Subgroups — #7583967

Order 512.

1491 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#45081	C₂	1	1	yes	maximal, characteristic
2	#35919	C₂	1	1	yes	maximal, characteristic, complemented
3	#31520	C₂	1	1	yes	maximal, characteristic, complemented
4	#31492	C₂	1	1	yes	maximal, characteristic, complemented
5	#31152	C₂	1	1	yes	maximal, characteristic, complemented
6	#30464	C₂	1	1	yes	maximal, characteristic
7	#29506	C₂	1	1	yes	maximal, characteristic, complemented
8	#29457	C₂	1	1	yes	maximal, characteristic, complemented
9	#28977	C₂	1	1	yes	maximal, characteristic, complemented
10	#28977	C₂	1	1	yes	maximal, characteristic, complemented
11	#28974	C₂	1	1	yes	maximal, characteristic, complemented
12	#27477	C₂	1	1	yes	maximal, characteristic, complemented
13	#27245	C₂	1	1	yes	maximal, characteristic
14	#27192	C₂	1	1	yes	maximal, characteristic, complemented
15	#27191	C₂	1	1	yes	maximal, characteristic, complemented
16	#26902	C₂	1	1	yes	maximal, characteristic, complemented
17	#26807	C₂	1	1	yes	maximal, characteristic, complemented
18	#26765	C₂	1	1	yes	maximal, characteristic, complemented
19	#26689	C₂	1	1	yes	maximal, characteristic, complemented
20	#26574	C₂	1	1	yes	maximal, characteristic, complemented
21	#26266	C₂	1	1	yes	maximal, characteristic, complemented
22	#24921	C₂	1	1	yes	maximal, characteristic
23	#24678	C₂	1	1	yes	maximal, characteristic, complemented
24	#24477	C₂	1	1	yes	maximal, characteristic
25	#23283	C₂	1	1	yes	maximal, characteristic, complemented
26	#23192	C₂	1	1	yes	maximal, characteristic, complemented
27	#23066	C₂	1	1	yes	maximal, characteristic, complemented
28	#22874	C₂	1	1	yes	maximal, characteristic
29	#22874	C₂	1	1	yes	maximal, characteristic
30	#21511	C₂	1	1	yes	maximal, characteristic, complemented
31	#21128	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#497	C₂²	1	1	yes	characteristic
33	C₂×#483	C₂²	1	1	yes	characteristic
34	C₂×#475	C₂²	1	1	yes	characteristic, complemented
35	C₂×#474	C₂²	1	1	yes	characteristic
36	C₂×#464	C₂²	1	1	yes	characteristic
37	C₂×#450	C₂²	1	1	yes	characteristic
38	C₂×#450	C₂²	1	1	yes	characteristic
39	C₂×#441	C₂²	1	1	yes	characteristic, complemented
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
43	C₂²×#102	C₂²	1	1	yes	characteristic
44	#2746	—	2	1	no	—
45	#2743	—	2	1	no	—
46	#2735	—	2	1	no	—
47	#2728	—	2	1	no	—
48	#2655	—	2	1	no	—
49	#2645	C₂²	1	1	yes	characteristic, complemented
50	#2588	—	2	1	no	—
51	#2575	—	2	1	no	—
52	#2561	—	2	1	no	—
53	#2542	C₂²	1	1	yes	characteristic
54	#2528	—	2	1	no	—
55	#2527	—	2	1	no	—
56	#2506	C₂²	1	1	yes	characteristic, complemented
57	#2497	C₂²	1	1	yes	characteristic
58	#2492	C₂²	1	1	yes	characteristic
59	#2492	C₂²	1	1	yes	characteristic
60	#2482	—	2	1	no	—
61	#2477	—	2	1	no	—
62	#2475	—	2	1	no	—
63	#2453	—	2	1	no	—
64	#2452	C₂²	1	1	yes	characteristic
65	#2451	C₂²	1	1	yes	characteristic, complemented
66	#2447	C₂²	1	1	yes	characteristic
67	#2447	C₂²	1	1	yes	characteristic
68	#2446	C₂²	1	1	yes	characteristic, complemented
