Subgroups — #11301625

Order 768.

1344 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2822	C₂	1	1	yes	maximal, characteristic, complemented
2	#83064	C₂	1	1	yes	maximal, characteristic
3	#83064	C₂	1	1	yes	maximal, characteristic
4	#83023	C₂	1	1	yes	maximal, characteristic, complemented
5	#83023	C₂	1	1	yes	maximal, characteristic, complemented
6	#78315	C₂	1	1	yes	maximal, characteristic, complemented
7	#78304	C₂	1	1	yes	maximal, characteristic
8	#78282	C₂	1	1	yes	maximal, characteristic, complemented
9	#78277	C₂	1	1	yes	maximal, characteristic
10	#78201	C₂	1	1	yes	maximal, characteristic
11	#78200	C₂	1	1	yes	maximal, characteristic
12	#78176	C₂	1	1	yes	maximal, characteristic, complemented
13	#78159	C₂	1	1	yes	maximal, characteristic, complemented
14	#78004	C₂	1	1	yes	maximal, characteristic
15	#78002	C₂	1	1	yes	maximal, characteristic
16	#77924	C₂	1	1	yes	maximal, characteristic, complemented
17	#77917	C₂	1	1	yes	maximal, characteristic, complemented
18	#77902	C₂	1	1	yes	maximal, characteristic
19	#77900	C₂	1	1	yes	maximal, characteristic
20	#77893	C₂	1	1	yes	maximal, characteristic
21	#77887	C₂	1	1	yes	maximal, characteristic
22	#77809	C₂	1	1	yes	maximal, characteristic
23	#77805	C₂	1	1	yes	maximal, characteristic, complemented
24	#77803	C₂	1	1	yes	maximal, characteristic, complemented
25	#77799	C₂	1	1	yes	maximal, characteristic, complemented
26	#77783	C₂	1	1	yes	maximal, characteristic
27	#77780	C₂	1	1	yes	maximal, characteristic, complemented
28	#77777	C₂	1	1	yes	maximal, characteristic, complemented
29	#77769	C₂	1	1	yes	maximal, characteristic, complemented
30	#74224	C₂	1	1	yes	maximal, characteristic
31	#74192	C₂	1	1	yes	maximal, characteristic, complemented
32	#47825	—	3	1	no	maximal, Sylow
33	C₂×C₃×#125	C₂²	1	1	yes	characteristic
34	C₂×C₃×#125	C₂²	1	1	yes	characteristic
35	C₂×#872	C₂²	1	1	yes	characteristic
36	C₃×#400	C₂²	1	1	yes	characteristic
37	C₃×#400	C₂²	1	1	yes	characteristic
38	C₃×#400	C₂²	1	1	yes	characteristic
39	C₃×#400	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×#398	C₂²	1	1	yes	characteristic
44	C₃×#398	C₂²	1	1	yes	characteristic
45	C₃×#398	C₂²	1	1	yes	characteristic
46	C₃×#398	C₂²	1	1	yes	characteristic
47	C₃×#398	C₂²	1	1	yes	characteristic
48	C₃×#382	C₂²	1	1	yes	characteristic
49	#4994	C₂²	1	1	yes	characteristic
50	#4994	C₂²	1	1	yes	characteristic
51	#4993	C₂²	1	1	yes	characteristic
52	#4993	C₂²	1	1	yes	characteristic
53	#4992	C₂²	1	1	yes	characteristic
54	#4992	C₂²	1	1	yes	characteristic
55	#4990	C₂²	1	1	yes	characteristic
56	#4990	C₂²	1	1	yes	characteristic
57	#4990	C₂²	1	1	yes	characteristic
58	#4990	C₂²	1	1	yes	characteristic
59	#4990	C₂²	1	1	yes	characteristic
60	#4990	C₂²	1	1	yes	characteristic
61	#4989	C₂²	1	1	yes	characteristic
62	#4989	C₂²	1	1	yes	characteristic
63	#4989	C₂²	1	1	yes	characteristic
64	#4989	C₂²	1	1	yes	characteristic
65	#4987	C₂²	1	1	yes	characteristic
