Subgroups — #6700979

Order 512.

1361 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#40099	C₂	1	1	yes	maximal, characteristic
2	#36448	C₂	1	1	yes	maximal, characteristic, complemented
3	#33069	C₂	1	1	yes	maximal, characteristic, complemented
4	#32543	C₂	1	1	yes	maximal, characteristic, complemented
5	#32434	C₂	1	1	yes	maximal, characteristic, complemented
6	#32393	C₂	1	1	yes	maximal, characteristic, complemented
7	#32308	C₂	1	1	yes	maximal, characteristic
8	#31903	C₂	1	1	yes	maximal, characteristic, complemented
9	#31611	C₂	1	1	yes	maximal, characteristic, complemented
10	#31496	C₂	1	1	yes	maximal, characteristic
11	#31442	C₂	1	1	yes	maximal, characteristic, complemented
12	#30377	C₂	1	1	yes	maximal, characteristic, complemented
13	#30135	C₂	1	1	yes	maximal, characteristic, complemented
14	#29092	C₂	1	1	yes	maximal, characteristic, complemented
15	#28846	C₂	1	1	yes	maximal, characteristic
16	#27556	C₂	1	1	yes	maximal, characteristic, complemented
17	#27554	C₂	1	1	yes	maximal, characteristic, complemented
18	#27037	C₂	1	1	yes	maximal, characteristic, complemented
19	#26375	C₂	1	1	yes	maximal, characteristic, complemented
20	#26189	C₂	1	1	yes	maximal, characteristic, complemented
21	#26116	C₂	1	1	yes	maximal, characteristic, complemented
22	#25965	C₂	1	1	yes	maximal, characteristic, complemented
23	#25169	C₂	1	1	yes	maximal, characteristic
24	#24918	C₂	1	1	yes	maximal, characteristic, complemented
25	#24894	C₂	1	1	yes	maximal, characteristic
26	#24826	C₂	1	1	yes	maximal, characteristic, complemented
27	#24528	C₂	1	1	yes	maximal, characteristic
28	#22871	C₂	1	1	yes	maximal, characteristic, complemented
29	#22679	C₂	1	1	yes	maximal, characteristic, complemented
30	#22345	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#464	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#479	C₂²	1	1	yes	characteristic
33	C₂×#464	C₂²	1	1	yes	characteristic
34	C₂×#451	C₂²	1	1	yes	characteristic
35	C₂×#448	C₂²	1	1	yes	characteristic
36	C₂×#441	C₂²	1	1	yes	characteristic
37	C₂×#441	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
40	C₂²×#103	C₂²	1	1	yes	characteristic
41	#2863	—	2	1	no	—
42	#2863	C₂²	1	1	yes	characteristic
43	#2859	C₂²	1	1	yes	characteristic
44	#2777	—	2	1	no	—
45	#2721	—	2	1	no	—
46	#2718	—	2	1	no	—
47	#2694	—	2	1	no	—
48	#2667	—	2	1	no	—
49	#2575	—	2	1	no	—
50	#2570	C₂²	1	1	yes	characteristic
51	#2565	C₂²	1	1	yes	characteristic
52	#2553	—	2	1	no	—
53	#2514	—	2	1	no	—
54	#2514	—	2	1	no	—
55	#2514	C₂²	1	1	yes	characteristic
56	#2514	C₂²	1	1	yes	characteristic
57	#2512	C₂²	1	1	yes	characteristic
58	#2511	—	2	1	no	—
59	#2511	C₂²	1	1	yes	characteristic
60	#2501	C₂²	1	1	yes	characteristic
61	#2496	—	2	1	no	—
62	#2496	C₂²	1	1	yes	characteristic
63	#2495	—	2	1	no	—
64	#2495	C₂²	1	1	yes	characteristic
65	#2494	—	2	1	no	—
