Subgroups — #6609102

Order 512.

1572 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36294	C₂	1	1	yes	maximal, characteristic, complemented
2	#36293	C₂	1	1	yes	maximal, characteristic, complemented
3	#33279	C₂	1	1	yes	maximal, characteristic, complemented
4	#33266	C₂	1	1	yes	maximal, characteristic, complemented
5	#33128	C₂	1	1	yes	maximal, characteristic, complemented
6	#29576	C₂	1	1	yes	maximal, characteristic, complemented
7	#29556	C₂	1	1	yes	maximal, characteristic, complemented
8	#29516	C₂	1	1	yes	maximal, characteristic, complemented
9	#29497	C₂	1	1	yes	maximal, characteristic, complemented
10	#29072	C₂	1	1	yes	maximal, characteristic, complemented
11	#29072	C₂	1	1	yes	maximal, characteristic, complemented
12	#29010	C₂	1	1	yes	maximal, characteristic, complemented
13	#29008	C₂	1	1	yes	maximal, characteristic, complemented
14	#28944	C₂	1	1	yes	maximal, characteristic, complemented
15	#28876	C₂	1	1	yes	maximal, characteristic, complemented
16	#28772	C₂	1	1	yes	maximal, characteristic, complemented
17	#28331	C₂	1	1	yes	maximal, characteristic
18	#28037	C₂	1	1	yes	maximal, characteristic, complemented
19	#27701	C₂	1	1	yes	maximal, characteristic, complemented
20	#27256	C₂	1	1	yes	maximal, characteristic, complemented
21	#26819	C₂	1	1	yes	maximal, characteristic, complemented
22	#24602	C₂	1	1	yes	maximal, characteristic, complemented
23	#24500	C₂	1	1	yes	maximal, characteristic
24	#23126	C₂	1	1	yes	maximal, characteristic, complemented
25	#22922	C₂	1	1	yes	maximal, characteristic, complemented
26	#22870	C₂	1	1	yes	maximal, characteristic
27	#22574	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#488	C₂	1	1	yes	maximal, characteristic, complemented
29	#21275	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#1934	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈×#117	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#488	C₂²	1	1	yes	characteristic
33	C₂×#484	C₂²	1	1	yes	characteristic
34	C₂×#465	C₂²	1	1	yes	characteristic
35	C₂×#447	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₈	C₂²	1	1	yes	characteristic
37	C₂×#431	C₂²	1	1	yes	characteristic
38	C₂²×#102	C₂²	1	1	yes	characteristic
39	C₂²×#102	C₂²	1	1	yes	characteristic
40	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
41	#2864	C₂²	1	1	yes	characteristic, complemented
42	#2861	C₂²	1	1	yes	characteristic
43	#2860	C₂²	1	1	yes	characteristic
44	#2860	C₂²	1	1	yes	characteristic, complemented
45	#2855	C₂²	1	1	yes	characteristic
46	#2854	C₂²	1	1	yes	characteristic
47	#2597	—	2	1	no	—
48	#2596	—	2	1	no	—
49	#2531	—	2	1	no	—
50	#2530	—	2	1	no	—
51	#2529	—	2	1	no	—
52	#2526	—	2	1	no	—
53	#2513	C₂²	1	1	yes	characteristic
54	#2513	C₂²	1	1	yes	characteristic, complemented
55	#2509	C₂²	1	1	yes	characteristic, complemented
56	#2508	C₂²	1	1	yes	characteristic, complemented
57	#2504	C₂²	1	1	yes	characteristic
58	#2498	—	2	1	no	—
59	#2482	—	2	1	no	—
60	#2481	—	2	1	no	—
61	#2480	—	2	1	no	—
62	#2479	—	2	1	no	—
63	#2478	—	2	1	no	—
64	#2454	C₂²	1	1	yes	characteristic
65	#2454	C₂²	1	1	yes	characteristic, complemented
66	#2448	C₂²	1	1	yes	characteristic
67	#2447	C₂²	1	1	yes	characteristic
68	#2442	C₂²	1	1	yes	characteristic
69	#2442	C₂²	1	1	yes	characteristic
70	#2435	C₂²	1	1	yes	characteristic
71	#2361	C₂²	1	1	yes	characteristic
72	#2360	C₂²	1	1	yes	characteristic
73	#2359	—	2	1	no	—
74	#2352	—	2	1	no	—
75	#2345	C₂²	1	1	yes	characteristic
76	#2342	—	2	1	no	—
77	#2342	—	2	1	no	—
78	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