69	#2437	—	2	1	no	—
70	#2435	C₂²	1	1	yes	characteristic
71	#2429	C₂²	1	1	yes	characteristic
72	#2423	C₂²	1	1	yes	characteristic
73	#2423	C₂²	1	1	yes	characteristic
74	#2401	C₂²	1	1	yes	characteristic
75	#2396	—	2	1	no	—
76	#2367	C₂²	1	1	yes	characteristic
77	#2365	C₂²	1	1	yes	characteristic, complemented
78	#2365	C₂²	1	1	yes	characteristic, complemented
79	#2360	C₂²	1	1	yes	characteristic
80	#2360	C₂²	1	1	yes	characteristic
81	#2355	C₂²	1	1	yes	characteristic, complemented
82	#2354	C₂²	1	1	yes	characteristic
83	#2344	C₂²	1	1	yes	characteristic
84	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	#2326	C₂²	1	1	yes	characteristic
87	#2319	C₂²	1	1	yes	characteristic
88	#2276	C₂²	1	1	yes	characteristic, complemented
89	#2096	C₂²	1	1	yes	characteristic, complemented
90	#2093	C₂²	1	1	yes	characteristic
91	#2087	C₂²	1	1	yes	characteristic, complemented
92	#2086	C₂²	1	1	yes	characteristic, complemented
93	#2084	C₂²	1	1	yes	characteristic, complemented
94	#2076	C₂²	1	1	yes	characteristic
95	#2076	C₂²	1	1	yes	characteristic
96	#2072	C₂²	1	1	yes	characteristic, complemented
97	#2072	C₂²	1	1	yes	characteristic, complemented
98	#2072	C₂²	1	1	yes	characteristic, complemented
99	#2068	C₂²	1	1	yes	characteristic, complemented
100	#2068	C₂²	1	1	yes	characteristic, complemented
101	#2065	C₂²	1	1	yes	characteristic
102	#2065	C₂²	1	1	yes	characteristic
103	#2058	C₂²	1	1	yes	characteristic, complemented
104	#2056	C₂²	1	1	yes	characteristic, complemented
105	#2055	C₂²	1	1	yes	characteristic
106	#2055	C₂²	1	1	yes	characteristic
107	#2055	C₂²	1	1	yes	characteristic
108	#2043	C₂²	1	1	yes	characteristic, complemented
109	#2042	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2042	C₂²	1	1	yes	characteristic
112	#2036	C₂²	1	1	yes	characteristic
113	#2036	C₂²	1	1	yes	characteristic
114	#2024	C₂²	1	1	yes	characteristic, complemented
115	#2024	C₂²	1	1	yes	characteristic, complemented
116	#2023	C₂²	1	1	yes	characteristic
117	#2015	C₂²	1	1	yes	characteristic
118	#2013	C₂²	1	1	yes	characteristic
119	#2001	C₂²	1	1	yes	characteristic
120	#2001	C₂²	1	1	yes	characteristic
121	#1990	C₂²	1	1	yes	characteristic, complemented
122	#1990	C₂²	1	1	yes	characteristic, complemented
123	#1983	C₂²	1	1	yes	characteristic
124	#1983	C₂²	1	1	yes	characteristic
125	#1981	C₂²	1	1	yes	characteristic, complemented
126	#1973	C₂²	1	1	yes	characteristic
127	#1971	C₂²	1	1	yes	characteristic, complemented
128	#1969	C₂²	1	1	yes	characteristic, complemented
129	#1969	C₂²	1	1	yes	characteristic, complemented
130	#1968	C₂²	1	1	yes	characteristic
131	#1968	C₂²	1	1	yes	characteristic
132	#1948	C₂²	1	1	yes	characteristic, complemented
133	#1948	C₂²	1	1	yes	characteristic, complemented
134	#1944	C₂²	1	1	yes	characteristic, complemented
135	#1943	C₂²	1	1	yes	characteristic, complemented
136	#1939	C₂²	1	1	yes	characteristic, complemented
137	#1936	C₂²	1	1	yes	characteristic
138	#1936	C₂²	1	1	yes	characteristic
139	#1934	C₂²	1	1	yes	characteristic
140	#1934	C₂²	1	1	yes	characteristic
