Subgroups — #6357964

Order 512.

1843 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62544	C₂	1	1	yes	maximal, characteristic, complemented
2	#62541	C₂	1	1	yes	maximal, characteristic, complemented
3	#62538	C₂	1	1	yes	maximal, characteristic, complemented
4	#62483	C₂	1	1	yes	maximal, characteristic, complemented
5	#61006	C₂	1	1	yes	maximal, characteristic, complemented
6	#60821	C₂	1	1	yes	maximal, characteristic, complemented
7	#19754	C₂	1	1	yes	maximal, characteristic, complemented
8	#19748	C₂	1	1	yes	maximal, characteristic, complemented
9	#19741	C₂	1	1	yes	maximal, characteristic, complemented
10	#19736	C₂	1	1	yes	maximal, characteristic, complemented
11	#19735	C₂	1	1	yes	maximal, characteristic, complemented
12	#19734	C₂	1	1	yes	maximal, characteristic, complemented
13	#19730	C₂	1	1	yes	maximal, characteristic, complemented
14	#19726	C₂	1	1	yes	maximal, characteristic, complemented
15	#19723	C₂	1	1	yes	maximal, characteristic, complemented
16	#19721	C₂	1	1	yes	maximal, characteristic, complemented
17	#19716	C₂	1	1	yes	maximal, characteristic, complemented
18	#19715	C₂	1	1	yes	maximal, characteristic, complemented
19	#19709	C₂	1	1	yes	maximal, characteristic, complemented
20	#19705	C₂	1	1	yes	maximal, characteristic, complemented
21	#19695	C₂	1	1	yes	maximal, characteristic, complemented
22	#19695	C₂	1	1	yes	maximal, characteristic, complemented
23	#19686	C₂	1	1	yes	maximal, characteristic, complemented
24	#19684	C₂	1	1	yes	maximal, characteristic, complemented
25	#19670	C₂	1	1	yes	maximal, characteristic, complemented
26	#19659	C₂	1	1	yes	maximal, characteristic, complemented
27	#19649	C₂	1	1	yes	maximal, characteristic, complemented
28	#19642	C₂	1	1	yes	maximal, characteristic, complemented
29	#19639	C₂	1	1	yes	maximal, characteristic, complemented
30	#19627	C₂	1	1	yes	maximal, characteristic, complemented
31	#17340	C₂	1	1	yes	maximal, characteristic, complemented
32	#3511	C₂²	1	1	yes	characteristic
33	#3509	C₂²	1	1	yes	characteristic
34	#3508	C₂²	1	1	yes	characteristic
35	#3499	C₂²	1	1	yes	characteristic
36	#3388	—	2	2	no	—
37	#3373	—	2	2	no	—
38	#3371	—	2	2	no	—
39	#3367	—	2	2	no	—
40	#3351	—	2	2	no	—
41	#3350	—	2	2	no	—
42	#3348	—	2	2	no	—
43	#3332	—	2	2	no	—
44	#3330	—	2	2	no	—
45	#3323	—	2	2	no	—
46	#3317	—	2	2	no	—
47	#3311	—	2	2	no	—
48	#3308	—	2	2	no	—
49	#3308	—	2	2	no	—
50	#3306	—	2	2	no	—
51	#3306	—	2	2	no	—
52	#3257	—	2	2	no	—
53	#3231	C₂²	1	1	yes	characteristic
54	#3231	C₂²	1	1	yes	characteristic
55	#3231	C₂²	1	1	yes	characteristic
56	#3231	C₂²	1	1	yes	characteristic, complemented
57	#3230	C₂²	1	1	yes	characteristic
58	#3230	C₂²	1	1	yes	characteristic, complemented
59	#3229	C₂²	1	1	yes	characteristic
60	#3229	C₂²	1	1	yes	characteristic, complemented
61	#3228	C₂²	1	1	yes	characteristic
62	#3228	C₂²	1	1	yes	characteristic
63	#3228	C₂²	1	1	yes	characteristic
64	#3228	C₂²	1	1	yes	characteristic, complemented
65	#3227	C₂²	1	1	yes	characteristic
66	#3227	C₂²	1	1	yes	characteristic
67	#3227	C₂²	1	1	yes	characteristic
68	#3227	C₂²	1	1	yes	characteristic
69	#3227	C₂²	1	1	yes	characteristic, complemented
70	#3226	C₂²	1	1	yes	characteristic
71	#3226	C₂²	1	1	yes	characteristic, complemented
72	#3223	—	2	2	no	—
73	#3223	—	2	2	no	—
74	#3210	C₂²	1	1	yes	characteristic
75	#3210	C₂²	1	1	yes	characteristic
76	#3210	C₂²	1	1	yes	characteristic
77	#3210	C₂²	1	1	yes	characteristic
78	#3210	C₂²	1	1	yes	characteristic, complemented
79	#3210	C₂²	1	1	yes	characteristic, complemented
80	#3209	C₂²	1	1	yes	characteristic
81	#3209	C₂²	1	1	yes	characteristic
82	#3209	C₂²	1	1	yes	characteristic, complemented
83	#3209	C₂²	1	1	yes	characteristic, complemented
84	#3208	C₂²	1	1	yes	characteristic
85	#3208	C₂²	1	1	yes	characteristic
86	#3207	C₂²	1	1	yes	characteristic
87	#3207	C₂²	1	1	yes	characteristic
88	#3207	C₂²	1	1	yes	characteristic
89	#3207	C₂²	1	1	yes	characteristic
90	#3207	C₂²	1	1	yes	characteristic
91	#3207	C₂²	1	1	yes	characteristic, complemented
92	#3206	C₂²	1	1	yes	characteristic, complemented
93	#3205	C₂²	1	1	yes	characteristic
94	#3205	C₂²	1	1	yes	characteristic
95	#3198	—	2	2	no	—
96	#3185	C₂²	1	1	yes	characteristic
97	#3184	C₂²	1	1	yes	characteristic
98	#3184	C₂²	1	1	yes	characteristic
99	#3184	C₂²	1	1	yes	characteristic
100	#3182	C₂²	1	1	yes	characteristic
101	#3182	C₂²	1	1	yes	characteristic
102	#3182	C₂²	1	1	yes	characteristic
103	#3182	C₂²	1	1	yes	characteristic, complemented
104	#3182	C₂²	1	1	yes	characteristic, complemented
105	#3182	C₂²	1	1	yes	characteristic, complemented
106	#3169	C₂²	1	1	yes	characteristic
107	#3169	C₂²	1	1	yes	characteristic, complemented
108	#3167	C₂²	1	1	yes	characteristic
109	#3167	C₂²	1	1	yes	characteristic
110	#3167	C₂²	1	1	yes	characteristic
111	#3167	C₂²	1	1	yes	characteristic
112	#3165	C₂²	1	1	yes	characteristic, complemented
113	#3165	C₂²	1	1	yes	characteristic, complemented
114	#3160	C₂²	1	1	yes	characteristic
