C₄	—	3	1	no	—
684	C₂×C₄⋊C₄	—	3	1	no	—
685	C₂×C₄⋊C₄	—	3	1	no	—
686	C₂×C₄⋊C₄	—	3	1	no	—
687	C₂×C₄⋊C₄	—	3	1	no	—
688	C₂×C₄⋊C₄	—	3	1	no	—
689	C₂×C₄⋊C₄	—	3	1	no	—
690	C₂×C₄⋊C₄	—	3	1	no	—
691	C₂×C₄⋊C₄	—	3	1	no	—
692	C₂×C₄⋊C₄	—	3	1	no	—
693	C₂×C₄⋊C₄	—	3	1	no	—
694	C₂×C₄⋊C₄	—	3	1	no	—
695	C₂×C₄⋊C₄	—	3	1	no	—
696	C₂×C₄⋊C₄	—	3	1	no	—
697	C₂×C₄⋊C₄	—	3	1	no	—
698	C₂×C₄⋊C₄	—	3	1	no	—
699	C₂×C₄⋊C₄	—	3	1	no	—
700	C₂×C₄⋊C₄	—	3	1	no	—
701	C₂×C₄⋊C₄	—	6	4	no	—
702	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	—	3	1	no	—
717	C₂×C₂²⋊C₄	—	3	1	no	—
718	C₂×C₂²⋊C₄	—	3	1	no	—
719	C₂×C₂²⋊C₄	—	3	1	no	—
720	C₂×C₂²⋊C₄	—	3	1	no	—
721	C₂×C₂²⋊C₄	—	3	1	no	—
722	C₂×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
728	C₂×C₄²	—	3	1	no	—
729	C₂×C₄²	—	3	1	no	—
730	C₂×C₄²	—	3	1	no	—
731	C₂×C₄²	—	3	1	no	—
732	C₂×C₄²	—	3	1	no	—
733	C₂×C₄²	—	3	1	no	—
734	C₂×C₄²	—	3	1	no	—
735	C₂×C₄²	—	3	1	no	—
736	C₂×C₄²	—	3	1	no	—
737	C₂×C₄²	—	3	1	no	—
738	C₂×C₄²	—	3	1	no	—
739	C₂×C₄²	—	3	1	no	—
740	C₂×C₄²	—	3	1	no	—
741	C₂×C₄²	—	3	1	no	—
742	C₂×C₄²	—	3	1	no	—
743	C₂×C₄²	—	3	1	no	—
744	C₂×C₄²	—	3	1	no	—
745	C₂×C₄²	—	3	1	no	—
746	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
747	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
748	#95	—	3	1	no	—
749	#95	—	3	1	no	—
750	#95	—	3	1	no	—
751	#95	—	3	1	no	—
752	#95	—	3	1	no	—
753	#95	—	3	1	no	—
754	#95	—	3	1	no	—
755	#95	—	3	1	no	—
756	#95	—	3	1	no	—
757	#95	—	3	1	no	—
758	#95	—	3	1	no	—
759	#95	—	3	1	no	—
760	#95	—	3	1	no	—
761	#95	—	3	1	no	—
762	#95	—	3	1	no	—
763	#95	—	3	1	no	—
764	#95	—	3	1	no	—
765	#95	—	3	1	no	—
766	#95	—	3	1	no	—
767	#95	—	3	1	no	—
768	#95	—	3	1	no	—
769	#95	—	3	1	no	—
770	#95	—	3	1	no	—
771	#95	—	3	1	no	—
772	#95	—	3	1	no	—
773	#95	—	3	1	no	—
774	#95	—	3	1	no	—
775	#95	—	3	1	no	—
776	#95	—	3	1	no	—
777	#95	—	3	1	no	—
778	#95	—	3	1	no	—
779	#95	—	3	1	no	—
780	#95	—	3	1	no	—
781	#95	—	3	1	no	—
782	#95	—	3	1	no	—
783	#95	—	3	1	no	—
784	#95	—	3	1	no	—
785	#95	—	3	1	no	—
786	#95	—	3	1	no	—
787	#95	—	3	1	no	—
788	#95	—	3	1	no	—
789	#95	—	3	1	no	—
790	#95	—	3	1	no	—
791	#95	—	3	1	no	—
792	#95	—	3	1	no	—
793	#95	—	3	1	no	—
794	#95	—	3	1	no	—
795	#95	—	3	1	no	—
796	#95	—	3	1	no	—
797	#95	—	3	1	no	—
798	#95	—	3	1	no	—
799	#95	—	3	1	no	—
800	#95	—	3	1	no	—
