Subgroups — #7489243

Order 512.

1466 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59653	C₂	1	1	yes	maximal, characteristic, complemented
2	#38985	C₂	1	1	yes	maximal, characteristic, complemented
3	#32618	C₂	1	1	yes	maximal, characteristic, complemented
4	#32605	C₂	1	1	yes	maximal, characteristic, complemented
5	#32559	C₂	1	1	yes	maximal, characteristic, complemented
6	#32546	C₂	1	1	yes	maximal, characteristic, complemented
7	#32192	C₂	1	1	yes	maximal, characteristic, complemented
8	#32167	C₂	1	1	yes	maximal, characteristic, complemented
9	#31652	C₂	1	1	yes	maximal, characteristic, complemented
10	#31640	C₂	1	1	yes	maximal, characteristic, complemented
11	#30762	C₂	1	1	yes	maximal, characteristic, complemented
12	#30759	C₂	1	1	yes	maximal, characteristic, complemented
13	#30746	C₂	1	1	yes	maximal, characteristic
14	#30745	C₂	1	1	yes	maximal, characteristic, complemented
15	#30045	C₂	1	1	yes	maximal, characteristic
16	#30041	C₂	1	1	yes	maximal, characteristic, complemented
17	#29375	C₂	1	1	yes	maximal, characteristic, complemented
18	#29370	C₂	1	1	yes	maximal, characteristic, complemented
19	#27578	C₂	1	1	yes	maximal, characteristic, complemented
20	#27559	C₂	1	1	yes	maximal, characteristic, complemented
21	#26710	C₂	1	1	yes	maximal, characteristic, complemented
22	#26694	C₂	1	1	yes	maximal, characteristic, complemented
23	#26603	C₂	1	1	yes	maximal, characteristic, complemented
24	#26587	C₂	1	1	yes	maximal, characteristic
25	#26181	C₂	1	1	yes	maximal, characteristic, complemented
26	#26165	C₂	1	1	yes	maximal, characteristic, complemented
27	#25640	C₂	1	1	yes	maximal, characteristic, complemented
28	#25636	C₂	1	1	yes	maximal, characteristic, complemented
29	#24205	C₂	1	1	yes	maximal, characteristic, complemented
30	#24187	C₂	1	1	yes	maximal, characteristic, complemented
31	#23364	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#557	C₂²	1	1	yes	characteristic
33	C₂×#556	C₂²	1	1	yes	characteristic
34	C₂×#497	C₂²	1	1	yes	characteristic
35	C₂×#495	C₂²	1	1	yes	characteristic
36	C₂×#464	C₂²	1	1	yes	characteristic
37	C₂×#464	C₂²	1	1	yes	characteristic
38	C₂×#463	C₂²	1	1	yes	characteristic
39	C₂×#461	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
42	#2858	C₂²	1	1	yes	characteristic
43	#2725	—	2	1	no	—
44	#2725	—	2	1	no	—
45	#2715	—	2	1	no	—
46	#2715	—	2	1	no	—
47	#2700	—	2	1	no	—
48	#2700	—	2	1	no	—
49	#2644	—	2	1	no	—
50	#2592	C₂²	1	1	yes	characteristic
51	#2592	C₂²	1	1	yes	characteristic
52	#2582	C₂²	1	1	yes	characteristic
53	#2567	C₂²	1	1	yes	characteristic
54	#2548	C₂²	1	1	yes	characteristic
55	#2545	C₂²	1	1	yes	characteristic
56	#2545	C₂²	1	1	yes	characteristic
57	#2538	C₂²	1	1	yes	characteristic
58	#2538	C₂²	1	1	yes	characteristic
59	#2538	C₂²	1	1	yes	characteristic
60	#2519	—	2	1	no	—
61	#2519	—	2	1	no	—
62	#2512	—	2	1	no	—
63	#2512	C₂²	1	1	yes	characteristic
64	#2512	C₂²	1	1	yes	characteristic
65	#2489	—	2	1	no	—
66	#2452	—	2	1	no	—
67	#2448	C₂²	1	1	yes	characteristic