66	#4987	C₂²	1	1	yes	characteristic
67	#4986	C₂²	1	1	yes	characteristic
68	#4985	C₂²	1	1	yes	characteristic
69	#4985	C₂²	1	1	yes	characteristic
70	#4985	C₂²	1	1	yes	characteristic
71	#4985	C₂²	1	1	yes	characteristic
72	#4984	C₂²	1	1	yes	characteristic
73	#4984	C₂²	1	1	yes	characteristic
74	#4984	C₂²	1	1	yes	characteristic
75	#4984	C₂²	1	1	yes	characteristic
76	#4984	C₂²	1	1	yes	characteristic
77	#4984	C₂²	1	1	yes	characteristic
78	#4984	C₂²	1	1	yes	characteristic
79	#4984	C₂²	1	1	yes	characteristic
80	#4984	C₂²	1	1	yes	characteristic
81	#4984	C₂²	1	1	yes	characteristic
82	#4984	C₂²	1	1	yes	characteristic
83	#4984	C₂²	1	1	yes	characteristic
84	#4984	C₂²	1	1	yes	characteristic
85	#4983	C₂²	1	1	yes	characteristic
86	#4983	C₂²	1	1	yes	characteristic
87	#4982	C₂²	1	1	yes	characteristic
88	#4982	C₂²	1	1	yes	characteristic
89	#4982	C₂²	1	1	yes	characteristic
90	#4982	C₂²	1	1	yes	characteristic
91	#4980	C₂²	1	1	yes	characteristic
92	#4980	C₂²	1	1	yes	characteristic
93	#4980	C₂²	1	1	yes	characteristic
94	#4980	C₂²	1	1	yes	characteristic
95	#4980	C₂²	1	1	yes	characteristic
96	#4980	C₂²	1	1	yes	characteristic
97	#4980	C₂²	1	1	yes	characteristic
98	#4980	C₂²	1	1	yes	characteristic
99	#4980	C₂²	1	1	yes	characteristic
100	#4980	C₂²	1	1	yes	characteristic
101	#4979	C₂²	1	1	yes	characteristic
102	#4978	C₂²	1	1	yes	characteristic
103	#4978	C₂²	1	1	yes	characteristic
104	#4978	C₂²	1	1	yes	characteristic
105	#4978	C₂²	1	1	yes	characteristic
106	#4977	C₂²	1	1	yes	characteristic
107	#4976	C₂²	1	1	yes	characteristic
108	#4976	C₂²	1	1	yes	characteristic
109	#4976	C₂²	1	1	yes	characteristic
110	#4976	C₂²	1	1	yes	characteristic
111	#4976	C₂²	1	1	yes	characteristic
112	#4976	C₂²	1	1	yes	characteristic
113	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	Dic₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	#4973	C₂²	1	1	yes	characteristic
121	#4935	C₂²	1	1	yes	characteristic
122	#4932	C₂²	1	1	yes	characteristic
123	#4932	C₂²	1	1	yes	characteristic
124	#4677	C₂²	1	1	yes	characteristic
125	#4675	C₂²	1	1	yes	characteristic
126	#4675	C₂²	1	1	yes	characteristic
127	#4674	C₂²	1	1	yes	characteristic
128	#4674	C₂²	1	1	yes	characteristic
129	#4673	C₂²	1	1	yes	characteristic
130	#4670	C₂²	1	1	yes	characteristic
131	#4670	C₂²	1	1	yes	characteristic
132	#4670	C₂²	1	1	yes	characteristic
133	#4670	C₂²	1	1	yes	characteristic
134	#4670	C₂²	1	1	yes	characteristic
135	#4670	C₂²	1	1	yes	characteristic
136	#4670	C₂²	1	1	yes	characteristic
137	#4670	C₂²	1	1	yes	characteristic
138	#4669	C₂²	1	1	yes	characteristic
139	#4669	C₂²	1	1	yes	characteristic
140	C₃⋊#401	C₂²	1	1	yes	characteristic
141	C₃⋊#401	C₂²	1	1	yes	characteristic
142	#4661	C₂²	1	1	yes	characteristic
143	#4661	C₂²	1	1	yes	characteristic
144	#4660	C₂²	1	1	yes	characteristic
145	#4660	C₂²	1	1	yes	characteristic
146	#4660	C₂²	1	1	yes	characteristic
147	#4660	C₂²	1	1	yes	characteristic
