Subgroups — #7003893

Order 512.

1452 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59197	C₂	1	1	yes	maximal, characteristic
2	#39154	C₂	1	1	yes	maximal, characteristic
3	#32421	C₂	1	1	yes	maximal, characteristic, complemented
4	#32272	C₂	1	1	yes	maximal, characteristic, complemented
5	#32258	C₂	1	1	yes	maximal, characteristic, complemented
6	#32216	C₂	1	1	yes	maximal, characteristic, complemented
7	#32025	C₂	1	1	yes	maximal, characteristic, complemented
8	#31793	C₂	1	1	yes	maximal, characteristic, complemented
9	#31444	C₂	1	1	yes	maximal, characteristic, complemented
10	#31079	C₂	1	1	yes	maximal, characteristic, complemented
11	#28775	C₂	1	1	yes	maximal, characteristic, complemented
12	#28073	C₂	1	1	yes	maximal, characteristic, complemented
13	#27854	C₂	1	1	yes	maximal, characteristic, complemented
14	#27664	C₂	1	1	yes	maximal, characteristic, complemented
15	#27454	C₂	1	1	yes	maximal, characteristic, complemented
16	#27176	C₂	1	1	yes	maximal, characteristic, complemented
17	#26344	C₂	1	1	yes	maximal, characteristic, complemented
18	#26312	C₂	1	1	yes	maximal, characteristic, complemented
19	#26210	C₂	1	1	yes	maximal, characteristic, complemented
20	#26129	C₂	1	1	yes	maximal, characteristic, complemented
21	#25994	C₂	1	1	yes	maximal, characteristic, complemented
22	#25353	C₂	1	1	yes	maximal, characteristic, complemented
23	#25234	C₂	1	1	yes	maximal, characteristic, complemented
24	#24947	C₂	1	1	yes	maximal, characteristic, complemented
25	#24556	C₂	1	1	yes	maximal, characteristic, complemented
26	#24552	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂×#2075	C₂	1	1	yes	maximal, characteristic, complemented
28	#22932	C₂	1	1	yes	maximal, characteristic, complemented
29	#22846	C₂	1	1	yes	maximal, characteristic
30	#22656	C₂	1	1	yes	maximal, characteristic, complemented
31	#21942	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#484	C₂²	1	1	yes	characteristic
33	C₂×#484	C₂²	1	1	yes	characteristic
34	C₂×#479	C₂²	1	1	yes	characteristic, complemented
35	C₂×#435	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
37	C₂×#427	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#107	C₂²	1	1	yes	characteristic
39	C₂×#407	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	#2848	C₂²	1	1	yes	characteristic
42	#2788	—	2	1	no	—
43	#2787	—	2	1	no	—
44	#2786	—	2	1	no	—
45	#2747	—	2	1	no	—
46	#2741	—	2	1	no	—
47	#2715	—	2	1	no	—
48	#2643	—	2	1	no	—
49	#2569	—	2	1	no	—
50	#2562	C₂²	1	1	yes	characteristic
51	#2547	C₂²	1	1	yes	characteristic
52	#2538	C₂²	1	1	yes	characteristic
53	#2510	—	2	1	no	—
54	#2498	—	2	1	no	—
55	#2496	C₂²	1	1	yes	characteristic
56	#2495	C₂²	1	1	yes	characteristic
57	#2494	C₂²	1	1	yes	characteristic
58	#2494	C₂²	1	1	yes	characteristic
59	#2493	—	2	1	no	—
60	#2492	C₂²	1	1	yes	characteristic
61	#2487	C₂²	1	1	yes	characteristic
62	#2486	C₂²	1	1	yes	characteristic
63	#2485	C₂²	1	1	yes	characteristic
64	#2485	C₂²	1	1	yes	characteristic
65	#2480	—	2	1	no	—
66	#2472	—	2	1	no	—
67	#2442	C₂²	1	1	yes	characteristic
68	#2442	C₂²	1	1	yes	characteristic
