Subgroups — #6556469

Order 512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36277	C₂	1	1	yes	maximal, characteristic, complemented
2	#36202	C₂	1	1	yes	maximal, characteristic
3	#30387	C₂	1	1	yes	maximal, characteristic, complemented
4	#30321	C₂	1	1	yes	maximal, characteristic, complemented
5	#30200	C₂	1	1	yes	maximal, characteristic, complemented
6	#29577	C₂	1	1	yes	maximal, characteristic, complemented
7	#29496	C₂	1	1	yes	maximal, characteristic, complemented
8	#29077	C₂	1	1	yes	maximal, characteristic, complemented
9	#29073	C₂	1	1	yes	maximal, characteristic, complemented
10	#29003	C₂	1	1	yes	maximal, characteristic, complemented
11	#29001	C₂	1	1	yes	maximal, characteristic, complemented
12	#28582	C₂	1	1	yes	maximal, characteristic, complemented
13	#28306	C₂	1	1	yes	maximal, characteristic, complemented
14	#28015	C₂	1	1	yes	maximal, characteristic, complemented
15	#28010	C₂	1	1	yes	maximal, characteristic, complemented
16	#27949	C₂	1	1	yes	maximal, characteristic, complemented
17	#27866	C₂	1	1	yes	maximal, characteristic, complemented
18	#25262	C₂	1	1	yes	maximal, characteristic, complemented
19	#25258	C₂	1	1	yes	maximal, characteristic
20	#25138	C₂	1	1	yes	maximal, characteristic
21	#25134	C₂	1	1	yes	maximal, characteristic, complemented
22	#25047	C₂	1	1	yes	maximal, characteristic, complemented
23	#25045	C₂	1	1	yes	maximal, characteristic, complemented
24	#23759	C₂	1	1	yes	maximal, characteristic, complemented
25	#23687	C₂	1	1	yes	maximal, characteristic, complemented
26	#23629	C₂	1	1	yes	maximal, characteristic, complemented
27	#22945	C₂	1	1	yes	maximal, characteristic, complemented
28	#22941	C₂	1	1	yes	maximal, characteristic, complemented
29	#22869	C₂	1	1	yes	maximal, characteristic, complemented
30	#22865	C₂	1	1	yes	maximal, characteristic, complemented
31	#20567	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#483	C₂²	1	1	yes	characteristic
33	C₂×#480	C₂²	1	1	yes	characteristic
34	C₂×#470	C₂²	1	1	yes	characteristic
35	C₂×#468	C₂²	1	1	yes	characteristic
36	C₂×#451	C₂²	1	1	yes	characteristic
37	C₂×#448	C₂²	1	1	yes	characteristic
38	C₂×#441	C₂²	1	1	yes	characteristic
39	C₂×#440	C₂²	1	1	yes	characteristic
40	C₂×#436	C₂²	1	1	yes	characteristic
41	C₂×#436	C₂²	1	1	yes	characteristic
42	C₂×#419	C₂²	1	1	yes	characteristic
43	C₂×#419	C₂²	1	1	yes	characteristic
44	#2864	C₂²	1	1	yes	characteristic
45	#2863	C₂²	1	1	yes	characteristic
46	#2857	C₂²	1	1	yes	characteristic
47	#2855	C₂²	1	1	yes	characteristic
48	#2850	C₂²	1	1	yes	characteristic
49	#2850	C₂²	1	1	yes	characteristic
50	#2607	—	2	1	no	—
51	#2605	—	2	1	no	—
52	#2589	—	2	1	no	—
53	#2588	—	2	1	no	—
54	#2578	—	2	1	no	—
55	#2569	—	2	1	no	—
56	#2564	—	2	1	no	—
57	#2531	—	2	1	no	—
58	#2525	—	2	1	no	—
59	#2516	—	2	1	no	—
60	#2512	C₂²	1	1	yes	characteristic
61	#2511	C₂²	1	1	yes	characteristic
62	#2511	C₂²	1	1	yes	characteristic
63	#2492	C₂²	1	1	yes	characteristic
64	#2487	C₂²	1	1	yes	characteristic
65	#2467	—	2	1	no	—
66	#2457	—	2	1	no	—