66	#2494	C₂²	1	1	yes	characteristic
67	#2454	C₂²	1	1	yes	characteristic
68	#2448	C₂²	1	1	yes	characteristic
69	#2442	C₂²	1	1	yes	characteristic
70	#2426	C₂²	1	1	yes	characteristic
71	#2423	C₂²	1	1	yes	characteristic
72	#2420	C₂²	1	1	yes	characteristic
73	#2360	C₂²	1	1	yes	characteristic
74	#2351	C₂²	1	1	yes	characteristic
75	#2351	C₂²	1	1	yes	characteristic
76	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
79	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
80	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	#2335	—	2	1	no	—
82	C₄×#126	—	2	1	no	—
83	C₄×#126	C₂²	1	1	yes	characteristic
84	C₄×#124	C₂²	1	1	yes	characteristic
85	C₄²×Q₈	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic
87	#2100	C₂²	1	1	yes	characteristic
88	#2100	C₂²	1	1	yes	characteristic
89	#2099	C₂²	1	1	yes	characteristic
90	#2097	C₂²	1	1	yes	characteristic
91	#2097	C₂²	1	1	yes	characteristic
92	#2096	C₂²	1	1	yes	characteristic
93	#2092	C₂²	1	1	yes	characteristic
94	#2092	C₂²	1	1	yes	characteristic
95	#2088	C₂²	1	1	yes	characteristic
96	#2088	C₂²	1	1	yes	characteristic
97	#2086	C₂²	1	1	yes	characteristic
98	#2085	C₂²	1	1	yes	characteristic
99	#2085	C₂²	1	1	yes	characteristic
100	#2084	C₂²	1	1	yes	characteristic
101	#2077	C₂²	1	1	yes	characteristic
102	#2077	C₂²	1	1	yes	characteristic
103	#2074	C₂²	1	1	yes	characteristic
104	#2072	C₂²	1	1	yes	characteristic
105	#2072	C₂²	1	1	yes	characteristic
106	#2071	C₂²	1	1	yes	characteristic
107	#2068	C₂²	1	1	yes	characteristic
108	#2068	C₂²	1	1	yes	characteristic
109	#2066	C₂²	1	1	yes	characteristic
110	#2066	C₂²	1	1	yes	characteristic
111	#2066	C₂²	1	1	yes	characteristic
112	#2065	C₂²	1	1	yes	characteristic
113	#2065	C₂²	1	1	yes	characteristic
114	#2059	C₂²	1	1	yes	characteristic
115	#2056	C₂²	1	1	yes	characteristic
116	#2055	C₂²	1	1	yes	characteristic
117	#2055	C₂²	1	1	yes	characteristic
118	#2055	C₂²	1	1	yes	characteristic
119	#2042	C₂²	1	1	yes	characteristic
120	#2036	C₂²	1	1	yes	characteristic
121	#2035	C₂²	1	1	yes	characteristic
122	#2034	C₂²	1	1	yes	characteristic
123	#2033	C₂²	1	1	yes	characteristic
124	#2026	C₂²	1	1	yes	characteristic
125	#2015	C₂²	1	1	yes	characteristic
126	#1992	C₂²	1	1	yes	characteristic
127	#1983	C₂²	1	1	yes	characteristic
128	#1973	C₂²	1	1	yes	characteristic
129	#1969	C₂²	1	1	yes	characteristic
130	#1949	C₂²	1	1	yes	characteristic
131	#1949	C₂²	1	1	yes	characteristic
132	#1947	C₂²	1	1	yes	characteristic
133	#1947	C₂²	1	1	yes	characteristic
134	#1944	C₂²	1	1	yes	characteristic
135	#1941	C₂²	1	1	yes	characteristic
136	#1941	C₂²	1	1	yes	characteristic
137	#1940	C₂²	1	1	yes	characteristic
138	#1939	C₂²	1	1	yes	characteristic
139	#1936	C₂²	1	1	yes	characteristic
140	#1935	C₂²	1	1	yes	characteristic
141	#1934	C₂²	1	1	yes	characteristic
142	#1933	C₂²	1	1	yes	characteristic
143	#1933	C₂²	1	1	yes	characteristic
