Subgroups — #7048079

Order 512.

1342 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59405	C₂	1	1	yes	maximal, characteristic
2	#59291	C₂	1	1	yes	maximal, characteristic, complemented
3	#32520	C₂	1	1	yes	maximal, characteristic, complemented
4	#32326	C₂	1	1	yes	maximal, characteristic, complemented
5	#32008	C₂	1	1	yes	maximal, characteristic, complemented
6	#31796	C₂	1	1	yes	maximal, characteristic
7	#31606	C₂	1	1	yes	maximal, characteristic, complemented
8	#31422	C₂	1	1	yes	maximal, characteristic, complemented
9	#31352	C₂	1	1	yes	maximal, characteristic, complemented
10	#31132	C₂	1	1	yes	maximal, characteristic, complemented
11	#29243	C₂	1	1	yes	maximal, characteristic, complemented
12	#29050	C₂	1	1	yes	maximal, characteristic, complemented
13	#28061	C₂	1	1	yes	maximal, characteristic, complemented
14	#27624	C₂	1	1	yes	maximal, characteristic, complemented
15	#27473	C₂	1	1	yes	maximal, characteristic, complemented
16	#27471	C₂	1	1	yes	maximal, characteristic, complemented
17	#27412	C₂	1	1	yes	maximal, characteristic, complemented
18	#27393	C₂	1	1	yes	maximal, characteristic, complemented
19	#27313	C₂	1	1	yes	maximal, characteristic, complemented
20	#27148	C₂	1	1	yes	maximal, characteristic, complemented
21	#27036	C₂	1	1	yes	maximal, characteristic, complemented
22	#26782	C₂	1	1	yes	maximal, characteristic, complemented
23	#26542	C₂	1	1	yes	maximal, characteristic, complemented
24	#26342	C₂	1	1	yes	maximal, characteristic, complemented
25	#26126	C₂	1	1	yes	maximal, characteristic
26	#24979	C₂	1	1	yes	maximal, characteristic, complemented
27	#23762	C₂	1	1	yes	maximal, characteristic, complemented
28	#22971	C₂	1	1	yes	maximal, characteristic, complemented
29	#22618	C₂	1	1	yes	maximal, characteristic, complemented
30	#22371	C₂	1	1	yes	maximal, characteristic, complemented
31	#22081	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#480	C₂²	1	1	yes	characteristic
33	C₂×#477	C₂²	1	1	yes	characteristic
34	C₂²×#107	C₂²	1	1	yes	characteristic
35	#2793	—	2	1	no	—
36	#2779	—	2	1	no	—
37	#2774	—	2	1	no	—
38	#2768	—	2	1	no	—
39	#2597	—	2	1	no	—
40	#2590	—	2	1	no	—
41	#2587	—	2	1	no	—
42	#2559	—	2	1	no	—
43	#2556	—	2	1	no	—
44	#2552	C₂²	1	1	yes	characteristic
45	#2536	C₂²	1	1	yes	characteristic
46	#2513	C₂²	1	1	yes	characteristic
47	#2509	C₂²	1	1	yes	characteristic
48	#2507	C₂²	1	1	yes	characteristic
49	#2507	C₂²	1	1	yes	characteristic
50	#2497	C₂²	1	1	yes	characteristic
51	#2497	C₂²	1	1	yes	characteristic
52	#2496	C₂²	1	1	yes	characteristic
53	#2487	C₂²	1	1	yes	characteristic
54	#2473	—	2	1	no	—
55	#2466	—	2	1	no	—
56	#2440	C₂²	1	1	yes	characteristic
57	#2440	C₂²	1	1	yes	characteristic
58	#2438	—	2	1	no	—
59	#2426	C₂²	1	1	yes	characteristic
60	#2426	C₂²	1	1	yes	characteristic
61	#2422	—	2	1	no	—
62	#2422	C₂²	1	1	yes	characteristic
63	#2417	—	2	1	no	—
64	#2416	C₂²	1	1	yes	characteristic
65	#2374	—	2	1	no	—
66	#2369	C₂²	1	1	yes	characteristic
