Subgroups — #6609260

Order 512.

1488 conjugacy classes of subgroups.

The subgroup lattice has 1229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36380	C₂	1	1	yes	maximal, characteristic, complemented
2	#36293	C₂	1	1	yes	maximal, characteristic
3	#33288	C₂	1	1	yes	maximal, characteristic, complemented
4	#33268	C₂	1	1	yes	maximal, characteristic, complemented
5	#33144	C₂	1	1	yes	maximal, characteristic, complemented
6	#29582	C₂	1	1	yes	maximal, characteristic, complemented
7	#29563	C₂	1	1	yes	maximal, characteristic, complemented
8	#29521	C₂	1	1	yes	maximal, characteristic, complemented
9	#29502	C₂	1	1	yes	maximal, characteristic, complemented
10	#29085	C₂	1	1	yes	maximal, characteristic, complemented
11	#29076	C₂	1	1	yes	maximal, characteristic, complemented
12	#29016	C₂	1	1	yes	maximal, characteristic, complemented
13	#29010	C₂	1	1	yes	maximal, characteristic, complemented
14	#28944	C₂	1	1	yes	maximal, characteristic, complemented
15	#28880	C₂	1	1	yes	maximal, characteristic, complemented
16	#28787	C₂	1	1	yes	maximal, characteristic, complemented
17	#28361	C₂	1	1	yes	maximal, characteristic
18	#28055	C₂	1	1	yes	maximal, characteristic, complemented
19	#27724	C₂	1	1	yes	maximal, characteristic, complemented
20	#27281	C₂	1	1	yes	maximal, characteristic
21	#26840	C₂	1	1	yes	maximal, characteristic, complemented
22	#24611	C₂	1	1	yes	maximal, characteristic, complemented
23	#24507	C₂	1	1	yes	maximal, characteristic
24	#23144	C₂	1	1	yes	maximal, characteristic, complemented
25	#22928	C₂	1	1	yes	maximal, characteristic, complemented
26	#22864	C₂	1	1	yes	maximal, characteristic
27	#22584	C₂	1	1	yes	maximal, characteristic
28	C₄×#489	C₂	1	1	yes	maximal, characteristic, complemented
29	#21288	C₂	1	1	yes	maximal, characteristic, complemented
30	#21095	C₂	1	1	yes	maximal, characteristic
31	#20480	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#489	C₂²	1	1	yes	characteristic
33	C₂×#485	C₂²	1	1	yes	characteristic
34	C₂×#470	C₂²	1	1	yes	characteristic
35	C₂×#450	C₂²	1	1	yes	characteristic
36	C₂×#440	C₂²	1	1	yes	characteristic
37	C₂×#432	C₂²	1	1	yes	characteristic
38	C₂×#418	C₂²	1	1	yes	characteristic
39	C₂×#418	C₂²	1	1	yes	characteristic
40	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
41	#2864	C₂²	1	1	yes	characteristic, complemented
42	#2863	C₂²	1	1	yes	characteristic, complemented
43	#2861	C₂²	1	1	yes	characteristic
44	#2860	C₂²	1	1	yes	characteristic
45	#2855	C₂²	1	1	yes	characteristic
46	#2855	C₂²	1	1	yes	characteristic
47	#2599	—	2	1	no	—
48	#2597	—	2	1	no	—
49	#2531	—	2	1	no	—
50	#2528	—	2	1	no	—
51	#2527	—	2	1	no	—
52	#2526	—	2	1	no	—
53	#2520	—	2	1	no	—
54	#2515	—	2	1	no	—
55	#2514	C₂²	1	1	yes	characteristic, complemented
56	#2513	C₂²	1	1	yes	characteristic
57	#2508	C₂²	1	1	yes	characteristic, complemented
58	#2506	C₂²	1	1	yes	characteristic, complemented
59	#2499	C₂²	1	1	yes	characteristic
60	#2482	—	2	1	no	—
61	#2480	—	2	1	no	—
62	#2479	—	2	1	no	—
63	#2475	—	2	1	no	—
64	#2454	C₂²	1	1	yes	characteristic
65	#2451	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	#2439	C₂²	1	1	yes	characteristic
70	#2435	C₂²	1	1	yes	characteristic
71	#2371	—	2	1	no	—
72	#2362	C₂²	1	1	yes	characteristic