79	C₄×#125	C₂²	1	1	yes	characteristic, complemented
80	C₄×#124	C₂²	1	1	yes	characteristic
81	#2293	C₂²	1	1	yes	characteristic
82	#2293	C₂²	1	1	yes	characteristic, complemented
83	C₂×#390	C₂²	1	1	yes	characteristic
84	C₂×#389	C₂²	1	1	yes	characteristic
85	C₄×#117	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2101	C₂²	1	1	yes	characteristic, complemented
88	#2092	C₂²	1	1	yes	characteristic
89	#2092	C₂²	1	1	yes	characteristic
90	#2087	C₂²	1	1	yes	characteristic, complemented
91	#2087	C₂²	1	1	yes	characteristic, complemented
92	#2085	C₂²	1	1	yes	characteristic, complemented
93	#2085	C₂²	1	1	yes	characteristic, complemented
94	#2073	C₂²	1	1	yes	characteristic
95	#2073	C₂²	1	1	yes	characteristic, complemented
96	#2068	C₂²	1	1	yes	characteristic, complemented
97	#2068	C₂²	1	1	yes	characteristic, complemented
98	#2067	C₂²	1	1	yes	characteristic
99	#2067	C₂²	1	1	yes	characteristic
100	#2059	C₂²	1	1	yes	characteristic, complemented
101	#2059	C₂²	1	1	yes	characteristic, complemented
102	#2054	C₂²	1	1	yes	characteristic
103	#2054	C₂²	1	1	yes	characteristic
104	#2042	C₂²	1	1	yes	characteristic
105	#2042	C₂²	1	1	yes	characteristic
106	#2025	C₂²	1	1	yes	characteristic
107	#2025	C₂²	1	1	yes	characteristic, complemented
108	#2012	C₂²	1	1	yes	characteristic
109	#2012	C₂²	1	1	yes	characteristic
110	#1991	C₂²	1	1	yes	characteristic, complemented
111	#1991	C₂²	1	1	yes	characteristic, complemented
112	#1991	C₂²	1	1	yes	characteristic, complemented
113	#1970	C₂²	1	1	yes	characteristic
114	#1970	C₂²	1	1	yes	characteristic
115	#1970	C₂²	1	1	yes	characteristic
116	#1970	C₂²	1	1	yes	characteristic
117	#1970	C₂²	1	1	yes	characteristic
118	#1968	C₂²	1	1	yes	characteristic, complemented
119	#1968	C₂²	1	1	yes	characteristic, complemented
120	#1958	C₂²	1	1	yes	characteristic
121	#1958	C₂²	1	1	yes	characteristic
122	#1958	C₂²	1	1	yes	characteristic
123	#1942	C₂²	1	1	yes	characteristic, complemented
124	#1942	C₂²	1	1	yes	characteristic, complemented
125	#1942	C₂²	1	1	yes	characteristic, complemented
126	#1942	C₂²	1	1	yes	characteristic, complemented
127	#1942	C₂²	1	1	yes	characteristic, complemented
128	#1941	C₂²	1	1	yes	characteristic, complemented
129	#1941	C₂²	1	1	yes	characteristic, complemented
130	#1934	C₂²	1	1	yes	characteristic
131	#1934	C₂²	1	1	yes	characteristic
132	#1934	C₂²	1	1	yes	characteristic
133	#1934	C₂²	1	1	yes	characteristic
134	#1934	C₂²	1	1	yes	characteristic
135	#1934	C₂²	1	1	yes	characteristic
136	#1934	C₂²	1	1	yes	characteristic
137	#1934	C₂²	1	1	yes	characteristic
138	#1934	C₂²	1	1	yes	characteristic
139	#1934	C₂²	1	1	yes	characteristic
140	#1934	C₂²	1	1	yes	characteristic
141	#1934	C₂²	1	1	yes	characteristic
142	#1934	C₂²	1	1	yes	characteristic
143	#1934	C₂²	1	1	yes	characteristic
144	#1934	C₂²	1	1	yes	characteristic
145	#1934	C₂²	1	1	yes	characteristic, complemented
146	#1934	C₂²	1	1	yes	characteristic, complemented
147	#1934	C₂²	1	1	yes	characteristic, complemented
148	#1934	C₂²	1	1	yes	characteristic, complemented
149	#1934	C₂²	1	1	yes	characteristic, complemented
150	#1933	C₂²	1	1	yes	characteristic, complemented
151	#1933	C₂²	1	1	yes	characteristic, complemented
152	#1933	C₂²	1	1	yes	characteristic, complemented
153	#1933	C₂²	1	1	yes	characteristic, complemented
154	#1933	C₂²	1	1	yes	characteristic, complemented
155	#1933	C₂²	1	1	yes	characteristic, complemented
156	#1928	C₂²	1	1	yes	characteristic, complemented
157	#1926	C₂²	1	1	yes	characteristic