144	#1928	C₂²	1	1	yes	characteristic
145	#1927	C₂²	1	1	yes	characteristic
146	#1925	C₂²	1	1	yes	characteristic
147	#1924	C₂²	1	1	yes	characteristic
148	#1924	C₂²	1	1	yes	characteristic
149	#1923	C₂²	1	1	yes	characteristic
150	#1921	C₂²	1	1	yes	characteristic
151	#1921	C₂²	1	1	yes	characteristic
152	#1921	C₂²	1	1	yes	characteristic
153	#1921	C₂²	1	1	yes	characteristic
154	#1920	C₂²	1	1	yes	characteristic
155	#1917	C₂²	1	1	yes	characteristic
156	#1916	C₂²	1	1	yes	characteristic
157	#1916	C₂²	1	1	yes	characteristic
158	#1893	C₂²	1	1	yes	characteristic
159	#1892	C₂²	1	1	yes	characteristic
160	#1880	C₂²	1	1	yes	characteristic
161	#1880	C₂²	1	1	yes	characteristic
162	#1880	C₂²	1	1	yes	characteristic
163	#1880	C₂²	1	1	yes	characteristic
164	#1878	C₂²	1	1	yes	characteristic
165	#1878	C₂²	1	1	yes	characteristic
166	#1878	C₂²	1	1	yes	characteristic
167	#1878	C₂²	1	1	yes	characteristic
168	#1878	C₂²	1	1	yes	characteristic
169	#1877	C₂²	1	1	yes	characteristic
170	#1865	C₂²	1	1	yes	characteristic
171	#1865	C₂²	1	1	yes	characteristic
172	#1865	C₂²	1	1	yes	characteristic
173	#1863	C₂²	1	1	yes	characteristic
174	#1863	C₂²	1	1	yes	characteristic
175	#1863	C₂²	1	1	yes	characteristic
176	#1863	C₂²	1	1	yes	characteristic
177	#1863	C₂²	1	1	yes	characteristic
178	#1863	C₂²	1	1	yes	characteristic
179	#1862	C₂²	1	1	yes	characteristic
180	#1853	C₂²	1	1	yes	characteristic
181	#1852	C₂²	1	1	yes	characteristic
182	#1850	C₂²	1	1	yes	characteristic
183	#1850	C₂²	1	1	yes	characteristic
184	#1847	C₂²	1	1	yes	characteristic
185	#1835	C₂²	1	1	yes	characteristic
186	#1831	C₂²	1	1	yes	characteristic
187	#1823	C₂²	1	1	yes	characteristic
188	#1808	C₂²	1	1	yes	characteristic
189	#1805	C₂²	1	1	yes	characteristic
190	#1805	C₂²	1	1	yes	characteristic
191	#1805	C₂²	1	1	yes	characteristic
192	#1803	C₂²	1	1	yes	characteristic
193	#1803	C₂²	1	1	yes	characteristic
194	#1803	C₂²	1	1	yes	characteristic
195	#1803	C₂²	1	1	yes	characteristic
196	#1787	C₂²	1	1	yes	characteristic
197	#1771	C₂²	1	1	yes	characteristic
198	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	C₄×#103	C₂²	1	1	yes	characteristic
201	C₄×#102	C₂²	1	1	yes	characteristic
202	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
203	C₂³×Q₈	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	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×#126	—	2	1	no	—
210	C₂×#126	—	2	1	no	—
211	C₂×#126	D₄	1	1	yes	characteristic
212	C₂×#125	—	2	1	no	—
213	C₂×#125	C₂³	1	1	yes	characteristic
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×#123	—	2	1	no	—
216	C₂×#123	—	2	1	no	—
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×#121	C₂³	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂³	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×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	#479	—	4	2	no	—