69	#2440	C₂²	1	1	yes	characteristic
70	#2421	C₂²	1	1	yes	characteristic
71	#2417	C₂²	1	1	yes	characteristic
72	#2415	C₂²	1	1	yes	characteristic
73	#2412	—	2	1	no	—
74	#2360	C₂²	1	1	yes	characteristic
75	#2352	C₂²	1	1	yes	characteristic
76	#2352	C₂²	1	1	yes	characteristic
77	#2352	C₂²	1	1	yes	characteristic
78	#2345	C₂²	1	1	yes	characteristic
79	#2344	C₂²	1	1	yes	characteristic
80	#2342	—	2	1	no	—
81	#2329	—	2	1	no	—
82	C₄×#120	C₂²	1	1	yes	characteristic
83	C₂×#380	C₂²	1	1	yes	characteristic
84	C₂×#380	C₂²	1	1	yes	characteristic
85	C₂×#380	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2101	C₂²	1	1	yes	characteristic, complemented
88	#2100	C₂²	1	1	yes	characteristic, complemented
89	#2097	C₂²	1	1	yes	characteristic, complemented
90	#2087	C₂²	1	1	yes	characteristic, complemented
91	#2087	C₂²	1	1	yes	characteristic, complemented
92	#2087	C₂²	1	1	yes	characteristic, complemented
93	#2086	C₂²	1	1	yes	characteristic, complemented
94	#2085	C₂²	1	1	yes	characteristic, complemented
95	#2085	C₂²	1	1	yes	characteristic, complemented
96	#2083	C₂²	1	1	yes	characteristic, complemented
97	#2077	C₂²	1	1	yes	characteristic, complemented
98	#2076	C₂²	1	1	yes	characteristic
99	#2076	C₂²	1	1	yes	characteristic
100	#2076	C₂²	1	1	yes	characteristic, complemented
101	#2075	C₂²	1	1	yes	characteristic
102	#2075	C₂²	1	1	yes	characteristic
103	#2075	C₂²	1	1	yes	characteristic
104	#2075	C₂²	1	1	yes	characteristic
105	#2075	C₂²	1	1	yes	characteristic
106	#2075	C₂²	1	1	yes	characteristic
107	#2075	C₂²	1	1	yes	characteristic
108	#2075	C₂²	1	1	yes	characteristic
109	#2075	C₂²	1	1	yes	characteristic
110	#2075	C₂²	1	1	yes	characteristic
111	#2075	C₂²	1	1	yes	characteristic, complemented
112	#2075	C₂²	1	1	yes	characteristic, complemented
113	#2074	C₂²	1	1	yes	characteristic, complemented
114	#2068	C₂²	1	1	yes	characteristic, complemented
115	#2068	C₂²	1	1	yes	characteristic, complemented
116	#2059	C₂²	1	1	yes	characteristic, complemented
117	#2059	C₂²	1	1	yes	characteristic, complemented
118	#2057	C₂²	1	1	yes	characteristic, complemented
119	#2057	C₂²	1	1	yes	characteristic, complemented
120	#2036	C₂²	1	1	yes	characteristic
121	#2036	C₂²	1	1	yes	characteristic
122	#2036	C₂²	1	1	yes	characteristic, complemented
123	#2036	C₂²	1	1	yes	characteristic, complemented
124	#2035	C₂²	1	1	yes	characteristic
125	#2035	C₂²	1	1	yes	characteristic
126	#1993	C₂²	1	1	yes	characteristic, complemented
127	#1992	C₂²	1	1	yes	characteristic, complemented
128	#1987	C₂²	1	1	yes	characteristic, complemented
129	#1955	C₂²	1	1	yes	characteristic
130	#1949	C₂²	1	1	yes	characteristic, complemented
131	#1949	C₂²	1	1	yes	characteristic, complemented
132	#1949	C₂²	1	1	yes	characteristic, complemented
133	#1947	C₂²	1	1	yes	characteristic, complemented
134	#1944	C₂²	1	1	yes	characteristic, complemented
135	#1943	C₂²	1	1	yes	characteristic, complemented
136	#1943	C₂²	1	1	yes	characteristic, complemented
137	#1942	C₂²	1	1	yes	characteristic, complemented
138	#1935	C₂²	1	1	yes	characteristic, complemented
139	#1933	C₂²	1	1	yes	characteristic, complemented