68	#2448	C₂²	1	1	yes	characteristic
69	#2447	C₂²	1	1	yes	characteristic
70	#2447	C₂²	1	1	yes	characteristic
71	#2446	C₂²	1	1	yes	characteristic
72	#2446	C₂²	1	1	yes	characteristic
73	#2441	—	2	1	no	—
74	#2429	—	2	1	no	—
75	#2369	C₂²	1	1	yes	characteristic
76	#2366	C₂²	1	1	yes	characteristic
77	#2362	—	2	1	no	—
78	#2351	C₂²	1	1	yes	characteristic
79	#2351	C₂²	1	1	yes	characteristic
80	#2319	—	2	1	no	—
81	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
83	C₄×#124	C₂²	1	1	yes	characteristic
84	#2295	C₂²	1	1	yes	characteristic
85	#2101	C₂²	1	1	yes	characteristic
86	#2100	C₂²	1	1	yes	characteristic
87	#2100	C₂²	1	1	yes	characteristic
88	#2099	C₂²	1	1	yes	characteristic
89	#2097	C₂²	1	1	yes	characteristic
90	#2095	C₂²	1	1	yes	characteristic
91	#2088	C₂²	1	1	yes	characteristic
92	#2087	C₂²	1	1	yes	characteristic
93	#2073	C₂²	1	1	yes	characteristic
94	#2073	C₂²	1	1	yes	characteristic
95	#2072	C₂²	1	1	yes	characteristic
96	#2071	C₂²	1	1	yes	characteristic
97	#2071	C₂²	1	1	yes	characteristic
98	#2071	C₂²	1	1	yes	characteristic
99	#2067	C₂²	1	1	yes	characteristic
100	#2067	C₂²	1	1	yes	characteristic
101	#2056	C₂²	1	1	yes	characteristic
102	#2055	C₂²	1	1	yes	characteristic
103	#2055	C₂²	1	1	yes	characteristic
104	#2054	C₂²	1	1	yes	characteristic
105	#2043	C₂²	1	1	yes	characteristic
106	#2043	C₂²	1	1	yes	characteristic
107	#2042	C₂²	1	1	yes	characteristic
108	#2042	C₂²	1	1	yes	characteristic
109	#2042	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2024	C₂²	1	1	yes	characteristic
112	#2024	C₂²	1	1	yes	characteristic
113	#2024	C₂²	1	1	yes	characteristic
114	#2023	C₂²	1	1	yes	characteristic
115	#2016	C₂²	1	1	yes	characteristic
116	#2016	C₂²	1	1	yes	characteristic
117	#2015	C₂²	1	1	yes	characteristic
118	#2015	C₂²	1	1	yes	characteristic
119	#2015	C₂²	1	1	yes	characteristic
120	#2014	C₂²	1	1	yes	characteristic
121	#2014	C₂²	1	1	yes	characteristic
122	#2014	C₂²	1	1	yes	characteristic
123	#2013	C₂²	1	1	yes	characteristic
124	#2013	C₂²	1	1	yes	characteristic
125	#2013	C₂²	1	1	yes	characteristic
126	#2013	C₂²	1	1	yes	characteristic
127	#2012	C₂²	1	1	yes	characteristic
128	#2012	C₂²	1	1	yes	characteristic
129	#2012	C₂²	1	1	yes	characteristic
130	#2012	C₂²	1	1	yes	characteristic
131	#2012	C₂²	1	1	yes	characteristic
132	#2011	C₂²	1	1	yes	characteristic
133	#1985	C₂²	1	1	yes	characteristic
134	#1985	C₂²	1	1	yes	characteristic
135	#1984	C₂²	1	1	yes	characteristic
136	#1984	C₂²	1	1	yes	characteristic
137	#1983	C₂²	1	1	yes	characteristic
138	#1981	C₂²	1	1	yes	characteristic
139	#1973	C₂²	1	1	yes	characteristic
140	#1970	C₂²	1	1	yes	characteristic
141	#1959	C₂²	1	1	yes	characteristic
142	#1956	C₂²	1	1	yes	characteristic
143	#1936	C₂²	1	1	yes	characteristic
144	#1936	C₂²	1	1	yes	characteristic
145	#1935	C₂²	1	1	yes	characteristic
146	#1934	C₂²	1	1	yes	characteristic
147	#1933	C₂²	1	1	yes	characteristic
148	#1933	C₂²	1	1	yes	characteristic
149	#1928	C₂²	1	1	yes	characteristic
150	#1928	C₂²	1	1	yes	characteristic