67	#2451	C₂²	1	1	yes	characteristic
68	#2423	C₂²	1	1	yes	characteristic
69	#2423	C₂²	1	1	yes	characteristic
70	#2422	C₂²	1	1	yes	characteristic
71	#2415	C₂²	1	1	yes	characteristic
72	#2414	C₂²	1	1	yes	characteristic
73	#2409	C₂²	1	1	yes	characteristic
74	#2374	—	2	1	no	—
75	#2373	—	2	1	no	—
76	#2368	—	2	1	no	—
77	#2363	C₂²	1	1	yes	characteristic
78	#2362	C₂²	1	1	yes	characteristic
79	#2353	—	2	1	no	—
80	#2345	C₂²	1	1	yes	characteristic
81	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
82	C₄×#124	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
84	#2295	C₂²	1	1	yes	characteristic
85	C₂×#391	C₂²	1	1	yes	characteristic
86	#2285	C₂²	1	1	yes	characteristic
87	#2283	C₂²	1	1	yes	characteristic
88	C₄²×D₄	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic
90	#2101	C₂²	1	1	yes	characteristic
91	#2097	C₂²	1	1	yes	characteristic
92	#2097	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic
94	#2087	C₂²	1	1	yes	characteristic
95	#2085	C₂²	1	1	yes	characteristic
96	#2085	C₂²	1	1	yes	characteristic
97	#2085	C₂²	1	1	yes	characteristic
98	#2085	C₂²	1	1	yes	characteristic
99	#2077	C₂²	1	1	yes	characteristic
100	#2075	C₂²	1	1	yes	characteristic
101	#2074	C₂²	1	1	yes	characteristic
102	#2074	C₂²	1	1	yes	characteristic
103	#2074	C₂²	1	1	yes	characteristic
104	#2074	C₂²	1	1	yes	characteristic
105	#2072	C₂²	1	1	yes	characteristic
106	#2072	C₂²	1	1	yes	characteristic
107	#2072	C₂²	1	1	yes	characteristic
108	#2072	C₂²	1	1	yes	characteristic
109	#2072	C₂²	1	1	yes	characteristic
110	#2071	C₂²	1	1	yes	characteristic
111	#2068	C₂²	1	1	yes	characteristic
112	#2068	C₂²	1	1	yes	characteristic
113	#2066	C₂²	1	1	yes	characteristic
114	#2065	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	#2036	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	#2024	C₂²	1	1	yes	characteristic
124	#2023	C₂²	1	1	yes	characteristic
125	#2015	C₂²	1	1	yes	characteristic
126	#2015	C₂²	1	1	yes	characteristic
127	#2001	C₂²	1	1	yes	characteristic
128	#2000	C₂²	1	1	yes	characteristic
129	#1990	C₂²	1	1	yes	characteristic
130	#1990	C₂²	1	1	yes	characteristic
131	#1969	C₂²	1	1	yes	characteristic
132	#1969	C₂²	1	1	yes	characteristic
133	#1969	C₂²	1	1	yes	characteristic
134	#1969	C₂²	1	1	yes	characteristic
135	#1968	C₂²	1	1	yes	characteristic
136	#1968	C₂²	1	1	yes	characteristic
137	#1968	C₂²	1	1	yes	characteristic
138	#1968	C₂²	1	1	yes	characteristic
139	#1944	C₂²	1	1	yes	characteristic
140	#1943	C₂²	1	1	yes	characteristic
141	#1942	C₂²	1	1	yes	characteristic
142	#1941	C₂²	1	1	yes	characteristic
143	#1935	C₂²	1	1	yes	characteristic
144	#1935	C₂²	1	1	yes	characteristic
145	#1934	C₂²	1	1	yes	characteristic
146	#1934	C₂²	1	1	yes	characteristic
147	#1933	C₂²	1	1	yes	characteristic
148	#1933	C₂²	1	1	yes	characteristic
149	#1933	C₂²	1	1	yes	characteristic
150	#1933	C₂²	1	1	yes	characteristic
151	#1928	C₂²	1	1	yes	characteristic
152	#1928	C₂²	1	1	yes	characteristic
153	#1927	C₂²	1	1	yes	characteristic
154	#1926	C₂²	1	1	yes	characteristic