67	#2367	C₂²	1	1	yes	characteristic
68	#2360	C₂²	1	1	yes	characteristic
69	#2359	—	2	1	no	—
70	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	#2345	C₂²	1	1	yes	characteristic
73	#2345	C₂²	1	1	yes	characteristic
74	#2345	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
76	C₄×#123	C₂²	1	1	yes	characteristic
77	C₄×#121	C₂²	1	1	yes	characteristic
78	C₂×#389	C₂²	1	1	yes	characteristic
79	#2285	C₂²	1	1	yes	characteristic
80	#2101	C₂²	1	1	yes	characteristic
81	#2100	C₂²	1	1	yes	characteristic
82	#2099	C₂²	1	1	yes	characteristic
83	#2099	C₂²	1	1	yes	characteristic
84	#2095	C₂²	1	1	yes	characteristic
85	#2093	C₂²	1	1	yes	characteristic
86	#2088	C₂²	1	1	yes	characteristic
87	#2088	C₂²	1	1	yes	characteristic
88	#2088	C₂²	1	1	yes	characteristic
89	#2088	C₂²	1	1	yes	characteristic
90	#2087	C₂²	1	1	yes	characteristic
91	#2086	C₂²	1	1	yes	characteristic
92	#2085	C₂²	1	1	yes	characteristic
93	#2084	C₂²	1	1	yes	characteristic
94	#2084	C₂²	1	1	yes	characteristic
95	#2083	C₂²	1	1	yes	characteristic
96	#2083	C₂²	1	1	yes	characteristic
97	#2077	C₂²	1	1	yes	characteristic
98	#2077	C₂²	1	1	yes	characteristic
99	#2075	C₂²	1	1	yes	characteristic
100	#2075	C₂²	1	1	yes	characteristic
101	#2075	C₂²	1	1	yes	characteristic
102	#2075	C₂²	1	1	yes	characteristic
103	#2072	C₂²	1	1	yes	characteristic
104	#2068	C₂²	1	1	yes	characteristic
105	#2068	C₂²	1	1	yes	characteristic
106	#2067	C₂²	1	1	yes	characteristic
107	#2065	C₂²	1	1	yes	characteristic
108	#2057	C₂²	1	1	yes	characteristic
109	#2042	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2036	C₂²	1	1	yes	characteristic
112	#2036	C₂²	1	1	yes	characteristic
113	#2035	C₂²	1	1	yes	characteristic
114	#2035	C₂²	1	1	yes	characteristic
115	#2034	C₂²	1	1	yes	characteristic
116	#2034	C₂²	1	1	yes	characteristic
117	#2033	C₂²	1	1	yes	characteristic
118	#2033	C₂²	1	1	yes	characteristic
119	#2023	C₂²	1	1	yes	characteristic
120	#1990	C₂²	1	1	yes	characteristic
121	#1983	C₂²	1	1	yes	characteristic
122	#1959	C₂²	1	1	yes	characteristic
123	#1955	C₂²	1	1	yes	characteristic
124	#1949	C₂²	1	1	yes	characteristic
125	#1948	C₂²	1	1	yes	characteristic
126	#1947	C₂²	1	1	yes	characteristic
127	#1947	C₂²	1	1	yes	characteristic
128	#1947	C₂²	1	1	yes	characteristic
129	#1944	C₂²	1	1	yes	characteristic
130	#1943	C₂²	1	1	yes	characteristic
131	#1943	C₂²	1	1	yes	characteristic
132	#1943	C₂²	1	1	yes	characteristic
133	#1943	C₂²	1	1	yes	characteristic
134	#1942	C₂²	1	1	yes	characteristic
135	#1940	C₂²	1	1	yes	characteristic
136	#1936	C₂²	1	1	yes	characteristic
137	#1936	C₂²	1	1	yes	characteristic
138	#1936	C₂²	1	1	yes	characteristic
139	#1934	C₂²	1	1	yes	characteristic
140	#1926	C₂²	1	1	yes	characteristic
141	#1925	C₂²	1	1	yes	characteristic
142	#1925	C₂²	1	1	yes	characteristic
143	#1925	C₂²	1	1	yes	characteristic
144	#1924	C₂²	1	1	yes	characteristic
145	#1924	C₂²	1	1	yes	characteristic
146	#1923	C₂²	1	1	yes	characteristic
147	#1923	C₂²	1	1	yes	characteristic