151	#1928	C₂²	1	1	yes	characteristic
152	#1928	C₂²	1	1	yes	characteristic
153	#1926	C₂²	1	1	yes	characteristic
154	#1925	C₂²	1	1	yes	characteristic
155	#1921	C₂²	1	1	yes	characteristic
156	#1918	C₂²	1	1	yes	characteristic
157	#1917	C₂²	1	1	yes	characteristic
158	#1917	C₂²	1	1	yes	characteristic
159	#1917	C₂²	1	1	yes	characteristic
160	#1917	C₂²	1	1	yes	characteristic
161	#1916	C₂²	1	1	yes	characteristic
162	#1916	C₂²	1	1	yes	characteristic
163	#1916	C₂²	1	1	yes	characteristic
164	#1916	C₂²	1	1	yes	characteristic
165	#1880	C₂²	1	1	yes	characteristic
166	#1880	C₂²	1	1	yes	characteristic
167	#1880	C₂²	1	1	yes	characteristic
168	#1880	C₂²	1	1	yes	characteristic
169	#1880	C₂²	1	1	yes	characteristic
170	#1880	C₂²	1	1	yes	characteristic
171	#1880	C₂²	1	1	yes	characteristic
172	#1880	C₂²	1	1	yes	characteristic
173	#1880	C₂²	1	1	yes	characteristic
174	#1880	C₂²	1	1	yes	characteristic
175	#1880	C₂²	1	1	yes	characteristic
176	#1879	C₂²	1	1	yes	characteristic
177	#1879	C₂²	1	1	yes	characteristic
178	#1879	C₂²	1	1	yes	characteristic
179	#1878	C₂²	1	1	yes	characteristic
180	#1878	C₂²	1	1	yes	characteristic
181	#1878	C₂²	1	1	yes	characteristic
182	#1878	C₂²	1	1	yes	characteristic
183	#1878	C₂²	1	1	yes	characteristic
184	#1878	C₂²	1	1	yes	characteristic
185	#1878	C₂²	1	1	yes	characteristic
186	#1878	C₂²	1	1	yes	characteristic
187	#1877	C₂²	1	1	yes	characteristic
188	#1877	C₂²	1	1	yes	characteristic
189	#1865	C₂²	1	1	yes	characteristic
190	#1865	C₂²	1	1	yes	characteristic
191	#1864	C₂²	1	1	yes	characteristic
192	#1863	C₂²	1	1	yes	characteristic
193	#1863	C₂²	1	1	yes	characteristic
194	#1863	C₂²	1	1	yes	characteristic
195	#1862	C₂²	1	1	yes	characteristic
196	#1862	C₂²	1	1	yes	characteristic
197	#1839	C₂²	1	1	yes	characteristic
198	#1839	C₂²	1	1	yes	characteristic
199	#1803	C₂²	1	1	yes	characteristic
200	#1803	C₂²	1	1	yes	characteristic
201	#1763	C₂²	1	1	yes	characteristic
202	C₄×#103	C₂²	1	1	yes	characteristic
203	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
212	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
213	C₂²×D₈	C₂³	1	1	yes	characteristic
214	C₂²×D₈	C₂³	1	1	yes	characteristic
215	#557	—	4	2	no	—
216	#557	—	4	2	no	—
217	#556	—	4	2	no	—
218	#556	—	4	2	no	—
219	C₂×C₄⋊Q₈	D₄	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂×#127	C₂³	1	1	yes	characteristic
225	C₂×#126	—	2	1	no	—
226	C₂×#126	—	2	1	no	—
227	C₂×#126	—	2	1	no	—
228	C₂×#126	—	2	1	no	—
229	C₂×#125	—	2	1	no	—
230	C₂×#125	—	2	1	no	—
231	C₂×#125	—	2	1	no	—
232	C₂×#124	—	2	1	no	—
233	C₂×#124	—	2	1	no	—
234	C₂×#124	C₂³	1	1	yes	characteristic
235	C₂×#124	C₂³	1	1	yes	characteristic
236	C₂×#124	C₂³	1	1	yes	characteristic
237	C₂×#124	C₂³	1	1	yes	characteristic
238	C₂×#124	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	—	2	1	no	—
240	C₂×C₂²⋊Q₈	—	2	1	no	—
241	C₂×C₂²⋊Q₈	—	2	1	no	—
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₄	—	2	1	no	—
255	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
258	C₂×#117	—	2	1	no	—
259	#497	—	4	2	no	—