140	#1928	C₂²	1	1	yes	characteristic, complemented
141	#1927	C₂²	1	1	yes	characteristic, complemented
142	#1924	C₂²	1	1	yes	characteristic
143	#1923	C₂²	1	1	yes	characteristic
144	#1921	C₂²	1	1	yes	characteristic, complemented
145	#1921	C₂²	1	1	yes	characteristic, complemented
146	#1919	C₂²	1	1	yes	characteristic, complemented
147	#1918	C₂²	1	1	yes	characteristic, complemented
148	#1918	C₂²	1	1	yes	characteristic, complemented
149	#1918	C₂²	1	1	yes	characteristic, complemented
150	#1918	C₂²	1	1	yes	characteristic, complemented
151	#1918	C₂²	1	1	yes	characteristic, complemented
152	#1894	C₂²	1	1	yes	characteristic
153	#1894	C₂²	1	1	yes	characteristic
154	#1892	C₂²	1	1	yes	characteristic
155	#1892	C₂²	1	1	yes	characteristic
156	#1892	C₂²	1	1	yes	characteristic, complemented
157	#1873	C₂²	1	1	yes	characteristic, complemented
158	#1872	C₂²	1	1	yes	characteristic
159	#1872	C₂²	1	1	yes	characteristic
160	#1870	C₂²	1	1	yes	characteristic
161	#1869	C₂²	1	1	yes	characteristic
162	#1869	C₂²	1	1	yes	characteristic
163	#1865	C₂²	1	1	yes	characteristic, complemented
164	#1863	C₂²	1	1	yes	characteristic, complemented
165	#1854	C₂²	1	1	yes	characteristic, complemented
166	#1854	C₂²	1	1	yes	characteristic, complemented
167	#1854	C₂²	1	1	yes	characteristic, complemented
168	#1853	C₂²	1	1	yes	characteristic
169	#1853	C₂²	1	1	yes	characteristic
170	#1853	C₂²	1	1	yes	characteristic
171	#1853	C₂²	1	1	yes	characteristic
172	#1853	C₂²	1	1	yes	characteristic
173	#1852	C₂²	1	1	yes	characteristic
174	#1852	C₂²	1	1	yes	characteristic
175	#1852	C₂²	1	1	yes	characteristic
176	#1852	C₂²	1	1	yes	characteristic
177	#1852	C₂²	1	1	yes	characteristic
178	#1851	C₂²	1	1	yes	characteristic
179	#1850	C₂²	1	1	yes	characteristic
180	#1846	C₂²	1	1	yes	characteristic, complemented
181	#1825	C₂²	1	1	yes	characteristic, complemented
182	#1825	C₂²	1	1	yes	characteristic, complemented
183	#1824	C₂²	1	1	yes	characteristic
184	#1824	C₂²	1	1	yes	characteristic
185	#1809	C₂²	1	1	yes	characteristic
186	#1809	C₂²	1	1	yes	characteristic
187	#1809	C₂²	1	1	yes	characteristic
188	#1809	C₂²	1	1	yes	characteristic
189	#1809	C₂²	1	1	yes	characteristic
190	#1809	C₂²	1	1	yes	characteristic
191	#1808	C₂²	1	1	yes	characteristic
192	#1808	C₂²	1	1	yes	characteristic
193	#1808	C₂²	1	1	yes	characteristic, complemented
194	#1808	C₂²	1	1	yes	characteristic, complemented
195	#1776	C₂²	1	1	yes	characteristic, complemented
196	C₄×#107	C₂²	1	1	yes	characteristic, complemented
197	#1763	C₂²	1	1	yes	characteristic, complemented
198	#1753	C₂²	1	1	yes	characteristic
199	#1752	C₂²	1	1	yes	characteristic
200	C₂×#340	C₂²	1	1	yes	characteristic
201	C₂×#340	C₂²	1	1	yes	characteristic
202	C₂×#340	C₂²	1	1	yes	characteristic
203	C₂⁴×C₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#126	—	2	1	no	—
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#124	—	2	1	no	—
213	C₂×#123	—	2	1	no	—
214	C₂×C₂²⋊Q₈	—	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×#120	D₄	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