158	#1926	C₂²	1	1	yes	characteristic
159	#1925	C₂²	1	1	yes	characteristic
160	#1921	C₂²	1	1	yes	characteristic, complemented
161	#1921	C₂²	1	1	yes	characteristic, complemented
162	#1920	C₂²	1	1	yes	characteristic, complemented
163	#1919	C₂²	1	1	yes	characteristic, complemented
164	#1893	C₂²	1	1	yes	characteristic
165	#1892	C₂²	1	1	yes	characteristic
166	#1880	C₂²	1	1	yes	characteristic, complemented
167	#1879	C₂²	1	1	yes	characteristic
168	#1879	C₂²	1	1	yes	characteristic
169	#1877	C₂²	1	1	yes	characteristic, complemented
170	#1874	C₂²	1	1	yes	characteristic
171	#1872	C₂²	1	1	yes	characteristic
172	#1864	C₂²	1	1	yes	characteristic
173	#1864	C₂²	1	1	yes	characteristic
174	#1863	C₂²	1	1	yes	characteristic, complemented
175	#1862	C₂²	1	1	yes	characteristic
176	#1852	C₂²	1	1	yes	characteristic
177	#1852	C₂²	1	1	yes	characteristic
178	#1835	C₂²	1	1	yes	characteristic, complemented
179	#1824	C₂²	1	1	yes	characteristic
180	#1807	C₂²	1	1	yes	characteristic
181	#1786	C₂²	1	1	yes	characteristic
182	C₄×#107	C₂²	1	1	yes	characteristic, complemented
183	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
184	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
185	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
186	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
187	C₄×#103	C₂²	1	1	yes	characteristic, complemented
188	C₄×#103	C₂²	1	1	yes	characteristic, complemented
189	C₄×#102	C₂²	1	1	yes	characteristic
190	C₄×#102	C₂²	1	1	yes	characteristic
191	C₄×#102	C₂²	1	1	yes	characteristic
192	C₄×#102	C₂²	1	1	yes	characteristic, complemented
193	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
194	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
195	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
196	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
197	#1744	C₂²	1	1	yes	characteristic, complemented
198	#1744	C₂²	1	1	yes	characteristic, complemented
199	C₂×#340	C₂²	1	1	yes	characteristic
200	C₂×#340	C₂²	1	1	yes	characteristic
201	C₄²×C₈	C₂²	1	1	yes	characteristic, complemented
202	C₄²×C₈	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×D₈	C₂³	1	1	yes	characteristic
206	C₂²×D₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×#126	—	2	1	no	—
210	C₂×#126	—	2	1	no	—
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#124	C₂³	1	1	yes	characteristic
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×#123	—	2	1	no	—
216	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×#121	C₂³	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	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×#117	—	2	1	no	—
224	C₂×#117	—	2	1	no	—
225	C₂×#117	D₄	1	1	yes	characteristic
226	C₂×#117	D₄	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
232	C₂²×C₂²⋊C₄	—	2	1	no	—
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	C₂²×C₄²	C₂³	1	1	yes	characteristic
235	#488	—	2	4	no	—
236	#484	—	2	4	no	—
237	#465	—	2	4	no	—
238	#447	—	2	4	no	—
239	C₄×D₈	—	2	4	no	—
240	#431	—	2	4	no	—
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×#107	C₂³	1	1	yes	characteristic
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	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×#103	C₂³	1	1	yes	characteristic
253	C₂×#103	C₂³	1	1	yes	characteristic
254	C₂×#103	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×#102	—	2	4	no	—
260	C₂×#102	—	2	4	no	—
261	C₂×#102	C₂³	1	1	yes	characteristic
262	C₂×#102	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×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄×C₈	—	2	4	no	—