148	#4659	C₂²	1	1	yes	characteristic
149	#4659	C₂²	1	1	yes	characteristic
150	#4658	C₂²	1	1	yes	characteristic
151	#4658	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	#4654	C₂²	1	1	yes	characteristic
161	#4654	C₂²	1	1	yes	characteristic
162	#4654	C₂²	1	1	yes	characteristic
163	#4654	C₂²	1	1	yes	characteristic
164	#4654	C₂²	1	1	yes	characteristic
165	#4654	C₂²	1	1	yes	characteristic
166	#4653	C₂²	1	1	yes	characteristic
167	#4653	C₂²	1	1	yes	characteristic
168	#4653	C₂²	1	1	yes	characteristic
169	#4653	C₂²	1	1	yes	characteristic
170	#4653	C₂²	1	1	yes	characteristic
171	#4653	C₂²	1	1	yes	characteristic
172	#4652	C₂²	1	1	yes	characteristic
173	#4652	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	#4650	C₂²	1	1	yes	characteristic
179	#4649	C₂²	1	1	yes	characteristic
180	#4649	C₂²	1	1	yes	characteristic
181	#4648	C₂²	1	1	yes	characteristic
182	#4647	C₂²	1	1	yes	characteristic
183	#4647	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	#2822	D₃	1	1	yes	characteristic, complemented
189	#2810	—	3	1	no	—
190	#2809	—	3	1	no	—
191	#2802	—	3	1	no	—
192	#2798	—	3	1	no	—
193	#2788	—	3	1	no	—
194	#2787	—	3	1	no	—
195	#2783	—	3	1	no	—
196	#2777	—	3	1	no	—
197	#2776	—	3	1	no	—
198	#2773	—	3	1	no	—
199	#2770	—	3	1	no	—
200	#2768	—	3	1	no	—
201	#2612	—	3	1	no	—
202	#2611	—	3	1	no	—
203	#2611	—	3	1	no	—
204	#2596	—	3	1	no	—
205	#2596	—	3	1	no	—
206	#2594	—	3	1	no	—
207	#2590	—	3	1	no	—
208	#2588	—	3	1	no	—
209	#2585	—	3	1	no	—
210	#2533	—	3	1	no	—
211	#2532	—	3	1	no	—
212	#2528	—	3	1	no	—
213	#2524	—	3	1	no	—
214	#2514	—	3	1	no	—
215	#2508	—	3	1	no	—
216	#2330	—	3	1	no	—
217	#2330	—	3	1	no	—
218	#2314	—	3	1	no	—
219	C₂²×C₄×D₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₆	C₂³	1	1	yes	characteristic
221	C₃×#125	—	2	4	no	—
222	C₃×#125	—	2	4	no	—
223	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊Dic₃	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×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×Dic₃⋊C₄	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	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
306	#872	—	2	4	no	—
307	C₃×#95	C₂³	1	1	yes	characteristic
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	C₂×#125	C₂×D₃	1	1	yes	characteristic
378	C₂×#125	C₂×D₃	1	1	yes	characteristic
379	C₂×#117	—	3	1	no	—
380	#401	—	3	1	no	—
381	#401	—	3	1	no	—
382	#400	—	3	1	no	—
383	#400	—	3	1	no	—
384	#400	—	3	1	no	—
385	#400	—	3	1	no	—
386	#400	—	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	C₂×D₃	1	1	yes	characteristic
396	#400	C₂×D₃	1	1	yes	characteristic
397	#400	C₂×D₃	1	1	yes	characteristic
398	#400	C₂×D₃	1	1	yes	characteristic
399	#399	—	3	1	no	—
400	#399	—	3	1	no	—
401	#399	—	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	C₂×D₃	1	1	yes	characteristic
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	#398	C₂×D₃	1	1	yes	characteristic
416	#398	C₂×D₃	1	1	yes	characteristic
