Subgroups — #6551229

Order 512.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#38212	C₂	1	1	yes	maximal, characteristic
2	#34482	C₂	1	1	yes	maximal, characteristic, complemented
3	#30156	C₂	1	1	yes	maximal, characteristic, complemented
4	#30027	C₂	1	1	yes	maximal, characteristic, complemented
5	#29769	C₂	1	1	yes	maximal, characteristic, complemented
6	#29538	C₂	1	1	yes	maximal, characteristic, complemented
7	#29430	C₂	1	1	yes	maximal, characteristic, complemented
8	#29252	C₂	1	1	yes	maximal, characteristic, complemented
9	#29251	C₂	1	1	yes	maximal, characteristic, complemented
10	#27460	C₂	1	1	yes	maximal, characteristic, complemented
11	#27391	C₂	1	1	yes	maximal, characteristic, complemented
12	#27322	C₂	1	1	yes	maximal, characteristic, complemented
13	#27105	C₂	1	1	yes	maximal, characteristic, complemented
14	#26934	C₂	1	1	yes	maximal, characteristic, complemented
15	#26869	C₂	1	1	yes	maximal, characteristic, complemented
16	#26719	C₂	1	1	yes	maximal, characteristic, complemented
17	#26222	C₂	1	1	yes	maximal, characteristic, complemented
18	#26173	C₂	1	1	yes	maximal, characteristic, complemented
19	#26140	C₂	1	1	yes	maximal, characteristic
20	#25560	C₂	1	1	yes	maximal, characteristic
21	#25546	C₂	1	1	yes	maximal, characteristic, complemented
22	#24765	C₂	1	1	yes	maximal, characteristic, complemented
23	#24615	C₂	1	1	yes	maximal, characteristic, complemented
24	#23778	C₂	1	1	yes	maximal, characteristic, complemented
25	#23704	C₂	1	1	yes	maximal, characteristic, complemented
26	#23667	C₂	1	1	yes	maximal, characteristic, complemented
27	#23145	C₂	1	1	yes	maximal, characteristic, complemented
28	#23024	C₂	1	1	yes	maximal, characteristic, complemented
29	#22942	C₂	1	1	yes	maximal, characteristic, complemented
30	#22921	C₂	1	1	yes	maximal, characteristic, complemented
31	#22756	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#552	C₂²	1	1	yes	characteristic
33	C₂×#485	C₂²	1	1	yes	characteristic
34	C₂×#482	C₂²	1	1	yes	characteristic
35	C₂×#482	C₂²	1	1	yes	characteristic
36	C₂×#468	C₂²	1	1	yes	characteristic
37	C₂×#467	C₂²	1	1	yes	characteristic
38	C₂×#464	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
40	C₂×#433	C₂²	1	1	yes	characteristic
41	C₂²×#107	C₂²	1	1	yes	characteristic
42	C₂×#424	C₂²	1	1	yes	characteristic
43	#2863	C₂²	1	1	yes	characteristic
44	#2796	—	2	1	no	—
45	#2795	—	2	1	no	—
46	#2772	—	2	1	no	—
47	#2711	—	2	1	no	—
48	#2624	C₂²	1	1	yes	characteristic
49	#2620	C₂²	1	1	yes	characteristic
50	#2578	—	2	1	no	—
51	#2518	—	2	1	no	—
52	#2506	C₂²	1	1	yes	characteristic
53	#2497	C₂²	1	1	yes	characteristic
54	#2476	—	2	1	no	—
55	#2448	C₂²	1	1	yes	characteristic
56	#2441	—	2	1	no	—
57	#2427	C₂²	1	1	yes	characteristic
58	#2416	C₂²	1	1	yes	characteristic
59	#2415	C₂²	1	1	yes	characteristic
60	#2382	—	2	1	no	—
61	#2376	—	2	1	no	—
62	#2373	—	2	1	no	—
63	#2370	C₂²	1	1	yes	characteristic
64	#2363	C₂²	1	1	yes	characteristic
65	#2362	C₂²	1	1	yes	characteristic
66	#2360	C₂²	1	1	yes	characteristic