148	#1921	C₂²	1	1	yes	characteristic
149	#1921	C₂²	1	1	yes	characteristic
150	#1921	C₂²	1	1	yes	characteristic
151	#1920	C₂²	1	1	yes	characteristic
152	#1919	C₂²	1	1	yes	characteristic
153	#1918	C₂²	1	1	yes	characteristic
154	#1918	C₂²	1	1	yes	characteristic
155	#1918	C₂²	1	1	yes	characteristic
156	#1918	C₂²	1	1	yes	characteristic
157	#1918	C₂²	1	1	yes	characteristic
158	#1918	C₂²	1	1	yes	characteristic
159	#1918	C₂²	1	1	yes	characteristic
160	#1917	C₂²	1	1	yes	characteristic
161	#1917	C₂²	1	1	yes	characteristic
162	#1893	C₂²	1	1	yes	characteristic
163	#1892	C₂²	1	1	yes	characteristic
164	#1874	C₂²	1	1	yes	characteristic
165	#1874	C₂²	1	1	yes	characteristic
166	#1872	C₂²	1	1	yes	characteristic
167	#1872	C₂²	1	1	yes	characteristic
168	#1872	C₂²	1	1	yes	characteristic
169	#1869	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	#1865	C₂²	1	1	yes	characteristic
174	#1864	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	#1853	C₂²	1	1	yes	characteristic
179	#1853	C₂²	1	1	yes	characteristic
180	#1852	C₂²	1	1	yes	characteristic
181	#1852	C₂²	1	1	yes	characteristic
182	#1852	C₂²	1	1	yes	characteristic
183	#1850	C₂²	1	1	yes	characteristic
184	#1836	C₂²	1	1	yes	characteristic
185	#1824	C₂²	1	1	yes	characteristic
186	#1824	C₂²	1	1	yes	characteristic
187	#1823	C₂²	1	1	yes	characteristic
188	#1807	C₂²	1	1	yes	characteristic
189	#1803	C₂²	1	1	yes	characteristic
190	#1802	C₂²	1	1	yes	characteristic
191	#1802	C₂²	1	1	yes	characteristic
192	#1797	C₂²	1	1	yes	characteristic
193	#1776	C₂²	1	1	yes	characteristic
194	#1776	C₂²	1	1	yes	characteristic
195	#1776	C₂²	1	1	yes	characteristic
196	#1770	C₂²	1	1	yes	characteristic
197	#1763	C₂²	1	1	yes	characteristic
198	#1763	C₂²	1	1	yes	characteristic
199	#1763	C₂²	1	1	yes	characteristic
200	C₄×#103	C₂²	1	1	yes	characteristic
201	#1752	C₂²	1	1	yes	characteristic
202	#1749	C₂²	1	1	yes	characteristic
203	C₂³×C₈	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
205	C₂×#126	—	2	1	no	—
206	C₂×#125	—	2	1	no	—
207	C₂×#124	C₂³	1	1	yes	characteristic
208	C₂×#123	—	2	1	no	—
209	C₂×#123	D₄	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	—	2	1	no	—
211	C₂×C₂²⋊Q₈	—	2	1	no	—
212	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×#121	—	2	1	no	—
215	C₂×#121	C₂³	1	1	yes	characteristic
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
224	C₂×#117	—	2	1	no	—
225	C₂²×C₄⋊C₄	—	2	1	no	—
226	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₄²	C₂³	1	1	yes	characteristic
231	#480	—	2	4	no	—
232	#477	—	2	4	no	—
233	C₂×#107	—	2	4	no	—
234	C₂×#107	C₂³	1	1	yes	characteristic
235	C₂×#107	C₂³	1	1	yes	characteristic
236	C₂×#107	C₂³	1	1	yes	characteristic
237	C₂×#107	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
256	C₂×#103	C₂³	1	1	yes	characteristic
257	C₂×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
264	C₂×#102	C₂³	1	1	yes	characteristic
265	C₂×#102	C₂³	1	1	yes	characteristic