73	#2360	C₂²	1	1	yes	characteristic
74	#2356	—	2	1	no	—
75	#2346	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
80	C₄×#124	C₂²	1	1	yes	characteristic
81	#2296	C₂²	1	1	yes	characteristic
82	#2295	C₂²	1	1	yes	characteristic, complemented
83	#2293	C₂²	1	1	yes	characteristic
84	C₂×#390	C₂²	1	1	yes	characteristic
85	C₄×#117	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2100	C₂²	1	1	yes	characteristic, complemented
88	#2094	C₂²	1	1	yes	characteristic
89	#2092	C₂²	1	1	yes	characteristic
90	#2088	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	#2074	C₂²	1	1	yes	characteristic, complemented
95	#2073	C₂²	1	1	yes	characteristic
96	#2068	C₂²	1	1	yes	characteristic, complemented
97	#2067	C₂²	1	1	yes	characteristic
98	#2067	C₂²	1	1	yes	characteristic
99	#2066	C₂²	1	1	yes	characteristic, complemented
100	#2059	C₂²	1	1	yes	characteristic, complemented
101	#2057	C₂²	1	1	yes	characteristic, complemented
102	#2055	C₂²	1	1	yes	characteristic
103	#2055	C₂²	1	1	yes	characteristic
104	#2042	C₂²	1	1	yes	characteristic
105	#2042	C₂²	1	1	yes	characteristic
106	#2026	C₂²	1	1	yes	characteristic, complemented
107	#2023	C₂²	1	1	yes	characteristic
108	#2015	C₂²	1	1	yes	characteristic
109	#2015	C₂²	1	1	yes	characteristic
110	#1993	C₂²	1	1	yes	characteristic, complemented
111	#1991	C₂²	1	1	yes	characteristic, complemented
112	#1991	C₂²	1	1	yes	characteristic, complemented
113	#1973	C₂²	1	1	yes	characteristic
114	#1973	C₂²	1	1	yes	characteristic
115	#1973	C₂²	1	1	yes	characteristic
116	#1971	C₂²	1	1	yes	characteristic, complemented
117	#1969	C₂²	1	1	yes	characteristic, complemented
118	#1968	C₂²	1	1	yes	characteristic
119	#1968	C₂²	1	1	yes	characteristic
120	#1959	C₂²	1	1	yes	characteristic
121	#1958	C₂²	1	1	yes	characteristic
122	#1958	C₂²	1	1	yes	characteristic
123	#1944	C₂²	1	1	yes	characteristic, complemented
124	#1943	C₂²	1	1	yes	characteristic, complemented
125	#1943	C₂²	1	1	yes	characteristic, complemented
126	#1943	C₂²	1	1	yes	characteristic, complemented
127	#1942	C₂²	1	1	yes	characteristic, complemented
128	#1942	C₂²	1	1	yes	characteristic, complemented
129	#1941	C₂²	1	1	yes	characteristic, complemented
130	#1936	C₂²	1	1	yes	characteristic
131	#1936	C₂²	1	1	yes	characteristic
132	#1936	C₂²	1	1	yes	characteristic
133	#1936	C₂²	1	1	yes	characteristic
134	#1936	C₂²	1	1	yes	characteristic
135	#1936	C₂²	1	1	yes	characteristic
136	#1936	C₂²	1	1	yes	characteristic
137	#1936	C₂²	1	1	yes	characteristic
138	#1936	C₂²	1	1	yes	characteristic
139	#1935	C₂²	1	1	yes	characteristic, complemented
140	#1935	C₂²	1	1	yes	characteristic, complemented
141	#1935	C₂²	1	1	yes	characteristic, complemented
142	#1935	C₂²	1	1	yes	characteristic, complemented
143	#1935	C₂²	1	1	yes	characteristic, complemented
144	#1935	C₂²	1	1	yes	characteristic, complemented
145	#1935	C₂²	1	1	yes	characteristic, complemented
146	#1934	C₂²	1	1	yes	characteristic
147	#1934	C₂²	1	1	yes	characteristic
148	#1934	C₂²	1	1	yes	characteristic
149	#1934	C₂²	1	1	yes	characteristic
150	#1934	C₂²	1	1	yes	characteristic
151	#1934	C₂²	1	1	yes	characteristic
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	#1925	C₂²	1	1	yes	characteristic
159	#1925	C₂²	1	1	yes	characteristic