115	#3152	C₂²	1	1	yes	characteristic, complemented
116	C₂×#494	C₂²	1	1	yes	characteristic, complemented
117	#3141	C₂²	1	1	yes	characteristic
118	#3141	C₂²	1	1	yes	characteristic
119	#3141	C₂²	1	1	yes	characteristic
120	#3141	C₂²	1	1	yes	characteristic
121	#3141	C₂²	1	1	yes	characteristic, complemented
122	#3139	C₂²	1	1	yes	characteristic, complemented
123	#3138	C₂²	1	1	yes	characteristic
124	#3131	C₂²	1	1	yes	characteristic
125	#3131	C₂²	1	1	yes	characteristic, complemented
126	C₂×#487	C₂²	1	1	yes	characteristic, complemented
127	C₂×#486	C₂²	1	1	yes	characteristic
128	#3119	—	2	2	no	—
129	#3118	—	2	2	no	—
130	#3044	—	2	2	no	—
131	#3011	—	2	2	no	—
132	#2965	C₂²	1	1	yes	characteristic
133	#2965	C₂²	1	1	yes	characteristic
134	#2922	C₂²	1	1	yes	characteristic
135	#1723	C₂²	1	1	yes	characteristic, complemented
136	#1723	C₂²	1	1	yes	characteristic, complemented
137	#1723	C₂²	1	1	yes	characteristic, complemented
138	#1723	C₂²	1	1	yes	characteristic, complemented
139	#1722	C₂²	1	1	yes	characteristic
140	#1722	C₂²	1	1	yes	characteristic
141	#1722	C₂²	1	1	yes	characteristic
142	#1722	C₂²	1	1	yes	characteristic, complemented
143	#1721	C₂²	1	1	yes	characteristic
144	#1721	C₂²	1	1	yes	characteristic
145	#1720	C₂²	1	1	yes	characteristic
146	#1720	C₂²	1	1	yes	characteristic
147	#1720	C₂²	1	1	yes	characteristic
148	#1720	C₂²	1	1	yes	characteristic
149	#1720	C₂²	1	1	yes	characteristic
150	#1720	C₂²	1	1	yes	characteristic
151	#1720	C₂²	1	1	yes	characteristic, complemented
152	#1720	C₂²	1	1	yes	characteristic, complemented
153	#1720	C₂²	1	1	yes	characteristic, complemented
154	#1720	C₂²	1	1	yes	characteristic, complemented
155	#1719	C₂²	1	1	yes	characteristic
156	#1719	C₂²	1	1	yes	characteristic
157	#1719	C₂²	1	1	yes	characteristic
158	#1719	C₂²	1	1	yes	characteristic
159	#1719	C₂²	1	1	yes	characteristic, complemented
160	#1719	C₂²	1	1	yes	characteristic, complemented
161	#1718	C₂²	1	1	yes	characteristic, complemented
162	#1718	C₂²	1	1	yes	characteristic, complemented
163	#1718	C₂²	1	1	yes	characteristic, complemented
164	#1718	C₂²	1	1	yes	characteristic, complemented
165	#1718	C₂²	1	1	yes	characteristic, complemented
166	#1718	C₂²	1	1	yes	characteristic, complemented
167	#1717	C₂²	1	1	yes	characteristic
168	#1717	C₂²	1	1	yes	characteristic
169	#1717	C₂²	1	1	yes	characteristic
170	#1717	C₂²	1	1	yes	characteristic
171	#1717	C₂²	1	1	yes	characteristic
172	#1717	C₂²	1	1	yes	characteristic, complemented
173	#1716	C₂²	1	1	yes	characteristic, complemented
174	#1716	C₂²	1	1	yes	characteristic, complemented
175	#1716	C₂²	1	1	yes	characteristic, complemented
176	#1715	C₂²	1	1	yes	characteristic
177	#1715	C₂²	1	1	yes	characteristic
178	#1715	C₂²	1	1	yes	characteristic, complemented
179	#1714	C₂²	1	1	yes	characteristic
180	#1714	C₂²	1	1	yes	characteristic
181	#1714	C₂²	1	1	yes	characteristic, complemented
182	#1714	C₂²	1	1	yes	characteristic, complemented
183	#1711	C₂²	1	1	yes	characteristic
184	#1711	C₂²	1	1	yes	characteristic
185	#1711	C₂²	1	1	yes	characteristic
186	#1711	C₂²	1	1	yes	characteristic, complemented
187	#1710	C₂²	1	1	yes	characteristic, complemented
188	#1709	C₂²	1	1	yes	characteristic
189	#1709	C₂²	1	1	yes	characteristic
190	#1709	C₂²	1	1	yes	characteristic
191	#1708	C₂²	1	1	yes	characteristic, complemented
192	#1707	C₂²	1	1	yes	characteristic, complemented
193	#1707	C₂²	1	1	yes	characteristic, complemented
194	#1707	C₂²	1	1	yes	characteristic, complemented
195	#1707	C₂²	1	1	yes	characteristic, complemented
196	#1706	C₂²	1	1	yes	characteristic
197	#1706	C₂²	1	1	yes	characteristic
198	#1705	C₂²	1	1	yes	characteristic, complemented
199	#1455	C₂²	1	1	yes	characteristic, complemented
200	#1454	C₂²	1	1	yes	characteristic
201	#1454	C₂²	1	1	yes	characteristic, complemented
202	#1453	C₂²	1	1	yes	characteristic
203	#1453	C₂²	1	1	yes	characteristic, complemented
204	#1453	C₂²	1	1	yes	characteristic, complemented
205	#1452	C₂²	1	1	yes	characteristic
206	#1451	C₂²	1	1	yes	characteristic, complemented
207	#1451	C₂²	1	1	yes	characteristic, complemented
208	#1450	C₂²	1	1	yes	characteristic, complemented
209	C₈×M₁₆	C₂²	1	1	yes	characteristic
210	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
211	C₂×2₋¹⁺⁴	—	2	1	no	—
212	C₂×#137	—	2	2	no	—
213	C₂²×Q₁₆	—	2	2	no	—
214	#559	—	2	1	no	—
215	#559	—	2	1	no	—
216	#557	—	2	1	no	—
217	#557	—	2	1	no	—
218	#556	—	2	1	no	—
219	#556	—	2	1	no	—
220	#556	—	2	1	no	—
221	#555	—	2	1	no	—
222	#554	—	2	1	no	—
223	#553	—	2	1	no	—
224	#553	—	2	1	no	—
225	#552	—	2	1	no	—
226	#552	—	2	1	no	—
227	#552	—	2	1	no	—
228	#552	—	2	1	no	—
229	#550	—	2	1	no	—
230	#550	—	2	1	no	—
231	D₄×Q₈	—	2	1	no	—
232	D₄×Q₈	—	2	1	no	—
233	#548	—	2	1	no	—
234	#548	—	2	1	no	—
235	#547	—	2	1	no	—
236	#547	—	2	1	no	—
237	#547	—	2	1	no	—
238	#547	—	2	1	no	—
239	#547	—	2	1	no	—
240	#547	—	2	1	no	—
241	#547	—	2	1	no	—
242	#546	—	2	1	no	—
243	#546	—	2	1	no	—
244	#546	—	2	1	no	—