266	C₂×#102	C₂³	1	1	yes	characteristic
267	C₂×#102	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×#97	C₂³	1	1	yes	characteristic
279	C₂×#97	C₂³	1	1	yes	characteristic
280	C₂×#97	C₂³	1	1	yes	characteristic
281	C₂×#97	C₂³	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
283	#400	—	2	1	no	—
284	#400	—	2	1	no	—
285	#400	—	2	1	no	—
286	#400	—	2	1	no	—
287	#400	—	2	1	no	—
288	#400	—	2	1	no	—
289	#399	—	2	1	no	—
290	#398	—	2	1	no	—
291	#398	—	2	1	no	—
292	#398	—	2	1	no	—
293	#398	—	2	1	no	—
294	#398	—	2	1	no	—
295	#398	—	2	1	no	—
296	#398	—	2	1	no	—
297	#398	—	2	1	no	—
298	#398	—	2	1	no	—
299	#397	—	2	1	no	—
300	#397	—	2	1	no	—
301	#397	—	2	1	no	—
302	#397	—	2	1	no	—
303	#396	—	2	1	no	—
304	#396	—	2	1	no	—
305	#396	—	2	1	no	—
306	#396	—	2	1	no	—
307	#396	—	2	1	no	—
308	#395	—	2	1	no	—
309	#395	—	2	1	no	—
310	#394	—	2	1	no	—
311	#394	—	2	1	no	—
312	#394	—	2	1	no	—
313	#394	—	2	1	no	—
314	#394	—	2	1	no	—
315	#391	—	2	1	no	—
316	#391	—	2	1	no	—
317	#391	C₂³	1	1	yes	characteristic
318	#390	—	2	1	no	—
319	#390	—	2	1	no	—
320	#390	C₂³	1	1	yes	characteristic
321	#390	C₂³	1	1	yes	characteristic
322	#390	C₂³	1	1	yes	characteristic
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	—	2	1	no	—
327	#389	—	2	1	no	—
328	#389	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
335	#389	C₂³	1	1	yes	characteristic
336	#389	C₂³	1	1	yes	characteristic
337	#389	C₂³	1	1	yes	characteristic
338	#389	C₂³	1	1	yes	characteristic
339	#389	C₂³	1	1	yes	characteristic
340	#389	C₂³	1	1	yes	characteristic
341	#389	C₂³	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	#388	—	2	1	no	—
351	#388	—	2	1	no	—
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	D₄	1	1	yes	characteristic
362	#388	D₄	1	1	yes	characteristic
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#387	—	2	1	no	—
369	#387	—	2	1	no	—
370	#387	—	2	1	no	—
371	#387	—	2	1	no	—
372	#387	—	2	1	no	—
373	#387	—	2	1	no	—
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	D₄	1	1	yes	characteristic
378	#387	D₄	1	1	yes	characteristic
379	#386	—	2	1	no	—
380	#386	—	2	1	no	—
381	#386	—	2	1	no	—
382	#386	D₄	1	1	yes	characteristic
383	#385	—	2	1	no	—
384	#385	—	2	1	no	—
385	#385	—	2	1	no	—
386	#385	—	2	1	no	—
387	#385	—	2	1	no	—
388	#385	—	2	1	no	—
389	#385	—	2	1	no	—
390	#385	—	2	1	no	—
391	#385	—	2	1	no	—
392	#385	D₄	1	1	yes	characteristic
393	#384	—	2	1	no	—
394	#384	C₂³	1	1	yes	characteristic
395	#384	C₂³	1	1	yes	characteristic
396	#384	C₂³	1	1	yes	characteristic
397	#384	C₂³	1	1	yes	characteristic
398	#384	C₂³	1	1	yes	characteristic
399	#382	—	2	1	no	—
400	#382	C₂³	1	1	yes	characteristic
401	#381	D₄	1	1	yes	characteristic
402	#380	—	2	1	no	—
403	#380	—	2	1	no	—
404	#380	—	2	1	no	—
405	#380	—	2	1	no	—
406	#380	C₂³	1	1	yes	characteristic
407	#380	C₂³	1	1	yes	characteristic
408	#380	C₂³	1	1	yes	characteristic
409	#380	C₂³	1	1	yes	characteristic
410	#380	C₂³	1	1	yes	characteristic
411	#380	C₂³	1	1	yes	characteristic