67	#2360	C₂²	1	1	yes	characteristic
68	#2352	C₂²	1	1	yes	characteristic
69	#2351	C₂²	1	1	yes	characteristic
70	#2346	—	2	1	no	—
71	#2346	C₂²	1	1	yes	characteristic
72	#2345	C₂²	1	1	yes	characteristic
73	#2335	—	2	1	no	—
74	#2334	—	2	1	no	—
75	#2330	—	2	1	no	—
76	#2323	C₂²	1	1	yes	characteristic
77	#2323	C₂²	1	1	yes	characteristic
78	#2323	C₂²	1	1	yes	characteristic
79	#2317	C₂²	1	1	yes	characteristic
80	#2317	C₂²	1	1	yes	characteristic
81	#2316	C₂²	1	1	yes	characteristic
82	#2314	—	2	1	no	—
83	C₄×#125	C₂²	1	1	yes	characteristic
84	#2295	C₂²	1	1	yes	characteristic
85	#2293	C₂²	1	1	yes	characteristic
86	#2293	C₂²	1	1	yes	characteristic
87	#2101	C₂²	1	1	yes	characteristic
88	#2092	C₂²	1	1	yes	characteristic
89	#2088	C₂²	1	1	yes	characteristic
90	#2088	C₂²	1	1	yes	characteristic
91	#2087	C₂²	1	1	yes	characteristic
92	#2087	C₂²	1	1	yes	characteristic
93	#2087	C₂²	1	1	yes	characteristic
94	#2087	C₂²	1	1	yes	characteristic
95	#2086	C₂²	1	1	yes	characteristic
96	#2086	C₂²	1	1	yes	characteristic
97	#2086	C₂²	1	1	yes	characteristic
98	#2086	C₂²	1	1	yes	characteristic
99	#2085	C₂²	1	1	yes	characteristic
100	#2084	C₂²	1	1	yes	characteristic
101	#2083	C₂²	1	1	yes	characteristic
102	#2076	C₂²	1	1	yes	characteristic
103	#2076	C₂²	1	1	yes	characteristic
104	#2074	C₂²	1	1	yes	characteristic
105	#2068	C₂²	1	1	yes	characteristic
106	#2068	C₂²	1	1	yes	characteristic
107	#2068	C₂²	1	1	yes	characteristic
108	#2067	C₂²	1	1	yes	characteristic
109	#2067	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	#2059	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	#2042	C₂²	1	1	yes	characteristic
118	#2042	C₂²	1	1	yes	characteristic
119	#2035	C₂²	1	1	yes	characteristic
120	#2035	C₂²	1	1	yes	characteristic
121	#2035	C₂²	1	1	yes	characteristic
122	#2033	C₂²	1	1	yes	characteristic
123	#2026	C₂²	1	1	yes	characteristic
124	#2025	C₂²	1	1	yes	characteristic
125	#2001	C₂²	1	1	yes	characteristic
126	#2000	C₂²	1	1	yes	characteristic
127	#1983	C₂²	1	1	yes	characteristic
128	#1969	C₂²	1	1	yes	characteristic
129	#1947	C₂²	1	1	yes	characteristic
130	#1943	C₂²	1	1	yes	characteristic
131	#1942	C₂²	1	1	yes	characteristic
132	#1942	C₂²	1	1	yes	characteristic
133	#1936	C₂²	1	1	yes	characteristic
134	#1934	C₂²	1	1	yes	characteristic
135	#1933	C₂²	1	1	yes	characteristic
136	#1933	C₂²	1	1	yes	characteristic
137	#1928	C₂²	1	1	yes	characteristic
138	#1928	C₂²	1	1	yes	characteristic
139	#1928	C₂²	1	1	yes	characteristic
140	#1927	C₂²	1	1	yes	characteristic
141	#1925	C₂²	1	1	yes	characteristic
142	#1925	C₂²	1	1	yes	characteristic
143	#1923	C₂²	1	1	yes	characteristic
144	#1923	C₂²	1	1	yes	characteristic
145	#1921	C₂²	1	1	yes	characteristic
146	#1921	C₂²	1	1	yes	characteristic
147	#1921	C₂²	1	1	yes	characteristic
148	#1921	C₂²	1	1	yes	characteristic
149	#1921	C₂²	1	1	yes	characteristic
150	#1920	C₂²	1	1	yes	characteristic
151	#1920	C₂²	1	1	yes	characteristic
152	#1920	C₂²	1	1	yes	characteristic
153	#1919	C₂²	1	1	yes	characteristic