283	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
290	C₂×C₄×C₈	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	#399	—	2	1	no	—
303	#399	—	2	1	no	—
304	#399	—	2	1	no	—
305	#398	—	2	1	no	—
306	#398	—	2	1	no	—
307	#398	—	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	#394	—	2	1	no	—
320	#394	—	2	1	no	—
321	#391	C₂³	1	1	yes	characteristic
322	#391	C₂³	1	1	yes	characteristic
323	#391	C₂³	1	1	yes	characteristic
324	#390	—	2	1	no	—
325	#390	—	2	1	no	—
326	#390	C₂³	1	1	yes	characteristic
327	#390	C₂³	1	1	yes	characteristic
328	#390	C₂³	1	1	yes	characteristic
329	#390	C₂³	1	1	yes	characteristic
330	#390	C₂³	1	1	yes	characteristic
331	#390	C₂³	1	1	yes	characteristic
332	#390	C₂³	1	1	yes	characteristic
333	#390	C₂³	1	1	yes	characteristic
334	#390	C₂³	1	1	yes	characteristic
335	#390	C₂³	1	1	yes	characteristic
336	#390	C₂³	1	1	yes	characteristic
337	#390	C₂³	1	1	yes	characteristic
338	#390	C₂³	1	1	yes	characteristic
339	#389	—	2	1	no	—
340	#389	—	2	1	no	—
341	#389	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	C₂³	1	1	yes	characteristic
344	#389	C₂³	1	1	yes	characteristic
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#389	C₂³	1	1	yes	characteristic
351	#389	C₂³	1	1	yes	characteristic
352	#389	C₂³	1	1	yes	characteristic
353	#389	C₂³	1	1	yes	characteristic
354	#389	C₂³	1	1	yes	characteristic
355	#389	C₂³	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#388	—	2	1	no	—
379	#388	—	2	1	no	—
380	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#386	—	2	1	no	—
401	#386	—	2	1	no	—
402	#386	—	2	1	no	—
403	#385	—	2	1	no	—
404	#385	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	—	2	1	no	—
410	#385	—	2	1	no	—
411	#382	—	2	1	no	—
412	#382	C₂³	1	1	yes	characteristic
413	#382	C₂³	1	1	yes	characteristic
414	#382	C₂³	1	1	yes	characteristic
415	#382	C₂³	1	1	yes	characteristic
416	#381	—	2	1	no	—
417	#381	—	2	1	no	—
418	#380	—	2	1	no	—
419	#380	—	2	1	no	—
420	#380	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	—	2	1	no	—
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#379	—	2	1	no	—
426	#379	—	2	1	no	—
427	#379	—	2	1	no	—
428	C₄×C₄⋊C₄	—	2	1	no	—
429	C₄×C₄⋊C₄	—	2	1	no	—
430	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
431	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	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	D₄	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	#376	D₄	1	1	yes	characteristic
449	#376	D₄	1	1	yes	characteristic
450	C₂×#95	—	2	1	no	—
451	C₄³	C₂³	1	1	yes	characteristic
452	C₄³	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	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
489	C₂²×D₄	—	2	2	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	4	1	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	C₂⁴	1	1	yes	characteristic
498	C₂²×D₄	C₂⁴	1	1	yes	characteristic
499	C₂²×D₄	C₂⁴	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
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	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	4	1	no	—
511	C₂×SD₁₆	—	4	1	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	2	2	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	4	1	no	—
516	C₂×D₈	—	4	1	no	—
517	C₂×D₈	—	4	1	no	—
518	C₂²×C₈	—	2	2	no	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	4	1	no	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	#41	1	4	yes	—
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	#126	—	8	2	no	—