141	#1933	C₂²	1	1	yes	characteristic, complemented
142	#1933	C₂²	1	1	yes	characteristic, complemented
143	#1928	C₂²	1	1	yes	characteristic, complemented
144	#1927	C₂²	1	1	yes	characteristic, complemented
145	#1927	C₂²	1	1	yes	characteristic, complemented
146	#1926	C₂²	1	1	yes	characteristic
147	#1926	C₂²	1	1	yes	characteristic
148	#1926	C₂²	1	1	yes	characteristic
149	#1926	C₂²	1	1	yes	characteristic
150	#1925	C₂²	1	1	yes	characteristic
151	#1924	C₂²	1	1	yes	characteristic
152	#1924	C₂²	1	1	yes	characteristic
153	#1924	C₂²	1	1	yes	characteristic
154	#1921	C₂²	1	1	yes	characteristic, complemented
155	#1921	C₂²	1	1	yes	characteristic, complemented
156	#1921	C₂²	1	1	yes	characteristic, complemented
157	#1920	C₂²	1	1	yes	characteristic, complemented
158	#1919	C₂²	1	1	yes	characteristic, complemented
159	#1918	C₂²	1	1	yes	characteristic, complemented
160	#1916	C₂²	1	1	yes	characteristic, complemented
161	#1916	C₂²	1	1	yes	characteristic, complemented
162	#1916	C₂²	1	1	yes	characteristic, complemented
163	#1892	C₂²	1	1	yes	characteristic
164	#1892	C₂²	1	1	yes	characteristic
165	#1892	C₂²	1	1	yes	characteristic
166	#1880	C₂²	1	1	yes	characteristic
167	#1880	C₂²	1	1	yes	characteristic
168	#1880	C₂²	1	1	yes	characteristic
169	#1880	C₂²	1	1	yes	characteristic
170	#1878	C₂²	1	1	yes	characteristic, complemented
171	#1878	C₂²	1	1	yes	characteristic, complemented
172	#1878	C₂²	1	1	yes	characteristic, complemented
173	#1877	C₂²	1	1	yes	characteristic
174	#1877	C₂²	1	1	yes	characteristic
175	#1877	C₂²	1	1	yes	characteristic
176	#1877	C₂²	1	1	yes	characteristic
177	#1877	C₂²	1	1	yes	characteristic
178	#1865	C₂²	1	1	yes	characteristic, complemented
179	#1865	C₂²	1	1	yes	characteristic, complemented
180	#1864	C₂²	1	1	yes	characteristic
181	#1864	C₂²	1	1	yes	characteristic
182	#1863	C₂²	1	1	yes	characteristic, complemented
183	#1862	C₂²	1	1	yes	characteristic
184	#1853	C₂²	1	1	yes	characteristic
185	#1853	C₂²	1	1	yes	characteristic
186	#1850	C₂²	1	1	yes	characteristic
187	#1803	C₂²	1	1	yes	characteristic, complemented
188	#1802	C₂²	1	1	yes	characteristic
189	#1786	C₂²	1	1	yes	characteristic
190	#1776	C₂²	1	1	yes	characteristic, complemented
191	#1776	C₂²	1	1	yes	characteristic, complemented
192	#1771	C₂²	1	1	yes	characteristic, complemented
193	#1770	C₂²	1	1	yes	characteristic, complemented
194	#1768	C₂²	1	1	yes	characteristic, complemented
195	#1762	C₂²	1	1	yes	characteristic
196	C₄×#103	C₂²	1	1	yes	characteristic, complemented
197	C₄×#103	C₂²	1	1	yes	characteristic, complemented
198	C₄×#102	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
201	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
202	#1746	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂³×C₈	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×#125	—	2	1	no	—
215	C₂×#124	C₂³	1	1	yes	characteristic
216	C₂×#124	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	—	2	1	no	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄×Q₈	—	2	1	no	—