154	#1918	C₂²	1	1	yes	characteristic
155	#1917	C₂²	1	1	yes	characteristic
156	#1916	C₂²	1	1	yes	characteristic
157	#1894	C₂²	1	1	yes	characteristic
158	#1893	C₂²	1	1	yes	characteristic
159	#1880	C₂²	1	1	yes	characteristic
160	#1880	C₂²	1	1	yes	characteristic
161	#1878	C₂²	1	1	yes	characteristic
162	#1877	C₂²	1	1	yes	characteristic
163	#1874	C₂²	1	1	yes	characteristic
164	#1874	C₂²	1	1	yes	characteristic
165	#1873	C₂²	1	1	yes	characteristic
166	#1873	C₂²	1	1	yes	characteristic
167	#1872	C₂²	1	1	yes	characteristic
168	#1872	C₂²	1	1	yes	characteristic
169	#1872	C₂²	1	1	yes	characteristic
170	#1870	C₂²	1	1	yes	characteristic
171	#1869	C₂²	1	1	yes	characteristic
172	#1865	C₂²	1	1	yes	characteristic
173	#1865	C₂²	1	1	yes	characteristic
174	#1865	C₂²	1	1	yes	characteristic
175	#1864	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	#1863	C₂²	1	1	yes	characteristic
180	#1854	C₂²	1	1	yes	characteristic
181	#1854	C₂²	1	1	yes	characteristic
182	#1853	C₂²	1	1	yes	characteristic
183	#1852	C₂²	1	1	yes	characteristic
184	#1852	C₂²	1	1	yes	characteristic
185	#1831	C₂²	1	1	yes	characteristic
186	#1825	C₂²	1	1	yes	characteristic
187	#1803	C₂²	1	1	yes	characteristic
188	#1798	C₂²	1	1	yes	characteristic
189	#1798	C₂²	1	1	yes	characteristic
190	C₄×#107	C₂²	1	1	yes	characteristic
191	C₄×#106	C₂²	1	1	yes	characteristic
192	C₄×#106	C₂²	1	1	yes	characteristic
193	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
194	#1763	C₂²	1	1	yes	characteristic
195	#1763	C₂²	1	1	yes	characteristic
196	C₄×#102	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	#1753	C₂²	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
200	#1736	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	#1735	C₂²	1	1	yes	characteristic
203	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	#552	—	2	4	no	—
208	#552	—	2	4	no	—
209	C₂×#126	—	2	1	no	—
210	C₂×#125	—	2	1	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#124	C₂³	1	1	yes	characteristic
214	C₂×#123	—	2	1	no	—
215	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×#121	—	2	1	no	—
220	C₂×#121	C₂³	1	1	yes	characteristic
221	C₂×#121	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×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×#117	—	2	1	no	—
229	C₂×#117	—	2	1	no	—
230	C₂×#117	C₂³	1	1	yes	characteristic
231	C₂×#117	C₂³	1	1	yes	characteristic
232	C₂×#117	C₂³	1	1	yes	characteristic
233	C₂×#117	C₂³	1	1	yes	characteristic
234	C₂×#117	C₂³	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	#485	—	2	4	no	—
239	#482	—	2	4	no	—
240	#482	—	4	2	no	—
241	#468	—	2	4	no	—
242	#467	—	2	4	no	—
243	#464	—	4	2	no	—
244	C₄×Q₁₆	—	4	2	no	—
245	#433	—	4	2	no	—
246	C₂×#107	—	4	2	no	—
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#107	C₂³	1	1	yes	characteristic
253	C₂×#107	C₂³	1	1	yes	characteristic
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#107	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×#106	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	#424	—	4	2	no	—