533	#126	—	8	2	no	—
534	#125	—	2	2	no	—
535	#125	—	4	1	no	—
536	#125	—	4	1	no	—
537	#125	—	4	1	no	—
538	#124	—	2	2	no	—
539	#124	—	4	1	no	—
540	#124	—	4	1	no	—
541	#124	—	4	1	no	—
542	#123	—	4	4	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	C₄×Q₈	—	4	1	no	—
548	C₄×Q₈	—	4	1	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	4	1	no	—
552	C₄×D₄	—	4	1	no	—
553	C₄×D₄	—	4	1	no	—
554	C₄×D₄	—	4	1	no	—
555	C₄×D₄	—	4	4	no	—
556	#117	—	2	4	no	—
557	#117	—	2	4	no	—
558	#117	—	8	2	no	—
559	#117	—	8	2	no	—
560	C₂×C₄⋊C₄	—	2	2	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	4	1	no	—
589	C₂×C₄⋊C₄	—	4	1	no	—
590	C₂×C₄⋊C₄	—	4	1	no	—
591	C₂×C₄⋊C₄	—	8	2	no	—
592	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×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	—	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	—	4	4	no	—
646	C₂×C₂²⋊C₄	—	4	4	no	—
647	C₂×C₂²⋊C₄	—	8	2	no	—
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	2	no	—
653	C₂×C₄²	—	2	2	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	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
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	C₂×C₄²	C₂⁴	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
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	#106	—	2	2	no	—
682	#106	—	4	1	no	—
683	#106	—	4	1	no	—
684	C₄⋊C₈	—	2	2	no	—
685	C₄⋊C₈	—	2	2	no	—
686	#103	—	2	2	no	—
687	#103	—	2	2	no	—
688	#103	—	2	2	no	—
689	#103	—	2	2	no	—
690	#103	—	2	2	no	—
691	#103	—	4	1	no	—
692	#103	—	4	1	no	—
693	#102	—	2	2	no	—
694	#102	—	2	2	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	2	2	no	—
699	#102	—	2	2	no	—
700	#102	—	2	2	no	—
701	#102	—	2	2	no	—
702	#102	—	2	2	no	—
703	#102	—	2	2	no	—
704	#102	—	2	2	no	—
705	#102	—	4	1	no	—
706	#102	—	4	1	no	—
707	#102	—	4	1	no	—
708	#102	—	4	1	no	—
709	#102	—	4	1	no	—
710	#102	—	4	1	no	—
711	#102	#41	1	4	yes	—
712	C₂²⋊C₈	—	2	2	no	—
713	C₂²⋊C₈	#41	1	4	yes	—
714	C₄×C₈	—	2	2	no	—
715	C₄×C₈	—	2	2	no	—
716	C₄×C₈	—	2	2	no	—
717	C₄×C₈	—	2	2	no	—
718	C₄×C₈	—	2	2	no	—
719	C₄×C₈	—	2	2	no	—
720	C₄×C₈	—	2	2	no	—
721	C₄×C₈	—	2	2	no	—
722	C₄×C₈	—	4	1	no	—
723	C₄×C₈	—	4	1	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	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	#95	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	C₂⁴	—	2	1	no	—
773	C₂⁴	—	2	1	no	—
774	C₂⁴	—	2	1	no	—
775	C₂⁴	—	4	2	no	—
776	C₂⁴	—	4	2	no	—
777	C₂⁴	—	4	2	no	—
778	C₂⁴	—	4	2	no	—
779	C₂⁴	—	8	1	no	—
780	C₂⁴	—	8	1	no	—
781	C₂⁴	—	8	1	no	—
782	C₂⁴	C₂²×D₄	1	1	yes	characteristic
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	4	4	no	—
807	C₂×D₄	—	4	4	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	—	4	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	8	2	no	—
814	C₂×D₄	—	8	2	no	—
815	C₂×D₄	—	8	1	no	—
816	C₂×D₄	C₂×#41	1	2	yes	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	2	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	—	4	1	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	8	1	no	—
849	C₂²×C₄	—	8	1	no	—
850	C₂²×C₄	—	8	1	no	—
851	C₂²×C₄	—	8	1	no	—
852	C₂²×C₄	—	8	1	no	—
853	C₂²×C₄	—	8	1	no	—
854	C₂²×C₄	—	8	1	no	—
855	C₂²×C₄	—	8	1	no	—
856	C₂²×C₄	—	8	1	no	—
857	C₂²×C₄	#135	1	4	yes	—
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
865	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
866	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
872	C₂²×C₄	C₂×#41	1	2	yes	—
873	C₂²×C₄	C₂⁵	1	1	yes	characteristic
874	SD₁₆	—	8	2	no	—
875	D₈	—	4	4	no	—