801	#95	—	3	1	no	—
802	#95	—	3	1	no	—
803	#95	—	3	1	no	—
804	#95	—	3	1	no	—
805	#95	—	3	1	no	—
806	#95	—	3	1	no	—
807	#95	—	3	1	no	—
808	#95	C₂²×D₃	1	1	yes	characteristic
809	#95	C₂²×D₃	1	1	yes	characteristic
810	#95	C₂²×D₃	1	1	yes	characteristic
811	#95	C₂²×D₃	1	1	yes	characteristic
812	#95	C₂²×D₃	1	1	yes	characteristic
813	#95	C₂²×D₃	1	1	yes	characteristic
814	#95	C₂²×D₃	1	1	yes	characteristic
815	#95	C₂²×D₃	1	1	yes	characteristic
816	#95	C₂²×D₃	1	1	yes	characteristic
817	#95	C₂²×D₃	1	1	yes	characteristic
818	#95	C₂²×D₃	1	1	yes	characteristic
819	#95	C₂²×D₃	1	1	yes	characteristic
820	C₂³×C₃	—	2	1	no	—
821	C₂³×C₃	—	2	1	no	—
822	C₂³×C₃	—	2	1	no	—
823	C₂³×C₃	—	2	1	no	—
824	C₂³×C₃	—	2	1	no	—
825	C₂³×C₃	—	2	1	no	—
826	C₂³×C₃	C₂×#41	1	2	yes	—
827	C₂³×C₃	C₂⁵	1	1	yes	characteristic
828	C₂×C₃×C₄	—	2	1	no	—
829	C₂×C₃×C₄	—	2	1	no	—
830	C₂×C₃×C₄	—	2	1	no	—
831	C₂×C₃×C₄	—	2	1	no	—
832	C₂×C₃×C₄	—	2	1	no	—
833	C₂×C₃×C₄	—	2	1	no	—
834	C₂×C₃×C₄	—	2	1	no	—
835	C₂×C₃×C₄	—	2	1	no	—
836	C₂×C₃×C₄	—	2	1	no	—
837	C₂×C₃×C₄	—	2	1	no	—
838	C₂×C₃×C₄	—	2	1	no	—
839	C₂×C₃×C₄	—	2	1	no	—
840	C₂×C₃×C₄	—	2	1	no	—
841	C₂×C₃×C₄	—	2	1	no	—
842	C₂×C₃×C₄	—	2	1	no	—
843	C₂×C₃×C₄	—	2	1	no	—
844	C₂×C₃×C₄	—	2	1	no	—
845	C₂×C₃×C₄	—	2	1	no	—
846	C₂×C₃×C₄	—	2	1	no	—
847	C₂×C₃×C₄	—	2	1	no	—
848	C₂×C₃×C₄	—	2	1	no	—
849	C₂×C₃×C₄	—	2	1	no	—
850	C₂×C₃×C₄	—	2	1	no	—
851	C₂×C₃×C₄	—	2	1	no	—
852	C₂×C₃×C₄	—	2	1	no	—
853	C₂×C₃×C₄	—	2	1	no	—
854	C₂×C₃×C₄	—	2	1	no	—
855	C₂×C₃×C₄	—	2	1	no	—
856	C₂×C₃×C₄	—	2	1	no	—
857	C₂×C₃×C₄	—	2	1	no	—
858	C₂×C₃×C₄	—	2	1	no	—
859	C₂×C₃×C₄	—	2	1	no	—
860	C₂×C₃×C₄	—	2	1	no	—
861	C₂×C₃×C₄	—	2	1	no	—
862	C₂×C₃×C₄	—	2	1	no	—
863	C₂×C₃×C₄	—	2	1	no	—
864	C₂×C₃×C₄	—	2	1	no	—
865	C₂×C₃×C₄	—	2	1	no	—
866	C₂×C₃×C₄	—	2	1	no	—
867	C₂×C₃×C₄	—	8	2	no	—
868	C₂×C₃×C₄	C₂×#41	1	2	yes	—
869	C₂×C₃×C₄	C₂×#41	1	2	yes	—
870	C₂×C₃×C₄	C₂×#41	1	2	yes	—
871	C₂×Dic₃	—	2	1	no	—
872	C₂×Dic₃	—	2	1	no	—
873	C₂×Dic₃	—	2	1	no	—
874	C₂×Dic₃	—	2	1	no	—
875	C₂×Dic₃	—	2	1	no	—
876	C₂×Dic₃	—	2	1	no	—
877	C₂×Dic₃	—	2	1	no	—
878	C₂×Dic₃	—	2	1	no	—
879	C₂×Dic₃	—	2	1	no	—
880	C₂×Dic₃	—	2	1	no	—
881	C₂×Dic₃	—	2	1	no	—
882	C₂×Dic₃	—	2	1	no	—
883	C₂×Dic₃	—	2	1	no	—
884	C₂×Dic₃	—	2	1	no	—
885	C₂×Dic₃	—	2	1	no	—
886	C₂×Dic₃	—	2	1	no	—
887	C₂×Dic₃	—	2	1	no	—