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	C₂×#117	C₂³	1	1	yes	characteristic
226	C₂×#117	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	C₂²×C₂²⋊C₄	—	2	1	no	—
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	#484	—	2	4	no	—
237	#484	—	4	2	no	—
238	#479	—	4	2	no	—
239	#435	—	4	2	no	—
240	C₈×D₄	—	2	4	no	—
241	#427	—	4	2	no	—
242	C₂×#107	—	4	2	no	—
243	C₂×#107	C₂³	1	1	yes	characteristic
244	C₂×#107	C₂³	1	1	yes	characteristic
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×#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×#107	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	C₂×#106	C₂³	1	1	yes	characteristic
262	C₂×#106	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×#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	#407	—	2	4	no	—
275	C₂×C₂²⋊C₈	—	4	2	no	—
276	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×#97	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
290	#401	—	2	1	no	—
291	#401	—	2	1	no	—
292	#400	—	2	1	no	—
293	#400	—	2	1	no	—
294	#400	—	2	1	no	—
295	#400	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#399	—	2	1	no	—
301	#398	—	2	1	no	—
302	#398	—	2	1	no	—
303	#398	—	2	1	no	—
304	#398	—	2	1	no	—
305	#398	—	2	1	no	—
306	#397	—	2	1	no	—
307	#397	—	2	1	no	—
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#397	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	2	1	no	—
317	#396	—	2	1	no	—
318	#396	—	2	1	no	—
319	#396	—	2	1	no	—
320	#395	—	2	1	no	—
321	#394	—	2	1	no	—
322	#394	—	2	1	no	—
323	#394	—	2	1	no	—
324	#394	—	2	1	no	—
325	#393	—	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	#390	—	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	#388	—	2	1	no	—
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#388	—	2	1	no	—
349	#388	—	2	1	no	—
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	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
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	#386	—	2	1	no	—
372	#386	—	2	1	no	—
373	#386	—	2	1	no	—
374	#386	—	2	1	no	—
375	#386	—	2	1	no	—
376	#386	D₄	1	1	yes	characteristic
377	#386	D₄	1	1	yes	characteristic
378	#386	D₄	1	1	yes	characteristic
379	#385	—	2	1	no	—
380	#385	—	2	1	no	—
381	#385	—	2	1	no	—
382	#385	—	2	1	no	—
383	#385	—	2	1	no	—
384	#385	—	2	1	no	—
385	#385	—	2	1	no	—
386	#385	—	2	1	no	—
387	#385	D₄	1	1	yes	characteristic
388	#385	D₄	1	1	yes	characteristic
389	#385	D₄	1	1	yes	characteristic
390	#384	C₂³	1	1	yes	characteristic
391	#383	—	2	1	no	—
392	#382	C₂³	1	1	yes	characteristic
393	#382	C₂³	1	1	yes	characteristic
394	#382	C₂³	1	1	yes	characteristic
395	#381	—	2	1	no	—
396	#381	—	2	1	no	—
397	#380	—	2	1	no	—
398	#380	—	2	1	no	—
399	#380	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	—	2	1	no	—
402	#380	—	2	1	no	—
403	#380	—	2	1	no	—
404	#380	—	2	1	no	—
405	#380	—	2	1	no	—
406	#380	—	2	1	no	—
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	#380	C₂³	1	1	yes	characteristic
415	#380	C₂³	1	1	yes	characteristic
416	#380	C₂³	1	1	yes	characteristic
417	#380	C₂³	1	1	yes	characteristic
418	#380	C₂³	1	1	yes	characteristic
419	#380	C₂³	1	1	yes	characteristic