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	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×#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×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×#97	C₂³	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
296	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#399	—	2	1	no	—
301	#399	—	2	1	no	—
302	#398	—	2	1	no	—
303	#397	—	2	1	no	—
304	#397	—	2	1	no	—
305	#397	—	2	1	no	—
306	#397	—	2	1	no	—
307	#396	—	2	1	no	—
308	#396	—	2	1	no	—
309	#396	—	2	1	no	—
310	#396	—	2	1	no	—
311	#394	—	2	1	no	—
312	#394	—	2	1	no	—
313	#394	—	2	1	no	—
314	#394	—	2	1	no	—
315	#394	—	2	1	no	—
316	#394	—	2	1	no	—
317	#394	—	2	1	no	—
318	#391	C₂³	1	1	yes	characteristic
319	#391	C₂³	1	1	yes	characteristic
320	#391	C₂³	1	1	yes	characteristic
321	#391	C₂³	1	1	yes	characteristic
322	#391	C₂³	1	1	yes	characteristic
323	#390	—	2	1	no	—
324	#390	D₄	1	1	yes	characteristic
325	#390	D₄	1	1	yes	characteristic
326	#390	C₂³	1	1	yes	characteristic
327	#390	C₂³	1	1	yes	characteristic
328	#390	C₂³	1	1	yes	characteristic
329	#389	—	2	1	no	—
330	#389	—	2	1	no	—
331	#389	—	2	1	no	—
332	#389	—	2	1	no	—
333	#389	—	2	1	no	—
334	#389	—	2	1	no	—
335	#389	—	2	1	no	—
336	#389	—	2	1	no	—
337	#389	—	2	1	no	—
338	#389	—	2	1	no	—
339	#389	—	2	1	no	—
340	#389	D₄	1	1	yes	characteristic
341	#389	D₄	1	1	yes	characteristic
342	#389	C₂³	1	1	yes	characteristic
343	#389	C₂³	1	1	yes	characteristic
344	#389	C₂³	1	1	yes	characteristic
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#389	C₂³	1	1	yes	characteristic
351	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
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	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	D₄	1	1	yes	characteristic
377	#388	D₄	1	1	yes	characteristic
378	#388	D₄	1	1	yes	characteristic
379	#388	D₄	1	1	yes	characteristic
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	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#386	—	2	1	no	—
401	#386	—	2	1	no	—
402	#386	—	2	1	no	—
403	#386	—	2	1	no	—
404	#385	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	—	2	1	no	—
410	#384	—	2	1	no	—
411	#384	—	2	1	no	—
412	#384	C₂³	1	1	yes	characteristic
413	#383	—	2	1	no	—
414	#382	—	2	1	no	—
415	#382	—	2	1	no	—
416	#382	—	2	1	no	—
417	#382	—	2	1	no	—
418	#382	C₂³	1	1	yes	characteristic
419	#380	—	2	1	no	—
420	#380	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	—	2	1	no	—
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	#380	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
447	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
449	#376	—	2	1	no	—
450	#376	—	2	1	no	—
451	C₄³	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	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	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	C₂⁴	1	1	yes	characteristic
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
495	C₂²×D₄	C₂⁴	1	1	yes	characteristic
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×Q₁₆	—	2	2	no	—