888	C₂×Dic₃	—	2	1	no	—
889	C₂×Dic₃	—	2	1	no	—
890	C₂×Dic₃	—	2	1	no	—
891	C₂×Dic₃	—	2	1	no	—
892	C₂×Dic₃	—	2	1	no	—
893	C₂×Dic₃	—	2	1	no	—
894	C₂×Dic₃	—	2	1	no	—
895	C₂×Dic₃	—	2	1	no	—
896	C₂×Dic₃	—	2	1	no	—
897	C₂×Dic₃	—	2	1	no	—
898	C₂×Dic₃	—	2	1	no	—
899	C₂×Dic₃	—	2	1	no	—
900	C₂×Dic₃	—	2	1	no	—
901	C₂×Dic₃	—	2	1	no	—
902	C₂×Dic₃	—	2	1	no	—
903	C₂×Dic₃	—	2	1	no	—
904	C₂×Dic₃	—	2	1	no	—
905	C₂×Dic₃	—	2	1	no	—
906	C₂×Dic₃	—	2	1	no	—
907	C₂×Dic₃	—	2	1	no	—
908	C₂×Dic₃	—	2	1	no	—
909	C₂×Dic₃	—	2	1	no	—
910	C₂×Dic₃	—	2	1	no	—
911	C₂×Dic₃	—	2	1	no	—
912	C₂×Dic₃	—	2	1	no	—
913	C₂×Dic₃	—	2	1	no	—
914	C₂×Dic₃	—	2	1	no	—
915	C₂×Dic₃	—	4	4	no	—
916	C₂×Dic₃	—	8	2	no	—
917	C₂×Dic₃	C₂×#41	1	2	yes	—
918	C₂×Dic₃	C₂×#41	1	2	yes	—
919	C₂×Dic₃	2₋¹⁺⁴	1	2	yes	—
920	C₂×Dic₃	2₋¹⁺⁴	1	2	yes	—
921	Dic₆	—	4	4	no	—
922	Dic₆	—	8	2	no	—
923	C₂⁴	C₂³×D₃	1	1	yes	characteristic
924	C₂×Q₈	—	6	2	no	—
925	C₂×Q₈	—	6	2	no	—
926	C₂×Q₈	—	6	2	no	—
927	C₂×Q₈	—	12	1	no	—
928	C₂×Q₈	—	12	1	no	—
929	C₂×Q₈	—	12	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	3	1	no	—
932	C₂²×C₄	—	3	1	no	—
933	C₂²×C₄	—	3	1	no	—
934	C₂²×C₄	—	3	1	no	—
935	C₂²×C₄	—	3	1	no	—
936	C₂²×C₄	—	3	1	no	—
937	C₂²×C₄	—	3	1	no	—
938	C₂²×C₄	—	3	1	no	—
939	C₂²×C₄	—	3	1	no	—
940	C₂²×C₄	—	3	1	no	—
941	C₂²×C₄	—	3	1	no	—
942	C₂²×C₄	—	3	1	no	—
943	C₂²×C₄	—	3	1	no	—
944	C₂²×C₄	—	3	1	no	—
945	C₂²×C₄	—	3	1	no	—
946	C₂²×C₄	—	3	1	no	—
947	C₂²×C₄	—	4	1	no	—
948	C₂²×C₄	—	4	1	no	—
949	C₂²×C₄	—	6	2	no	—
950	C₂²×C₄	—	6	2	no	—
951	C₂²×C₄	—	6	2	no	—
952	C₂²×C₄	—	12	1	no	—
953	C₂²×C₄	—	12	1	no	—
954	C₂²×C₄	—	12	1	no	—
955	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
956	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
957	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
958	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
959	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
960	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
961	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
962	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
963	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
964	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
965	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