160	#1920	C₂²	1	1	yes	characteristic, complemented
161	#1920	C₂²	1	1	yes	characteristic, complemented
162	#1920	C₂²	1	1	yes	characteristic, complemented
163	#1918	C₂²	1	1	yes	characteristic, complemented
164	#1894	C₂²	1	1	yes	characteristic
165	#1894	C₂²	1	1	yes	characteristic
166	#1880	C₂²	1	1	yes	characteristic
167	#1878	C₂²	1	1	yes	characteristic, complemented
168	#1878	C₂²	1	1	yes	characteristic, complemented
169	#1877	C₂²	1	1	yes	characteristic
170	#1873	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	#1854	C₂²	1	1	yes	characteristic
177	#1852	C₂²	1	1	yes	characteristic
178	#1836	C₂²	1	1	yes	characteristic, complemented
179	#1825	C₂²	1	1	yes	characteristic
180	#1809	C₂²	1	1	yes	characteristic
181	#1786	C₂²	1	1	yes	characteristic
182	#1776	C₂²	1	1	yes	characteristic, complemented
183	#1770	C₂²	1	1	yes	characteristic, complemented
184	#1770	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	#1763	C₂²	1	1	yes	characteristic, complemented
188	#1762	C₂²	1	1	yes	characteristic
189	C₄×#103	C₂²	1	1	yes	characteristic, complemented
190	C₄×#103	C₂²	1	1	yes	characteristic, complemented
191	C₄×#102	C₂²	1	1	yes	characteristic
192	C₄×#102	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	#1753	C₂²	1	1	yes	characteristic
197	#1745	C₂²	1	1	yes	characteristic, complemented
198	#1745	C₂²	1	1	yes	characteristic, complemented
199	#1736	C₂²	1	1	yes	characteristic
200	#1736	C₂²	1	1	yes	characteristic
201	C₄×#97	C₂²	1	1	yes	characteristic, complemented
202	C₄×#97	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂²×M₁₆	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#126	—	2	1	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#124	C₂³	1	1	yes	characteristic
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₄×Q₈	—	2	1	no	—
218	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
222	C₂×#117	—	2	1	no	—
223	C₂×#117	D₄	1	1	yes	characteristic
224	C₂×#117	D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
229	C₂²×C₂²⋊C₄	—	2	1	no	—
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂²×C₄²	C₂³	1	1	yes	characteristic
232	#489	—	2	4	no	—
233	#485	—	2	4	no	—
234	#470	—	2	4	no	—
235	#450	—	2	4	no	—
236	#440	—	2	4	no	—
237	#432	—	2	4	no	—
238	C₂×#107	C₂³	1	1	yes	characteristic
239	C₂×#107	C₂³	1	1	yes	characteristic
240	C₂×#107	C₂³	1	1	yes	characteristic
241	C₂×#107	C₂³	1	1	yes	characteristic
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#106	C₂³	1	1	yes	characteristic
244	C₂×#106	C₂³	1	1	yes	characteristic
245	C₂×#106	C₂³	1	1	yes	characteristic
246	C₂×#106	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	#418	—	2	4	no	—
250	#418	—	2	4	no	—
251	C₂×#103	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×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#102	C₂³	1	1	yes	characteristic
264	C₂×#102	C₂³	1	1	yes	characteristic
265	C₂×#102	C₂³	1	1	yes	characteristic
266	C₂×#102	C₂³	1	1	yes	characteristic
267	C₂×#102	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₄×M₁₆	—	2	4	no	—
280	C₂×#97	C₂³	1	1	yes	characteristic
281	C₂×#97	C₂³	1	1	yes	characteristic
282	C₂×#97	C₂³	1	1	yes	characteristic
283	C₂×#97	C₂³	1	1	yes	characteristic
284	C₂×#97	C₂³	1	1	yes	characteristic