224	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
233	C₂×#117	—	2	1	no	—
234	C₂×#117	—	2	1	no	—
235	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₂²⋊C₄	—	2	1	no	—
237	C₂²×C₂²⋊C₄	—	2	1	no	—
238	#497	—	2	4	no	—
239	#483	—	4	2	no	—
240	#475	—	4	2	no	—
241	#474	—	2	4	no	—
242	#464	—	2	4	no	—
243	#450	—	2	4	no	—
244	#450	—	2	4	no	—
245	#441	—	4	2	no	—
246	#440	—	2	4	no	—
247	C₄×SD₁₆	—	4	2	no	—
248	C₄×SD₁₆	—	4	2	no	—
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×#106	C₂³	1	1	yes	characteristic
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#102	—	4	2	no	—
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×#97	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
303	#401	—	2	1	no	—
304	#401	D₄	1	1	yes	characteristic
305	#400	—	2	1	no	—
306	#400	—	2	1	no	—
307	#400	—	2	1	no	—
308	#400	—	2	1	no	—
309	#400	—	2	1	no	—
310	#400	—	2	1	no	—
311	#400	—	2	1	no	—
312	#400	—	2	1	no	—
313	#400	D₄	1	1	yes	characteristic
314	#400	D₄	1	1	yes	characteristic
315	#400	D₄	1	1	yes	characteristic
316	#399	—	2	1	no	—
317	#399	—	2	1	no	—
318	#399	—	2	1	no	—
319	#399	—	2	1	no	—
320	#398	—	2	1	no	—
321	#398	—	2	1	no	—
322	#398	—	2	1	no	—
323	#398	—	2	1	no	—
324	#398	—	2	1	no	—
325	#398	—	2	1	no	—
326	#397	—	2	1	no	—
327	#397	—	2	1	no	—
328	#397	—	2	1	no	—
329	#397	—	2	1	no	—
330	#397	D₄	1	1	yes	characteristic
331	#397	D₄	1	1	yes	characteristic
332	#397	D₄	1	1	yes	characteristic
333	#396	—	2	1	no	—
334	#396	—	2	1	no	—
335	#396	—	2	1	no	—
336	#396	D₄	1	1	yes	characteristic
337	#395	—	2	1	no	—
338	#394	—	2	1	no	—
339	#394	—	2	1	no	—
340	#393	—	2	1	no	—
341	#393	—	2	1	no	—
342	#393	—	2	1	no	—
343	#391	—	2	1	no	—
344	#391	—	2	1	no	—
345	#391	—	2	1	no	—
346	#391	—	2	1	no	—
347	#391	C₂³	1	1	yes	characteristic
348	#391	C₂³	1	1	yes	characteristic
349	#391	C₂³	1	1	yes	characteristic
350	#391	C₂³	1	1	yes	characteristic
351	#391	C₂³	1	1	yes	characteristic
352	#391	C₂³	1	1	yes	characteristic
353	#391	C₂³	1	1	yes	characteristic
354	#391	C₂³	1	1	yes	characteristic
355	#391	C₂³	1	1	yes	characteristic
356	#390	C₂³	1	1	yes	characteristic
357	#390	C₂³	1	1	yes	characteristic
358	#390	C₂³	1	1	yes	characteristic
359	#390	C₂³	1	1	yes	characteristic
360	#390	C₂³	1	1	yes	characteristic
361	#390	C₂³	1	1	yes	characteristic
362	#389	—	2	1	no	—
363	#389	—	2	1	no	—
364	#389	—	2	1	no	—
365	#389	—	2	1	no	—
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#389	C₂³	1	1	yes	characteristic
369	#389	C₂³	1	1	yes	characteristic
370	#389	C₂³	1	1	yes	characteristic
371	#389	C₂³	1	1	yes	characteristic
372	#389	C₂³	1	1	yes	characteristic
373	#389	C₂³	1	1	yes	characteristic
374	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	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	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#386	—	2	1	no	—
407	#386	—	2	1	no	—
408	#386	—	2	1	no	—
409	#386	—	2	1	no	—
410	#385	—	2	1	no	—
411	#385	—	2	1	no	—
412	#385	—	2	1	no	—
413	#385	—	2	1	no	—
414	#385	—	2	1	no	—
415	#385	—	2	1	no	—
416	#385	—	2	1	no	—
417	#385	—	2	1	no	—