417	#398	C₂×D₃	1	1	yes	characteristic
418	#397	—	3	1	no	—
419	#397	—	3	1	no	—
420	#397	—	3	1	no	—
421	#397	—	3	1	no	—
422	#397	—	3	1	no	—
423	#397	—	3	1	no	—
424	#396	—	3	1	no	—
425	#396	—	3	1	no	—
426	#395	—	3	1	no	—
427	#393	—	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	#389	—	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	—	3	1	no	—
449	#389	—	3	1	no	—
450	#389	—	3	1	no	—
451	#389	—	3	1	no	—
452	#389	—	3	1	no	—
453	#389	—	3	1	no	—
454	#388	—	3	1	no	—
455	#388	—	3	1	no	—
456	#388	—	3	1	no	—
457	#388	—	3	1	no	—
458	#388	—	3	1	no	—
459	#388	—	3	1	no	—
460	#388	—	3	1	no	—
461	#388	—	3	1	no	—
462	#388	—	3	1	no	—
463	#388	—	3	1	no	—
464	#388	—	3	1	no	—
465	#388	—	3	1	no	—
466	#388	—	3	1	no	—
467	#388	—	3	1	no	—
468	#388	—	3	1	no	—
469	#388	—	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	—	3	1	no	—
495	#387	—	3	1	no	—
496	#387	—	3	1	no	—
497	#387	—	3	1	no	—
498	#387	—	3	1	no	—
499	#387	—	3	1	no	—
500	#387	—	3	1	no	—
501	#387	—	3	1	no	—
502	#387	—	3	1	no	—
503	#387	—	3	1	no	—
504	#387	—	3	1	no	—
505	#387	—	3	1	no	—
506	#385	—	3	1	no	—
507	#385	—	3	1	no	—
508	#385	—	3	1	no	—
509	#385	—	3	1	no	—
510	#384	—	3	1	no	—
511	#383	—	3	1	no	—
512	#383	—	3	1	no	—
513	#383	—	3	1	no	—
514	#382	—	3	1	no	—
515	#382	—	3	1	no	—
516	#382	—	3	1	no	—
517	#382	C₂×D₃	1	1	yes	characteristic
518	#380	—	3	1	no	—
519	#380	—	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×C₄⋊C₄	—	3	1	no	—
526	C₄×C₄⋊C₄	—	3	1	no	—
527	C₄×C₄⋊C₄	—	3	1	no	—
528	C₄×C₄⋊C₄	—	3	1	no	—
529	#376	—	3	1	no	—
530	#376	—	3	1	no	—
531	#376	—	3	1	no	—
532	C₂³×D₃	C₂⁴	1	1	yes	characteristic
533	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
534	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
535	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
536	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
537	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
538	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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×Dic₃	C₂⁴	1	1	yes	characteristic
549	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
550	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
551	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
552	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
553	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
554	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
555	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
556	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
557	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
558	C₂²×Dic₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×D₃	—	2	2	no	—
564	C₂×C₄×D₃	—	4	1	no	—
565	C₂×C₄×D₃	—	4	1	no	—
566	C₂×Dic₆	—	2	2	no	—
567	C₂×Dic₆	—	4	1	no	—
568	C₂×Dic₆	—	4	1	no	—
569	C₃×C₄⋊C₄	—	2	2	no	—
570	C₃×C₄⋊C₄	—	2	2	no	—
571	C₃×C₄⋊C₄	—	2	2	no	—
572	C₃×C₄⋊C₄	—	2	2	no	—
573	C₃×C₄⋊C₄	—	2	2	no	—