285	C₂×#97	C₂³	1	1	yes	characteristic
286	C₂×#97	C₂³	1	1	yes	characteristic
287	C₂×#97	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	#401	—	2	1	no	—
295	#400	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#399	—	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	#397	—	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	#396	—	2	1	no	—
313	#396	—	2	1	no	—
314	#395	—	2	1	no	—
315	#394	—	2	1	no	—
316	#394	—	2	1	no	—
317	#393	—	2	1	no	—
318	#391	—	2	1	no	—
319	#391	—	2	1	no	—
320	#391	—	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	#391	C₂³	1	1	yes	characteristic
325	#391	C₂³	1	1	yes	characteristic
326	#391	C₂³	1	1	yes	characteristic
327	#391	C₂³	1	1	yes	characteristic
328	#391	C₂³	1	1	yes	characteristic
329	#390	—	2	1	no	—
330	#390	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
342	#389	C₂³	1	1	yes	characteristic
343	#389	C₂³	1	1	yes	characteristic
344	#389	C₂³	1	1	yes	characteristic
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#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	#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	#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	#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	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#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	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#384	C₂³	1	1	yes	characteristic
409	#383	—	2	1	no	—
410	#383	—	2	1	no	—
411	#382	—	2	1	no	—
412	#382	—	2	1	no	—
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	#381	—	2	1	no	—
419	#380	—	2	1	no	—
420	#380	—	2	1	no	—
421	#380	C₂³	1	1	yes	characteristic
422	#380	C₂³	1	1	yes	characteristic
423	#379	—	2	1	no	—
424	#379	—	2	1	no	—
425	#379	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
447	#376	—	2	1	no	—
448	#376	—	2	1	no	—
449	#376	D₄	1	1	yes	characteristic
450	#376	D₄	1	1	yes	characteristic
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	—	2	1	no	—
489	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
490	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
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	C₂×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×Q₁₆	—	2	2	no	—
507	C₂×Q₁₆	—	4	1	no	—
508	C₂×Q₁₆	—	4	1	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	4	1	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂×M₁₆	—	4	1	no	—
520	C₂×M₁₆	#41	1	4	yes	—
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	4	1	no	—
531	#126	—	8	2	no	—
532	#125	—	4	1	no	—
533	#125	—	4	1	no	—
534	#125	—	4	4	no	—
535	#124	—	2	2	no	—
536	#124	—	4	1	no	—
537	#124	—	4	1	no	—
538	#124	—	4	1	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	4	1	no	—
545	C₄×Q₈	—	4	4	no	—
546	C₄×Q₈	—	4	1	no	—
547	C₄×Q₈	—	4	1	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	4	1	no	—
550	C₄×D₄	—	4	1	no	—
551	C₄×D₄	—	4	1	no	—
552	#117	—	2	2	no	—
553	#117	—	2	2	no	—
554	#117	—	2	2	no	—
555	#117	—	4	2	no	—
556	#117	—	4	2	no	—
557	#117	—	4	1	no	—
558	#117	—	8	2	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	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	—	4	1	no	—
586	C₂×C₄⋊C₄	—	4	1	no	—
587	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	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	—	4	4	no	—