412	#380	C₂³	1	1	yes	characteristic
413	#380	C₂³	1	1	yes	characteristic
414	C₄×C₄⋊C₄	—	2	1	no	—
415	C₄×C₄⋊C₄	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	—	2	1	no	—
418	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
428	C₄×C₂²⋊C₄	—	2	1	no	—
429	C₄×C₂²⋊C₄	—	2	1	no	—
430	C₄×C₂²⋊C₄	—	2	1	no	—
431	C₄×C₂²⋊C₄	—	2	1	no	—
432	C₄×C₂²⋊C₄	—	2	1	no	—
433	C₄×C₂²⋊C₄	—	2	1	no	—
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
438	C₂×#95	—	2	1	no	—
439	#340	C₂³	1	1	yes	characteristic
440	#340	C₂³	1	1	yes	characteristic
441	#340	C₂³	1	1	yes	characteristic
442	#340	C₂³	1	1	yes	characteristic
443	#340	C₂³	1	1	yes	characteristic
444	#340	C₂³	1	1	yes	characteristic
445	#340	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	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	#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	C₂²×Q₈	—	2	1	no	—
482	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
486	C₂²×D₄	C₂⁴	1	1	yes	characteristic
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
493	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
494	C₂³×C₄	C₂⁴	1	1	yes	characteristic
495	C₂³×C₄	C₂⁴	1	1	yes	characteristic
496	C₂²×C₈	—	2	2	no	—
497	C₂²×C₈	—	4	1	no	—
498	C₂²×C₈	—	4	1	no	—
499	C₂²×C₈	C₂⁴	1	1	yes	characteristic
500	C₂²×C₈	C₂⁴	1	1	yes	characteristic
501	C₂²×C₈	C₂⁴	1	1	yes	characteristic
502	C₂²×C₈	C₂⁴	1	1	yes	characteristic
503	C₂²×C₈	C₂⁴	1	1	yes	characteristic
504	C₂²×C₈	C₂⁴	1	1	yes	characteristic
505	C₂²×C₈	C₂⁴	1	1	yes	characteristic
506	C₂²×C₈	C₂⁴	1	1	yes	characteristic
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	—	4	1	no	—
509	#126	—	8	2	no	—
510	#125	—	8	2	no	—
511	#124	—	2	2	no	—
512	#124	—	4	1	no	—
513	#123	—	2	4	no	—
514	#123	—	4	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	4	1	no	—
518	C₂²⋊Q₈	—	4	1	no	—
519	C₂²⋊Q₈	—	8	2	no	—
520	C₂²⋊Q₈	—	8	2	no	—
521	#121	—	2	2	no	—
522	#121	—	4	1	no	—
523	#121	—	4	1	no	—
524	#121	—	4	1	no	—
525	#121	—	8	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	4	1	no	—
528	C₄×Q₈	—	4	1	no	—
529	C₄×Q₈	—	4	1	no	—
530	C₄×Q₈	—	4	1	no	—
531	C₄×Q₈	—	4	1	no	—
532	C₄×D₄	—	4	1	no	—
533	C₄×D₄	—	4	1	no	—
534	C₄×D₄	—	4	1	no	—
535	C₄×D₄	—	4	1	no	—
536	C₄×D₄	—	8	2	no	—
537	C₄×D₄	—	8	2	no	—
538	#117	—	8	2	no	—
539	C₂×C₄⋊C₄	—	2	2	no	—
540	C₂×C₄⋊C₄	—	2	2	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	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	—	4	1	no	—
579	C₂×C₄⋊C₄	—	4	1	no	—
580	C₂×C₄⋊C₄	—	4	1	no	—
581	C₂×C₄⋊C₄	—	4	1	no	—
582	C₂×C₄⋊C₄	—	4	1	no	—
583	C₂×C₄⋊C₄	—	8	2	no	—
584	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
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	—	4	1	no	—
644	C₂×C₄²	—	4	1	no	—
645	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
646	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
647	C₂×C₄²	C₂⁴	1	1	yes	characteristic
648	C₂×C₄²	C₂⁴	1	1	yes	characteristic
649	C₂×C₄²	C₂⁴	1	1	yes	characteristic
650	C₂×C₄²	C₂⁴	1	1	yes	characteristic