260	#495	—	4	2	no	—
261	#464	—	4	2	no	—
262	#464	—	4	2	no	—
263	#463	—	4	2	no	—
264	#461	—	4	2	no	—
265	#440	—	4	2	no	—
266	C₄×SD₁₆	—	4	2	no	—
267	C₂×#107	C₂³	1	1	yes	characteristic
268	C₂×#107	C₂³	1	1	yes	characteristic
269	C₂×#107	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×#102	C₂³	1	1	yes	characteristic
303	C₂×#102	C₂³	1	1	yes	characteristic
304	C₂×#102	C₂³	1	1	yes	characteristic
305	C₂×#102	C₂³	1	1	yes	characteristic
306	C₂×#102	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
311	#400	—	2	1	no	—
312	#400	—	2	1	no	—
313	#399	—	2	1	no	—
314	#399	—	2	1	no	—
315	#398	—	2	1	no	—
316	#398	—	2	1	no	—
317	#398	—	2	1	no	—
318	#398	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#397	—	2	1	no	—
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#397	—	2	1	no	—
326	#397	—	2	1	no	—
327	#397	—	2	1	no	—
328	#397	—	2	1	no	—
329	#396	—	2	1	no	—
330	#396	—	2	1	no	—
331	#396	—	2	1	no	—
332	#396	—	2	1	no	—
333	#396	—	2	1	no	—
334	#396	—	2	1	no	—
335	#396	—	2	1	no	—
336	#396	—	2	1	no	—
337	#396	—	2	1	no	—
338	#396	—	2	1	no	—
339	#396	—	2	1	no	—
340	#396	—	2	1	no	—
341	#395	—	2	1	no	—
342	#395	—	2	1	no	—
343	#394	—	2	1	no	—
344	#394	—	2	1	no	—
345	#393	—	2	1	no	—
346	#393	—	2	1	no	—
347	#391	—	2	1	no	—
348	#391	—	2	1	no	—
349	#391	—	2	1	no	—
350	#391	D₄	1	1	yes	characteristic
351	#391	D₄	1	1	yes	characteristic
352	#391	C₂³	1	1	yes	characteristic
353	#391	C₂³	1	1	yes	characteristic
354	#391	C₂³	1	1	yes	characteristic
355	#391	C₂³	1	1	yes	characteristic
356	#391	C₂³	1	1	yes	characteristic
357	#391	C₂³	1	1	yes	characteristic
358	#391	C₂³	1	1	yes	characteristic
359	#391	C₂³	1	1	yes	characteristic
360	#391	C₂³	1	1	yes	characteristic
361	#390	—	2	1	no	—
362	#390	—	2	1	no	—
363	#390	—	2	1	no	—
364	#390	—	2	1	no	—
365	#390	—	2	1	no	—
366	#390	C₂³	1	1	yes	characteristic
367	#390	C₂³	1	1	yes	characteristic
368	#390	C₂³	1	1	yes	characteristic
369	#390	C₂³	1	1	yes	characteristic
370	#390	C₂³	1	1	yes	characteristic
371	#390	C₂³	1	1	yes	characteristic
372	#390	C₂³	1	1	yes	characteristic
373	#390	C₂³	1	1	yes	characteristic
374	#390	C₂³	1	1	yes	characteristic
375	#390	C₂³	1	1	yes	characteristic
376	#390	C₂³	1	1	yes	characteristic
377	#389	—	2	1	no	—
378	#389	—	2	1	no	—
379	#389	—	2	1	no	—
380	#389	—	2	1	no	—
381	#389	—	2	1	no	—
382	#389	—	2	1	no	—
383	#389	—	2	1	no	—
384	#389	—	2	1	no	—
385	#389	—	2	1	no	—
386	#389	—	2	1	no	—
387	#389	D₄	1	1	yes	characteristic
388	#389	D₄	1	1	yes	characteristic
389	#389	D₄	1	1	yes	characteristic
390	#389	D₄	1	1	yes	characteristic
391	#389	C₂³	1	1	yes	characteristic
392	#389	C₂³	1	1	yes	characteristic
393	#389	C₂³	1	1	yes	characteristic
394	#389	C₂³	1	1	yes	characteristic
395	#389	C₂³	1	1	yes	characteristic
396	#389	C₂³	1	1	yes	characteristic
397	#389	C₂³	1	1	yes	characteristic
398	#389	C₂³	1	1	yes	characteristic
399	#388	—	2	1	no	—
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	—	2	1	no	—
404	#388	—	2	1	no	—
405	#388	—	2	1	no	—
406	#388	—	2	1	no	—