245	#546	—	2	1	no	—
246	#542	—	2	1	no	—
247	#542	—	2	1	no	—
248	#541	—	2	1	no	—
249	#541	—	2	1	no	—
250	#540	—	2	1	no	—
251	#540	—	2	1	no	—
252	#537	—	2	1	no	—
253	#536	—	2	1	no	—
254	#536	—	2	1	no	—
255	#536	—	2	1	no	—
256	#536	—	2	1	no	—
257	#535	—	2	1	no	—
258	#533	C₂³	1	1	yes	characteristic
259	#533	C₂³	1	1	yes	characteristic
260	#533	C₂³	1	1	yes	characteristic
261	#533	C₂³	1	1	yes	characteristic
262	#533	C₂³	1	1	yes	characteristic
263	#533	C₂³	1	1	yes	characteristic
264	#533	C₂³	1	1	yes	characteristic
265	#533	C₂³	1	1	yes	characteristic
266	#532	C₂³	1	1	yes	characteristic
267	#532	C₂³	1	1	yes	characteristic
268	#532	C₂³	1	1	yes	characteristic
269	#532	C₂³	1	1	yes	characteristic
270	#532	C₂³	1	1	yes	characteristic
271	#532	C₂³	1	1	yes	characteristic
272	#532	C₂³	1	1	yes	characteristic
273	#532	C₂³	1	1	yes	characteristic
274	#532	C₂³	1	1	yes	characteristic
275	#532	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
281	C₂×#127	C₂³	1	1	yes	characteristic
282	#520	—	2	1	no	—
283	#519	—	2	1	no	—
284	#518	—	2	1	no	—
285	C₄×#41	C₂³	1	1	yes	characteristic
286	#501	—	2	2	no	—
287	#501	—	2	2	no	—
288	#500	C₂³	1	1	yes	characteristic
289	#500	C₂³	1	1	yes	characteristic
290	#500	C₂³	1	1	yes	characteristic
291	#500	C₂³	1	1	yes	characteristic
292	#500	C₂³	1	1	yes	characteristic
293	#500	C₂³	1	1	yes	characteristic
294	#500	C₂³	1	1	yes	characteristic
295	#500	C₂³	1	1	yes	characteristic
296	#500	C₂³	1	1	yes	characteristic
297	#500	C₂³	1	1	yes	characteristic
298	#499	—	2	2	no	—
299	#498	C₂³	1	1	yes	characteristic
300	#498	C₂³	1	1	yes	characteristic
301	#498	C₂³	1	1	yes	characteristic
302	#498	C₂³	1	1	yes	characteristic
303	#498	C₂³	1	1	yes	characteristic
304	#498	C₂³	1	1	yes	characteristic
305	#498	C₂³	1	1	yes	characteristic
306	#498	C₂³	1	1	yes	characteristic
307	#498	C₂³	1	1	yes	characteristic
308	#498	C₂³	1	1	yes	characteristic
309	#498	C₂³	1	1	yes	characteristic
310	#498	C₂³	1	1	yes	characteristic
311	#497	—	2	2	no	—
312	#494	—	2	2	no	—
313	#494	C₂³	1	1	yes	characteristic
314	#494	C₂³	1	1	yes	characteristic
315	#494	C₂³	1	1	yes	characteristic
316	#494	C₂³	1	1	yes	characteristic
317	#494	C₂³	1	1	yes	characteristic
318	#494	C₂³	1	1	yes	characteristic
319	#494	C₂³	1	1	yes	characteristic
320	#493	C₂³	1	1	yes	characteristic
321	#493	C₂³	1	1	yes	characteristic
322	#493	C₂³	1	1	yes	characteristic
323	#493	C₂³	1	1	yes	characteristic
324	#493	C₂³	1	1	yes	characteristic
325	#492	C₂³	1	1	yes	characteristic
326	#492	C₂³	1	1	yes	characteristic
327	#492	C₂³	1	1	yes	characteristic
328	#492	C₂³	1	1	yes	characteristic
329	#492	C₂³	1	1	yes	characteristic
330	#492	C₂³	1	1	yes	characteristic
331	#492	C₂³	1	1	yes	characteristic
332	#492	C₂³	1	1	yes	characteristic
333	#492	C₂³	1	1	yes	characteristic
334	#492	C₂³	1	1	yes	characteristic
335	#491	—	2	2	no	—
336	#490	—	2	2	no	—
337	#489	—	2	2	no	—
338	#489	—	2	2	no	—
339	#489	—	2	2	no	—
340	#489	—	2	2	no	—
341	#489	—	2	2	no	—
342	#488	—	2	2	no	—
343	#488	—	2	2	no	—
344	#487	—	2	2	no	—
345	#487	C₂³	1	1	yes	characteristic
346	#487	C₂³	1	1	yes	characteristic
347	#487	C₂³	1	1	yes	characteristic
348	#487	C₂³	1	1	yes	characteristic
349	#487	C₂³	1	1	yes	characteristic
350	#487	C₂³	1	1	yes	characteristic
351	#487	C₂³	1	1	yes	characteristic
352	#487	C₂³	1	1	yes	characteristic
353	#487	C₂³	1	1	yes	characteristic
354	#487	C₂³	1	1	yes	characteristic
355	#487	C₂³	1	1	yes	characteristic
356	#487	C₂³	1	1	yes	characteristic
357	#487	C₂³	1	1	yes	characteristic
358	#487	C₂³	1	1	yes	characteristic
359	#487	C₂³	1	1	yes	characteristic
360	#487	C₂³	1	1	yes	characteristic
361	#487	C₂³	1	1	yes	characteristic
362	#487	C₂³	1	1	yes	characteristic
363	#487	C₂³	1	1	yes	characteristic
364	#487	C₂³	1	1	yes	characteristic
365	#487	C₂³	1	1	yes	characteristic
366	#487	C₂³	1	1	yes	characteristic
367	#487	C₂³	1	1	yes	characteristic
368	#487	C₂³	1	1	yes	characteristic
369	#486	—	2	2	no	—
370	#486	C₂³	1	1	yes	characteristic
371	#486	C₂³	1	1	yes	characteristic
372	#486	C₂³	1	1	yes	characteristic
373	#486	C₂³	1	1	yes	characteristic
374	#486	C₂³	1	1	yes	characteristic
375	#486	C₂³	1	1	yes	characteristic
376	#486	C₂³	1	1	yes	characteristic
377	#486	C₂³	1	1	yes	characteristic
378	#486	C₂³	1	1	yes	characteristic
379	#486	C₂³	1	1	yes	characteristic
380	#486	C₂³	1	1	yes	characteristic
381	#486	C₂³	1	1	yes	characteristic
382	#486	C₂³	1	1	yes	characteristic
383	#486	C₂³	1	1	yes	characteristic
384	#486	C₂³	1	1	yes	characteristic
385	#486	C₂³	1	1	yes	characteristic
386	#486	C₂³	1	1	yes	characteristic
387	#486	C₂³	1	1	yes	characteristic
388	#486	C₂³	1	1	yes	characteristic
389	#486	C₂³	1	1	yes	characteristic
390	#486	C₂³	1	1	yes	characteristic
391	#486	C₂³	1	1	yes	characteristic
392	#486	C₂³	1	1	yes	characteristic
393	#486	C₂³	1	1	yes	characteristic
394	#486	C₂³	1	1	yes	characteristic
395	#486	C₂³	1	1	yes	characteristic
396	#486	C₂³	1	1	yes	characteristic
397	#486	C₂³	1	1	yes	characteristic