966	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
967	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
968	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	3	4	no	—
978	C₄⋊C₄	—	4	1	no	—
979	C₄⋊C₄	—	4	1	no	—
980	C₄⋊C₄	—	4	1	no	—
981	C₄⋊C₄	—	4	1	no	—
982	C₄⋊C₄	—	4	1	no	—
983	C₄⋊C₄	—	4	1	no	—
984	C₄⋊C₄	—	6	2	no	—
985	C₄⋊C₄	—	6	2	no	—
986	C₄⋊C₄	—	6	2	no	—
987	C₄⋊C₄	—	6	2	no	—
988	C₄⋊C₄	—	6	2	no	—
989	C₄⋊C₄	—	6	2	no	—
990	C₄⋊C₄	—	6	2	no	—
991	C₄⋊C₄	—	6	2	no	—
992	C₄⋊C₄	—	6	2	no	—
993	C₄⋊C₄	—	6	2	no	—
994	C₄⋊C₄	—	6	2	no	—
995	C₄⋊C₄	—	6	2	no	—
996	C₄⋊C₄	—	6	2	no	—
997	C₄⋊C₄	—	6	2	no	—
998	C₄⋊C₄	—	12	1	no	—
999	C₄⋊C₄	—	12	1	no	—
1000	C₄⋊C₄	—	12	1	no	—
1001	C₄⋊C₄	—	12	1	no	—
1002	C₄⋊C₄	—	12	1	no	—
1003	C₄⋊C₄	—	12	1	no	—
1004	C₄⋊C₄	—	12	1	no	—
1005	C₄⋊C₄	—	12	1	no	—
1006	C₄⋊C₄	—	12	1	no	—
1007	C₄⋊C₄	—	12	1	no	—
1008	C₄⋊C₄	—	12	1	no	—
1009	C₄⋊C₄	—	12	1	no	—
1010	C₄⋊C₄	—	12	1	no	—
1011	C₄⋊C₄	—	12	1	no	—
1012	C₄⋊C₄	—	12	1	no	—
1013	C₄⋊C₄	—	12	1	no	—
1014	C₄⋊C₄	—	12	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	4	1	no	—
1020	C₂²⋊C₄	—	6	2	no	—
1021	C₂²⋊C₄	—	6	2	no	—
1022	C₂²⋊C₄	—	6	2	no	—
1023	C₂²⋊C₄	—	12	1	no	—
1024	C₂²⋊C₄	—	12	1	no	—
1025	C₂²⋊C₄	—	12	1	no	—
1026	C₂²⋊C₄	#237	1	4	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	6	2	no	—
1030	C₄²	—	6	2	no	—
1031	C₄²	—	6	2	no	—
1032	C₄²	—	6	2	no	—
1033	C₄²	—	6	2	no	—
1034	C₄²	—	6	2	no	—
1035	C₄²	—	6	2	no	—
1036	C₄²	—	6	2	no	—
1037	C₄²	—	12	1	no	—
1038	C₄²	—	12	1	no	—
1039	C₄²	—	12	1	no	—
1040	C₄²	—	12	1	no	—
1041	C₄²	—	12	1	no	—
1042	C₄²	—	12	1	no	—
1043	C₄²	—	12	1	no	—
1044	C₄²	—	12	1	no	—
1045	C₄²	—	12	1	no	—
1046	C₄²	—	12	1	no	—
1047	C₂²×C₃	—	2	2	no	—
1048	C₂²×C₃	—	2	2	no	—
1049	C₂²×C₃	—	2	2	no	—
1050	C₂²×C₃	—	4	1	no	—
1051	C₂²×C₃	—	4	1	no	—
1052	C₂²×C₃	—	4	1	no	—
1053	C₂²×C₃	—	4	1	no	—
1054	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1055	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1056	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1057	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1058	C₂²×C₃	#585	1	1	yes	characteristic
1059	C₂²×C₃	#585	1	1	yes	characteristic
1060	C₂²×C₃	#585	1	1	yes	characteristic
1061	C₃×C₄	—	2	2	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	4	1	no	—
1065	C₃×C₄	—	4	1	no	—