231	#464	—	2	4	no	—
232	#451	—	2	4	no	—
233	#448	—	4	2	no	—
234	#441	—	2	4	no	—
235	#441	—	4	2	no	—
236	C₄×Q₁₆	—	4	2	no	—
237	C₄×SD₁₆	—	4	2	no	—
238	C₂×#107	C₂³	1	1	yes	characteristic
239	C₂×#107	C₂³	1	1	yes	characteristic
240	C₂×#107	C₂³	1	1	yes	characteristic
241	C₂×#107	C₂³	1	1	yes	characteristic
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#107	C₂³	1	1	yes	characteristic
244	C₂×#106	C₂³	1	1	yes	characteristic
245	C₂×#106	C₂³	1	1	yes	characteristic
246	C₂×#106	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×#106	C₂³	1	1	yes	characteristic
249	C₂×#106	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₂×#103	—	4	2	no	—
258	C₂×#103	C₂³	1	1	yes	characteristic
259	C₂×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×#97	C₂³	1	1	yes	characteristic
286	C₂×#97	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
290	#401	—	2	1	no	—
291	#401	—	2	1	no	—
292	#401	—	2	1	no	—
293	#400	—	2	1	no	—
294	#400	—	2	1	no	—
295	#400	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#399	—	2	1	no	—
302	#399	—	2	1	no	—
303	#399	—	2	1	no	—
304	#399	—	2	1	no	—
305	#399	—	2	1	no	—
306	#398	—	2	1	no	—
307	#398	—	2	1	no	—
308	#398	—	2	1	no	—
309	#398	—	2	1	no	—
310	#398	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	2	1	no	—
317	#396	—	2	1	no	—
318	#396	—	2	1	no	—
319	#396	—	2	1	no	—
320	#394	—	2	1	no	—
321	#394	—	2	1	no	—
322	#391	—	2	1	no	—
323	#391	—	2	1	no	—
324	#391	—	2	1	no	—
325	#391	—	2	1	no	—
326	#391	—	2	1	no	—
327	#391	—	2	1	no	—
328	#391	C₂³	1	1	yes	characteristic
329	#391	C₂³	1	1	yes	characteristic
330	#391	C₂³	1	1	yes	characteristic
331	#391	C₂³	1	1	yes	characteristic
332	#391	C₂³	1	1	yes	characteristic
333	#391	C₂³	1	1	yes	characteristic
334	#391	C₂³	1	1	yes	characteristic
335	#391	C₂³	1	1	yes	characteristic
336	#390	—	2	1	no	—
337	#390	C₂³	1	1	yes	characteristic
338	#390	C₂³	1	1	yes	characteristic
339	#390	C₂³	1	1	yes	characteristic
340	#390	C₂³	1	1	yes	characteristic
341	#389	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	—	2	1	no	—
344	#389	—	2	1	no	—
345	#389	—	2	1	no	—
346	#389	—	2	1	no	—
347	#389	—	2	1	no	—
348	#389	—	2	1	no	—
349	#389	—	2	1	no	—
350	#389	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	C₂³	1	1	yes	characteristic
353	#389	C₂³	1	1	yes	characteristic
354	#389	C₂³	1	1	yes	characteristic
355	#389	C₂³	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#389	C₂³	1	1	yes	characteristic
360	#389	C₂³	1	1	yes	characteristic
361	#389	C₂³	1	1	yes	characteristic
362	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#388	D₄	1	1	yes	characteristic
374	#388	D₄	1	1	yes	characteristic
375	#388	D₄	1	1	yes	characteristic
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	D₄	1	1	yes	characteristic
392	#387	D₄	1	1	yes	characteristic
393	#387	D₄	1	1	yes	characteristic
394	#386	—	2	1	no	—