398	#485	—	2	2	no	—
399	#485	—	2	2	no	—
400	#485	—	2	2	no	—
401	#485	—	2	2	no	—
402	#484	—	2	2	no	—
403	#484	—	2	2	no	—
404	#483	—	2	2	no	—
405	#483	—	2	2	no	—
406	#482	—	2	2	no	—
407	#482	—	2	2	no	—
408	#482	—	2	2	no	—
409	#482	—	2	2	no	—
410	#481	—	2	2	no	—
411	#481	—	2	2	no	—
412	#481	—	2	2	no	—
413	#481	—	2	2	no	—
414	#481	—	2	2	no	—
415	#480	—	2	2	no	—
416	#480	—	2	2	no	—
417	#479	—	2	2	no	—
418	#479	—	2	2	no	—
419	#479	—	2	2	no	—
420	#479	—	2	2	no	—
421	#478	—	2	2	no	—
422	#478	—	2	2	no	—
423	#478	—	2	2	no	—
424	#478	—	2	2	no	—
425	#477	—	2	2	no	—
426	#477	—	2	2	no	—
427	#476	—	2	2	no	—
428	#476	—	2	2	no	—
429	#476	—	2	2	no	—
430	#476	—	2	2	no	—
431	#476	—	2	2	no	—
432	#475	—	2	2	no	—
433	#475	—	2	2	no	—
434	#474	—	2	2	no	—
435	#474	—	2	2	no	—
436	#470	—	2	2	no	—
437	#469	—	2	2	no	—
438	#469	—	2	2	no	—
439	#469	—	2	2	no	—
440	#468	—	2	2	no	—
441	#468	—	2	2	no	—
442	#468	—	2	2	no	—
443	#468	—	2	2	no	—
444	#468	—	2	2	no	—
445	#468	—	2	2	no	—
446	#466	—	2	2	no	—
447	#466	—	2	2	no	—
448	#465	—	2	2	no	—
449	#465	—	2	2	no	—
450	#465	—	2	2	no	—
451	#465	—	2	2	no	—
452	#464	—	2	2	no	—
453	#464	—	2	2	no	—
454	#464	—	2	2	no	—
455	#464	—	2	2	no	—
456	#464	—	2	2	no	—
457	#464	—	2	2	no	—
458	#463	—	2	2	no	—
459	#463	—	2	2	no	—
460	#463	—	2	2	no	—
461	#463	—	2	2	no	—
462	#463	—	2	2	no	—
463	#463	—	2	2	no	—
464	#462	—	2	2	no	—
465	#462	—	2	2	no	—
466	#462	—	2	2	no	—
467	#462	—	2	2	no	—
468	#461	—	2	2	no	—
469	#460	—	2	2	no	—
470	#460	—	2	2	no	—
471	#459	—	2	2	no	—
472	#459	—	2	2	no	—
473	#452	—	2	2	no	—
474	#452	—	2	2	no	—
475	#452	—	2	2	no	—
476	#452	—	2	2	no	—
477	#452	—	2	2	no	—
478	#452	—	2	2	no	—
479	#451	—	2	2	no	—
480	#451	—	2	2	no	—
481	#451	—	2	2	no	—
482	#451	—	2	2	no	—
483	#450	—	2	2	no	—
484	#450	—	2	2	no	—
485	#449	—	2	2	no	—
486	#449	—	2	2	no	—
487	#449	—	2	2	no	—
488	#449	—	2	2	no	—
489	#449	—	2	2	no	—
490	#449	—	2	2	no	—
491	#448	—	2	2	no	—
492	#447	—	2	2	no	—
493	#447	—	2	2	no	—
494	#446	D₄	1	2	yes	—
495	#446	D₄	1	2	yes	—
496	#442	—	2	2	no	—
497	#442	—	2	2	no	—
498	#442	—	2	2	no	—
499	#441	—	2	2	no	—
500	#440	—	2	2	no	—
501	#440	—	2	2	no	—
502	#440	—	2	2	no	—
503	#440	—	2	2	no	—
504	#440	—	2	2	no	—
505	#440	—	2	2	no	—
506	C₄×SD₁₆	—	2	2	no	—
507	C₄×SD₁₆	—	2	2	no	—
508	C₄×SD₁₆	—	2	2	no	—
509	C₄×SD₁₆	—	2	2	no	—
510	C₄×D₈	—	2	2	no	—
511	C₄×D₈	—	2	2	no	—
512	#436	D₄	1	2	yes	—
513	#436	D₄	1	2	yes	—
514	#435	D₄	1	2	yes	—
515	#435	D₄	1	2	yes	—
516	#435	D₄	1	2	yes	—
517	#435	D₄	1	2	yes	—
518	#433	D₄	1	2	yes	—
519	#433	D₄	1	2	yes	—
520	#431	C₂³	1	1	yes	characteristic
521	#431	C₂³	1	1	yes	characteristic
522	#431	C₂³	1	1	yes	characteristic
523	#431	C₂³	1	1	yes	characteristic
524	#431	C₂³	1	1	yes	characteristic
525	#431	C₂³	1	1	yes	characteristic
526	#431	C₂³	1	1	yes	characteristic
527	#431	C₂³	1	1	yes	characteristic
528	#431	C₂³	1	1	yes	characteristic
529	#431	C₂³	1	1	yes	characteristic
530	#428	—	2	2	no	—
531	#428	—	2	2	no	—
532	#427	—	2	2	no	—
533	#424	D₄	1	2	yes	—
534	#419	—	2	2	no	—
535	#418	—	2	2	no	—
536	#417	—	2	2	no	—
537	#417	—	2	2	no	—
538	#417	—	2	2	no	—
539	#417	—	2	2	no	—
540	#417	—	2	2	no	—
541	#416	—	2	2	no	—
542	#416	—	2	2	no	—
543	C₂×#103	—	2	2	no	—
544	C₂×#102	—	2	2	no	—
545	#408	D₄	1	2	yes	—
546	C₄×M₁₆	C₂³	1	1	yes	characteristic
547	C₄×M₁₆	C₂³	1	1	yes	characteristic
548	C₄×M₁₆	C₂³	1	1	yes	characteristic
549	C₄×M₁₆	C₂³	1	1	yes	characteristic
550	C₄×M₁₆	C₂³	1	1	yes	characteristic
551	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
552	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
553	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
554	#322	C₂³	1	1	yes	characteristic
555	#322	C₂³	1	1	yes	characteristic
556	#322	C₂³	1	1	yes	characteristic
557	#322	C₂³	1	1	yes	characteristic
558	#322	C₂³	1	1	yes	characteristic
559	#322	C₂³	1	1	yes	characteristic
560	#322	C₂³	1	1	yes	characteristic
561	#322	C₂³	1	1	yes	characteristic
562	#322	C₂³	1	1	yes	characteristic
563	#322	C₂³	1	1	yes	characteristic
564	#322	C₂³	1	1	yes	characteristic
565	#322	C₂³	1	1	yes	characteristic
566	C₈²	C₂³	1	1	yes	characteristic
567	C₈²	C₂³	1	1	yes	characteristic
568	C₈²	C₂³	1	1	yes	characteristic
569	C₈²	C₂³	1	1	yes	characteristic
570	2₋¹⁺⁴	—	8	4	no	—
571	C₂×#41	—	2	1	no	—
572	C₂×#41	—	2	1	no	—
573	C₂×#41	—	2	1	no	—
574	C₂×#41	—	2	1	no	—
575	C₂×#41	—	2	1	no	—
576	C₂×#41	—	2	1	no	—
577	C₂×#41	—	2	1	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	4	1	no	—
582	C₂×#41	—	4	1	no	—
583	C₂×#41	—	4	1	no	—
584	C₂×#41	C₂×D₄	1	1	yes	characteristic
585	C₂²×Q₈	—	2	1	no	—
586	C₂²×Q₈	—	2	1	no	—
587	C₂²×Q₈	—	2	1	no	—
588	C₂²×Q₈	—	2	1	no	—
589	C₂²×Q₈	—	2	1	no	—
590	C₂²×Q₈	—	4	1	no	—
591	C₂²×D₄	—	2	1	no	—
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	2	1	no	—
594	#137	—	8	4	no	—
595	C₂×Q₁₆	—	2	2	no	—
596	C₂×Q₁₆	—	2	2	no	—
597	C₂×Q₁₆	—	2	2	no	—
598	C₂×Q₁₆	—	2	2	no	—
599	C₂×Q₁₆	—	2	2	no	—
600	C₂×Q₁₆	—	2	2	no	—
601	C₂×Q₁₆	—	2	2	no	—
602	C₂×Q₁₆	—	8	4	no	—
603	C₂×SD₁₆	—	2	2	no	—