155	#1921	C₂²	1	1	yes	characteristic
156	#1920	C₂²	1	1	yes	characteristic
157	#1920	C₂²	1	1	yes	characteristic
158	#1918	C₂²	1	1	yes	characteristic
159	#1895	C₂²	1	1	yes	characteristic
160	#1895	C₂²	1	1	yes	characteristic
161	#1895	C₂²	1	1	yes	characteristic
162	#1894	C₂²	1	1	yes	characteristic
163	#1894	C₂²	1	1	yes	characteristic
164	#1894	C₂²	1	1	yes	characteristic
165	#1894	C₂²	1	1	yes	characteristic
166	#1894	C₂²	1	1	yes	characteristic
167	#1880	C₂²	1	1	yes	characteristic
168	#1878	C₂²	1	1	yes	characteristic
169	#1878	C₂²	1	1	yes	characteristic
170	#1877	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	#1862	C₂²	1	1	yes	characteristic
175	#1854	C₂²	1	1	yes	characteristic
176	#1854	C₂²	1	1	yes	characteristic
177	#1854	C₂²	1	1	yes	characteristic
178	#1854	C₂²	1	1	yes	characteristic
179	#1845	C₂²	1	1	yes	characteristic
180	#1844	C₂²	1	1	yes	characteristic
181	#1809	C₂²	1	1	yes	characteristic
182	#1809	C₂²	1	1	yes	characteristic
183	C₄×#107	C₂²	1	1	yes	characteristic
184	C₄×#106	C₂²	1	1	yes	characteristic
185	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
186	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
187	#1767	C₂²	1	1	yes	characteristic
188	#1763	C₂²	1	1	yes	characteristic
189	#1762	C₂²	1	1	yes	characteristic
190	C₄×#103	C₂²	1	1	yes	characteristic
191	C₄×#103	C₂²	1	1	yes	characteristic
192	#1753	C₂²	1	1	yes	characteristic
193	#1753	C₂²	1	1	yes	characteristic
194	#1753	C₂²	1	1	yes	characteristic
195	#1753	C₂²	1	1	yes	characteristic
196	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
197	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
198	#1744	C₂²	1	1	yes	characteristic
199	#1736	C₂²	1	1	yes	characteristic
200	#1736	C₂²	1	1	yes	characteristic
201	#1728	C₂²	1	1	yes	characteristic
202	#1728	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	C₂²×M₁₆	C₂³	1	1	yes	characteristic
209	C₂²×M₁₆	C₂³	1	1	yes	characteristic
210	C₂²×M₁₆	C₂³	1	1	yes	characteristic
211	C₂²×M₁₆	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×#126	—	2	1	no	—
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×#123	—	2	1	no	—
216	C₂×C₂²⋊Q₈	—	2	1	no	—
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×#121	C₂³	1	1	yes	characteristic
222	C₂×#121	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	D₄	1	1	yes	characteristic
227	C₂×C₄×D₄	D₄	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×#117	C₂³	1	1	yes	characteristic
231	C₂×#117	C₂³	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₄²	C₂³	1	1	yes	characteristic
234	C₂²×C₄²	C₂³	1	1	yes	characteristic
235	#483	—	2	4	no	—
236	#480	—	2	4	no	—
237	#470	—	4	2	no	—
238	#468	—	4	2	no	—
239	#451	—	2	4	no	—
240	#448	—	2	4	no	—
241	#441	—	4	2	no	—
242	#440	—	4	2	no	—
243	#436	—	2	4	no	—
244	#436	—	2	4	no	—
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	C₂³	1	1	yes	characteristic
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×#106	C₂³	1	1	yes	characteristic
252	C₂×#106	C₂³	1	1	yes	characteristic
253	C₂×#106	C₂³	1	1	yes	characteristic