651	C₂×C₄²	C₂⁴	1	1	yes	characteristic
652	#107	—	2	2	no	—
653	#107	—	2	2	no	—
654	#107	—	2	2	no	—
655	#107	—	2	2	no	—
656	#107	—	2	2	no	—
657	#107	—	4	1	no	—
658	#107	—	4	1	no	—
659	#107	—	4	1	no	—
660	#107	—	4	1	no	—
661	#107	#41	1	4	yes	—
662	#106	—	4	1	no	—
663	#106	—	4	1	no	—
664	#106	—	4	1	no	—
665	#106	—	4	1	no	—
666	#106	—	4	1	no	—
667	#106	—	4	1	no	—
668	C₄⋊C₈	—	2	2	no	—
669	C₄⋊C₈	—	4	1	no	—
670	C₄⋊C₈	—	4	1	no	—
671	C₄⋊C₈	—	4	1	no	—
672	C₄⋊C₈	—	4	1	no	—
673	#103	—	2	2	no	—
674	#103	—	2	2	no	—
675	#103	—	2	2	no	—
676	#103	—	2	2	no	—
677	#103	—	4	1	no	—
678	#103	—	4	1	no	—
679	#103	—	4	1	no	—
680	#103	—	4	1	no	—
681	#102	—	2	2	no	—
682	#102	—	2	2	no	—
683	#102	—	4	1	no	—
684	#102	—	4	1	no	—
685	#102	—	4	1	no	—
686	#102	—	4	1	no	—
687	#102	—	4	1	no	—
688	#102	—	4	1	no	—
689	C₂²⋊C₈	—	2	2	no	—
690	C₂²⋊C₈	—	4	1	no	—
691	C₂²⋊C₈	—	4	1	no	—
692	C₂²⋊C₈	—	4	1	no	—
693	C₂²⋊C₈	—	4	1	no	—
694	C₂²⋊C₈	—	4	1	no	—
695	C₂²⋊C₈	—	4	1	no	—
696	#97	—	4	1	no	—
697	#97	—	4	1	no	—
698	#97	—	4	1	no	—
699	#97	—	4	1	no	—
700	C₄×C₈	—	4	1	no	—
701	#95	—	2	1	no	—
702	#95	—	2	1	no	—
703	#95	—	2	1	no	—
704	#95	—	2	1	no	—
705	#95	—	2	1	no	—
706	#95	—	2	1	no	—
707	#95	—	2	1	no	—
708	#95	—	2	1	no	—
709	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
738	#95	C₂×D₄	1	1	yes	characteristic
739	#95	C₂×D₄	1	1	yes	characteristic
740	#95	C₂×D₄	1	1	yes	characteristic
741	#95	C₂×D₄	1	1	yes	characteristic
742	#95	C₂×D₄	1	1	yes	characteristic
743	#95	C₂×D₄	1	1	yes	characteristic
744	#95	C₂×D₄	1	1	yes	characteristic
745	#95	C₂×D₄	1	1	yes	characteristic
746	#95	C₂×D₄	1	1	yes	characteristic
747	C₂⁴	—	2	1	no	—
748	C₂⁴	C₂²×D₄	1	1	yes	characteristic
749	C₂⁴	C₂²×D₄	1	1	yes	characteristic
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	—	8	1	no	—
757	C₂×Q₈	—	8	1	no	—
758	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	4	1	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	—	8	1	no	—
772	C₂×D₄	—	8	1	no	—
773	C₂×D₄	—	8	1	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	4	1	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	8	1	no	—
814	C₂²×C₄	—	8	1	no	—
815	C₂²×C₄	—	8	1	no	—
816	C₂²×C₄	—	8	1	no	—
817	C₂²×C₄	—	8	1	no	—
818	C₂²×C₄	—	8	1	no	—
819	C₂²×C₄	—	8	1	no	—
820	C₂²×C₄	—	8	1	no	—
821	C₂²×C₄	—	8	1	no	—
822	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
823	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
824	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
825	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
826	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
827	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
828	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
829	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
830	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
831	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
832	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