604	C₂×SD₁₆	—	2	2	no	—
605	C₂×SD₁₆	—	2	2	no	—
606	C₂×SD₁₆	—	2	2	no	—
607	C₂×SD₁₆	—	2	2	no	—
608	C₂×SD₁₆	—	2	2	no	—
609	C₂×SD₁₆	—	2	2	no	—
610	C₂×SD₁₆	—	2	2	no	—
611	C₂×SD₁₆	—	2	2	no	—
612	C₂×SD₁₆	—	2	2	no	—
613	C₂×D₈	—	2	2	no	—
614	C₂×D₈	—	2	2	no	—
615	C₂×D₈	—	2	2	no	—
616	C₂×D₈	—	2	2	no	—
617	C₂×D₈	—	2	2	no	—
618	C₂×M₁₆	C₂×D₄	1	2	yes	—
619	C₂×M₁₆	C₂×D₄	1	2	yes	—
620	C₂×M₁₆	C₂×D₄	1	2	yes	—
621	C₂×M₁₆	C₂×D₄	1	2	yes	—
622	C₂×M₁₆	C₂×D₄	1	2	yes	—
623	C₂²×C₈	C₂×D₄	1	2	yes	—
624	C₂²×C₈	C₂×D₄	1	2	yes	—
625	C₂²×C₈	C₂×D₄	1	2	yes	—
626	C₄⋊Q₈	—	2	1	no	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	1	no	—
629	C₄⋊Q₈	—	2	1	no	—
630	C₄⋊Q₈	—	2	1	no	—
631	C₄⋊Q₈	—	2	1	no	—
632	C₄⋊Q₈	—	2	1	no	—
633	C₄⋊Q₈	—	2	1	no	—
634	C₄⋊Q₈	—	2	1	no	—
635	C₄⋊Q₈	—	2	1	no	—
636	C₄⋊Q₈	—	2	1	no	—
637	C₄⋊Q₈	—	2	1	no	—
638	C₄⋊Q₈	—	2	1	no	—
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	—	4	1	no	—
642	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
643	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
644	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
645	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
646	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
647	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
648	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
649	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
650	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
651	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
652	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
653	C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
654	#127	—	2	1	no	—
655	#127	—	2	1	no	—
656	#127	—	2	1	no	—
657	#127	—	4	1	no	—
658	#127	C₂⁴	1	1	yes	characteristic
659	#127	C₂⁴	1	1	yes	characteristic
660	#127	C₂⁴	1	1	yes	characteristic
661	#127	C₂⁴	1	1	yes	characteristic
662	#126	—	4	1	no	—
663	#126	—	4	1	no	—
664	#126	—	4	1	no	—
665	#126	—	4	1	no	—
666	#126	—	4	1	no	—
667	#126	—	4	1	no	—
668	#125	—	2	1	no	—
669	#125	—	2	1	no	—
670	#125	—	2	1	no	—
671	#125	—	2	1	no	—
672	#125	—	2	1	no	—
673	#125	—	2	1	no	—
674	#125	—	2	1	no	—
675	#125	—	2	1	no	—
676	#125	—	4	1	no	—
677	#125	—	4	1	no	—
678	#125	—	4	1	no	—
679	#125	—	4	1	no	—
680	#124	—	2	1	no	—
681	#124	—	2	1	no	—
682	#124	—	2	1	no	—
683	#124	—	2	1	no	—
684	#124	—	2	1	no	—
685	#124	—	2	1	no	—
686	#124	—	2	1	no	—
687	#124	—	2	1	no	—
688	#124	—	2	1	no	—
689	#124	—	2	1	no	—
690	#124	—	4	1	no	—
691	#124	—	4	1	no	—
692	#124	—	4	1	no	—
693	#124	—	4	1	no	—
694	#123	—	4	1	no	—
695	#123	—	4	1	no	—
696	#123	—	4	1	no	—
697	#123	—	4	1	no	—
698	#123	—	4	1	no	—
699	#123	—	4	1	no	—
700	#123	—	4	1	no	—
701	#123	—	4	1	no	—
702	#123	—	4	1	no	—
703	#123	—	4	1	no	—
704	#123	—	4	1	no	—
705	#123	—	4	1	no	—
706	#123	—	4	1	no	—
707	#123	—	4	1	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	1	no	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	1	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	1	no	—
715	C₂²⋊Q₈	—	2	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	2	1	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	4	1	no	—
725	C₂²⋊Q₈	—	4	1	no	—
726	C₂²⋊Q₈	—	4	1	no	—
727	C₂²⋊Q₈	—	4	1	no	—
728	C₂²⋊Q₈	—	4	1	no	—
729	C₂²⋊Q₈	—	4	1	no	—
730	C₂²⋊Q₈	—	4	1	no	—
731	C₂²⋊Q₈	—	4	1	no	—
732	C₂²⋊Q₈	—	4	1	no	—
733	#121	—	2	1	no	—
734	#121	—	2	1	no	—
735	#121	—	2	1	no	—
736	#121	—	2	1	no	—
737	#121	—	2	1	no	—
738	#121	—	2	1	no	—
739	#121	—	2	1	no	—
740	#121	—	2	1	no	—
741	#121	—	2	1	no	—
742	#121	—	2	1	no	—
743	#121	—	2	1	no	—
744	#121	—	2	1	no	—
745	#121	—	2	1	no	—
746	#121	—	2	1	no	—
747	#121	—	2	1	no	—
748	#121	—	2	1	no	—
749	#121	—	2	1	no	—
750	#121	—	2	1	no	—
751	#121	—	2	1	no	—
752	#121	—	2	1	no	—
753	#121	—	4	1	no	—
754	#121	—	4	1	no	—
755	#121	—	4	1	no	—
756	#121	—	4	1	no	—
757	#121	—	4	1	no	—
758	#121	—	4	1	no	—
759	#121	—	4	1	no	—
760	#120	—	4	1	no	—
761	#120	—	4	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	4	1	no	—
779	C₄×Q₈	—	4	1	no	—
780	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
781	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	4	1	no	—
803	C₄×D₄	—	4	1	no	—
804	C₄×D₄	—	4	1	no	—
805	C₄×D₄	—	4	1	no	—
806	C₄×D₄	C₂×D₄	1	1	yes	characteristic
807	C₄×D₄	C₂×D₄	1	1	yes	characteristic
808	C₄×D₄	C₂×D₄	1	1	yes	characteristic
809	C₄×D₄	C₂×D₄	1	1	yes	characteristic
810	C₄×D₄	C₂×D₄	1	1	yes	characteristic
811	C₄×D₄	C₂×D₄	1	1	yes	characteristic
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	4	1	no	—
821	#117	—	4	1	no	—
822	#117	—	4	1	no	—
823	#117	C₂×D₄	1	1	yes	characteristic
824	#117	C₂×D₄	1	1	yes	characteristic
825	#117	C₂×D₄	1	1	yes	characteristic
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	4	1	no	—
837	C₂×C₂²⋊C₄	—	4	1	no	—
838	C₂×C₂²⋊C₄	—	4	1	no	—
839	C₂×C₄²	C₂⁴	1	1	yes	characteristic
840	C₂×C₄²	C₂⁴	1	1	yes	characteristic
841	C₂×C₄²	C₂⁴	1	1	yes	characteristic
842	#107	—	2	2	no	—
843	#107	—	2	2	no	—
844	#107	—	2	2	no	—
845	#107	—	2	2	no	—
846	#107	—	2	2	no	—
847	#107	—	2	2	no	—