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	#419	—	4	2	no	—
260	#419	—	4	2	no	—
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×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	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×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
296	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#400	—	2	1	no	—
302	#400	—	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	#397	—	2	1	no	—
310	#397	—	2	1	no	—
311	#397	—	2	1	no	—
312	#396	—	2	1	no	—
313	#395	—	2	1	no	—
314	#395	—	2	1	no	—
315	#394	—	2	1	no	—
316	#394	—	2	1	no	—
317	#394	—	2	1	no	—
318	#393	—	2	1	no	—
319	#393	—	2	1	no	—
320	#392	—	2	1	no	—
321	#391	—	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	#391	C₂³	1	1	yes	characteristic
337	#391	C₂³	1	1	yes	characteristic
338	#391	C₂³	1	1	yes	characteristic
339	#390	—	2	1	no	—
340	#390	—	2	1	no	—
341	#390	C₂³	1	1	yes	characteristic
342	#390	C₂³	1	1	yes	characteristic
343	#390	C₂³	1	1	yes	characteristic
344	#389	—	2	1	no	—
345	#389	—	2	1	no	—
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	#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	—	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	#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	—	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	—	2	1	no	—
392	#387	—	2	1	no	—
393	#386	—	2	1	no	—
394	#386	—	2	1	no	—
395	#386	—	2	1	no	—
396	#386	—	2	1	no	—
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#385	—	2	1	no	—
401	#385	—	2	1	no	—
402	#385	—	2	1	no	—
403	#385	—	2	1	no	—
404	#385	—	2	1	no	—
405	#384	C₂³	1	1	yes	characteristic
406	#384	C₂³	1	1	yes	characteristic
407	#384	C₂³	1	1	yes	characteristic
408	#383	—	2	1	no	—
409	#383	—	2	1	no	—
410	#382	C₂³	1	1	yes	characteristic
411	#382	C₂³	1	1	yes	characteristic
412	#382	C₂³	1	1	yes	characteristic
413	#381	—	2	1	no	—
414	#381	—	2	1	no	—
415	#380	—	2	1	no	—
416	#380	—	2	1	no	—
417	#380	—	2	1	no	—
418	#380	—	2	1	no	—
419	#380	—	2	1	no	—
420	#380	C₂³	1	1	yes	characteristic
421	#380	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
432	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
439	C₄×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	#376	—	2	1	no	—
452	#376	—	2	1	no	—
453	C₂×#95	—	2	1	no	—
454	C₂×#95	—	2	1	no	—
455	C₄³	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	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	—	2	2	no	—
493	C₂²×Q₈	—	2	2	no	—
494	C₂²×Q₈	—	2	2	no	—
495	C₂²×Q₈	—	4	1	no	—
496	C₂²×Q₈	—	4	1	no	—
497	C₂²×Q₈	—	4	1	no	—
498	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
500	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
504	C₂²×D₄	C₂⁴	1	1	yes	characteristic
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂⁴	1	1	yes	characteristic
513	C₂³×C₄	C₂⁴	1	1	yes	characteristic
514	C₂×Q₁₆	—	2	2	no	—
515	C₂×Q₁₆	—	2	2	no	—
516	C₂×Q₁₆	—	2	2	no	—
517	C₂×Q₁₆	—	4	1	no	—
518	C₂×Q₁₆	—	4	1	no	—
519	C₂×Q₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×M₁₆	—	2	2	no	—