876	D₈	—	8	2	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	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	—	4	4	no	—
897	C₂×C₈	—	4	4	no	—
898	C₂×C₈	C₂×#41	1	2	yes	—
899	C₂×C₈	C₂×#41	1	2	yes	—
900	C₂×C₈	C₂×#41	1	2	yes	—
901	C₂×C₈	C₂×#41	1	2	yes	—
902	C₂×C₈	C₂×#41	1	2	yes	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	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	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	—	8	1	no	—
945	C₄⋊C₄	—	8	1	no	—
946	C₄⋊C₄	—	8	1	no	—
947	C₄⋊C₄	—	8	1	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	C₂×#41	1	2	yes	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	8	1	no	—
980	C₂²⋊C₄	—	8	1	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	—	8	1	no	—
984	C₂²⋊C₄	—	8	1	no	—
985	C₂²⋊C₄	—	8	1	no	—
986	C₂²⋊C₄	—	8	1	no	—
987	C₂²⋊C₄	—	8	1	no	—
988	C₂²⋊C₄	—	8	1	no	—
989	C₂²⋊C₄	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	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	#135	1	4	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	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	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	4	1	no	—
1018	C₄²	—	4	1	no	—
1019	C₄²	—	4	2	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	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	2	no	—
1029	C₂³	—	4	1	no	—
1030	C₂³	—	4	1	no	—
1031	C₂³	—	4	1	no	—
1032	C₂³	—	4	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	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	—	8	4	no	—
1050	C₂³	—	8	4	no	—
1051	C₂³	—	8	4	no	—
1052	C₂³	—	8	4	no	—
1053	C₂³	—	16	2	no	—
1054	C₂³	—	16	2	no	—
1055	C₂³	—	16	2	no	—
1056	C₂³	#532	1	2	yes	—
1057	C₂³	C₂×#135	1	2	yes	—
1058	C₂³	C₂×#135	1	2	yes	—
1059	C₂³	C₂³×D₄	1	1	yes	characteristic
1060	Q₈	—	4	1	no	—
1061	Q₈	—	4	1	no	—
1062	Q₈	—	4	1	no	—
1063	Q₈	—	4	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	8	4	no	—
1077	D₄	—	8	4	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	8	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	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	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	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	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	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	4	4	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	4	no	—
1157	C₂×C₄	—	8	4	no	—
1158	C₂×C₄	—	8	4	no	—
1159	C₂×C₄	—	16	2	no	—
1160	C₂×C₄	—	16	2	no	—
1161	C₂×C₄	—	16	2	no	—
1162	C₂×C₄	#532	1	2	yes	—
1163	C₂×C₄	C₂×#135	1	2	yes	—
1164	C₂×C₄	C₂×#135	1	2	yes	—
1165	C₂×C₄	C₂×#135	1	2	yes	—
1166	C₂×C₄	C₂×#135	1	2	yes	—
1167	C₂×C₄	#576	1	2	yes	—
1168	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1169	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1170	C₂×C₄	C₂²×#41	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	—	2	2	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	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	8	1	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	8	1	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	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	—	8	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	—	8	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	16	8	no	—
1210	C₂²	#3168	1	4	yes	—
1211	C₂²	C₂×#532	1	1	yes	characteristic
1212	C₂²	D₄×#41	1	1	yes	characteristic
1213	C₂²	#3500	1	1	yes	characteristic
1214	C₂²	C₂²×#135	1	1	yes	characteristic
1215	C₂²	C₂²×#135	1	1	yes	characteristic
1216	C₂²	C₂×#576	1	1	yes	characteristic