407	#388	—	2	1	no	—
408	#388	—	2	1	no	—
409	#388	—	2	1	no	—
410	#388	—	2	1	no	—
411	#388	—	2	1	no	—
412	#388	—	2	1	no	—
413	#388	—	2	1	no	—
414	#388	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	—	2	1	no	—
421	#386	—	2	1	no	—
422	#386	—	2	1	no	—
423	#385	—	2	1	no	—
424	#385	—	2	1	no	—
425	#384	D₄	1	1	yes	characteristic
426	#384	C₂³	1	1	yes	characteristic
427	#384	C₂³	1	1	yes	characteristic
428	#384	C₂³	1	1	yes	characteristic
429	#382	—	2	1	no	—
430	#382	—	2	1	no	—
431	#382	C₂³	1	1	yes	characteristic
432	#381	—	2	1	no	—
433	#381	—	2	1	no	—
434	#380	—	2	1	no	—
435	#380	—	2	1	no	—
436	#380	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	—	2	1	no	—
439	C₄×C₄⋊C₄	—	2	1	no	—
440	C₄×C₄⋊C₄	—	2	1	no	—
441	C₄×C₄⋊C₄	—	2	1	no	—
442	C₄×C₄⋊C₄	—	2	1	no	—
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	—	2	1	no	—
451	C₄×C₂²⋊C₄	—	2	1	no	—
452	#376	—	2	1	no	—
453	C₄³	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#336	C₂³	1	1	yes	characteristic
471	#336	C₂³	1	1	yes	characteristic
472	#336	C₂³	1	1	yes	characteristic
473	#336	C₂³	1	1	yes	characteristic
474	#336	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
492	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
493	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	C₂⁴	1	1	yes	characteristic
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	2	2	no	—
507	C₂×Q₁₆	—	4	1	no	—
508	C₂×Q₁₆	—	4	1	no	—
509	C₂×Q₁₆	—	4	1	no	—
510	C₂×Q₁₆	—	4	1	no	—
511	C₂×Q₁₆	—	4	1	no	—
512	C₂×Q₁₆	—	4	1	no	—
513	C₂×Q₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	2	2	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	4	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×SD₁₆	—	4	1	no	—
528	C₂×SD₁₆	—	4	1	no	—
529	C₂×SD₁₆	—	4	1	no	—
530	C₂×SD₁₆	—	4	1	no	—
531	C₂×SD₁₆	—	4	1	no	—
532	C₂×SD₁₆	—	4	1	no	—
533	C₂×SD₁₆	—	4	1	no	—
534	C₂×SD₁₆	—	4	1	no	—
535	C₂×D₈	—	4	1	no	—
536	C₂×D₈	—	4	1	no	—
537	C₂×D₈	—	4	1	no	—
538	C₂×D₈	—	4	1	no	—
539	C₂×D₈	—	4	1	no	—
540	C₂×D₈	—	4	1	no	—
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	C₂²×C₈	C₂⁴	1	1	yes	characteristic
548	C₂²×C₈	C₂⁴	1	1	yes	characteristic
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	4	1	no	—
554	C₄⋊Q₈	—	4	1	no	—
555	C₄⋊Q₈	—	4	1	no	—
556	C₄⋊Q₈	—	4	1	no	—
557	C₄⋊Q₈	—	4	2	no	—
558	#127	—	4	1	no	—
559	#127	—	4	1	no	—
560	#126	—	4	4	no	—
561	#126	—	4	4	no	—
562	#126	—	8	2	no	—
563	#126	—	8	2	no	—
564	#125	—	4	4	no	—
565	#125	—	4	4	no	—
566	#125	—	4	4	no	—
567	#124	—	2	2	no	—
568	#124	—	2	2	no	—
569	#124	—	4	1	no	—
570	#124	—	4	1	no	—
571	#124	—	4	1	no	—
572	#124	—	4	1	no	—
573	#124	—	4	1	no	—
574	#124	—	4	1	no	—
575	#124	—	4	1	no	—
576	#124	—	4	1	no	—
577	#124	—	8	2	no	—
578	#124	—	8	2	no	—
579	C₂²⋊Q₈	—	4	4	no	—
580	C₂²⋊Q₈	—	4	4	no	—
581	C₂²⋊Q₈	—	8	2	no	—
582	C₂²⋊Q₈	—	8	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	4	1	no	—
588	C₄×Q₈	—	4	1	no	—
589	C₄×Q₈	—	4	1	no	—
590	C₄×Q₈	—	4	1	no	—
591	C₄×Q₈	—	4	1	no	—
592	C₄×Q₈	—	4	1	no	—
593	C₄×Q₈	—	4	1	no	—
594	C₄×Q₈	—	4	1	no	—
595	C₄×Q₈	—	4	1	no	—