418	#384	C₂³	1	1	yes	characteristic
419	#384	C₂³	1	1	yes	characteristic
420	#384	C₂³	1	1	yes	characteristic
421	#382	—	2	1	no	—
422	#381	—	2	1	no	—
423	#381	—	2	1	no	—
424	#381	—	2	1	no	—
425	#381	—	2	1	no	—
426	#380	—	2	1	no	—
427	#380	—	2	1	no	—
428	#380	C₂³	1	1	yes	characteristic
429	#380	C₂³	1	1	yes	characteristic
430	#380	C₂³	1	1	yes	characteristic
431	#379	—	2	1	no	—
432	#379	—	2	1	no	—
433	#379	—	2	1	no	—
434	#379	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	—	2	1	no	—
439	C₄×C₄⋊C₄	—	2	1	no	—
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	—	2	1	no	—
451	C₄×C₂²⋊C₄	—	2	1	no	—
452	C₄×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
456	#376	—	2	1	no	—
457	#376	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	#336	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	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂⁵	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	—	4	1	no	—
502	C₂²×D₄	—	4	1	no	—
503	C₂²×D₄	C₂⁴	1	1	yes	characteristic
504	C₂²×D₄	C₂⁴	1	1	yes	characteristic
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×Q₁₆	—	2	2	no	—
512	C₂×Q₁₆	—	2	2	no	—
513	C₂×Q₁₆	—	2	2	no	—
514	C₂×Q₁₆	—	4	1	no	—
515	C₂×Q₁₆	—	4	1	no	—
516	C₂×Q₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×SD₁₆	—	4	1	no	—
528	C₂×SD₁₆	#41	1	4	yes	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	—	4	1	no	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₂²×C₈	C₂⁴	1	1	yes	characteristic
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	4	1	no	—
543	C₄⋊Q₈	—	4	1	no	—
544	C₄⋊Q₈	—	4	1	no	—
545	C₄⋊Q₈	—	4	1	no	—
546	#125	—	8	2	no	—
547	#124	—	2	2	no	—
548	#124	—	2	2	no	—
549	#124	—	4	1	no	—
550	#124	—	4	1	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	4	1	no	—
554	C₂²⋊Q₈	—	4	1	no	—
555	C₂²⋊Q₈	—	4	1	no	—
556	C₂²⋊Q₈	—	4	1	no	—
557	C₂²⋊Q₈	—	8	2	no	—
558	C₂²⋊Q₈	—	8	2	no	—
559	C₂²⋊Q₈	—	8	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	4	1	no	—
565	C₄×Q₈	—	4	1	no	—
566	C₄×Q₈	—	4	1	no	—
567	C₄×Q₈	—	4	1	no	—
568	C₄×Q₈	—	4	1	no	—
569	C₄×Q₈	—	4	1	no	—
570	C₄×Q₈	—	8	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	4	1	no	—
574	C₄×D₄	—	4	1	no	—
575	C₄×D₄	—	4	1	no	—
576	C₄×D₄	—	4	1	no	—
577	C₄×D₄	—	4	1	no	—
578	C₄×D₄	—	4	1	no	—
579	#117	—	8	2	no	—
580	#117	—	8	2	no	—
581	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	4	1	no	—
611	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	8	2	no	—
655	C₂×C₂²⋊C₄	—	8	2	no	—
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	—	2	1	no	—
671	C₂×C₄²	—	2	1	no	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	C₂×C₄²	C₂⁴	1	1	yes	characteristic
678	C₂×C₄²	C₂⁴	1	1	yes	characteristic
679	C₂×C₄²	C₂⁴	1	1	yes	characteristic
680	#107	—	2	2	no	—
681	#107	—	2	2	no	—
682	#107	—	2	2	no	—
683	#107	—	4	1	no	—
684	#106	—	2	2	no	—
685	#106	—	2	2	no	—
686	#106	—	2	2	no	—
687	#106	—	4	1	no	—
688	#106	—	4	1	no	—
689	#106	—	4	1	no	—
690	C₄⋊C₈	—	2	2	no	—
691	C₄⋊C₈	—	2	2	no	—
692	C₄⋊C₈	—	4	1	no	—
693	C₄⋊C₈	—	4	1	no	—
694	C₄⋊C₈	—	4	1	no	—
695	#103	—	2	2	no	—