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	#380	C₂³	1	1	yes	characteristic
427	#379	—	2	1	no	—
428	#379	D₄	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	—	2	1	no	—
437	C₄×C₂²⋊C₄	—	2	1	no	—
438	C₄×C₂²⋊C₄	—	2	1	no	—
439	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
442	C₂×#95	—	2	1	no	—
443	C₂×#95	—	2	1	no	—
444	C₂×#95	—	2	1	no	—
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	#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	#340	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	C₂⁵	C₂×D₄	1	1	yes	characteristic
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
490	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
491	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
492	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
493	C₂³×C₄	—	2	2	no	—
494	C₂³×C₄	—	2	2	no	—
495	C₂³×C₄	—	2	1	no	—
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	—	2	1	no	—
501	C₂³×C₄	—	4	1	no	—
502	C₂³×C₄	—	4	1	no	—
503	C₂³×C₄	—	4	1	no	—
504	C₂³×C₄	—	4	1	no	—
505	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
506	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂⁴	1	1	yes	characteristic
509	C₂³×C₄	C₂⁴	1	1	yes	characteristic
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂³×C₄	C₂⁴	1	1	yes	characteristic
512	C₂×M₁₆	—	2	2	no	—
513	C₂×M₁₆	—	2	2	no	—
514	C₂×M₁₆	—	4	1	no	—
515	C₂×M₁₆	—	4	1	no	—
516	C₂×M₁₆	—	4	1	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂²×C₈	—	2	2	no	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	2	2	no	—
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	2	2	no	—
523	C₂²×C₈	—	4	1	no	—
524	C₂²×C₈	—	4	1	no	—
525	C₂²×C₈	—	4	1	no	—
526	C₂²×C₈	—	4	1	no	—
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₄⋊Q₈	—	4	1	no	—
536	C₄⋊Q₈	—	4	1	no	—
537	#126	—	8	2	no	—
538	#125	—	4	1	no	—
539	#125	—	4	1	no	—
540	#124	—	8	2	no	—
541	#123	—	8	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	4	4	no	—
545	C₂²⋊Q₈	—	4	1	no	—
546	C₂²⋊Q₈	—	4	1	no	—
547	C₂²⋊Q₈	—	4	1	no	—
548	C₂²⋊Q₈	—	4	1	no	—
549	C₂²⋊Q₈	—	4	1	no	—
550	C₂²⋊Q₈	—	4	1	no	—
551	#120	—	4	2	no	—
552	C₄×Q₈	—	4	1	no	—
553	C₄×Q₈	—	4	1	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	4	1	no	—
557	C₄×D₄	—	4	1	no	—
558	C₄×D₄	—	4	1	no	—
559	C₄×D₄	—	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	—	8	2	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	—	2	2	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	4	1	no	—
594	C₂×C₄⋊C₄	—	4	1	no	—
595	C₂×C₄⋊C₄	—	4	1	no	—
596	C₂×C₄⋊C₄	—	4	1	no	—
597	C₂×C₄⋊C₄	—	4	1	no	—
598	C₂×C₄⋊C₄	—	4	1	no	—
599	C₂×C₄⋊C₄	—	4	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	C₂×D₄	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×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×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	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	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	4	4	no	—
648	C₂×C₂²⋊C₄	—	8	2	no	—
649	C₂×C₂²⋊C₄	—	8	2	no	—
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×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