503	C₂×Q₁₆	—	2	2	no	—
504	C₂×Q₁₆	—	4	1	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	4	1	no	—
507	C₂×SD₁₆	—	4	1	no	—
508	C₂×M₁₆	—	2	2	no	—
509	C₂×M₁₆	—	4	1	no	—
510	C₂×M₁₆	—	4	1	no	—
511	C₂²×C₈	—	2	2	no	—
512	C₂²×C₈	—	2	2	no	—
513	C₂²×C₈	—	4	1	no	—
514	C₂²×C₈	C₂⁴	1	1	yes	characteristic
515	C₂²×C₈	C₂⁴	1	1	yes	characteristic
516	C₂²×C₈	C₂⁴	1	1	yes	characteristic
517	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	#126	—	2	8	no	—
523	#125	—	2	8	no	—
524	#125	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	8	2	no	—
527	#124	—	4	1	no	—
528	#124	—	4	1	no	—
529	#123	—	2	8	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	4	1	no	—
537	C₂²⋊Q₈	#41	1	4	yes	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	4	1	no	—
541	#121	—	4	1	no	—
542	#121	—	8	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	4	1	no	—
546	C₄×Q₈	—	4	1	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×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	4	1	no	—
555	#117	—	2	8	no	—
556	#117	—	2	2	no	—
557	#117	—	2	2	no	—
558	#117	—	4	1	no	—
559	#117	—	4	1	no	—
560	#117	—	4	1	no	—
561	#117	—	4	1	no	—
562	#117	—	4	1	no	—
563	#117	—	4	1	no	—
564	#117	—	4	1	no	—
565	#117	—	8	2	no	—
566	#117	#41	1	4	yes	—
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	2	no	—
574	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	4	1	no	—
601	C₂×C₄⋊C₄	—	4	1	no	—
602	C₂×C₄⋊C₄	—	4	1	no	—
603	C₂×C₄⋊C₄	—	4	1	no	—
604	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	C₂×C₄²	C₂⁴	1	1	yes	characteristic
678	C₂×C₄²	C₂⁴	1	1	yes	characteristic
679	#107	—	2	2	no	—
680	#107	—	2	2	no	—
681	#107	—	2	2	no	—
682	#107	—	2	2	no	—
683	#107	—	2	2	no	—
684	#107	—	2	2	no	—
685	#107	—	4	1	no	—
686	#107	—	4	1	no	—
687	#107	—	4	1	no	—
688	#106	—	2	2	no	—
689	#106	—	2	2	no	—
690	#106	—	2	2	no	—
691	#106	—	4	1	no	—
692	#106	—	4	1	no	—
693	C₄⋊C₈	—	2	2	no	—
694	C₄⋊C₈	—	2	2	no	—
695	C₄⋊C₈	—	4	1	no	—
696	C₄⋊C₈	—	4	1	no	—
697	C₄⋊C₈	—	4	1	no	—
698	C₄⋊C₈	—	4	1	no	—
699	#103	—	2	2	no	—
700	#103	—	2	2	no	—
701	#103	—	2	2	no	—
702	#103	—	2	2	no	—
703	#103	—	2	2	no	—
704	#103	—	2	2	no	—
705	#103	—	4	1	no	—
706	#103	—	4	1	no	—
707	#103	—	4	1	no	—
708	#103	—	4	1	no	—
709	#103	—	4	1	no	—
710	#103	—	4	1	no	—
711	#103	—	4	1	no	—
712	#102	—	2	2	no	—
713	#102	—	2	2	no	—
714	#102	—	2	2	no	—
715	#102	—	2	2	no	—
716	#102	—	4	1	no	—
717	#102	—	4	1	no	—
718	#102	—	4	1	no	—
719	C₂²⋊C₈	—	2	2	no	—
720	C₂²⋊C₈	—	2	2	no	—
721	C₂²⋊C₈	—	2	2	no	—
722	C₂²⋊C₈	—	4	1	no	—
723	C₂²⋊C₈	—	4	1	no	—
724	C₂²⋊C₈	—	4	1	no	—
725	#97	—	4	1	no	—
726	C₄×C₈	—	2	2	no	—
727	C₄×C₈	—	4	1	no	—
728	C₄×C₈	—	4	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	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	C₂×D₄	1	1	yes	characteristic
769	#95	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	#95	C₂×D₄	1	1	yes	characteristic
773	#95	C₂×D₄	1	1	yes	characteristic
774	C₂⁴	—	2	1	no	—
775	C₂⁴	C₂²×D₄	1	1	yes	characteristic