696	#103	—	2	2	no	—
697	#103	—	2	2	no	—
698	#103	—	4	1	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	#103	—	4	1	no	—
705	#103	—	4	1	no	—
706	#103	—	4	1	no	—
707	#103	—	4	1	no	—
708	#103	—	4	1	no	—
709	#103	—	4	1	no	—
710	#103	—	4	1	no	—
711	#102	—	2	2	no	—
712	#102	—	2	2	no	—
713	#102	—	2	2	no	—
714	#102	—	2	2	no	—
715	#102	—	2	2	no	—
716	#102	—	2	2	no	—
717	#102	—	2	2	no	—
718	#102	—	4	1	no	—
719	#102	—	4	1	no	—
720	#102	—	4	1	no	—
721	#102	—	4	1	no	—
722	#102	#41	1	4	yes	—
723	C₂²⋊C₈	—	2	2	no	—
724	C₂²⋊C₈	—	2	2	no	—
725	C₂²⋊C₈	—	4	1	no	—
726	#97	—	2	2	no	—
727	#97	—	2	2	no	—
728	#97	—	4	1	no	—
729	C₄×C₈	—	4	1	no	—
730	C₄×C₈	—	4	1	no	—
731	C₄×C₈	—	4	1	no	—
732	C₄×C₈	—	4	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	#95	C₂×D₄	1	1	yes	characteristic
773	#95	C₂×D₄	1	1	yes	characteristic
774	#95	C₂×D₄	1	1	yes	characteristic
775	#95	C₂×D₄	1	1	yes	characteristic
776	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
778	#95	C₂×D₄	1	1	yes	characteristic
779	#95	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
781	#95	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	C₂⁴	—	2	1	no	—
787	C₂⁴	—	2	1	no	—
788	C₂⁴	—	4	2	no	—
789	C₂⁴	—	4	2	no	—
790	C₂⁴	—	4	2	no	—
791	C₂⁴	—	8	1	no	—
792	C₂⁴	—	8	1	no	—
793	C₂⁴	—	8	1	no	—
794	C₂⁴	—	8	1	no	—
795	C₂⁴	C₂²×D₄	1	1	yes	characteristic
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	4	2	no	—
814	C₂×Q₈	—	4	2	no	—
815	C₂×Q₈	—	4	2	no	—
816	C₂×Q₈	—	8	1	no	—
817	C₂×Q₈	—	8	1	no	—
818	C₂×Q₈	—	8	1	no	—
819	C₂×Q₈	C₂×#41	1	2	yes	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	4	no	—
833	C₂×D₄	—	8	1	no	—
834	C₂×D₄	—	8	2	no	—
835	C₂×D₄	—	8	2	no	—
836	C₂×D₄	—	8	2	no	—
837	C₂×D₄	C₂×#41	1	2	yes	—
838	C₂×D₄	C₂×#41	1	2	yes	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	8	1	no	—
866	C₂²×C₄	—	8	1	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	—	8	1	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
871	C₂²×C₄	—	8	1	no	—
872	C₂²×C₄	—	8	1	no	—
873	C₂²×C₄	—	8	1	no	—
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂⁵	1	1	yes	characteristic
888	Q₁₆	—	4	4	no	—
889	Q₁₆	—	8	2	no	—
890	SD₁₆	—	4	4	no	—
891	SD₁₆	—	4	4	no	—
892	SD₁₆	—	4	4	no	—
893	SD₁₆	—	8	2	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	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	8	2	no	—
917	C₂×C₈	C₂×#41	1	2	yes	—
918	C₂×C₈	C₂×#41	1	2	yes	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	4	1	no	—
944	C₄⋊C₄	—	4	1	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	2	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	2	no	—
953	C₄⋊C₄	—	4	2	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	4	2	no	—
959	C₄⋊C₄	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₄⋊C₄	—	8	1	no	—
962	C₄⋊C₄	—	8	1	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	—	8	1	no	—
967	C₄⋊C₄	—	8	1	no	—
968	C₄⋊C₄	—	8	1	no	—
969	C₄⋊C₄	—	8	1	no	—
970	C₄⋊C₄	—	8	1	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	—	8	1	no	—
973	C₄⋊C₄	C₂×#41	1	2	yes	—