848	#107	—	2	2	no	—
849	#107	—	2	2	no	—
850	#107	—	2	2	no	—
851	#107	—	2	2	no	—
852	#106	—	2	2	no	—
853	#106	—	2	2	no	—
854	#106	—	2	2	no	—
855	#106	—	2	2	no	—
856	#106	—	2	2	no	—
857	#106	—	2	2	no	—
858	#106	—	2	2	no	—
859	#106	—	2	2	no	—
860	#106	—	2	2	no	—
861	#106	—	2	2	no	—
862	#106	—	2	2	no	—
863	#106	—	2	2	no	—
864	C₄⋊C₈	C₂×D₄	1	2	yes	—
865	C₄⋊C₈	C₂×D₄	1	2	yes	—
866	C₄⋊C₈	C₂×D₄	1	2	yes	—
867	C₄⋊C₈	C₂×D₄	1	2	yes	—
868	C₄⋊C₈	C₂×D₄	1	2	yes	—
869	C₄⋊C₈	C₂×D₄	1	2	yes	—
870	C₄⋊C₈	C₂×D₄	1	2	yes	—
871	C₄⋊C₈	C₂×D₄	1	2	yes	—
872	C₄⋊C₈	C₂×D₄	1	2	yes	—
873	C₄⋊C₈	C₂×D₄	1	2	yes	—
874	#103	—	2	2	no	—
875	#103	—	2	2	no	—
876	#103	—	2	2	no	—
877	#103	—	2	2	no	—
878	#103	—	2	2	no	—
879	#103	—	2	2	no	—
880	#103	—	2	2	no	—
881	#103	—	2	2	no	—
882	#103	—	2	2	no	—
883	#103	—	2	2	no	—
884	#103	—	2	2	no	—
885	#103	—	2	2	no	—
886	#103	—	2	2	no	—
887	#103	—	2	2	no	—
888	#103	—	2	2	no	—
889	#103	—	2	2	no	—
890	#103	—	2	2	no	—
891	#103	—	2	2	no	—
892	#103	—	2	2	no	—
893	#103	—	2	2	no	—
894	#103	—	2	2	no	—
895	#103	—	2	2	no	—
896	#103	—	2	2	no	—
897	#103	—	2	2	no	—
898	#102	—	2	2	no	—
899	#102	—	2	2	no	—
900	#102	—	2	2	no	—
901	#102	—	2	2	no	—
902	#102	—	2	2	no	—
903	#102	—	2	2	no	—
904	#102	—	2	2	no	—
905	#102	—	2	2	no	—
906	#102	—	2	2	no	—
907	#102	—	2	2	no	—
908	#102	—	2	2	no	—
909	#102	—	2	2	no	—
910	#102	—	2	2	no	—
911	#102	—	2	2	no	—
912	#102	—	2	2	no	—
913	#102	—	2	2	no	—
914	#102	—	2	2	no	—
915	#102	—	2	2	no	—
916	#102	—	2	2	no	—
917	#102	—	2	2	no	—
918	#102	—	2	2	no	—
919	#102	—	2	2	no	—
920	#102	—	2	2	no	—
921	#102	—	2	2	no	—
922	#102	—	2	2	no	—
923	#102	—	2	2	no	—
924	#102	—	2	2	no	—
925	#102	—	2	2	no	—
926	C₂²⋊C₈	C₂×D₄	1	2	yes	—
927	C₂²⋊C₈	C₂×D₄	1	2	yes	—
928	C₂²⋊C₈	C₂×D₄	1	2	yes	—
929	C₂²⋊C₈	C₂×D₄	1	2	yes	—
930	C₂²⋊C₈	C₂×D₄	1	2	yes	—
931	C₂²⋊C₈	C₂×D₄	1	2	yes	—
932	C₂²⋊C₈	C₂×D₄	1	2	yes	—
933	C₂²⋊C₈	C₂×D₄	1	2	yes	—
934	C₂²⋊C₈	C₂×D₄	1	2	yes	—
935	C₂²⋊C₈	C₂×D₄	1	2	yes	—
936	#97	C₂×D₄	1	2	yes	—
937	#97	C₂×D₄	1	2	yes	—
938	#97	C₂×D₄	1	2	yes	—
939	#97	C₂×D₄	1	2	yes	—
940	#97	C₂×D₄	1	2	yes	—
941	C₄×C₈	C₂×D₄	1	2	yes	—
942	C₄×C₈	C₂×D₄	1	2	yes	—
943	C₄×C₈	C₂×D₄	1	2	yes	—
944	C₄×C₈	C₂⁴	1	1	yes	characteristic
945	C₄×C₈	C₂⁴	1	1	yes	characteristic
946	C₄×C₈	C₂⁴	1	1	yes	characteristic
947	C₄×C₈	C₂⁴	1	1	yes	characteristic
948	C₄×C₈	C₂⁴	1	1	yes	characteristic
949	C₄×C₈	C₂⁴	1	1	yes	characteristic
950	C₄×C₈	C₂⁴	1	1	yes	characteristic
951	C₄×C₈	C₂⁴	1	1	yes	characteristic
952	C₄×C₈	C₂⁴	1	1	yes	characteristic
953	C₄×C₈	C₂⁴	1	1	yes	characteristic
954	C₄×C₈	C₂⁴	1	1	yes	characteristic
955	C₄×C₈	C₂⁴	1	1	yes	characteristic
956	C₂⁴	—	4	1	no	—
957	#41	—	4	2	no	—
958	#41	—	4	4	no	—
959	#41	—	8	2	no	—
960	#41	—	8	2	no	—
961	#41	—	8	2	no	—
962	#41	—	8	2	no	—
963	#41	—	8	2	no	—
964	#41	—	8	2	no	—
965	#41	—	8	2	no	—
966	#41	—	8	2	no	—
967	#41	—	8	2	no	—
968	#41	—	8	4	no	—
969	#41	—	8	4	no	—
970	#41	—	8	4	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	1	no	—
974	C₂×Q₈	—	2	1	no	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	1	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	2	1	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	4	4	no	—
984	C₂×Q₈	—	4	4	no	—
985	C₂×Q₈	—	4	1	no	—
986	C₂×Q₈	—	4	1	no	—
987	C₂×Q₈	—	4	1	no	—
988	C₂×Q₈	—	4	1	no	—
989	C₂×Q₈	—	4	1	no	—
990	C₂×Q₈	—	8	2	no	—
991	C₂×Q₈	—	8	2	no	—
992	C₂×Q₈	—	8	2	no	—
993	C₂×Q₈	—	8	4	no	—
994	C₂×Q₈	#127	1	1	yes	characteristic
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	4	1	no	—
1008	C₂×D₄	—	4	1	no	—
1009	C₂×D₄	—	4	1	no	—
1010	C₂×D₄	—	4	1	no	—
1011	C₂×D₄	—	4	1	no	—
1012	C₂×D₄	—	4	1	no	—
1013	C₂×D₄	—	4	1	no	—
1014	C₂×D₄	—	4	1	no	—
1015	C₂×D₄	—	4	1	no	—
1016	C₂×D₄	—	4	1	no	—
1017	C₂×D₄	—	4	1	no	—
1018	C₂×D₄	—	4	1	no	—
1019	C₂×D₄	—	4	1	no	—
1020	C₂×D₄	—	8	2	no	—
1021	C₂×D₄	—	8	2	no	—
1022	C₂×D₄	—	8	2	no	—
1023	C₂×D₄	#127	1	1	yes	characteristic
1024	C₂×D₄	#127	1	1	yes	characteristic
1025	C₂×D₄	#127	1	1	yes	characteristic
1026	C₂²×C₄	—	4	1	no	—
1027	C₂²×C₄	—	4	1	no	—
1028	C₂²×C₄	—	4	1	no	—
1029	C₂²×C₄	—	4	1	no	—
1030	C₂²×C₄	—	4	1	no	—
1031	C₂²×C₄	—	4	1	no	—
1032	C₂²×C₄	—	4	1	no	—
1033	C₂²×C₄	—	4	1	no	—
1034	C₂²×C₄	—	4	1	no	—
1035	C₂²×C₄	—	4	1	no	—
1036	C₂²×C₄	—	4	1	no	—
1037	C₂²×C₄	—	4	1	no	—
1038	C₂²×C₄	—	4	1	no	—
1039	C₂²×C₄	—	4	1	no	—
1040	C₂²×C₄	—	4	1	no	—
1041	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1048	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1050	Q₁₆	—	8	2	no	—
1051	Q₁₆	—	8	2	no	—
1052	Q₁₆	—	8	2	no	—
1053	Q₁₆	—	8	2	no	—
1054	Q₁₆	—	8	2	no	—
1055	Q₁₆	—	8	2	no	—
1056	Q₁₆	—	8	2	no	—
1057	SD₁₆	—	4	4	no	—
1058	SD₁₆	—	8	2	no	—
1059	SD₁₆	—	8	2	no	—
1060	SD₁₆	—	8	2	no	—
1061	SD₁₆	—	8	2	no	—
1062	SD₁₆	—	8	2	no	—
1063	SD₁₆	—	8	2	no	—
1064	SD₁₆	—	8	2	no	—
1065	SD₁₆	—	8	2	no	—
1066	SD₁₆	—	8	2	no	—
1067	D₈	—	8	2	no	—
1068	D₈	—	8	2	no	—
1069	D₈	—	8	2	no	—
1070	D₈	—	8	2	no	—
1071	D₈	—	8	2	no	—
1072	M₁₆	—	4	2	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	M₁₆	—	4	2	no	—
1076	M₁₆	—	4	2	no	—