776	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	C₂×#41	1	2	yes	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	1	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	8	1	no	—
800	C₂×D₄	—	8	1	no	—
801	C₂×D₄	—	8	1	no	—
802	C₂×D₄	—	8	1	no	—
803	C₂×D₄	—	8	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	4	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	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	8	1	no	—
833	C₂²×C₄	—	8	1	no	—
834	C₂²×C₄	—	8	1	no	—
835	C₂²×C₄	—	8	1	no	—
836	C₂²×C₄	—	8	1	no	—
837	C₂²×C₄	—	8	1	no	—
838	C₂²×C₄	—	8	1	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
846	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
847	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂×#41	1	2	yes	—
854	C₂²×C₄	C₂×#41	1	2	yes	—
855	C₂²×C₄	C₂⁵	1	1	yes	characteristic
856	Q₁₆	—	4	4	no	—
857	SD₁₆	—	8	2	no	—
858	M₁₆	—	8	2	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	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	4	4	no	—
883	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	2	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	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	4	1	no	—
914	C₄⋊C₄	—	4	1	no	—
915	C₄⋊C₄	—	4	1	no	—
916	C₄⋊C₄	—	4	1	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	1	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	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	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	C₂×#41	1	2	yes	—
945	C₄⋊C₄	C₂×#41	1	2	yes	—
946	C₄⋊C₄	C₂×#41	1	2	yes	—
947	C₄⋊C₄	2₋¹⁺⁴	1	2	yes	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	4	1	no	—
956	C₂²⋊C₄	—	4	1	no	—
957	C₂²⋊C₄	—	4	1	no	—
958	C₂²⋊C₄	—	4	1	no	—
959	C₂²⋊C₄	—	4	1	no	—
960	C₂²⋊C₄	—	4	1	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	8	1	no	—
968	C₂²⋊C₄	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₂²⋊C₄	—	8	1	no	—
978	C₂²⋊C₄	—	8	1	no	—
979	C₂²⋊C₄	—	8	1	no	—
980	C₄²	—	2	4	no	—
981	C₄²	—	2	4	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	4	1	no	—
994	C₄²	—	4	1	no	—
995	C₄²	—	4	1	no	—
996	C₄²	—	4	2	no	—
997	C₄²	—	4	2	no	—
998	C₄²	—	8	1	no	—
999	C₄²	—	8	1	no	—
1000	C₄²	—	8	1	no	—
1001	C₄²	—	8	1	no	—
1002	C₄²	—	8	1	no	—
1003	C₄²	—	8	1	no	—
1004	C₄²	—	8	1	no	—
1005	C₄²	—	8	1	no	—
1006	C₄²	—	8	1	no	—
1007	C₄²	—	8	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	#525	1	2	yes	—
1029	C₂³	C₂³×D₄	1	1	yes	characteristic
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	4	1	no	—
1033	Q₈	—	4	1	no	—
1034	Q₈	—	4	1	no	—
1035	Q₈	—	4	1	no	—
1036	Q₈	—	4	1	no	—
1037	Q₈	—	4	1	no	—
1038	D₄	—	4	1	no	—
1039	D₄	—	4	1	no	—
1040	D₄	—	4	1	no	—
1041	D₄	—	4	1	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	16	2	no	—
1044	D₄	—	16	2	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	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	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	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	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	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	8	4	no	—