574	C₃×C₄⋊C₄	—	2	2	no	—
575	C₃×C₄⋊C₄	—	2	2	no	—
576	C₃×C₄⋊C₄	—	2	2	no	—
577	C₃×C₄⋊C₄	—	2	2	no	—
578	C₃×C₄⋊C₄	—	2	2	no	—
579	C₃×C₄⋊C₄	—	2	2	no	—
580	C₃×C₄⋊C₄	—	2	2	no	—
581	C₃×C₄⋊C₄	—	4	1	no	—
582	C₃×C₄⋊C₄	—	4	1	no	—
583	C₃×C₄⋊C₄	—	4	1	no	—
584	C₃×C₄⋊C₄	—	4	1	no	—
585	C₃×C₄⋊C₄	—	4	1	no	—
586	C₃×C₄⋊C₄	—	4	1	no	—
587	C₃×C₄²	#41	1	4	yes	—
588	(C₂×D₃)⋊C₄	—	2	2	no	—
589	(C₂×D₃)⋊C₄	—	2	2	no	—
590	(C₂×D₃)⋊C₄	—	2	2	no	—
591	(C₂×D₃)⋊C₄	—	2	2	no	—
592	(C₂×D₃)⋊C₄	—	4	1	no	—
593	(C₂×D₃)⋊C₄	—	4	1	no	—
594	(C₂×D₃)⋊C₄	—	4	1	no	—
595	(C₂×D₃)⋊C₄	—	4	1	no	—
596	(C₂×D₃)⋊C₄	—	4	1	no	—
597	(C₂×D₃)⋊C₄	—	4	1	no	—
598	(C₂×D₃)⋊C₄	—	4	1	no	—
599	(C₂×D₃)⋊C₄	—	4	1	no	—
600	(C₂×D₃)⋊C₄	—	4	1	no	—
601	(C₂×D₃)⋊C₄	—	4	1	no	—
602	C₄⋊Dic₃	—	2	2	no	—
603	C₄⋊Dic₃	—	4	1	no	—
604	C₄⋊Dic₃	—	4	1	no	—
605	C₄⋊Dic₃	—	4	1	no	—
606	C₄⋊Dic₃	—	4	1	no	—
607	C₄⋊Dic₃	—	4	1	no	—
608	C₄⋊Dic₃	—	4	1	no	—
609	C₄⋊Dic₃	—	4	1	no	—
610	C₄⋊Dic₃	—	4	1	no	—
611	C₄⋊Dic₃	—	4	1	no	—
612	C₄⋊Dic₃	—	4	1	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	Dic₃⋊C₄	—	2	2	no	—
620	Dic₃⋊C₄	—	2	2	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	—	4	1	no	—
626	Dic₃⋊C₄	—	4	1	no	—
627	Dic₃⋊C₄	—	4	1	no	—
628	Dic₃⋊C₄	—	4	1	no	—
629	Dic₃⋊C₄	—	4	1	no	—
630	Dic₃⋊C₄	—	4	1	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	C₄×Dic₃	—	2	2	no	—
636	C₄×Dic₃	—	2	2	no	—
637	C₄×Dic₃	—	2	2	no	—
638	C₄×Dic₃	—	4	1	no	—
639	C₄×Dic₃	—	4	1	no	—
640	C₄×Dic₃	—	4	1	no	—
641	C₄×Dic₃	—	4	1	no	—
642	C₄×Dic₃	—	4	1	no	—
643	C₄×Dic₃	—	4	1	no	—
644	C₄×Dic₃	—	4	1	no	—
645	C₄×Dic₃	—	4	1	no	—
646	C₄×Dic₃	—	4	1	no	—
647	C₄×Dic₃	—	4	1	no	—
648	C₄×Dic₃	—	4	1	no	—
649	C₄×Dic₃	—	4	1	no	—
650	C₄×Dic₃	—	4	1	no	—
651	C₄×Dic₃	—	4	1	no	—
652	C₂²×Q₈	—	3	1	no	—
653	C₂³×C₄	—	3	1	no	—
654	#125	—	2	4	no	—
655	#125	—	2	4	no	—
656	#117	—	6	4	no	—
657	C₂×C₄⋊C₄	—	3	1	no	—
658	C₂×C₄⋊C₄	—	3	1	no	—
659	C₂×C₄⋊C₄	—	3	1	no	—
660	C₂×C₄⋊C₄	—	3	1	no	—
661	C₂×C₄⋊C₄	—	3	1	no	—
662	C₂×C₄⋊C₄	—	3	1	no	—
663	C₂×C₄⋊C₄	—	3	1	no	—
664	C₂×C₄⋊C₄	—	3	1	no	—
665	C₂×C₄⋊C₄	—	3	1	no	—
666	C₂×C₄⋊C₄	—	3	1	no	—
667	C₂×C₄⋊C₄	—	3	1	no	—
668	C₂×C₄⋊C₄	—	3	1	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	C₂²×D₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	3	1	no	—
709	C₂×C₂²⋊C₄	—	3	1	no	—
710	C₂×C₂²⋊C₄	—	3	1	no	—
711	C₂×C₂²⋊C₄	—	3	1	no	—
712	C₂×C₂²⋊C₄	—	3	1	no	—
713	C₂×C₂²⋊C₄	—	3	1	no	—
714	C₂×C₂²⋊C₄	—	3	1	no	—
715	C₂×C₂²⋊C₄	—	3	1	no	—
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×C₄²	—	3	1	no	—
723	C₂×C₄²	—	3	1	no	—
724	C₂×C₄²	—	3	1	no	—
725	C₂×C₄²	—	3	1	no	—
726	C₂×C₄²	—	3	1	no	—
727	C₂×C₄²	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
740	#95	—	3	1	no	—
741	#95	—	3	1	no	—
742	#95	—	3	1	no	—
743	#95	—	3	1	no	—
744	#95	—	3	1	no	—
745	#95	—	3	1	no	—
746	#95	—	3	1	no	—
747	#95	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
795	#95	C₂²×D₃	1	1	yes	characteristic
796	#95	C₂²×D₃	1	1	yes	characteristic