1077	C₂×C₈	—	4	2	no	—
1078	C₂×C₈	—	4	2	no	—
1079	C₂×C₈	—	4	2	no	—
1080	C₂×C₈	C₂²×D₄	1	2	yes	—
1081	C₂×C₈	C₂²×D₄	1	2	yes	—
1082	C₂×C₈	C₂²×D₄	1	2	yes	—
1083	C₂×C₈	C₂²×D₄	1	2	yes	—
1084	C₂×C₈	C₂²×D₄	1	2	yes	—
1085	C₂×C₈	C₂²×D₄	1	2	yes	—
1086	C₂×C₈	C₂²×D₄	1	2	yes	—
1087	C₂×C₈	C₂²×D₄	1	2	yes	—
1088	C₂×C₈	C₂²×D₄	1	2	yes	—
1089	C₂×C₈	C₂²×D₄	1	2	yes	—
1090	C₂×C₈	C₂²×D₄	1	2	yes	—
1091	C₂×C₈	C₂²×D₄	1	2	yes	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	1	no	—
1109	C₄⋊C₄	—	2	1	no	—
1110	C₄⋊C₄	—	2	1	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	1	no	—
1113	C₄⋊C₄	—	2	1	no	—
1114	C₄⋊C₄	—	2	1	no	—
1115	C₄⋊C₄	—	2	1	no	—
1116	C₄⋊C₄	—	4	1	no	—
1117	C₄⋊C₄	—	4	1	no	—
1118	C₄⋊C₄	—	4	1	no	—
1119	C₄⋊C₄	—	4	1	no	—
1120	C₄⋊C₄	—	4	1	no	—
1121	C₄⋊C₄	—	4	1	no	—
1122	C₄⋊C₄	—	4	1	no	—
1123	C₄⋊C₄	—	4	1	no	—
1124	C₄⋊C₄	—	4	1	no	—
1125	C₄⋊C₄	—	4	1	no	—
1126	C₄⋊C₄	—	4	1	no	—
1127	C₄⋊C₄	—	4	1	no	—
1128	C₄⋊C₄	—	4	1	no	—
1129	C₄⋊C₄	—	4	1	no	—
1130	C₄⋊C₄	—	4	1	no	—
1131	C₄⋊C₄	—	4	1	no	—
1132	C₄⋊C₄	—	4	1	no	—
1133	C₄⋊C₄	—	4	1	no	—
1134	C₄⋊C₄	—	4	1	no	—
1135	C₄⋊C₄	—	4	1	no	—
1136	C₄⋊C₄	—	4	1	no	—
1137	C₄⋊C₄	—	4	1	no	—
1138	C₄⋊C₄	—	4	1	no	—
1139	C₄⋊C₄	—	4	1	no	—
1140	C₄⋊C₄	—	4	1	no	—
1141	C₄⋊C₄	—	4	1	no	—
1142	C₄⋊C₄	#127	1	1	yes	characteristic
1143	C₄⋊C₄	#127	1	1	yes	characteristic
1144	C₄⋊C₄	#127	1	1	yes	characteristic
1145	C₄⋊C₄	#127	1	1	yes	characteristic
1146	C₄⋊C₄	#127	1	1	yes	characteristic
1147	C₄⋊C₄	#127	1	1	yes	characteristic
1148	C₂²⋊C₄	—	4	1	no	—
1149	C₂²⋊C₄	—	4	1	no	—
1150	C₂²⋊C₄	—	4	1	no	—
1151	C₂²⋊C₄	—	4	1	no	—
1152	C₂²⋊C₄	—	4	1	no	—
1153	C₂²⋊C₄	—	4	1	no	—
1154	C₂²⋊C₄	—	4	1	no	—
1155	C₂²⋊C₄	—	4	1	no	—
1156	C₂²⋊C₄	—	4	1	no	—
1157	C₂²⋊C₄	—	4	1	no	—
1158	C₂²⋊C₄	—	4	1	no	—
1159	C₂²⋊C₄	—	4	1	no	—
1160	C₂²⋊C₄	—	4	1	no	—
1161	C₂²⋊C₄	—	4	1	no	—
1162	C₂²⋊C₄	—	4	1	no	—
1163	C₂²⋊C₄	—	4	1	no	—
1164	C₂²⋊C₄	—	4	1	no	—
1165	C₂²⋊C₄	—	4	1	no	—
1166	C₂²⋊C₄	—	4	1	no	—
1167	C₂²⋊C₄	—	4	1	no	—
1168	C₂²⋊C₄	—	4	1	no	—
1169	C₂²⋊C₄	—	4	1	no	—
1170	C₂²⋊C₄	—	4	1	no	—
1171	C₂²⋊C₄	—	4	1	no	—
1172	C₂²⋊C₄	—	4	1	no	—
1173	C₂²⋊C₄	—	4	1	no	—
1174	C₂²⋊C₄	—	4	1	no	—
1175	C₂²⋊C₄	—	4	1	no	—
1176	C₂²⋊C₄	#127	1	1	yes	characteristic
1177	C₂²⋊C₄	#127	1	1	yes	characteristic
1178	C₂²⋊C₄	#127	1	1	yes	characteristic
1179	C₂²⋊C₄	#127	1	1	yes	characteristic
1180	C₂²⋊C₄	#127	1	1	yes	characteristic
1181	C₂²⋊C₄	#127	1	1	yes	characteristic
1182	C₄²	—	4	1	no	—
1183	C₄²	—	4	1	no	—
1184	C₄²	—	4	1	no	—
1185	C₄²	—	4	1	no	—
1186	C₄²	—	4	1	no	—
1187	C₄²	—	4	1	no	—
1188	C₄²	—	4	1	no	—
1189	C₄²	—	4	1	no	—
1190	C₄²	C₂²×D₄	1	1	yes	characteristic
1191	C₄²	C₂²×D₄	1	1	yes	characteristic
1192	C₄²	C₂²×D₄	1	1	yes	characteristic
1193	C₄²	C₂²×D₄	1	1	yes	characteristic
1194	C₄²	C₂²×D₄	1	1	yes	characteristic
1195	C₄²	C₂²×D₄	1	1	yes	characteristic
1196	C₄²	C₂²×D₄	1	1	yes	characteristic
1197	C₄²	C₂²×D₄	1	1	yes	characteristic
1198	C₄²	C₂²×D₄	1	1	yes	characteristic
1199	C₄²	C₂⁵	1	1	yes	characteristic
1200	C₂³	—	4	1	no	—
1201	C₂³	—	4	1	no	—
1202	C₂³	—	4	1	no	—
1203	C₂³	—	4	1	no	—
1204	C₂³	—	8	2	no	—
1205	C₂³	—	16	1	no	—
1206	C₂³	—	16	1	no	—
1207	C₂³	C₂×#127	1	1	yes	characteristic
1208	C₂³	C₂×#127	1	1	yes	characteristic
1209	C₂³	C₂×#127	1	1	yes	characteristic
1210	Q₈	—	4	1	no	—
1211	Q₈	—	4	2	no	—
1212	Q₈	—	4	2	no	—
1213	Q₈	—	4	2	no	—
1214	Q₈	—	4	2	no	—
1215	Q₈	—	4	2	no	—
1216	Q₈	—	4	2	no	—
1217	Q₈	—	4	2	no	—
1218	Q₈	—	4	2	no	—
1219	Q₈	—	4	2	no	—
1220	Q₈	—	4	2	no	—
1221	Q₈	—	4	2	no	—
1222	Q₈	—	4	2	no	—
1223	Q₈	—	8	2	no	—
1224	Q₈	—	8	2	no	—
1225	Q₈	—	8	2	no	—
1226	Q₈	—	8	2	no	—
1227	Q₈	—	16	1	no	—
1228	D₄	—	4	1	no	—
1229	D₄	—	4	1	no	—
1230	D₄	—	4	1	no	—
1231	D₄	—	4	2	no	—
1232	D₄	—	4	2	no	—
1233	D₄	—	4	2	no	—
1234	D₄	—	4	2	no	—
1235	D₄	—	4	2	no	—
1236	D₄	—	4	2	no	—
1237	D₄	—	4	2	no	—
1238	D₄	—	4	2	no	—
1239	D₄	—	4	2	no	—
1240	D₄	—	4	2	no	—
1241	D₄	—	4	2	no	—
1242	D₄	—	4	2	no	—
1243	D₄	—	8	2	no	—
1244	D₄	—	8	2	no	—
1245	D₄	—	8	2	no	—
1246	D₄	—	8	2	no	—
1247	D₄	—	8	2	no	—
1248	D₄	—	16	1	no	—
1249	D₄	—	16	1	no	—
1250	D₄	—	16	1	no	—
1251	D₄	—	16	1	no	—
1252	D₄	—	16	1	no	—
1253	D₄	—	16	1	no	—
1254	D₄	—	16	1	no	—
1255	D₄	—	16	1	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	2	no	—
1259	C₂×C₄	—	2	2	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	2	no	—
1262	C₂×C₄	—	2	2	no	—
1263	C₂×C₄	—	2	2	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	4	1	no	—
1266	C₂×C₄	—	4	1	no	—
1267	C₂×C₄	—	4	1	no	—
1268	C₂×C₄	—	4	1	no	—
1269	C₂×C₄	—	4	1	no	—
1270	C₂×C₄	—	4	1	no	—
1271	C₂×C₄	—	4	1	no	—
1272	C₂×C₄	—	4	1	no	—
1273	C₂×C₄	—	4	1	no	—
1274	C₂×C₄	—	4	1	no	—
1275	C₂×C₄	—	4	1	no	—
1276	C₂×C₄	—	4	1	no	—
1277	C₂×C₄	—	8	2	no	—
1278	C₂×C₄	—	8	2	no	—
1279	C₂×C₄	—	8	2	no	—
1280	C₂×C₄	—	8	2	no	—
1281	C₂×C₄	—	8	2	no	—
1282	C₂×C₄	—	8	2	no	—
1283	C₂×C₄	—	8	2	no	—
1284	C₂×C₄	—	8	2	no	—
1285	C₂×C₄	—	16	1	no	—
1286	C₂×C₄	—	16	1	no	—
1287	C₂×C₄	—	16	1	no	—
1288	C₂×C₄	—	16	1	no	—
1289	C₂×C₄	—	16	1	no	—
1290	C₂×C₄	—	16	1	no	—
1291	C₂×C₄	—	16	1	no	—
1292	C₂×C₄	C₂×#127	1	1	yes	characteristic