395	#385	—	2	1	no	—
396	#385	—	2	1	no	—
397	#385	—	2	1	no	—
398	#384	—	2	1	no	—
399	#384	—	2	1	no	—
400	#384	C₂³	1	1	yes	characteristic
401	#384	C₂³	1	1	yes	characteristic
402	#384	C₂³	1	1	yes	characteristic
403	#384	C₂³	1	1	yes	characteristic
404	#383	—	2	1	no	—
405	#383	—	2	1	no	—
406	#383	—	2	1	no	—
407	#383	—	2	1	no	—
408	#383	D₄	1	1	yes	characteristic
409	#382	—	2	1	no	—
410	#382	—	2	1	no	—
411	#382	—	2	1	no	—
412	#382	C₂³	1	1	yes	characteristic
413	#382	C₂³	1	1	yes	characteristic
414	#382	C₂³	1	1	yes	characteristic
415	#382	C₂³	1	1	yes	characteristic
416	#381	—	2	1	no	—
417	#380	—	2	1	no	—
418	#380	—	2	1	no	—
419	#380	—	2	1	no	—
420	#380	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	C₂³	1	1	yes	characteristic
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	C₄×C₄⋊C₄	—	2	1	no	—
427	C₄×C₄⋊C₄	—	2	1	no	—
428	C₄×C₄⋊C₄	—	2	1	no	—
429	C₄×C₄⋊C₄	—	2	1	no	—
430	C₄×C₄⋊C₄	—	2	1	no	—
431	C₄×C₄⋊C₄	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	—	2	1	no	—
441	C₄×C₂²⋊C₄	—	2	1	no	—
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	—	2	1	no	—
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
449	C₄³	—	2	1	no	—
450	C₄³	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	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	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	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	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	—	2	2	no	—
490	C₂²×Q₈	—	2	2	no	—
491	C₂²×Q₈	—	4	1	no	—
492	C₂²×Q₈	—	4	1	no	—
493	C₂²×Q₈	—	4	1	no	—
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	C₂⁴	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	C₂⁴	1	1	yes	characteristic
503	C₂×Q₁₆	—	2	2	no	—
504	C₂×Q₁₆	—	2	2	no	—
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	4	1	no	—
507	C₂×Q₁₆	—	4	1	no	—
508	C₂×Q₁₆	#41	1	4	yes	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	4	1	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂²×C₈	—	4	1	no	—
516	C₂²×C₈	—	4	1	no	—
517	C₂²×C₈	—	4	1	no	—
518	C₂²×C₈	C₂⁴	1	1	yes	characteristic
519	C₂²×C₈	C₂⁴	1	1	yes	characteristic
520	C₂²×C₈	C₂⁴	1	1	yes	characteristic
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	#126	—	4	2	no	—
527	#126	—	4	4	no	—
528	#126	—	8	2	no	—
529	#125	—	4	1	no	—
530	#125	—	4	1	no	—
531	#125	—	8	2	no	—
532	#124	—	2	2	no	—
533	#124	—	4	1	no	—
534	#123	—	4	4	no	—
535	#123	—	8	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	4	1	no	—
538	#121	—	4	1	no	—
539	#121	—	4	1	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	4	1	no	—
548	C₄×Q₈	—	4	1	no	—
549	C₄×Q₈	—	4	1	no	—
550	C₄×Q₈	—	4	1	no	—
551	C₄×Q₈	—	4	1	no	—
552	C₄×Q₈	—	4	1	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	1	no	—
558	C₄×D₄	—	4	1	no	—
559	C₄×D₄	—	4	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	4	1	no	—
594	C₂×C₄⋊C₄	—	4	1	no	—