527	C₂×M₁₆	—	2	2	no	—
528	C₂×M₁₆	—	2	2	no	—
529	C₂×M₁₆	—	2	2	no	—
530	C₂×M₁₆	—	4	1	no	—
531	C₂×M₁₆	—	4	1	no	—
532	C₂×M₁₆	—	4	1	no	—
533	C₂×M₁₆	—	4	1	no	—
534	C₂×M₁₆	—	4	1	no	—
535	C₂×M₁₆	—	4	1	no	—
536	C₂×M₁₆	—	4	1	no	—
537	C₂×M₁₆	—	4	1	no	—
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₄⋊Q₈	—	4	1	no	—
547	C₄⋊Q₈	—	4	1	no	—
548	#126	—	4	4	no	—
549	#124	—	4	1	no	—
550	#124	—	4	1	no	—
551	#123	—	4	4	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	4	1	no	—
556	C₂²⋊Q₈	—	4	4	no	—
557	C₂²⋊Q₈	—	4	1	no	—
558	C₂²⋊Q₈	—	4	1	no	—
559	C₂²⋊Q₈	—	4	1	no	—
560	C₂²⋊Q₈	—	4	1	no	—
561	#121	—	2	2	no	—
562	#121	—	2	2	no	—
563	#121	—	4	1	no	—
564	#121	—	4	1	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	4	1	no	—
567	C₄×Q₈	—	4	1	no	—
568	C₄×Q₈	—	4	1	no	—
569	C₄×Q₈	—	4	1	no	—
570	C₄×Q₈	—	4	1	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	4	1	no	—
575	C₄×D₄	—	4	1	no	—
576	C₄×D₄	—	4	2	no	—
577	#117	—	4	1	no	—
578	#117	—	4	1	no	—
579	#117	—	4	1	no	—
580	#117	—	4	1	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
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×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	—	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×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
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	—	4	1	no	—
662	C₂×C₄²	—	4	1	no	—
663	C₂×C₄²	—	4	1	no	—
664	C₂×C₄²	—	4	1	no	—
665	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	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	#107	—	2	2	no	—
679	#107	—	2	2	no	—
680	#107	—	4	1	no	—
681	#107	—	4	1	no	—
682	#107	—	4	1	no	—
683	#107	—	4	1	no	—
684	#106	—	2	2	no	—
685	#106	—	2	2	no	—
686	#106	—	4	1	no	—
687	#106	—	4	1	no	—
688	#106	—	4	1	no	—
689	#106	—	4	1	no	—
690	C₄⋊C₈	—	2	2	no	—
691	C₄⋊C₈	—	2	2	no	—
692	#103	—	2	2	no	—
693	#103	—	2	2	no	—
694	#103	—	2	2	no	—
695	#103	—	2	2	no	—
696	#103	—	2	2	no	—
697	#103	—	2	2	no	—
698	#103	—	2	2	no	—
699	#103	—	2	2	no	—
700	#103	—	2	2	no	—
701	#103	—	2	2	no	—
702	#103	—	4	1	no	—
703	#103	—	4	1	no	—
704	#103	—	4	1	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	#102	—	2	2	no	—
711	#102	—	2	2	no	—
712	#102	—	4	1	no	—
713	#102	—	4	1	no	—
714	#102	—	4	1	no	—
715	#102	—	4	1	no	—
716	C₂²⋊C₈	—	2	2	no	—
717	C₂²⋊C₈	—	2	2	no	—
718	C₂²⋊C₈	#41	1	4	yes	—
719	C₂²⋊C₈	#41	1	4	yes	—
720	#97	—	4	1	no	—
721	#97	—	4	1	no	—
722	C₄×C₈	—	2	2	no	—
723	C₄×C₈	—	2	2	no	—
724	C₄×C₈	—	4	1	no	—
725	C₄×C₈	—	4	1	no	—
726	C₄×C₈	—	4	1	no	—
727	C₄×C₈	—	4	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	—	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	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
778	#95	C₂×D₄	1	1	yes	characteristic
779	#95	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
781	#95	C₂×D₄	1	1	yes	characteristic
782	C₂⁴	—	2	1	no	—
783	C₂⁴	C₂²×D₄	1	1	yes	characteristic
784	C₂⁴	C₂²×D₄	1	1	yes	characteristic
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	4	2	no	—
803	C₂×Q₈	—	4	4	no	—
804	C₂×Q₈	—	4	4	no	—