1133	C₂×C₄	—	8	4	no	—
1134	C₂×C₄	—	16	2	no	—
1135	C₂×C₄	—	16	2	no	—
1136	C₂×C₄	#525	1	2	yes	—
1137	C₂×C₄	#578	1	2	yes	—
1138	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1139	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1140	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1141	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1142	C₂×C₄	#585	1	1	yes	characteristic
1143	C₂×C₄	#585	1	1	yes	characteristic
1144	C₈	—	2	2	no	—
1145	C₈	—	4	1	no	—
1146	C₈	—	4	1	no	—
1147	C₈	—	4	1	no	—
1148	C₈	—	4	1	no	—
1149	C₈	—	4	1	no	—
1150	C₈	—	4	1	no	—
1151	C₈	—	4	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	8	1	no	—
1167	C₂²	—	8	1	no	—
1168	C₂²	—	8	1	no	—
1169	C₂²	—	8	1	no	—
1170	C₂²	—	8	1	no	—
1171	C₂²	—	8	1	no	—
1172	C₂²	—	8	1	no	—
1173	C₂²	C₂×#525	1	1	yes	characteristic
1174	C₂²	#3489	1	1	yes	characteristic
1175	C₂²	#3496	1	1	yes	characteristic
1176	C₂²	C₂×#578	1	1	yes	characteristic
1177	C₂²	#3584	1	1	yes	characteristic
1178	C₂²	#3584	1	1	yes	characteristic
1179	C₂²	#3585	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	2	no	—
1197	C₄	—	8	1	no	—
1198	C₄	—	8	1	no	—
1199	C₄	—	8	1	no	—
1200	C₄	—	8	1	no	—
1201	C₄	—	8	1	no	—
1202	C₄	—	8	1	no	—
1203	C₄	—	8	1	no	—
1204	C₄	—	8	1	no	—
1205	C₄	—	8	1	no	—
1206	C₄	—	8	1	no	—
1207	C₄	#3511	1	1	yes	characteristic
1208	C₄	#3512	1	1	yes	characteristic
1209	C₄	#3513	1	1	yes	characteristic
1210	C₄	#3515	1	1	yes	characteristic
1211	C₂	—	4	2	no	—
1212	C₂	—	8	1	no	—
1213	C₂	—	16	1	no	—
1214	C₂	#35807	1	1	yes	characteristic
1215	C₂	#60573	1	1	yes	characteristic
1216	C₂	#60587	1	1	yes	characteristic
1217	C₂	#62165	1	1	yes	characteristic
1218	C₂	#62210	1	1	yes	characteristic
1219	C₂	#62325	1	1	yes	characteristic
1220	C₂	#62351	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2416	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2293 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #34482	C₂	semidirect
3. #30156	C₂	semidirect
4. #30027	C₂	semidirect
5. #29769	C₂	semidirect
6. #29538	C₂	semidirect
7. #29430	C₂	semidirect
8. #29252	C₂	semidirect
9. #29251	C₂	semidirect
10. #27460	C₂	semidirect
11. #27391	C₂	semidirect
12. #27322	C₂	semidirect
13. #27105	C₂	semidirect
14. #26934	C₂	semidirect
15. #26869	C₂	semidirect
16. #26719	C₂	semidirect
17. #26222	C₂	semidirect
18. #26173	C₂	semidirect
21. #25546	C₂	semidirect
22. #24765	C₂	semidirect
23. #24615	C₂	semidirect
24. #23778	C₂	semidirect
25. #23704	C₂	semidirect
26. #23667	C₂	semidirect
27. #23145	C₂	semidirect
28. #23024	C₂	semidirect
29. #22942	C₂	semidirect
30. #22921	C₂	semidirect
31. #22756	C₂	semidirect

Maximal subgroups

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

subgroup	index
#38212	2
#34482	2
#30156	2
#30027	2
#29769	2
#29538	2
#29430	2
#29252	2
#29251	2
#27460	2
#27391	2
#27322	2
#27105	2
#26934	2
#26869	2
#26719	2
#26222	2
#26173	2
#26140	2
#25560	2
#25546	2
#24765	2
#24615	2
#23778	2
#23704	2
#23667	2
#23145	2
#23024	2
#22942	2
#22921	2
#22756	2