833	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂²×C₄	C₂⁵	1	1	yes	characteristic
835	C₂×C₈	—	2	1	no	—
836	C₂×C₈	—	2	1	no	—
837	C₂×C₈	—	2	1	no	—
838	C₂×C₈	—	2	1	no	—
839	C₂×C₈	—	2	1	no	—
840	C₂×C₈	—	2	1	no	—
841	C₂×C₈	—	2	1	no	—
842	C₂×C₈	—	2	1	no	—
843	C₂×C₈	—	2	1	no	—
844	C₂×C₈	—	2	1	no	—
845	C₂×C₈	—	2	1	no	—
846	C₂×C₈	—	2	1	no	—
847	C₂×C₈	—	2	1	no	—
848	C₂×C₈	—	2	1	no	—
849	C₂×C₈	—	2	1	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	—	4	4	no	—
859	C₂×C₈	C₂×#41	1	2	yes	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	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	—	4	1	no	—
889	C₄⋊C₄	—	4	1	no	—
890	C₄⋊C₄	—	4	1	no	—
891	C₄⋊C₄	—	4	2	no	—
892	C₄⋊C₄	—	4	2	no	—
893	C₄⋊C₄	—	4	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	—	4	2	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	8	1	no	—
905	C₄⋊C₄	—	8	1	no	—
906	C₄⋊C₄	—	8	1	no	—
907	C₄⋊C₄	—	8	1	no	—
908	C₄⋊C₄	—	8	1	no	—
909	C₄⋊C₄	—	8	1	no	—
910	C₄⋊C₄	—	8	1	no	—
911	C₄⋊C₄	—	8	1	no	—
912	C₄⋊C₄	—	8	1	no	—
913	C₄⋊C₄	—	8	1	no	—
914	C₄⋊C₄	—	8	1	no	—
915	C₄⋊C₄	—	8	1	no	—
916	C₄⋊C₄	—	8	1	no	—
917	C₄⋊C₄	—	8	1	no	—
918	C₄⋊C₄	—	8	1	no	—
919	C₄⋊C₄	—	8	1	no	—
920	C₄⋊C₄	—	8	1	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	C₂×#41	1	2	yes	—
928	C₄⋊C₄	C₂×#41	1	2	yes	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	4	1	no	—
933	C₂²⋊C₄	—	4	1	no	—
934	C₂²⋊C₄	—	4	1	no	—
935	C₂²⋊C₄	—	4	1	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
949	C₂²⋊C₄	—	8	1	no	—
950	C₂²⋊C₄	—	8	1	no	—
951	C₂²⋊C₄	—	8	1	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	#137	1	4	yes	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	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	—	4	1	no	—
969	C₄²	—	4	1	no	—
970	C₄²	—	4	2	no	—
971	C₄²	—	8	1	no	—
972	C₄²	—	8	1	no	—
973	C₄²	—	8	1	no	—
974	C₄²	—	8	1	no	—
975	C₄²	—	8	1	no	—
976	C₄²	—	8	1	no	—
977	C₄²	—	8	1	no	—
978	C₄²	—	8	1	no	—
979	C₄²	—	8	1	no	—
980	C₄²	—	8	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	4	1	no	—
994	C₂³	—	4	1	no	—
995	C₂³	—	4	1	no	—
996	C₂³	—	4	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	4	1	no	—
999	C₂³	—	4	1	no	—
1000	C₂³	C₂×#137	1	2	yes	—
1001	C₂³	#576	1	2	yes	—
1002	C₂³	C₂³×D₄	1	1	yes	characteristic
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	2	no	—
1005	Q₈	—	4	1	no	—
1006	Q₈	—	4	1	no	—
1007	Q₈	—	16	2	no	—
1008	D₄	—	4	4	no	—
1009	D₄	—	4	1	no	—
1010	D₄	—	4	1	no	—
1011	D₄	—	4	1	no	—
1012	D₄	—	4	1	no	—
1013	D₄	—	8	4	no	—
1014	D₄	—	16	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	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	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	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	—	4	4	no	—
1053	C₂×C₄	—	4	1	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	1	no	—
1060	C₂×C₄	—	4	1	no	—
1061	C₂×C₄	—	4	1	no	—
1062	C₂×C₄	—	4	1	no	—
1063	C₂×C₄	—	4	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	—	8	2	no	—
1104	C₂×C₄	—	8	4	no	—
1105	C₂×C₄	—	16	2	no	—