797	#95	C₂²×D₃	1	1	yes	characteristic
798	#95	C₂²×D₃	1	1	yes	characteristic
799	#95	C₂²×D₃	1	1	yes	characteristic
800	#95	C₂²×D₃	1	1	yes	characteristic
801	#95	C₂²×D₃	1	1	yes	characteristic
802	#95	C₂²×D₃	1	1	yes	characteristic
803	#95	C₂²×D₃	1	1	yes	characteristic
804	#95	C₂²×D₃	1	1	yes	characteristic
805	#95	C₂²×D₃	1	1	yes	characteristic
806	#95	C₂²×D₃	1	1	yes	characteristic
807	#95	C₂²×D₃	1	1	yes	characteristic
808	#95	C₂²×D₃	1	1	yes	characteristic
809	#95	C₂²×D₃	1	1	yes	characteristic
810	C₂³×C₃	C₂⁵	1	1	yes	characteristic
811	C₂²×D₃	—	2	1	no	—
812	C₂²×D₃	—	2	1	no	—
813	C₂²×D₃	—	2	1	no	—
814	C₂²×D₃	—	2	1	no	—
815	C₂²×D₃	—	2	1	no	—
816	C₂²×D₃	—	2	1	no	—
817	C₂²×D₃	—	2	1	no	—
818	C₂×C₃×C₄	—	2	1	no	—
819	C₂×C₃×C₄	—	2	1	no	—
820	C₂×C₃×C₄	—	2	1	no	—
821	C₂×C₃×C₄	—	2	1	no	—
822	C₂×C₃×C₄	—	2	1	no	—
823	C₂×C₃×C₄	—	2	1	no	—
824	C₂×C₃×C₄	—	2	1	no	—
825	C₂×C₃×C₄	—	2	1	no	—
826	C₂×C₃×C₄	—	2	1	no	—
827	C₂×C₃×C₄	—	2	1	no	—
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	C₂×#41	1	2	yes	—
861	C₂×C₃×C₄	C₂×#41	1	2	yes	—
862	C₂×C₃×C₄	C₂×#41	1	2	yes	—
863	C₂×Dic₃	—	2	1	no	—
864	C₂×Dic₃	—	2	1	no	—
865	C₂×Dic₃	—	2	1	no	—
866	C₂×Dic₃	—	2	1	no	—
867	C₂×Dic₃	—	2	1	no	—
868	C₂×Dic₃	—	2	1	no	—
869	C₂×Dic₃	—	2	1	no	—
870	C₂×Dic₃	—	2	1	no	—
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⁺⁴	1	2	yes	—
907	C₂×Dic₃	2₋¹⁺⁴	1	2	yes	—
908	C₄×D₃	—	4	4	no	—
909	Dic₆	—	8	2	no	—
910	C₂⁴	—	3	1	no	—
911	C₂×Q₈	—	6	2	no	—
912	C₂×Q₈	—	12	1	no	—
913	C₂×Q₈	—	12	1	no	—
914	C₂²×C₄	—	3	1	no	—
915	C₂²×C₄	—	3	1	no	—
916	C₂²×C₄	—	3	1	no	—
917	C₂²×C₄	—	3	1	no	—
918	C₂²×C₄	—	3	1	no	—
919	C₂²×C₄	—	3	1	no	—
920	C₂²×C₄	—	3	1	no	—
921	C₂²×C₄	—	3	1	no	—
922	C₂²×C₄	—	3	1	no	—
923	C₂²×C₄	—	3	1	no	—
924	C₂²×C₄	—	3	1	no	—
925	C₂²×C₄	—	3	1	no	—
926	C₂²×C₄	—	3	1	no	—
927	C₂²×C₄	—	3	1	no	—
928	C₂²×C₄	—	3	1	no	—
929	C₂²×C₄	—	6	2	no	—
930	C₂²×C₄	—	12	1	no	—
931	C₂²×C₄	—	12	1	no	—
932	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
933	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
935	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
936	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
937	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
938	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
939	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
940	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
941	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
944	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
946	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	4	1	no	—
960	C₄⋊C₄	—	4	1	no	—
961	C₄⋊C₄	—	4	1	no	—
962	C₄⋊C₄	—	4	1	no	—
963	C₄⋊C₄	—	4	1	no	—
964	C₄⋊C₄	—	4	1	no	—
965	C₄⋊C₄	—	6	2	no	—
966	C₄⋊C₄	—	6	2	no	—
967	C₄⋊C₄	—	6	2	no	—
968	C₄⋊C₄	—	6	2	no	—
969	C₄⋊C₄	—	6	2	no	—
970	C₄⋊C₄	—	6	2	no	—
971	C₄⋊C₄	—	6	2	no	—
972	C₄⋊C₄	—	12	1	no	—
973	C₄⋊C₄	—	12	1	no	—
974	C₄⋊C₄	—	12	1	no	—
975	C₄⋊C₄	—	12	1	no	—
976	C₄⋊C₄	—	12	1	no	—