805	C₂×Q₈	—	4	2	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	—	8	1	no	—
808	C₂×Q₈	—	8	1	no	—
809	C₂×Q₈	—	8	1	no	—
810	C₂×Q₈	—	8	2	no	—
811	C₂×Q₈	—	8	2	no	—
812	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	4	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	8	1	no	—
825	C₂×D₄	—	8	1	no	—
826	C₂×D₄	—	8	1	no	—
827	C₂×D₄	—	8	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	1	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	1	no	—
862	C₂²×C₄	—	4	1	no	—
863	C₂²×C₄	—	4	1	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
871	C₂²×C₄	—	8	1	no	—
872	C₂²×C₄	—	8	1	no	—
873	C₂²×C₄	—	8	1	no	—
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂×#41	1	2	yes	—
887	C₂²×C₄	C₂×#41	1	2	yes	—
888	C₂²×C₄	C₂⁵	1	1	yes	characteristic
889	Q₁₆	—	4	4	no	—
890	Q₁₆	—	8	2	no	—
891	SD₁₆	—	4	4	no	—
892	SD₁₆	—	8	2	no	—
893	M₁₆	—	8	2	no	—
894	M₁₆	—	8	2	no	—
895	M₁₆	—	8	2	no	—
896	M₁₆	—	8	2	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	C₂×#41	1	2	yes	—
918	C₂×C₈	C₂×#41	1	2	yes	—
919	C₂×C₈	C₂×#41	1	2	yes	—
920	C₂×C₈	C₂×#41	1	2	yes	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	2	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	2	no	—
953	C₄⋊C₄	—	4	2	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	8	1	no	—
959	C₄⋊C₄	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₄⋊C₄	—	8	1	no	—
962	C₄⋊C₄	—	8	1	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	—	8	1	no	—
967	C₄⋊C₄	—	8	1	no	—
968	C₄⋊C₄	—	8	1	no	—
969	C₄⋊C₄	—	8	1	no	—
970	C₄⋊C₄	—	8	1	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	#137	1	4	yes	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	4	1	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	4	1	no	—
1014	C₄²	—	4	1	no	—
1015	C₄²	—	4	1	no	—
1016	C₄²	—	4	1	no	—
1017	C₄²	—	4	1	no	—
1018	C₄²	—	4	1	no	—
1019	C₄²	—	4	1	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	—	4	2	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	1	no	—
1024	C₄²	—	8	1	no	—
1025	C₄²	—	8	1	no	—
1026	C₄²	—	8	1	no	—
1027	C₄²	—	8	1	no	—
1028	C₄²	—	8	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	—	4	1	no	—
1045	C₂³	—	4	1	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	#532	1	2	yes	—
1050	C₂³	C₂³×D₄	1	1	yes	characteristic
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	4	1	no	—
1054	Q₈	—	4	1	no	—
1055	Q₈	—	4	1	no	—
1056	Q₈	—	4	1	no	—
1057	Q₈	—	4	1	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	1	no	—
1061	Q₈	—	4	1	no	—
1062	Q₈	—	4	1	no	—
1063	Q₈	—	8	4	no	—
1064	Q₈	—	16	2	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	16	2	no	—
1071	D₄	—	16	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	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	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	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	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	4	no	—
1161	C₂×C₄	—	16	2	no	—
1162	C₂×C₄	—	16	2	no	—
1163	C₂×C₄	#532	1	2	yes	—
1164	C₂×C₄	C₂×#137	1	2	yes	—
1165	C₂×C₄	C₂×#137	1	2	yes	—