671	C₂×C₄²	C₂⁴	1	1	yes	characteristic
672	C₂×C₄²	C₂⁴	1	1	yes	characteristic
673	#107	—	2	2	no	—
674	#107	—	2	2	no	—
675	#107	—	2	2	no	—
676	#107	—	2	2	no	—
677	#107	—	2	2	no	—
678	#107	—	4	1	no	—
679	#107	—	4	1	no	—
680	#107	—	4	1	no	—
681	#107	—	4	1	no	—
682	#107	—	4	1	no	—
683	#107	—	4	1	no	—
684	#107	—	4	1	no	—
685	#107	—	4	1	no	—
686	#107	—	4	1	no	—
687	#106	—	4	1	no	—
688	#106	—	4	1	no	—
689	#106	—	4	1	no	—
690	#106	—	4	1	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	#103	—	2	2	no	—
697	#103	—	2	2	no	—
698	#103	—	2	2	no	—
699	#103	—	4	1	no	—
700	#103	—	4	1	no	—
701	#103	—	4	1	no	—
702	#103	—	4	1	no	—
703	#103	—	4	1	no	—
704	C₂²⋊C₈	—	2	2	no	—
705	C₂²⋊C₈	—	2	2	no	—
706	C₂²⋊C₈	—	2	2	no	—
707	C₂²⋊C₈	—	2	2	no	—
708	C₂²⋊C₈	—	2	2	no	—
709	C₂²⋊C₈	—	2	2	no	—
710	C₂²⋊C₈	—	4	1	no	—
711	C₂²⋊C₈	—	4	1	no	—
712	C₂²⋊C₈	—	4	1	no	—
713	C₂²⋊C₈	—	4	1	no	—
714	C₂²⋊C₈	#41	1	4	yes	—
715	#97	—	4	1	no	—
716	#97	—	4	1	no	—
717	C₄×C₈	—	2	2	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	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	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	#95	C₂×D₄	1	1	yes	characteristic
767	#95	C₂×D₄	1	1	yes	characteristic
768	#95	C₂×D₄	1	1	yes	characteristic
769	C₂⁴	—	2	2	no	—
770	C₂⁴	—	2	2	no	—
771	C₂⁴	—	2	2	no	—
772	C₂⁴	—	2	2	no	—
773	C₂⁴	—	4	1	no	—
774	C₂⁴	—	4	1	no	—
775	C₂⁴	—	4	1	no	—
776	C₂⁴	C₂²×D₄	1	1	yes	characteristic
777	C₂⁴	C₂²×D₄	1	1	yes	characteristic
778	C₂⁴	C₂²×D₄	1	1	yes	characteristic
779	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	4	2	no	—
787	C₂×Q₈	—	8	1	no	—
788	C₂×Q₈	—	8	1	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	4	1	no	—
794	C₂×D₄	—	4	1	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	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	2	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	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	—	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	—	4	1	no	—
840	C₂²×C₄	—	4	1	no	—
841	C₂²×C₄	—	4	1	no	—
842	C₂²×C₄	—	4	1	no	—
843	C₂²×C₄	—	4	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	8	2	no	—
854	C₂²×C₄	—	8	2	no	—
855	C₂²×C₄	—	8	2	no	—
856	C₂²×C₄	—	8	2	no	—
857	C₂²×C₄	—	8	1	no	—
858	C₂²×C₄	—	8	1	no	—
859	C₂²×C₄	—	8	1	no	—
860	C₂²×C₄	—	8	1	no	—
861	C₂²×C₄	—	8	1	no	—
862	C₂²×C₄	—	8	1	no	—
863	C₂²×C₄	—	8	1	no	—
864	C₂²×C₄	—	8	1	no	—
865	C₂²×C₄	—	8	1	no	—
866	C₂²×C₄	—	8	1	no	—
867	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
868	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
869	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
878	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
879	C₂²×C₄	C₂⁵	1	1	yes	characteristic
880	M₁₆	—	8	2	no	—
881	M₁₆	—	8	2	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	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	—	4	4	no	—
904	C₂×C₈	—	4	4	no	—
905	C₂×C₈	—	8	2	no	—
906	C₂×C₈	C₂×#41	1	2	yes	—
907	C₂×C₈	C₂×#41	1	2	yes	—
908	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	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	—	4	1	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	—	8	1	no	—