1217	C₂²	#3584	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	2	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	2	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	—	8	1	no	—
1244	C₄	#3475	1	1	yes	characteristic
1245	C₄	#3475	1	1	yes	characteristic
1246	C₄	#3491	1	1	yes	characteristic
1247	C₄	#3521	1	1	yes	characteristic
1248	C₂	—	2	4	no	—
1249	C₂	—	8	2	no	—
1250	C₂	—	16	1	no	—
1251	C₂	—	16	1	no	—
1252	C₂	#36267	1	1	yes	characteristic
1253	C₂	C₂×#3168	1	1	yes	characteristic
1254	C₂	#60707	1	1	yes	characteristic
1255	C₂	#61428	1	1	yes	characteristic
1256	C₂	#61431	1	1	yes	characteristic
1257	C₂	#62527	1	1	yes	characteristic
1258	C₂	#62533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#447	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #36294	C₂	semidirect
2. #36293	C₂	semidirect
3. #33279	C₂	semidirect
4. #33266	C₂	semidirect
5. #33128	C₂	semidirect
6. #29576	C₂	semidirect
7. #29556	C₂	semidirect
8. #29516	C₂	semidirect
9. #29497	C₂	semidirect
10. #29072	C₂	semidirect
11. #29072	C₂	semidirect
12. #29010	C₂	semidirect
13. #29008	C₂	semidirect
14. #28944	C₂	semidirect
15. #28876	C₂	semidirect
16. #28772	C₂	semidirect
18. #28037	C₂	semidirect
19. #27701	C₂	semidirect
20. #27256	C₂	semidirect
21. #26819	C₂	semidirect
22. #24602	C₂	semidirect
24. #23126	C₂	semidirect
25. #22922	C₂	semidirect
27. #22574	C₂	semidirect
28. C₄×#488	C₂	semidirect
29. #21275	C₂	semidirect
30. C₂×#1934	C₂	semidirect
31. C₈×#117	C₂	semidirect
41. #2864	C₂²	semidirect
44. #2860	C₂²	semidirect
54. #2513	C₂²	semidirect
55. #2509	C₂²	semidirect
56. #2508	C₂²	semidirect
65. #2454	C₂²	semidirect
79. C₄×#125	C₂²	semidirect
82. #2293	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
90. #2087	C₂²	semidirect
91. #2087	C₂²	semidirect
92. #2085	C₂²	semidirect
93. #2085	C₂²	semidirect
95. #2073	C₂²	semidirect
96. #2068	C₂²	semidirect
97. #2068	C₂²	semidirect
100. #2059	C₂²	semidirect
101. #2059	C₂²	semidirect
107. #2025	C₂²	semidirect
110. #1991	C₂²	semidirect
111. #1991	C₂²	semidirect
112. #1991	C₂²	semidirect
118. #1968	C₂²	semidirect
119. #1968	C₂²	semidirect
123. #1942	C₂²	semidirect
124. #1942	C₂²	semidirect
125. #1942	C₂²	semidirect
126. #1942	C₂²	semidirect
127. #1942	C₂²	semidirect
128. #1941	C₂²	semidirect
129. #1941	C₂²	semidirect
145. #1934	C₂²	semidirect
146. #1934	C₂²	semidirect
147. #1934	C₂²	semidirect
148. #1934	C₂²	semidirect
149. #1934	C₂²	semidirect
150. #1933	C₂²	semidirect
151. #1933	C₂²	semidirect
152. #1933	C₂²	semidirect
153. #1933	C₂²	semidirect
154. #1933	C₂²	semidirect
155. #1933	C₂²	semidirect
156. #1928	C₂²	semidirect
160. #1921	C₂²	semidirect
161. #1921	C₂²	semidirect
162. #1920	C₂²	semidirect
163. #1919	C₂²	semidirect
166. #1880	C₂²	semidirect
169. #1877	C₂²	semidirect
174. #1863	C₂²	semidirect
178. #1835	C₂²	semidirect
182. C₄×#107	C₂²	semidirect
183. C₈×C₄⋊C₄	C₂²	semidirect
184. C₈×C₄⋊C₄	C₂²	semidirect
185. C₈×C₄⋊C₄	C₂²	semidirect
186. C₈×C₄⋊C₄	C₂²	semidirect
187. C₄×#103	C₂²	semidirect
188. C₄×#103	C₂²	semidirect
192. C₄×#102	C₂²	semidirect
197. #1744	C₂²	semidirect
198. #1744	C₂²	semidirect
201. C₄²×C₈	C₂²	semidirect
202. C₄²×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36294	2
#36293	2
#33279	2
#33266	2
#33128	2
#29576	2
#29556	2
#29516	2
#29497	2
#29072	2
#29010	2
#29008	2
#28944	2
#28876	2
#28772	2
#28331	2
#28037	2
#27701	2
#27256	2
#26819	2
#24602	2
#24500	2
#23126	2
#22922	2
#22870	2
#22574	2
C₄×#488	2
#21275	2
C₂×#1934	2
C₈×#117	2