974	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	4	1	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	1	no	—
1006	C₂²⋊C₄	—	8	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	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	4	2	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	—	4	2	no	—
1022	C₄²	—	4	2	no	—
1023	C₄²	—	4	2	no	—
1024	C₄²	—	8	1	no	—
1025	C₄²	—	8	1	no	—
1026	C₄²	—	8	1	no	—
1027	C₄²	—	8	1	no	—
1028	C₄²	—	8	1	no	—
1029	C₄²	—	8	1	no	—
1030	C₄²	—	8	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	2	no	—
1038	C₂³	—	2	2	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	—	4	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	8	4	no	—
1052	C₂³	—	8	4	no	—
1053	C₂³	—	8	4	no	—
1054	C₂³	—	16	2	no	—
1055	C₂³	—	16	2	no	—
1056	C₂³	—	16	2	no	—
1057	C₂³	—	16	2	no	—
1058	C₂³	#578	1	2	yes	—
1059	C₂³	C₂³×D₄	1	1	yes	characteristic
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	4	1	no	—
1063	Q₈	—	4	1	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	4	1	no	—
1066	Q₈	—	4	1	no	—
1067	Q₈	—	4	1	no	—
1068	Q₈	—	4	1	no	—
1069	Q₈	—	4	1	no	—
1070	Q₈	—	4	1	no	—
1071	Q₈	—	4	1	no	—
1072	Q₈	—	8	4	no	—
1073	Q₈	—	16	2	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	4	1	no	—
1079	D₄	—	4	1	no	—
1080	D₄	—	4	1	no	—
1081	D₄	—	4	1	no	—
1082	D₄	—	8	4	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	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	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	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	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	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	8	4	no	—
1167	C₂×C₄	—	8	4	no	—
1168	C₂×C₄	—	16	2	no	—
1169	C₂×C₄	—	16	2	no	—
1170	C₂×C₄	—	16	2	no	—
1171	C₂×C₄	#577	1	2	yes	—
1172	C₂×C₄	#577	1	2	yes	—
1173	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1174	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1175	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1176	C₂×C₄	#585	1	1	yes	characteristic
1177	C₂×C₄	#585	1	1	yes	characteristic
1178	C₂×C₄	#585	1	1	yes	characteristic
1179	C₈	—	2	2	no	—
1180	C₈	—	2	2	no	—
1181	C₈	—	4	1	no	—
1182	C₈	—	4	1	no	—
1183	C₈	—	4	1	no	—
1184	C₈	—	4	1	no	—
1185	C₈	—	4	1	no	—
1186	C₈	—	4	1	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	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	2	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	—	16	8	no	—
1209	C₂²	D₄×#41	1	1	yes	characteristic
1210	C₂²	D₄×#41	1	1	yes	characteristic
1211	C₂²	#3488	1	1	yes	characteristic
1212	C₂²	C₂×#577	1	1	yes	characteristic
1213	C₂²	C₂×#577	1	1	yes	characteristic
1214	C₂²	C₂×#578	1	1	yes	characteristic
1215	C₂²	#3585	1	1	yes	characteristic
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	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	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	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	#3481	1	1	yes	characteristic
1244	C₄	#3491	1	1	yes	characteristic
1245	C₄	#3510	1	1	yes	characteristic
1246	C₄	#3562	1	1	yes	characteristic