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	1	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
650	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
651	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
652	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄²	C₂⁴	1	1	yes	characteristic
654	C₂×C₄²	C₂⁴	1	1	yes	characteristic
655	C₂×C₄²	C₂⁴	1	1	yes	characteristic
656	C₂×C₄²	C₂⁴	1	1	yes	characteristic
657	C₂×C₄²	C₂⁴	1	1	yes	characteristic
658	C₂×C₄²	C₂⁴	1	1	yes	characteristic
659	#107	—	4	1	no	—
660	#107	—	4	1	no	—
661	#107	—	4	1	no	—
662	#107	—	4	1	no	—
663	#107	—	4	1	no	—
664	#107	—	4	1	no	—
665	#106	—	2	2	no	—
666	#106	—	4	1	no	—
667	#106	—	4	1	no	—
668	#106	—	4	1	no	—
669	#106	—	4	1	no	—
670	#106	—	4	1	no	—
671	C₄⋊C₈	—	2	2	no	—
672	C₄⋊C₈	—	4	1	no	—
673	C₄⋊C₈	—	4	1	no	—
674	C₄⋊C₈	—	4	1	no	—
675	C₄⋊C₈	—	4	1	no	—
676	C₄⋊C₈	—	4	1	no	—
677	C₄⋊C₈	—	4	1	no	—
678	#103	—	2	2	no	—
679	#103	—	2	2	no	—
680	#103	—	2	2	no	—
681	#103	—	2	2	no	—
682	#103	—	2	2	no	—
683	#103	—	2	2	no	—
684	#103	—	2	2	no	—
685	#103	—	2	2	no	—
686	#103	—	2	2	no	—
687	#103	—	4	1	no	—
688	#103	—	4	1	no	—
689	#103	—	4	1	no	—
690	#103	—	4	1	no	—
691	#103	—	4	1	no	—
692	#103	—	4	1	no	—
693	#103	—	4	1	no	—
694	#103	—	4	1	no	—
695	#103	—	4	1	no	—
696	#102	—	2	2	no	—
697	#102	—	4	1	no	—
698	#102	—	4	1	no	—
699	#102	—	4	1	no	—
700	#102	—	4	1	no	—
701	#102	—	4	1	no	—
702	C₂²⋊C₈	—	2	2	no	—
703	C₂²⋊C₈	—	4	1	no	—
704	C₂²⋊C₈	—	4	1	no	—
705	#97	—	2	2	no	—
706	#97	—	4	1	no	—
707	C₄×C₈	—	4	1	no	—
708	C₄×C₈	—	4	1	no	—
709	C₄×C₈	—	4	1	no	—
710	#95	—	2	1	no	—
711	#95	—	2	1	no	—
712	#95	—	2	1	no	—
713	#95	—	2	1	no	—
714	#95	—	2	1	no	—
715	#95	—	2	1	no	—
716	#95	—	2	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	C₂×D₄	1	1	yes	characteristic
755	#95	C₂×D₄	1	1	yes	characteristic
756	#95	C₂×D₄	1	1	yes	characteristic
757	#95	C₂×D₄	1	1	yes	characteristic
758	#95	C₂×D₄	1	1	yes	characteristic
759	#95	C₂×D₄	1	1	yes	characteristic
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	C₂⁴	—	2	1	no	—
767	C₂⁴	C₂²×D₄	1	1	yes	characteristic
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	4	2	no	—
783	C₂×Q₈	—	4	2	no	—
784	C₂×Q₈	—	4	2	no	—
785	C₂×Q₈	—	4	4	no	—
786	C₂×Q₈	—	8	2	no	—
787	C₂×Q₈	—	8	2	no	—
788	C₂×Q₈	—	8	2	no	—
789	C₂×Q₈	C₂×#41	1	2	yes	—
790	C₂×Q₈	C₂×#41	1	2	yes	—
791	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
792	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	8	1	no	—
801	C₂×D₄	—	8	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	8	1	no	—
829	C₂²×C₄	—	8	1	no	—
830	C₂²×C₄	—	8	1	no	—
831	C₂²×C₄	—	8	1	no	—
832	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
833	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
835	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
836	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