1066	C₃×C₄	—	4	1	no	—
1067	C₃×C₄	—	4	1	no	—
1068	C₃×C₄	—	4	1	no	—
1069	C₃×C₄	—	4	1	no	—
1070	C₃×C₄	—	4	1	no	—
1071	C₃×C₄	—	4	1	no	—
1072	C₃×C₄	—	4	1	no	—
1073	C₃×C₄	—	4	1	no	—
1074	C₃×C₄	—	4	1	no	—
1075	Dic₃	—	2	2	no	—
1076	Dic₃	—	2	2	no	—
1077	Dic₃	—	2	2	no	—
1078	Dic₃	—	2	2	no	—
1079	Dic₃	—	4	1	no	—
1080	Dic₃	—	4	1	no	—
1081	Dic₃	—	4	1	no	—
1082	Dic₃	—	4	1	no	—
1083	Dic₃	—	4	1	no	—
1084	Dic₃	—	4	1	no	—
1085	Dic₃	—	4	1	no	—
1086	Dic₃	—	4	1	no	—
1087	Dic₃	—	4	1	no	—
1088	Dic₃	—	4	1	no	—
1089	Dic₃	—	4	1	no	—
1090	Dic₃	—	4	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	C₂×#237	1	2	yes	—
1098	C₂³	C₂⁴×D₃	1	1	yes	characteristic
1099	Q₈	—	12	4	no	—
1100	Q₈	—	24	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	3	2	no	—
1141	C₂×C₄	—	3	2	no	—
1142	C₂×C₄	—	3	2	no	—
1143	C₂×C₄	—	3	2	no	—
1144	C₂×C₄	—	6	1	no	—
1145	C₂×C₄	—	6	1	no	—
1146	C₂×C₄	—	6	1	no	—
1147	C₂×C₄	—	6	1	no	—
1148	C₂×C₄	—	6	1	no	—
1149	C₂×C₄	—	6	1	no	—
1150	C₂×C₄	—	6	1	no	—
1151	C₂×C₄	—	6	1	no	—
1152	C₂×C₄	—	6	1	no	—
1153	C₂×C₄	—	6	1	no	—
1154	C₂×C₄	—	6	1	no	—
1155	C₂×C₄	—	6	1	no	—
1156	C₂×C₄	—	6	1	no	—
1157	C₂×C₄	—	6	1	no	—
1158	C₂×C₄	—	6	1	no	—
1159	C₂×C₄	—	6	1	no	—
1160	C₂×C₄	—	6	1	no	—
1161	C₂×C₄	—	6	1	no	—
1162	C₂×C₄	—	6	1	no	—
1163	C₂×C₄	—	6	1	no	—
1164	C₂×C₄	—	6	1	no	—
1165	C₂×C₄	—	6	1	no	—
1166	C₂×C₄	—	6	1	no	—
1167	C₂×C₄	—	6	1	no	—
1168	C₂×C₄	—	6	1	no	—
1169	C₂×C₄	—	6	1	no	—
1170	C₂×C₄	—	6	1	no	—
1171	C₂×C₄	—	6	1	no	—
1172	C₂×C₄	—	6	1	no	—
1173	C₂×C₄	—	6	1	no	—
1174	C₂×C₄	—	6	1	no	—
1175	C₂×C₄	—	6	1	no	—
1176	C₂×C₄	—	6	1	no	—
1177	C₂×C₄	—	6	1	no	—
1178	C₂×C₄	—	6	1	no	—
1179	C₂×C₄	—	6	1	no	—
1180	C₂×C₄	—	6	1	no	—
1181	C₂×C₄	—	6	1	no	—
1182	C₂×C₄	—	6	1	no	—
1183	C₂×C₄	—	6	1	no	—
1184	C₂×C₄	—	6	1	no	—
1185	C₂×C₄	—	6	1	no	—
1186	C₂×C₄	—	6	1	no	—
1187	C₂×C₄	—	6	1	no	—
1188	C₂×C₄	—	8	2	no	—
1189	C₂×C₄	—	12	4	no	—
1190	C₂×C₄	—	24	2	no	—
1191	C₂×C₄	C₂×#237	1	2	yes	—
1192	C₂×C₄	C₂×#237	1	2	yes	—
1193	C₂×C₄	D₃×#41	1	2	yes	—
1194	C₂×C₃	—	4	2	no	—
1195	C₂×C₃	#3461	1	1	yes	characteristic
1196	C₂×C₃	#3475	1	1	yes	characteristic
1197	C₂×C₃	#3515	1	1	yes	characteristic
1198	C₂×C₃	#3521	1	1	yes	characteristic
1199	C₂×C₃	#3523	1	1	yes	characteristic
1200	C₂×C₃	#3564	1	1	yes	characteristic
1201	C₂×C₃	#3565	1	1	yes	characteristic