632	C₂×C₂²⋊C₄	—	4	4	no	—
633	C₂×C₂²⋊C₄	—	8	2	no	—
634	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₂×C₄²	—	2	2	no	—
639	C₂×C₄²	—	2	2	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
649	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
650	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
651	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
652	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂⁴	1	1	yes	characteristic
659	C₂×C₄²	C₂⁴	1	1	yes	characteristic
660	C₂×C₄²	C₂⁴	1	1	yes	characteristic
661	C₂×C₄²	C₂⁴	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	#107	—	2	2	no	—
665	#107	—	2	2	no	—
666	#107	—	4	1	no	—
667	#107	—	4	1	no	—
668	#107	—	4	1	no	—
669	#106	—	2	2	no	—
670	#106	—	2	2	no	—
671	#106	—	4	1	no	—
672	#106	—	4	1	no	—
673	C₄⋊C₈	—	2	2	no	—
674	C₄⋊C₈	—	2	2	no	—
675	#103	—	2	2	no	—
676	#103	—	2	2	no	—
677	#103	—	2	2	no	—
678	#103	—	2	2	no	—
679	#103	—	2	2	no	—
680	#103	—	2	2	no	—
681	#103	—	2	2	no	—
682	#103	—	4	1	no	—
683	#103	—	4	1	no	—
684	#103	—	4	1	no	—
685	#103	—	4	1	no	—
686	#103	—	4	1	no	—
687	#102	—	2	2	no	—
688	#102	—	2	2	no	—
689	#102	—	2	2	no	—
690	#102	—	2	2	no	—
691	#102	—	2	2	no	—
692	#102	—	2	2	no	—
693	#102	—	2	2	no	—
694	#102	—	2	2	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	4	1	no	—
698	#102	—	4	1	no	—
699	#102	—	4	1	no	—
700	#102	#41	1	4	yes	—
701	C₂²⋊C₈	—	2	2	no	—
702	C₂²⋊C₈	#41	1	4	yes	—
703	#97	—	2	2	no	—
704	#97	—	2	2	no	—
705	#97	—	2	2	no	—
706	#97	—	2	2	no	—
707	#97	—	2	2	no	—
708	#97	—	2	2	no	—
709	#97	—	4	1	no	—
710	#97	—	4	1	no	—
711	C₄×C₈	—	2	2	no	—
712	C₄×C₈	—	2	2	no	—
713	C₄×C₈	—	4	1	no	—
714	C₄×C₈	—	4	1	no	—
715	C₄×C₈	—	4	1	no	—
716	C₄×C₈	—	4	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	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	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
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	1	no	—
770	C₂⁴	—	2	1	no	—
771	C₂⁴	—	4	2	no	—
772	C₂⁴	—	4	2	no	—
773	C₂⁴	—	4	2	no	—
774	C₂⁴	—	4	2	no	—
775	C₂⁴	—	8	1	no	—
776	C₂⁴	—	8	1	no	—
777	C₂⁴	—	8	1	no	—
778	C₂⁴	C₂²×D₄	1	1	yes	characteristic
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	—	8	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	—	4	4	no	—
806	C₂×D₄	—	4	4	no	—
807	C₂×D₄	—	4	2	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂×D₄	—	8	2	no	—
810	C₂×D₄	—	8	2	no	—
811	C₂×D₄	—	8	1	no	—
812	C₂×D₄	C₂×#41	1	2	yes	—
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	2	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	4	1	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	8	1	no	—
842	C₂²×C₄	—	8	1	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	—	8	1	no	—
845	C₂²×C₄	—	8	1	no	—
846	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
847	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂×#41	1	2	yes	—
860	C₂²×C₄	C₂×#41	1	2	yes	—
861	C₂²×C₄	C₂⁵	1	1	yes	characteristic
862	Q₁₆	—	8	2	no	—
863	SD₁₆	—	4	4	no	—
864	SD₁₆	—	8	2	no	—
865	M₁₆	—	4	4	no	—
866	M₁₆	—	4	4	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	C₂×#41	1	2	yes	—
887	C₂×C₈	C₂×#41	1	2	yes	—
888	C₂×C₈	C₂×#41	1	2	yes	—
889	C₂×C₈	C₂×#41	1	2	yes	—