837	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
838	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
839	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
840	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
841	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
842	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
843	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
844	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
845	C₂²×C₄	C₂⁵	1	1	yes	characteristic
846	Q₁₆	—	2	8	no	—
847	Q₁₆	—	8	2	no	—
848	SD₁₆	—	4	4	no	—
849	SD₁₆	—	8	2	no	—
850	C₂×C₈	—	2	1	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	2	1	no	—
855	C₂×C₈	—	2	1	no	—
856	C₂×C₈	—	2	1	no	—
857	C₂×C₈	—	2	1	no	—
858	C₂×C₈	—	2	1	no	—
859	C₂×C₈	—	2	1	no	—
860	C₂×C₈	—	2	1	no	—
861	C₂×C₈	—	2	1	no	—
862	C₂×C₈	—	2	1	no	—
863	C₂×C₈	—	2	1	no	—
864	C₂×C₈	—	2	1	no	—
865	C₂×C₈	—	2	1	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	8	2	no	—
874	C₂×C₈	C₂×#41	1	2	yes	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	4	1	no	—
902	C₄⋊C₄	—	4	1	no	—
903	C₄⋊C₄	—	4	1	no	—
904	C₄⋊C₄	—	4	1	no	—
905	C₄⋊C₄	—	4	2	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	8	1	no	—
922	C₄⋊C₄	—	8	1	no	—
923	C₄⋊C₄	—	8	1	no	—
924	C₄⋊C₄	—	8	1	no	—
925	C₄⋊C₄	—	8	1	no	—
926	C₄⋊C₄	—	8	1	no	—
927	C₄⋊C₄	—	8	1	no	—
928	C₄⋊C₄	—	8	1	no	—
929	C₄⋊C₄	—	8	1	no	—
930	C₄⋊C₄	—	8	1	no	—
931	C₄⋊C₄	—	8	1	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	4	1	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	8	1	no	—
953	C₂²⋊C₄	—	8	1	no	—
954	C₂²⋊C₄	—	8	1	no	—
955	C₂²⋊C₄	—	8	1	no	—
956	C₂²⋊C₄	—	8	1	no	—
957	C₂²⋊C₄	—	8	1	no	—
958	C₂²⋊C₄	—	8	1	no	—
959	C₂²⋊C₄	—	8	1	no	—
960	C₂²⋊C₄	—	8	1	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	4	1	no	—
976	C₄²	—	4	1	no	—
977	C₄²	—	4	2	no	—
978	C₄²	—	4	2	no	—
979	C₄²	—	4	2	no	—
980	C₄²	—	4	2	no	—
981	C₄²	—	4	2	no	—
982	C₄²	—	4	2	no	—
983	C₄²	—	4	2	no	—
984	C₄²	—	4	2	no	—
985	C₄²	—	4	2	no	—
986	C₄²	—	8	1	no	—
987	C₄²	—	8	1	no	—
988	C₄²	—	8	1	no	—
989	C₄²	—	8	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	4	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	4	1	no	—
999	C₂³	—	4	1	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	—	4	1	no	—
1003	C₂³	#575	1	2	yes	—
1004	C₂³	C₂³×D₄	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	4	1	no	—
1011	Q₈	—	4	1	no	—
1012	Q₈	—	4	1	no	—
1013	Q₈	—	4	1	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	4	1	no	—
1016	Q₈	—	8	4	no	—
1017	Q₈	#539	1	4	yes	—
1018	D₄	—	4	1	no	—
1019	D₄	—	4	1	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	16	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	1	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	1	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	8	4	no	—
1110	C₂×C₄	—	16	2	no	—
1111	C₂×C₄	—	16	2	no	—
1112	C₂×C₄	#577	1	2	yes	—