1247	C₂	—	4	2	no	—
1248	C₂	—	8	2	no	—
1249	C₂	—	8	2	no	—
1250	C₂	#59177	1	1	yes	characteristic
1251	C₂	#61497	1	1	yes	characteristic
1252	C₂	#61497	1	1	yes	characteristic
1253	C₂	#61522	1	1	yes	characteristic
1254	C₂	#61554	1	1	yes	characteristic
1255	C₂	#62017	1	1	yes	characteristic
1256	C₂	#62055	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 ◁ #2401 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #35919	C₂	semidirect
3. #31520	C₂	semidirect
4. #31492	C₂	semidirect
5. #31152	C₂	semidirect
7. #29506	C₂	semidirect
8. #29457	C₂	semidirect
9. #28977	C₂	semidirect
10. #28977	C₂	semidirect
11. #28974	C₂	semidirect
12. #27477	C₂	semidirect
14. #27192	C₂	semidirect
15. #27191	C₂	semidirect
16. #26902	C₂	semidirect
17. #26807	C₂	semidirect
18. #26765	C₂	semidirect
19. #26689	C₂	semidirect
20. #26574	C₂	semidirect
21. #26266	C₂	semidirect
23. #24678	C₂	semidirect
25. #23283	C₂	semidirect
26. #23192	C₂	semidirect
27. #23066	C₂	semidirect
30. #21511	C₂	semidirect
31. #21128	C₂	semidirect
34. C₂×#475	C₂²	semidirect
39. C₂×#441	C₂²	semidirect
49. #2645	C₂²	semidirect
56. #2506	C₂²	semidirect
65. #2451	C₂²	semidirect
68. #2446	C₂²	semidirect
77. #2365	C₂²	semidirect
78. #2365	C₂²	semidirect
81. #2355	C₂²	semidirect
88. #2276	C₂²	semidirect
89. #2096	C₂²	semidirect
91. #2087	C₂²	semidirect
92. #2086	C₂²	semidirect
93. #2084	C₂²	semidirect
96. #2072	C₂²	semidirect
97. #2072	C₂²	semidirect
98. #2072	C₂²	semidirect
99. #2068	C₂²	semidirect
100. #2068	C₂²	semidirect
103. #2058	C₂²	semidirect
104. #2056	C₂²	semidirect
108. #2043	C₂²	semidirect
114. #2024	C₂²	semidirect
115. #2024	C₂²	semidirect
121. #1990	C₂²	semidirect
122. #1990	C₂²	semidirect
125. #1981	C₂²	semidirect
127. #1971	C₂²	semidirect
128. #1969	C₂²	semidirect
129. #1969	C₂²	semidirect
132. #1948	C₂²	semidirect
133. #1948	C₂²	semidirect
134. #1944	C₂²	semidirect
135. #1943	C₂²	semidirect
136. #1939	C₂²	semidirect
141. #1933	C₂²	semidirect
142. #1933	C₂²	semidirect
143. #1928	C₂²	semidirect
144. #1927	C₂²	semidirect
145. #1927	C₂²	semidirect
154. #1921	C₂²	semidirect
155. #1921	C₂²	semidirect
156. #1921	C₂²	semidirect
157. #1920	C₂²	semidirect
158. #1919	C₂²	semidirect
159. #1918	C₂²	semidirect
160. #1916	C₂²	semidirect
161. #1916	C₂²	semidirect
162. #1916	C₂²	semidirect
170. #1878	C₂²	semidirect
171. #1878	C₂²	semidirect
172. #1878	C₂²	semidirect
178. #1865	C₂²	semidirect
179. #1865	C₂²	semidirect
182. #1863	C₂²	semidirect
187. #1803	C₂²	semidirect
190. #1776	C₂²	semidirect
191. #1776	C₂²	semidirect
192. #1771	C₂²	semidirect
193. #1770	C₂²	semidirect
194. #1768	C₂²	semidirect
196. C₄×#103	C₂²	semidirect
197. C₄×#103	C₂²	semidirect
202. #1746	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#45081	2
#35919	2
#31520	2
#31492	2
#31152	2
#30464	2
#29506	2
#29457	2
#28977	2
#28974	2
#27477	2
#27245	2
#27192	2
#27191	2
#26902	2
#26807	2
#26765	2
#26689	2
#26574	2
#26266	2
#24921	2
#24678	2
#24477	2
#23283	2
#23192	2
#23066	2
#22874	2
#21511	2
#21128	2