890	C₂×C₈	C₂×#41	1	2	yes	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	C₂×#41	1	2	yes	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	4	1	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	—	4	1	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	2	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	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	—	8	1	no	—
966	C₂²⋊C₄	—	8	1	no	—
967	C₂²⋊C₄	—	8	1	no	—
968	C₂²⋊C₄	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	4	1	no	—
993	C₄²	—	4	1	no	—
994	C₄²	—	4	1	no	—
995	C₄²	—	4	1	no	—
996	C₄²	—	4	1	no	—
997	C₄²	—	4	1	no	—
998	C₄²	—	4	1	no	—
999	C₄²	—	4	2	no	—
1000	C₄²	—	4	2	no	—
1001	C₄²	—	4	2	no	—
1002	C₄²	—	4	2	no	—
1003	C₄²	—	4	2	no	—
1004	C₄²	—	4	2	no	—
1005	C₄²	—	8	1	no	—
1006	C₄²	—	8	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	4	1	no	—
1015	C₂³	—	4	1	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	8	4	no	—
1028	C₂³	—	8	4	no	—
1029	C₂³	—	8	4	no	—
1030	C₂³	—	8	4	no	—
1031	C₂³	—	16	2	no	—
1032	C₂³	—	16	2	no	—
1033	C₂³	—	16	2	no	—
1034	C₂³	#532	1	2	yes	—
1035	C₂³	C₂³×D₄	1	1	yes	characteristic
1036	Q₈	—	4	1	no	—
1037	Q₈	—	4	1	no	—
1038	Q₈	—	4	1	no	—
1039	Q₈	—	4	1	no	—
1040	Q₈	—	4	1	no	—
1041	Q₈	—	4	1	no	—
1042	Q₈	—	4	1	no	—
1043	Q₈	—	4	1	no	—
1044	Q₈	—	8	4	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	4	1	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	4	1	no	—
1050	D₄	—	4	1	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	4	1	no	—
1053	D₄	—	8	4	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	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	2	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	—	4	4	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	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	—	8	2	no	—
1138	C₂×C₄	—	8	4	no	—
1139	C₂×C₄	—	16	2	no	—
1140	C₂×C₄	—	16	2	no	—
1141	C₂×C₄	#532	1	2	yes	—
1142	C₂×C₄	#575	1	2	yes	—
1143	C₂×C₄	#575	1	2	yes	—
1144	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1145	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1146	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1147	C₂×C₄	#585	1	1	yes	characteristic
1148	C₂×C₄	#585	1	1	yes	characteristic
1149	C₂×C₄	#585	1	1	yes	characteristic
1150	C₈	—	2	2	no	—
1151	C₈	—	2	2	no	—
1152	C₈	—	2	2	no	—
1153	C₈	—	2	2	no	—
1154	C₈	—	2	2	no	—
1155	C₈	—	4	1	no	—
1156	C₈	—	4	1	no	—
1157	C₈	—	4	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	8	1	no	—
1169	C₂²	—	8	1	no	—
1170	C₂²	—	8	1	no	—
1171	C₂²	—	8	1	no	—
1172	C₂²	—	8	1	no	—
1173	C₂²	—	8	1	no	—
1174	C₂²	—	8	1	no	—
1175	C₂²	—	8	1	no	—
1176	C₂²	—	8	1	no	—
1177	C₂²	—	8	1	no	—
1178	C₂²	—	8	1	no	—
1179	C₂²	—	16	8	no	—
1180	C₂²	C₂×#532	1	1	yes	characteristic
1181	C₂²	D₄×#41	1	1	yes	characteristic
1182	C₂²	#3500	1	1	yes	characteristic
1183	C₂²	C₂×#575	1	1	yes	characteristic
1184	C₂²	C₂×#575	1	1	yes	characteristic
1185	C₂²	#3585	1	1	yes	characteristic
1186	C₂²	#3586	1	1	yes	characteristic
1187	C₄	—	2	2	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	8	1	no	—
1202	C₄	—	8	1	no	—
1203	C₄	—	8	1	no	—
1204	C₄	—	8	1	no	—
1205	C₄	—	8	1	no	—
1206	C₄	—	8	1	no	—
1207	C₄	—	8	1	no	—
1208	C₄	—	8	1	no	—
1209	C₄	—	8	1	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	—	8	1	no	—