596	C₄×Q₈	—	4	1	no	—
597	C₄×Q₈	—	4	1	no	—
598	C₄×Q₈	—	4	1	no	—
599	C₄×Q₈	—	4	1	no	—
600	C₄×Q₈	—	4	1	no	—
601	C₄×Q₈	—	4	1	no	—
602	C₄×Q₈	—	4	1	no	—
603	C₄×Q₈	—	4	4	no	—
604	C₄×D₄	—	4	1	no	—
605	C₄×D₄	—	4	1	no	—
606	C₄×D₄	—	4	1	no	—
607	C₄×D₄	—	4	1	no	—
608	C₄×D₄	—	4	1	no	—
609	C₄×D₄	—	4	1	no	—
610	C₄×D₄	—	4	4	no	—
611	#117	—	4	4	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	1	no	—
688	C₂×C₂²⋊C₄	—	2	1	no	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	—	2	1	no	—
696	C₂×C₂²⋊C₄	—	2	1	no	—
697	C₂×C₂²⋊C₄	—	2	1	no	—
698	C₂×C₂²⋊C₄	—	2	1	no	—
699	C₂×C₄²	—	2	1	no	—
700	C₂×C₄²	—	2	1	no	—
701	C₂×C₄²	—	2	1	no	—
702	C₂×C₄²	—	2	1	no	—
703	C₂×C₄²	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
711	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
712	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
713	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
714	C₂×C₄²	C₂⁴	1	1	yes	characteristic
715	C₂×C₄²	C₂⁴	1	1	yes	characteristic
716	C₂×C₄²	C₂⁴	1	1	yes	characteristic
717	C₂×C₄²	C₂⁴	1	1	yes	characteristic
718	C₂×C₄²	C₂⁴	1	1	yes	characteristic
719	C₂×C₄²	C₂⁴	1	1	yes	characteristic
720	C₂×C₄²	C₂⁴	1	1	yes	characteristic
721	#107	—	4	1	no	—
722	#107	—	4	1	no	—
723	#107	—	4	1	no	—
724	#106	—	4	1	no	—
725	C₄⋊C₈	—	4	1	no	—
726	C₄⋊C₈	—	4	1	no	—
727	C₄⋊C₈	—	4	1	no	—
728	C₄⋊C₈	—	4	1	no	—
729	#103	—	2	2	no	—
730	#103	—	2	2	no	—
731	#103	—	4	1	no	—
732	#103	—	4	1	no	—
733	#103	—	4	1	no	—
734	#103	—	4	1	no	—
735	#103	—	4	1	no	—
736	#103	—	4	1	no	—
737	#103	—	4	1	no	—
738	#103	—	4	1	no	—
739	#103	—	4	1	no	—
740	#103	—	4	1	no	—
741	#103	—	4	1	no	—
742	#103	—	4	1	no	—
743	#103	—	4	1	no	—
744	#103	—	4	1	no	—
745	#103	—	4	1	no	—
746	#103	—	4	1	no	—
747	#103	—	4	1	no	—
748	#102	—	4	1	no	—
749	#102	—	4	1	no	—
750	#102	—	4	1	no	—
751	#102	—	4	1	no	—
752	#102	—	4	1	no	—
753	#102	—	4	1	no	—
754	#102	—	4	1	no	—
755	#102	—	4	1	no	—
756	#102	—	4	1	no	—
757	#102	—	4	1	no	—
758	#102	—	4	1	no	—
759	#102	—	4	1	no	—
760	#102	—	4	1	no	—
761	#97	—	4	1	no	—
762	#97	—	4	1	no	—
763	C₄×C₈	—	4	1	no	—
764	C₄×C₈	—	4	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	C₂×D₄	1	1	yes	characteristic
797	#95	C₂×D₄	1	1	yes	characteristic
798	#95	C₂×D₄	1	1	yes	characteristic
799	#95	C₂×D₄	1	1	yes	characteristic
800	#95	C₂×D₄	1	1	yes	characteristic
801	#95	C₂×D₄	1	1	yes	characteristic
802	#95	C₂×D₄	1	1	yes	characteristic
803	#95	C₂×D₄	1	1	yes	characteristic
804	C₂⁴	—	2	1	no	—
805	C₂⁴	—	2	1	no	—
806	C₂⁴	—	2	1	no	—
807	C₂×Q₈	—	2	2	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	1	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	4	1	no	—
833	C₂×Q₈	—	4	1	no	—
834	C₂×Q₈	—	4	1	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	8	1	no	—
837	C₂×Q₈	—	8	1	no	—
838	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
839	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	2	no	—
860	C₂×D₄	—	4	2	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	8	1	no	—
863	C₂×D₄	—	8	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	8	1	no	—