950	C₄⋊C₄	—	8	1	no	—
951	C₄⋊C₄	—	8	1	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	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	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	4	1	no	—
974	C₂²⋊C₄	—	4	1	no	—
975	C₂²⋊C₄	—	4	1	no	—
976	C₂²⋊C₄	—	4	1	no	—
977	C₂²⋊C₄	—	4	1	no	—
978	C₂²⋊C₄	—	4	1	no	—
979	C₂²⋊C₄	—	4	1	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	—	4	2	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	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	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	—	8	1	no	—
1013	C₄²	—	8	1	no	—
1014	C₄²	—	8	1	no	—
1015	C₄²	—	8	1	no	—
1016	C₄²	—	8	1	no	—
1017	C₄²	—	8	1	no	—
1018	C₄²	—	8	1	no	—
1019	C₄²	—	8	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	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	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	4	4	no	—
1047	C₂³	—	4	4	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	#547	1	2	yes	—
1052	C₂³	#575	1	2	yes	—
1053	C₂³	#576	1	2	yes	—
1054	C₂³	#578	1	2	yes	—
1055	C₂³	C₂³×D₄	1	1	yes	characteristic
1056	Q₈	—	4	1	no	—
1057	Q₈	—	4	1	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	16	2	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	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	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	—	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	—	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	—	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	—	4	1	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	—	16	2	no	—
1164	C₂×C₄	—	16	2	no	—
1165	C₂×C₄	—	16	2	no	—
1166	C₂×C₄	#547	1	2	yes	—
1167	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1168	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1169	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1170	C₂×C₄	#585	1	1	yes	characteristic
1171	C₂×C₄	#585	1	1	yes	characteristic
1172	C₂×C₄	#585	1	1	yes	characteristic
1173	C₈	—	2	2	no	—
1174	C₈	—	2	2	no	—
1175	C₈	—	2	2	no	—
1176	C₈	—	4	1	no	—
1177	C₈	—	4	1	no	—
1178	C₈	—	4	1	no	—
1179	C₈	—	4	1	no	—
1180	C₈	—	4	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	2	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	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	8	8	no	—
1209	C₂²	#3349	1	4	yes	—
1210	C₂²	C₂×#547	1	1	yes	characteristic
1211	C₂²	#3485	1	1	yes	characteristic
1212	C₂²	#3496	1	1	yes	characteristic
1213	C₂²	C₂×#575	1	1	yes	characteristic
1214	C₂²	C₂×#576	1	1	yes	characteristic
1215	C₂²	C₂×#578	1	1	yes	characteristic
1216	C₂²	#3586	1	1	yes	characteristic
1217	C₄	—	2	2	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	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	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	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	#3513	1	1	yes	characteristic
1244	C₄	#3521	1	1	yes	characteristic
1245	C₄	#3561	1	1	yes	characteristic
1246	C₄	#3564	1	1	yes	characteristic
1247	C₂	—	2	4	no	—
1248	C₂	—	4	2	no	—
1249	C₂	—	8	1	no	—
1250	C₂	—	8	1	no	—
1251	C₂	#43018	1	1	yes	characteristic