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	C₂²×#237	1	1	yes	characteristic
1210	C₂²	C₂×D₃×#41	1	1	yes	characteristic
1211	C₂²	#5964	1	1	yes	characteristic
1212	C₂²	#5966	1	1	yes	characteristic
1213	C₂²	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1214	C₂²	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1215	C₂²	#5968	1	1	yes	characteristic
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	2	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	6	2	no	—
1231	C₄	—	6	2	no	—
1232	C₄	—	6	2	no	—
1233	C₄	—	6	2	no	—
1234	C₄	—	12	1	no	—
1235	C₄	—	12	1	no	—
1236	C₄	—	12	1	no	—
1237	C₄	—	12	1	no	—
1238	C₄	—	12	1	no	—
1239	C₄	—	12	1	no	—
1240	C₄	—	12	1	no	—
1241	C₄	—	12	1	no	—
1242	C₄	—	12	1	no	—
1243	C₄	—	12	1	no	—
1244	C₄	—	12	1	no	—
1245	C₄	—	12	1	no	—
1246	C₃	#38345	1	1	yes	characteristic, complemented, Sylow
1247	C₂	—	4	2	no	—
1248	C₂	#86365	1	1	yes	characteristic
1249	C₂	#86505	1	1	yes	characteristic
1250	C₂	#86514	1	1	yes	characteristic
1251	C₂	#86675	1	1	yes	characteristic
1252	C₂	#86682	1	1	yes	characteristic
1253	C₂	#86800	1	1	yes	characteristic
1254	C₂	#87138	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₃
commutator, socle, cosocle	C₂³×C₃	C₂⁵
Fitting	C₃×#2722	C₂
prime radical	C₂⁴×C₃	C₂⁴
hypercenter	#2722	D₃
hypocenter	C₃	#38345
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #2722

Complements

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

N	H ≅ G/N	type
6. #77917	C₂	semidirect
7. #77916	C₂	semidirect
8. #77836	C₂	semidirect
9. #77814	C₂	semidirect
10. #77778	C₂	semidirect
11. #77777	C₂	semidirect
12. #77774	C₂	semidirect
13. #77751	C₂	semidirect
18. #76141	C₂	semidirect
19. #76058	C₂	semidirect
20. #76043	C₂	semidirect
21. #75962	C₂	semidirect
22. #75291	C₂	semidirect
23. #75190	C₂	semidirect
24. #75134	C₂	semidirect
25. #74958	C₂	semidirect
1246. C₃	#38345	semidirect

Maximal subgroups

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

subgroup	index
C₃×#2722	2
#83093	2
#83091	2
#83075	2
Dic₃×#126	2
#77917	2
#77916	2
#77836	2
#77814	2
#77778	2
#77777	2
#77774	2
#77751	2
#77557	2
#77506	2
#77502	2
#77496	2
#76141	2
#76058	2
#76043	2
#75962	2
#75291	2
#75190	2
#75134	2
#74958	2
#74574	2
#74396	2
#73931	2
#73921	2
#73908	2
#73867	2
#38345	3