977	C₄⋊C₄	—	12	1	no	—
978	C₄⋊C₄	—	12	1	no	—
979	C₄⋊C₄	—	12	1	no	—
980	C₄⋊C₄	—	12	1	no	—
981	C₄⋊C₄	—	12	1	no	—
982	C₄⋊C₄	—	12	1	no	—
983	C₄⋊C₄	—	12	1	no	—
984	C₄⋊C₄	—	12	1	no	—
985	C₄⋊C₄	—	12	1	no	—
986	C₄⋊C₄	—	12	1	no	—
987	C₄⋊C₄	—	12	1	no	—
988	C₄⋊C₄	—	12	1	no	—
989	C₄⋊C₄	—	12	1	no	—
990	C₄⋊C₄	—	12	1	no	—
991	C₄⋊C₄	—	12	1	no	—
992	C₄⋊C₄	—	12	1	no	—
993	C₄⋊C₄	—	12	1	no	—
994	C₄⋊C₄	—	12	1	no	—
995	C₄⋊C₄	—	12	1	no	—
996	C₄⋊C₄	—	12	1	no	—
997	C₄⋊C₄	—	12	1	no	—
998	C₂²⋊C₄	—	6	2	no	—
999	C₂²⋊C₄	—	6	2	no	—
1000	C₂²⋊C₄	—	6	2	no	—
1001	C₂²⋊C₄	—	6	2	no	—
1002	C₂²⋊C₄	—	12	1	no	—
1003	C₂²⋊C₄	—	12	1	no	—
1004	C₂²⋊C₄	—	12	1	no	—
1005	C₂²⋊C₄	—	12	1	no	—
1006	C₂²⋊C₄	—	12	1	no	—
1007	C₂²⋊C₄	—	12	1	no	—
1008	C₂²⋊C₄	—	12	1	no	—
1009	C₂²⋊C₄	—	12	1	no	—
1010	C₂²⋊C₄	—	12	1	no	—
1011	C₂²⋊C₄	—	12	1	no	—
1012	C₄²	—	6	2	no	—
1013	C₄²	—	6	2	no	—
1014	C₄²	—	6	2	no	—
1015	C₄²	—	12	1	no	—
1016	C₄²	—	12	1	no	—
1017	C₄²	—	12	1	no	—
1018	C₄²	—	12	1	no	—
1019	C₄²	—	12	1	no	—
1020	C₄²	—	12	1	no	—
1021	C₄²	—	12	1	no	—
1022	C₄²	—	12	1	no	—
1023	C₄²	—	12	1	no	—
1024	C₄²	—	12	1	no	—
1025	C₄²	—	12	1	no	—
1026	C₄²	—	12	1	no	—
1027	C₄²	—	12	1	no	—
1028	C₄²	—	12	1	no	—
1029	C₄²	#237	1	4	yes	—
1030	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1031	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1032	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1033	C₂²×C₃	#585	1	1	yes	characteristic
1034	C₂²×C₃	#585	1	1	yes	characteristic
1035	C₂²×C₃	#585	1	1	yes	characteristic
1036	C₂²×C₃	#585	1	1	yes	characteristic
1037	C₂×D₃	—	4	1	no	—
1038	C₂×D₃	—	4	1	no	—
1039	C₂×D₃	—	4	1	no	—
1040	C₂×D₃	—	4	1	no	—
1041	C₂×D₃	—	4	1	no	—
1042	C₂×D₃	—	4	1	no	—
1043	C₂×D₃	—	4	1	no	—
1044	C₃×C₄	—	2	2	no	—
1045	C₃×C₄	—	2	2	no	—
1046	C₃×C₄	—	2	2	no	—
1047	C₃×C₄	—	4	1	no	—
1048	C₃×C₄	—	4	1	no	—
1049	C₃×C₄	—	4	1	no	—
1050	C₃×C₄	—	4	1	no	—
1051	C₃×C₄	—	4	1	no	—
1052	C₃×C₄	—	4	1	no	—
1053	C₃×C₄	—	4	1	no	—
1054	C₃×C₄	—	4	1	no	—
1055	C₃×C₄	—	4	1	no	—
1056	C₃×C₄	—	4	1	no	—
1057	C₃×C₄	—	4	1	no	—
1058	C₃×C₄	—	4	1	no	—
1059	Dic₃	—	2	2	no	—
1060	Dic₃	—	2	2	no	—
1061	Dic₃	—	4	1	no	—
1062	Dic₃	—	4	1	no	—
1063	Dic₃	—	4	1	no	—
1064	Dic₃	—	4	1	no	—
1065	Dic₃	—	4	1	no	—
1066	Dic₃	—	4	1	no	—
1067	Dic₃	—	4	1	no	—
1068	Dic₃	—	4	1	no	—
1069	Dic₃	—	4	1	no	—
1070	Dic₃	—	4	1	no	—
1071	Dic₃	—	4	1	no	—
1072	Dic₃	—	4	1	no	—
1073	Dic₃	—	4	1	no	—
1074	C₂³	—	6	1	no	—
1075	C₂³	—	6	1	no	—
1076	C₂³	—	6	1	no	—
1077	C₂³	—	6	1	no	—
1078	C₂³	—	6	1	no	—
1079	C₂³	—	6	1	no	—
1080	C₂³	—	6	1	no	—
1081	C₂³	C₂⁴×D₃	1	1	yes	characteristic
1082	Q₈	—	24	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	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	—	3	2	no	—
1126	C₂×C₄	—	3	2	no	—
1127	C₂×C₄	—	6	1	no	—
1128	C₂×C₄	—	6	1	no	—
1129	C₂×C₄	—	6	1	no	—
1130	C₂×C₄	—	6	1	no	—
1131	C₂×C₄	—	6	1	no	—
1132	C₂×C₄	—	6	1	no	—
1133	C₂×C₄	—	6	1	no	—
1134	C₂×C₄	—	6	1	no	—
1135	C₂×C₄	—	6	1	no	—
1136	C₂×C₄	—	6	1	no	—