883	C₂²×C₄	—	8	1	no	—
884	C₂²×C₄	—	8	1	no	—
885	C₂²×C₄	—	8	1	no	—
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₂⁵	1	1	yes	characteristic
901	Q₁₆	—	8	2	no	—
902	Q₁₆	—	8	2	no	—
903	Q₁₆	—	8	2	no	—
904	SD₁₆	—	4	4	no	—
905	SD₁₆	—	4	4	no	—
906	SD₁₆	—	8	2	no	—
907	SD₁₆	—	8	2	no	—
908	SD₁₆	—	8	2	no	—
909	SD₁₆	—	8	2	no	—
910	SD₁₆	—	8	2	no	—
911	D₈	—	8	2	no	—
912	D₈	—	8	2	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	2	1	no	—
936	C₂×C₈	—	2	1	no	—
937	C₄⋊C₄	—	2	4	no	—
938	C₄⋊C₄	—	2	4	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	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	—	4	1	no	—
966	C₄⋊C₄	—	4	1	no	—
967	C₄⋊C₄	—	4	1	no	—
968	C₄⋊C₄	—	4	1	no	—
969	C₄⋊C₄	—	4	1	no	—
970	C₄⋊C₄	—	4	1	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	—	4	2	no	—
982	C₄⋊C₄	—	4	2	no	—
983	C₄⋊C₄	—	4	2	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₄⋊C₄	—	4	2	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	—	8	1	no	—
992	C₄⋊C₄	—	8	1	no	—
993	C₄⋊C₄	—	8	1	no	—
994	C₄⋊C₄	—	8	1	no	—
995	C₄⋊C₄	—	8	1	no	—
996	C₄⋊C₄	—	8	1	no	—
997	C₄⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	2	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	8	1	no	—
1015	C₂²⋊C₄	—	8	1	no	—
1016	C₂²⋊C₄	—	8	1	no	—
1017	C₂²⋊C₄	—	8	1	no	—
1018	C₂²⋊C₄	—	8	1	no	—
1019	C₂²⋊C₄	—	8	1	no	—
1020	C₂²⋊C₄	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	—	8	1	no	—
1027	C₂²⋊C₄	—	8	1	no	—
1028	C₂²⋊C₄	—	8	1	no	—
1029	C₂²⋊C₄	—	8	1	no	—
1030	C₂²⋊C₄	—	8	1	no	—
1031	C₂²⋊C₄	—	8	1	no	—
1032	C₂²⋊C₄	—	8	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	4	1	no	—
1050	C₄²	—	4	1	no	—
1051	C₄²	—	4	2	no	—
1052	C₄²	—	4	2	no	—
1053	C₄²	—	4	2	no	—
1054	C₄²	—	4	2	no	—
1055	C₄²	—	4	2	no	—
1056	C₄²	—	4	2	no	—
1057	C₄²	—	4	2	no	—
1058	C₄²	—	4	2	no	—
1059	C₄²	—	4	2	no	—
1060	C₄²	—	8	1	no	—
1061	C₄²	—	8	1	no	—
1062	C₂³	—	4	1	no	—
1063	C₂³	—	4	1	no	—
1064	C₂³	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	4	1	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	4	1	no	—
1077	C₂³	—	4	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	—	4	1	no	—
1081	C₂³	—	4	1	no	—
1082	C₂³	—	4	1	no	—
1083	C₂³	C₂³×D₄	1	1	yes	characteristic
1084	Q₈	—	2	2	no	—
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	4	4	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	1	no	—
1095	Q₈	—	4	1	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	1	no	—
1098	Q₈	—	4	1	no	—
1099	Q₈	—	4	1	no	—
1100	Q₈	—	4	1	no	—
1101	Q₈	—	8	2	no	—
1102	Q₈	—	16	2	no	—
1103	D₄	—	4	1	no	—
1104	D₄	—	4	1	no	—
1105	D₄	—	4	1	no	—
1106	D₄	—	4	1	no	—
1107	D₄	—	4	1	no	—
1108	D₄	—	4	1	no	—
1109	D₄	—	4	1	no	—
1110	D₄	—	4	1	no	—
1111	D₄	—	4	1	no	—
1112	D₄	—	4	1	no	—
1113	D₄	—	4	1	no	—
1114	D₄	—	4	1	no	—
1115	D₄	—	8	4	no	—
1116	D₄	—	16	2	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	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	1	no	—
1192	C₂×C₄	—	4	1	no	—
1193	C₂×C₄	—	4	1	no	—
1194	C₂×C₄	—	4	1	no	—
1195	C₂×C₄	—	8	4	no	—
1196	C₂×C₄	—	16	2	no	—