1113	C₂×C₄	#578	1	2	yes	—
1114	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1115	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1116	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1117	C₂×C₄	#585	1	1	yes	characteristic
1118	C₂×C₄	#585	1	1	yes	characteristic
1119	C₂×C₄	#585	1	1	yes	characteristic
1120	C₈	—	2	2	no	—
1121	C₈	—	4	1	no	—
1122	C₈	—	4	1	no	—
1123	C₈	—	4	1	no	—
1124	C₈	—	4	1	no	—
1125	C₈	—	4	1	no	—
1126	C₈	—	4	1	no	—
1127	C₈	—	4	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	8	1	no	—
1136	C₂²	—	8	1	no	—
1137	C₂²	—	8	1	no	—
1138	C₂²	—	8	1	no	—
1139	C₂²	—	8	1	no	—
1140	C₂²	—	8	1	no	—
1141	C₂²	—	8	1	no	—
1142	C₂²	D₄×#41	1	1	yes	characteristic
1143	C₂²	#3488	1	1	yes	characteristic
1144	C₂²	#3489	1	1	yes	characteristic
1145	C₂²	C₂×#575	1	1	yes	characteristic
1146	C₂²	C₂×#577	1	1	yes	characteristic
1147	C₂²	C₂×#578	1	1	yes	characteristic
1148	C₂²	#3584	1	1	yes	characteristic
1149	C₄	—	2	4	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	8	1	no	—
1165	C₄	—	8	1	no	—
1166	C₄	—	8	1	no	—
1167	C₄	—	8	1	no	—
1168	C₄	—	8	1	no	—
1169	C₄	—	8	1	no	—
1170	C₄	—	8	1	no	—
1171	C₄	—	8	1	no	—
1172	C₄	—	8	1	no	—
1173	C₄	—	8	1	no	—
1174	C₄	—	8	1	no	—
1175	C₄	—	8	1	no	—
1176	C₄	—	8	1	no	—
1177	C₄	C₂×#539	1	1	yes	characteristic
1178	C₄	#3521	1	1	yes	characteristic
1179	C₄	#3560	1	1	yes	characteristic
1180	C₄	#3564	1	1	yes	characteristic
1181	C₂	—	4	2	no	—
1182	C₂	—	16	1	no	—
1183	C₂	#37724	1	1	yes	characteristic
1184	C₂	#61446	1	1	yes	characteristic
1185	C₂	#61495	1	1	yes	characteristic
1186	C₂	#61981	1	1	yes	characteristic
1187	C₂	#62065	1	1	yes	characteristic
1188	C₂	#62140	1	1	yes	characteristic
1189	C₂	#62204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#121	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#126 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #36448	C₂	semidirect
3. #33069	C₂	semidirect
4. #32543	C₂	semidirect
5. #32434	C₂	semidirect
6. #32393	C₂	semidirect
8. #31903	C₂	semidirect
9. #31611	C₂	semidirect
11. #31442	C₂	semidirect
12. #30377	C₂	semidirect
13. #30135	C₂	semidirect
14. #29092	C₂	semidirect
16. #27556	C₂	semidirect
17. #27554	C₂	semidirect
18. #27037	C₂	semidirect
19. #26375	C₂	semidirect
20. #26189	C₂	semidirect
21. #26116	C₂	semidirect
22. #25965	C₂	semidirect
24. #24918	C₂	semidirect
26. #24826	C₂	semidirect
28. #22871	C₂	semidirect
29. #22679	C₂	semidirect
30. #22345	C₂	semidirect
31. C₄×#464	C₂	semidirect

Maximal subgroups

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

subgroup	index
#40099	2
#36448	2
#33069	2
#32543	2
#32434	2
#32393	2
#32308	2
#31903	2
#31611	2
#31496	2
#31442	2
#30377	2
#30135	2
#29092	2
#28846	2
#27556	2
#27554	2
#27037	2
#26375	2
#26189	2
#26116	2
#25965	2
#25169	2
#24918	2
#24894	2
#24826	2
#24528	2
#22871	2
#22679	2
#22345	2
C₄×#464	2