1137	C₂×C₄	—	6	1	no	—
1138	C₂×C₄	—	6	1	no	—
1139	C₂×C₄	—	6	1	no	—
1140	C₂×C₄	—	6	1	no	—
1141	C₂×C₄	—	6	1	no	—
1142	C₂×C₄	—	6	1	no	—
1143	C₂×C₄	—	6	1	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	—	12	4	no	—
1171	C₂×C₄	C₂×#237	1	2	yes	—
1172	C₂×C₄	C₂×#237	1	2	yes	—
1173	C₂×C₄	C₂×#237	1	2	yes	—
1174	C₂×C₃	#3493	1	1	yes	characteristic
1175	C₂×C₃	#3507	1	1	yes	characteristic
1176	C₂×C₃	#3507	1	1	yes	characteristic
1177	C₂×C₃	#3563	1	1	yes	characteristic
1178	C₂×C₃	#3564	1	1	yes	characteristic
1179	C₂×C₃	#3565	1	1	yes	characteristic
1180	C₂×C₃	#3567	1	1	yes	characteristic
1181	D₃	—	8	1	no	—
1182	C₂²	—	12	1	no	—
1183	C₂²	—	12	1	no	—
1184	C₂²	—	12	1	no	—
1185	C₂²	—	12	1	no	—
1186	C₂²	—	12	1	no	—
1187	C₂²	—	12	1	no	—
1188	C₂²	—	12	1	no	—
1189	C₂²	C₂²×#237	1	1	yes	characteristic
1190	C₂²	#5966	1	1	yes	characteristic
1191	C₂²	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1192	C₂²	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1193	C₂²	#5968	1	1	yes	characteristic
1194	C₂²	#5968	1	1	yes	characteristic
1195	C₂²	#5968	1	1	yes	characteristic
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	6	2	no	—
1212	C₄	—	6	2	no	—
1213	C₄	—	12	1	no	—
1214	C₄	—	12	1	no	—
1215	C₄	—	12	1	no	—
1216	C₄	—	12	1	no	—
1217	C₄	—	12	1	no	—
1218	C₄	—	12	1	no	—
1219	C₄	—	12	1	no	—
1220	C₄	—	12	1	no	—
1221	C₄	—	12	1	no	—
1222	C₄	—	12	1	no	—
1223	C₄	—	12	1	no	—
1224	C₄	—	12	1	no	—
1225	C₄	—	12	1	no	—
1226	C₃	#47825	1	1	yes	characteristic, complemented, Sylow
1227	C₂	—	24	1	no	—
1228	C₂	#86342	1	1	yes	characteristic
1229	C₂	#86342	1	1	yes	characteristic
1230	C₂	#86366	1	1	yes	characteristic
1231	C₂	#87124	1	1	yes	characteristic
1232	C₂	#87138	1	1	yes	characteristic
1233	C₂	#87141	1	1	yes	characteristic
1234	C₂	#87144	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₃
commutator, socle, cosocle	C₂³×C₃	C₂⁵
Fitting	C₃×#2822	C₂
prime radical	C₂³×D₃	C₂⁴
hypercenter	#2822	D₃
hypocenter	C₃	#47825
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #2822

Complements

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

N	H ≅ G/N	type
1. C₃×#2822	C₂	semidirect
4. #83023	C₂	semidirect
5. #83023	C₂	semidirect
6. #78315	C₂	semidirect
8. #78282	C₂	semidirect
12. #78176	C₂	semidirect
13. #78159	C₂	semidirect
16. #77924	C₂	semidirect
17. #77917	C₂	semidirect
23. #77805	C₂	semidirect
24. #77803	C₂	semidirect
25. #77799	C₂	semidirect
27. #77780	C₂	semidirect
28. #77777	C₂	semidirect
29. #77769	C₂	semidirect
31. #74192	C₂	semidirect
188. #2822	D₃	semidirect
1226. C₃	#47825	semidirect

Maximal subgroups

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

subgroup	index
C₃×#2822	2
#83064	2
#83023	2
#78315	2
#78304	2
#78282	2
#78277	2
#78201	2
#78200	2
#78176	2
#78159	2
#78004	2
#78002	2
#77924	2
#77917	2
#77902	2
#77900	2
#77893	2
#77887	2
#77809	2
#77805	2
#77803	2
#77799	2
#77783	2
#77780	2
#77777	2
#77769	2
#74224	2
#74192	2
#47825	3