1197	C₂×C₄	—	16	2	no	—
1198	C₂×C₄	#575	1	2	yes	—
1199	C₂×C₄	#577	1	2	yes	—
1200	C₂×C₄	#578	1	2	yes	—
1201	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1202	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1203	C₂×C₄	#585	1	1	yes	characteristic
1204	C₂×C₄	#585	1	1	yes	characteristic
1205	C₂×C₄	#585	1	1	yes	characteristic
1206	C₂×C₄	#585	1	1	yes	characteristic
1207	C₈	—	4	1	no	—
1208	C₈	—	4	1	no	—
1209	C₈	—	4	1	no	—
1210	C₈	—	4	1	no	—
1211	C₈	—	4	1	no	—
1212	C₈	—	4	1	no	—
1213	C₈	—	4	1	no	—
1214	C₈	—	4	1	no	—
1215	C₂²	—	8	1	no	—
1216	C₂²	—	8	1	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	8	1	no	—
1222	C₂²	—	8	1	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	—	8	1	no	—
1229	C₂²	—	8	1	no	—
1230	C₂²	—	8	1	no	—
1231	C₂²	—	8	1	no	—
1232	C₂²	—	8	1	no	—
1233	C₂²	—	8	1	no	—
1234	C₂²	—	8	1	no	—
1235	C₂²	—	8	1	no	—
1236	C₂²	#3484	1	1	yes	characteristic
1237	C₂²	#3487	1	1	yes	characteristic
1238	C₂²	#3487	1	1	yes	characteristic
1239	C₂²	C₂×#575	1	1	yes	characteristic
1240	C₂²	C₂×#577	1	1	yes	characteristic
1241	C₂²	C₂×#578	1	1	yes	characteristic
1242	C₂²	#3585	1	1	yes	characteristic
1243	C₄	—	2	2	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	—	8	1	no	—
1266	C₄	—	8	1	no	—
1267	C₄	—	8	1	no	—
1268	C₄	—	8	1	no	—
1269	C₄	—	8	1	no	—
1270	C₄	#3533	1	1	yes	characteristic
1271	C₄	#3533	1	1	yes	characteristic
1272	C₄	#3560	1	1	yes	characteristic
1273	C₄	#3560	1	1	yes	characteristic
1274	C₂	—	16	1	no	—
1275	C₂	—	16	1	no	—
1276	C₂	—	16	1	no	—
1277	C₂	#52010	1	1	yes	characteristic
1278	C₂	#61594	1	1	yes	characteristic
1279	C₂	#61687	1	1	yes	characteristic
1280	C₂	#61896	1	1	yes	characteristic
1281	C₂	#61905	1	1	yes	characteristic
1282	C₂	#61921	1	1	yes	characteristic
1283	C₂	#61934	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2011	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊Q₈ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #59653	C₂	semidirect
2. #38985	C₂	semidirect
3. #32618	C₂	semidirect
4. #32605	C₂	semidirect
5. #32559	C₂	semidirect
6. #32546	C₂	semidirect
7. #32192	C₂	semidirect
8. #32167	C₂	semidirect
9. #31652	C₂	semidirect
10. #31640	C₂	semidirect
11. #30762	C₂	semidirect
12. #30759	C₂	semidirect
14. #30745	C₂	semidirect
16. #30041	C₂	semidirect
17. #29375	C₂	semidirect
18. #29370	C₂	semidirect
19. #27578	C₂	semidirect
20. #27559	C₂	semidirect
21. #26710	C₂	semidirect
22. #26694	C₂	semidirect
23. #26603	C₂	semidirect
25. #26181	C₂	semidirect
26. #26165	C₂	semidirect
27. #25640	C₂	semidirect
28. #25636	C₂	semidirect
29. #24205	C₂	semidirect
30. #24187	C₂	semidirect
31. #23364	C₂	semidirect

Maximal subgroups

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

subgroup	index
#59653	2
#38985	2
#32618	2
#32605	2
#32559	2
#32546	2
#32192	2
#32167	2
#31652	2
#31640	2
#30762	2
#30759	2
#30746	2
#30745	2
#30045	2
#30041	2
#29375	2
#29370	2
#27578	2
#27559	2
#26710	2
#26694	2
#26603	2
#26587	2
#26181	2
#26165	2
#25640	2
#25636	2
#24205	2
#24187	2
#23364	2