1166	C₂×C₄	C₂×#137	1	2	yes	—
1167	C₂×C₄	#575	1	2	yes	—
1168	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1169	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1170	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1171	C₂×C₄	#585	1	1	yes	characteristic
1172	C₂×C₄	#585	1	1	yes	characteristic
1173	C₂×C₄	#585	1	1	yes	characteristic
1174	C₈	—	2	2	no	—
1175	C₈	—	2	2	no	—
1176	C₈	—	2	2	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	4	1	no	—
1179	C₈	—	4	1	no	—
1180	C₈	—	4	1	no	—
1181	C₈	—	4	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	8	1	no	—
1197	C₂²	—	8	1	no	—
1198	C₂²	—	8	1	no	—
1199	C₂²	—	8	1	no	—
1200	C₂²	—	8	1	no	—
1201	C₂²	—	8	1	no	—
1202	C₂²	—	8	1	no	—
1203	C₂²	C₂×#532	1	1	yes	characteristic
1204	C₂²	#3485	1	1	yes	characteristic
1205	C₂²	#3488	1	1	yes	characteristic
1206	C₂²	C₂²×#137	1	1	yes	characteristic
1207	C₂²	C₂×#575	1	1	yes	characteristic
1208	C₂²	#3584	1	1	yes	characteristic
1209	C₂²	#3584	1	1	yes	characteristic
1210	C₄	—	2	2	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	8	1	no	—
1224	C₄	—	8	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	—	8	1	no	—
1228	C₄	—	8	1	no	—
1229	C₄	—	8	1	no	—
1230	C₄	—	8	1	no	—
1231	C₄	—	8	1	no	—
1232	C₄	—	8	1	no	—
1233	C₄	—	8	1	no	—
1234	C₄	—	8	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	#3513	1	1	yes	characteristic
1238	C₄	#3513	1	1	yes	characteristic
1239	C₄	#3521	1	1	yes	characteristic
1240	C₄	#3521	1	1	yes	characteristic
1241	C₂	—	4	2	no	—
1242	C₂	—	8	1	no	—
1243	C₂	—	16	1	no	—
1244	C₂	#35850	1	1	yes	characteristic
1245	C₂	#60701	1	1	yes	characteristic
1246	C₂	#60713	1	1	yes	characteristic
1247	C₂	#61732	1	1	yes	characteristic
1248	C₂	#61742	1	1	yes	characteristic
1249	C₂	#62005	1	1	yes	characteristic
1250	C₂	#62006	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2414	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄²×D₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #36277	C₂	semidirect
3. #30387	C₂	semidirect
4. #30321	C₂	semidirect
5. #30200	C₂	semidirect
6. #29577	C₂	semidirect
7. #29496	C₂	semidirect
8. #29077	C₂	semidirect
9. #29073	C₂	semidirect
10. #29003	C₂	semidirect
11. #29001	C₂	semidirect
12. #28582	C₂	semidirect
13. #28306	C₂	semidirect
14. #28015	C₂	semidirect
15. #28010	C₂	semidirect
16. #27949	C₂	semidirect
17. #27866	C₂	semidirect
18. #25262	C₂	semidirect
21. #25134	C₂	semidirect
22. #25047	C₂	semidirect
23. #25045	C₂	semidirect
24. #23759	C₂	semidirect
25. #23687	C₂	semidirect
26. #23629	C₂	semidirect
27. #22945	C₂	semidirect
28. #22941	C₂	semidirect
29. #22869	C₂	semidirect
30. #22865	C₂	semidirect
31. #20567	C₂	semidirect

Maximal subgroups

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

subgroup	index
#36277	2
#36202	2
#30387	2
#30321	2
#30200	2
#29577	2
#29496	2
#29077	2
#29073	2
#29003	2
#29001	2
#28582	2
#28306	2
#28015	2
#28010	2
#27949	2
#27866	2
#25262	2
#25258	2
#25138	2
#25134	2
#25047	2
#25045	2
#23759	2
#23687	2
#23629	2
#22945	2
#22941	2
#22869	2
#22865	2
#20567	2