1252	C₂	C₂×#3349	1	1	yes	characteristic
1253	C₂	#61270	1	1	yes	characteristic
1254	C₂	#61727	1	1	yes	characteristic
1255	C₂	#61757	1	1	yes	characteristic
1256	C₂	#62272	1	1	yes	characteristic
1257	C₂	#62302	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#120	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#120 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #32421	C₂	semidirect
4. #32272	C₂	semidirect
5. #32258	C₂	semidirect
6. #32216	C₂	semidirect
7. #32025	C₂	semidirect
8. #31793	C₂	semidirect
9. #31444	C₂	semidirect
10. #31079	C₂	semidirect
11. #28775	C₂	semidirect
12. #28073	C₂	semidirect
13. #27854	C₂	semidirect
14. #27664	C₂	semidirect
15. #27454	C₂	semidirect
16. #27176	C₂	semidirect
17. #26344	C₂	semidirect
18. #26312	C₂	semidirect
19. #26210	C₂	semidirect
20. #26129	C₂	semidirect
21. #25994	C₂	semidirect
22. #25353	C₂	semidirect
23. #25234	C₂	semidirect
24. #24947	C₂	semidirect
25. #24556	C₂	semidirect
26. #24552	C₂	semidirect
27. C₂×#2075	C₂	semidirect
28. #22932	C₂	semidirect
30. #22656	C₂	semidirect
31. #21942	C₂	semidirect
34. C₂×#479	C₂²	semidirect
37. C₂×#427	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
88. #2100	C₂²	semidirect
89. #2097	C₂²	semidirect
90. #2087	C₂²	semidirect
91. #2087	C₂²	semidirect
92. #2087	C₂²	semidirect
93. #2086	C₂²	semidirect
94. #2085	C₂²	semidirect
95. #2085	C₂²	semidirect
96. #2083	C₂²	semidirect
97. #2077	C₂²	semidirect
100. #2076	C₂²	semidirect
111. #2075	C₂²	semidirect
112. #2075	C₂²	semidirect
113. #2074	C₂²	semidirect
114. #2068	C₂²	semidirect
115. #2068	C₂²	semidirect
116. #2059	C₂²	semidirect
117. #2059	C₂²	semidirect
118. #2057	C₂²	semidirect
119. #2057	C₂²	semidirect
122. #2036	C₂²	semidirect
123. #2036	C₂²	semidirect
126. #1993	C₂²	semidirect
127. #1992	C₂²	semidirect
128. #1987	C₂²	semidirect
130. #1949	C₂²	semidirect
131. #1949	C₂²	semidirect
132. #1949	C₂²	semidirect
133. #1947	C₂²	semidirect
134. #1944	C₂²	semidirect
135. #1943	C₂²	semidirect
136. #1943	C₂²	semidirect
137. #1942	C₂²	semidirect
138. #1935	C₂²	semidirect
139. #1933	C₂²	semidirect
140. #1928	C₂²	semidirect
141. #1927	C₂²	semidirect
144. #1921	C₂²	semidirect
145. #1921	C₂²	semidirect
146. #1919	C₂²	semidirect
147. #1918	C₂²	semidirect
148. #1918	C₂²	semidirect
149. #1918	C₂²	semidirect
150. #1918	C₂²	semidirect
151. #1918	C₂²	semidirect
156. #1892	C₂²	semidirect
157. #1873	C₂²	semidirect
163. #1865	C₂²	semidirect
164. #1863	C₂²	semidirect
165. #1854	C₂²	semidirect
166. #1854	C₂²	semidirect
167. #1854	C₂²	semidirect
180. #1846	C₂²	semidirect
181. #1825	C₂²	semidirect
182. #1825	C₂²	semidirect
193. #1808	C₂²	semidirect
194. #1808	C₂²	semidirect
195. #1776	C₂²	semidirect
196. C₄×#107	C₂²	semidirect
197. #1763	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#59197	2
#39154	2
#32421	2
#32272	2
#32258	2
#32216	2
#32025	2
#31793	2
#31444	2
#31079	2
#28775	2
#28073	2
#27854	2
#27664	2
#27454	2
#27176	2
#26344	2
#26312	2
#26210	2
#26129	2
#25994	2
#25353	2
#25234	2
#24947	2
#24556	2
#24552	2
C₂×#2075	2
#22932	2
#22846	2
#22656	2
#21942	2