1293	C₂×C₄	C₂×#127	1	1	yes	characteristic
1294	C₂×C₄	C₂×#127	1	1	yes	characteristic
1295	C₂×C₄	C₂×#127	1	1	yes	characteristic
1296	C₂×C₄	C₂×#127	1	1	yes	characteristic
1297	C₂×C₄	C₂×#127	1	1	yes	characteristic
1298	C₂×C₄	C₂×#127	1	1	yes	characteristic
1299	C₂×C₄	C₂×#127	1	1	yes	characteristic
1300	C₂×C₄	C₂×#127	1	1	yes	characteristic
1301	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1302	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1303	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1304	C₈	—	2	2	no	—
1305	C₈	—	2	2	no	—
1306	C₈	—	2	2	no	—
1307	C₈	—	2	2	no	—
1308	C₈	—	2	2	no	—
1309	C₈	—	2	2	no	—
1310	C₈	—	2	2	no	—
1311	C₈	—	2	2	no	—
1312	C₈	—	2	2	no	—
1313	C₈	—	2	2	no	—
1314	C₈	—	2	2	no	—
1315	C₈	—	2	2	no	—
1316	C₂²	—	2	1	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	2	1	no	—
1319	C₂²	—	2	1	no	—
1320	C₂²	—	2	1	no	—
1321	C₂²	—	2	1	no	—
1322	C₂²	—	2	1	no	—
1323	C₂²	—	2	1	no	—
1324	C₂²	—	2	1	no	—
1325	C₂²	—	8	1	no	—
1326	C₂²	—	8	1	no	—
1327	C₂²	—	8	1	no	—
1328	C₂²	—	8	1	no	—
1329	C₂²	—	8	1	no	—
1330	C₂²	—	8	1	no	—
1331	C₂²	—	8	1	no	—
1332	C₂²	—	8	1	no	—
1333	C₂²	—	8	1	no	—
1334	C₂²	—	8	1	no	—
1335	C₂²	—	8	1	no	—
1336	C₂²	—	8	1	no	—
1337	C₂²	—	32	2	no	—
1338	C₂²	C₂²×#127	1	1	yes	characteristic
1339	C₄	—	2	1	no	—
1340	C₄	—	2	1	no	—
1341	C₄	—	2	1	no	—
1342	C₄	—	2	1	no	—
1343	C₄	—	2	1	no	—
1344	C₄	—	2	1	no	—
1345	C₄	—	2	1	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	1	no	—
1348	C₄	—	8	1	no	—
1349	C₄	—	8	1	no	—
1350	C₄	—	8	1	no	—
1351	C₄	—	8	1	no	—
1352	C₄	—	8	1	no	—
1353	C₄	—	8	1	no	—
1354	C₄	—	8	1	no	—
1355	C₄	—	8	1	no	—
1356	C₄	—	8	1	no	—
1357	C₄	—	8	1	no	—
1358	C₄	—	8	1	no	—
1359	C₄	—	8	1	no	—
1360	C₄	#3584	1	2	yes	—
1361	C₄	#3585	1	2	yes	—
1362	C₄	#3586	1	2	yes	—
1363	C₂	—	4	1	no	—
1364	C₂	—	4	1	no	—
1365	C₂	—	4	1	no	—
1366	C₂	—	16	1	no	—
1367	C₂	—	16	1	no	—
1368	C₂	—	16	1	no	—
1369	C₂	—	16	1	no	—
1370	C₂	#60644	1	1	yes	characteristic
1371	C₂	#60649	1	1	yes	characteristic
1372	C₂	#60651	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#127
commutator, Frattini, cosocle	C₄²	C₂⁵
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62544	C₂	semidirect
2. #62541	C₂	semidirect
3. #62538	C₂	semidirect
4. #62483	C₂	semidirect
5. #61006	C₂	semidirect
6. #60821	C₂	semidirect
7. #19754	C₂	semidirect
8. #19748	C₂	semidirect
9. #19741	C₂	semidirect
10. #19736	C₂	semidirect
11. #19735	C₂	semidirect
12. #19734	C₂	semidirect
13. #19730	C₂	semidirect
14. #19726	C₂	semidirect
15. #19723	C₂	semidirect
16. #19721	C₂	semidirect
17. #19716	C₂	semidirect
18. #19715	C₂	semidirect
19. #19709	C₂	semidirect
20. #19705	C₂	semidirect
21. #19695	C₂	semidirect
22. #19695	C₂	semidirect
23. #19686	C₂	semidirect
24. #19684	C₂	semidirect
25. #19670	C₂	semidirect
26. #19659	C₂	semidirect
27. #19649	C₂	semidirect
28. #19642	C₂	semidirect
29. #19639	C₂	semidirect
30. #19627	C₂	semidirect
31. #17340	C₂	semidirect
56. #3231	C₂²	semidirect
58. #3230	C₂²	semidirect
60. #3229	C₂²	semidirect
64. #3228	C₂²	semidirect
69. #3227	C₂²	semidirect
71. #3226	C₂²	semidirect
78. #3210	C₂²	semidirect
79. #3210	C₂²	semidirect
82. #3209	C₂²	semidirect
83. #3209	C₂²	semidirect
91. #3207	C₂²	semidirect
92. #3206	C₂²	semidirect
103. #3182	C₂²	semidirect
104. #3182	C₂²	semidirect
105. #3182	C₂²	semidirect
107. #3169	C₂²	semidirect
112. #3165	C₂²	semidirect
113. #3165	C₂²	semidirect
115. #3152	C₂²	semidirect
116. C₂×#494	C₂²	semidirect
121. #3141	C₂²	semidirect
122. #3139	C₂²	semidirect
125. #3131	C₂²	semidirect
126. C₂×#487	C₂²	semidirect
135. #1723	C₂²	semidirect
136. #1723	C₂²	semidirect
137. #1723	C₂²	semidirect
138. #1723	C₂²	semidirect
142. #1722	C₂²	semidirect
151. #1720	C₂²	semidirect
152. #1720	C₂²	semidirect
153. #1720	C₂²	semidirect
154. #1720	C₂²	semidirect
159. #1719	C₂²	semidirect
160. #1719	C₂²	semidirect
161. #1718	C₂²	semidirect
162. #1718	C₂²	semidirect
163. #1718	C₂²	semidirect
164. #1718	C₂²	semidirect
165. #1718	C₂²	semidirect
166. #1718	C₂²	semidirect
172. #1717	C₂²	semidirect
173. #1716	C₂²	semidirect
174. #1716	C₂²	semidirect
175. #1716	C₂²	semidirect
178. #1715	C₂²	semidirect
181. #1714	C₂²	semidirect
182. #1714	C₂²	semidirect
186. #1711	C₂²	semidirect
187. #1710	C₂²	semidirect
191. #1708	C₂²	semidirect
192. #1707	C₂²	semidirect
193. #1707	C₂²	semidirect
194. #1707	C₂²	semidirect
195. #1707	C₂²	semidirect
198. #1705	C₂²	semidirect
199. #1455	C₂²	semidirect
201. #1454	C₂²	semidirect
203. #1453	C₂²	semidirect
204. #1453	C₂²	semidirect
206. #1451	C₂²	semidirect
207. #1451	C₂²	semidirect
208. #1450	C₂²	semidirect
210. C₈×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#62544	2
#62541	2
#62538	2
#62483	2
#61006	2
#60821	2
#19754	2
#19748	2
#19741	2
#19736	2
#19735	2
#19734	2
#19730	2
#19726	2
#19723	2
#19721	2
#19716	2
#19715	2
#19709	2
#19705	2
#19695	2
#19686	2
#19684	2
#19670	2
#19659	2
#19649	2
#19642	2
#19639	2
#19627	2
#17340	2