1213	C₄	—	8	1	no	—
1214	C₄	#3475	1	1	yes	characteristic
1215	C₄	#3475	1	1	yes	characteristic
1216	C₄	#3491	1	1	yes	characteristic
1217	C₄	#3521	1	1	yes	characteristic
1218	C₂	—	4	2	no	—
1219	C₂	—	8	2	no	—
1220	C₂	—	16	1	no	—
1221	C₂	#36267	1	1	yes	characteristic
1222	C₂	#60702	1	1	yes	characteristic
1223	C₂	#60709	1	1	yes	characteristic
1224	C₂	#61463	1	1	yes	characteristic
1225	C₂	#61464	1	1	yes	characteristic
1226	C₂	#62580	1	1	yes	characteristic
1227	C₂	#62585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
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. #36380	C₂	semidirect
3. #33288	C₂	semidirect
4. #33268	C₂	semidirect
5. #33144	C₂	semidirect
6. #29582	C₂	semidirect
7. #29563	C₂	semidirect
8. #29521	C₂	semidirect
9. #29502	C₂	semidirect
10. #29085	C₂	semidirect
11. #29076	C₂	semidirect
12. #29016	C₂	semidirect
13. #29010	C₂	semidirect
14. #28944	C₂	semidirect
15. #28880	C₂	semidirect
16. #28787	C₂	semidirect
18. #28055	C₂	semidirect
19. #27724	C₂	semidirect
21. #26840	C₂	semidirect
22. #24611	C₂	semidirect
24. #23144	C₂	semidirect
25. #22928	C₂	semidirect
28. C₄×#489	C₂	semidirect
29. #21288	C₂	semidirect
31. #20480	C₂	semidirect
41. #2864	C₂²	semidirect
42. #2863	C₂²	semidirect
55. #2514	C₂²	semidirect
57. #2508	C₂²	semidirect
58. #2506	C₂²	semidirect
65. #2451	C₂²	semidirect
79. C₄×C₄⋊Q₈	C₂²	semidirect
82. #2295	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2100	C₂²	semidirect
90. #2088	C₂²	semidirect
91. #2087	C₂²	semidirect
92. #2085	C₂²	semidirect
93. #2085	C₂²	semidirect
94. #2074	C₂²	semidirect
96. #2068	C₂²	semidirect
99. #2066	C₂²	semidirect
100. #2059	C₂²	semidirect
101. #2057	C₂²	semidirect
106. #2026	C₂²	semidirect
110. #1993	C₂²	semidirect
111. #1991	C₂²	semidirect
112. #1991	C₂²	semidirect
116. #1971	C₂²	semidirect
117. #1969	C₂²	semidirect
123. #1944	C₂²	semidirect
124. #1943	C₂²	semidirect
125. #1943	C₂²	semidirect
126. #1943	C₂²	semidirect
127. #1942	C₂²	semidirect
128. #1942	C₂²	semidirect
129. #1941	C₂²	semidirect
139. #1935	C₂²	semidirect
140. #1935	C₂²	semidirect
141. #1935	C₂²	semidirect
142. #1935	C₂²	semidirect
143. #1935	C₂²	semidirect
144. #1935	C₂²	semidirect
145. #1935	C₂²	semidirect
152. #1933	C₂²	semidirect
153. #1933	C₂²	semidirect
154. #1933	C₂²	semidirect
155. #1933	C₂²	semidirect
156. #1928	C₂²	semidirect
160. #1920	C₂²	semidirect
161. #1920	C₂²	semidirect
162. #1920	C₂²	semidirect
163. #1918	C₂²	semidirect
167. #1878	C₂²	semidirect
168. #1878	C₂²	semidirect
174. #1863	C₂²	semidirect
178. #1836	C₂²	semidirect
182. #1776	C₂²	semidirect
183. #1770	C₂²	semidirect
184. #1770	C₂²	semidirect
185. C₈×C₄⋊C₄	C₂²	semidirect
186. C₈×C₄⋊C₄	C₂²	semidirect
187. #1763	C₂²	semidirect
189. C₄×#103	C₂²	semidirect
190. C₄×#103	C₂²	semidirect
197. #1745	C₂²	semidirect
198. #1745	C₂²	semidirect
201. C₄×#97	C₂²	semidirect
202. C₄×#97	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36380	2
#36293	2
#33288	2
#33268	2
#33144	2
#29582	2
#29563	2
#29521	2
#29502	2
#29085	2
#29076	2
#29016	2
#29010	2
#28944	2
#28880	2
#28787	2
#28361	2
#28055	2
#27724	2
#27281	2
#26840	2
#24611	2
#24507	2
#23144	2
#22928	2
#22864	2
#22584	2
C₄×#489	2
#21288	2
#21095	2
#20480	2