1106	C₂×C₄	—	16	2	no	—
1107	C₂×C₄	—	16	2	no	—
1108	C₂×C₄	—	16	2	no	—
1109	C₂×C₄	C₂×#137	1	2	yes	—
1110	C₂×C₄	C₂×#137	1	2	yes	—
1111	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1112	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1113	C₂×C₄	#585	1	1	yes	characteristic
1114	C₂×C₄	#585	1	1	yes	characteristic
1115	C₂×C₄	#585	1	1	yes	characteristic
1116	C₂×C₄	#585	1	1	yes	characteristic
1117	C₈	—	2	2	no	—
1118	C₈	—	4	1	no	—
1119	C₈	—	4	1	no	—
1120	C₈	—	4	1	no	—
1121	C₈	—	4	1	no	—
1122	C₈	—	4	1	no	—
1123	C₈	—	4	1	no	—
1124	C₈	—	4	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	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	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	8	1	no	—
1140	C₂²	—	8	1	no	—
1141	C₂²	—	8	1	no	—
1142	C₂²	—	8	1	no	—
1143	C₂²	—	8	1	no	—
1144	C₂²	—	8	1	no	—
1145	C₂²	—	8	1	no	—
1146	C₂²	D₄×#41	1	1	yes	characteristic
1147	C₂²	#3485	1	1	yes	characteristic
1148	C₂²	#3489	1	1	yes	characteristic
1149	C₂²	C₂²×#137	1	1	yes	characteristic
1150	C₂²	C₂×#576	1	1	yes	characteristic
1151	C₂²	#3585	1	1	yes	characteristic
1152	C₂²	#3586	1	1	yes	characteristic
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	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	—	8	1	no	—
1178	C₄	—	8	1	no	—
1179	C₄	—	8	1	no	—
1180	C₄	#3493	1	1	yes	characteristic
1181	C₄	#3516	1	1	yes	characteristic
1182	C₄	#3553	1	1	yes	characteristic
1183	C₄	#3567	1	1	yes	characteristic
1184	C₂	—	4	2	no	—
1185	C₂	—	4	2	no	—
1186	C₂	—	16	1	no	—
1187	C₂	#43538	1	1	yes	characteristic
1188	C₂	#61457	1	1	yes	characteristic
1189	C₂	#61519	1	1	yes	characteristic
1190	C₂	#61726	1	1	yes	characteristic
1191	C₂	#61782	1	1	yes	characteristic
1192	C₂	#62112	1	1	yes	characteristic
1193	C₂	#62170	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 ◁ C₄×#123 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #59291	C₂	semidirect
3. #32520	C₂	semidirect
4. #32326	C₂	semidirect
5. #32008	C₂	semidirect
7. #31606	C₂	semidirect
8. #31422	C₂	semidirect
9. #31352	C₂	semidirect
10. #31132	C₂	semidirect
11. #29243	C₂	semidirect
12. #29050	C₂	semidirect
13. #28061	C₂	semidirect
14. #27624	C₂	semidirect
15. #27473	C₂	semidirect
16. #27471	C₂	semidirect
17. #27412	C₂	semidirect
18. #27393	C₂	semidirect
19. #27313	C₂	semidirect
20. #27148	C₂	semidirect
21. #27036	C₂	semidirect
22. #26782	C₂	semidirect
23. #26542	C₂	semidirect
24. #26342	C₂	semidirect
26. #24979	C₂	semidirect
27. #23762	C₂	semidirect
28. #22971	C₂	semidirect
29. #22618	C₂	semidirect
30. #22371	C₂	semidirect
31. #22081	C₂	semidirect

Maximal subgroups

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

subgroup	index
#59405	2
#59291	2
#32520	2
#32326	2
#32008	2
#31796	2
#31606	2
#31422	2
#31352	2
#31132	2
#29243	2
#29050	2
#28061	2
#27624	2
#27473	2
#27471	2
#27412	2
#27393	2
#27313	2
#27148	2
#27036	2
#26782	2
#26542	2
#26342	2
#26126	2
#24979	2
#23762	2
#22971	2
#22618	2
#22371	2
#22081	2