Subgroups — #7124580

Order 512.

1661 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	C₂×#3336	C₂	1	1	yes	maximal, characteristic
2	C₂×#3242	C₂	1	1	yes	maximal, characteristic, complemented
3	#45185	C₂	1	1	yes	maximal, characteristic
4	#42978	C₂	1	1	yes	maximal, characteristic
5	#31236	C₂	1	1	yes	maximal, characteristic, complemented
6	#31097	C₂	1	1	yes	maximal, characteristic, complemented
7	#30953	C₂	1	1	yes	maximal, characteristic, complemented
8	#30952	C₂	1	1	yes	maximal, characteristic, complemented
9	#30814	C₂	1	1	yes	maximal, characteristic, complemented
10	#30793	C₂	1	1	yes	maximal, characteristic, complemented
11	#30672	C₂	1	1	yes	maximal, characteristic, complemented
12	#30649	C₂	1	1	yes	maximal, characteristic, complemented
13	#28911	C₂	1	1	yes	maximal, characteristic, complemented
14	#28820	C₂	1	1	yes	maximal, characteristic, complemented
15	#27943	C₂	1	1	yes	maximal, characteristic, complemented
16	#26831	C₂	1	1	yes	maximal, characteristic, complemented
17	#26807	C₂	1	1	yes	maximal, characteristic, complemented
18	#26383	C₂	1	1	yes	maximal, characteristic, complemented
19	#26344	C₂	1	1	yes	maximal, characteristic, complemented
20	#26067	C₂	1	1	yes	maximal, characteristic, complemented
21	#26050	C₂	1	1	yes	maximal, characteristic, complemented
22	#25562	C₂	1	1	yes	maximal, characteristic
23	#25512	C₂	1	1	yes	maximal, characteristic, complemented
24	#25234	C₂	1	1	yes	maximal, characteristic
25	#25208	C₂	1	1	yes	maximal, characteristic, complemented
26	#24613	C₂	1	1	yes	maximal, characteristic, complemented
27	#24586	C₂	1	1	yes	maximal, characteristic, complemented
28	#24111	C₂	1	1	yes	maximal, characteristic
29	#23557	C₂	1	1	yes	maximal, characteristic, complemented
30	#22928	C₂	1	1	yes	maximal, characteristic, complemented
31	#22901	C₂	1	1	yes	maximal, characteristic
32	C₂×#552	C₂²	1	1	yes	characteristic
33	C₂×#552	C₂²	1	1	yes	characteristic
34	C₂×#544	C₂²	1	1	yes	characteristic
35	C₂×#541	C₂²	1	1	yes	characteristic
36	#3336	—	2	8	no	—
37	#3242	—	2	8	no	—
38	C₂×#501	C₂²	1	1	yes	characteristic
39	C₂×#499	C₂²	1	1	yes	characteristic
40	C₂×#499	C₂²	1	1	yes	characteristic
41	C₂×#491	C₂²	1	1	yes	characteristic
42	C₂×#487	C₂²	1	1	yes	characteristic
43	C₂×#484	C₂²	1	1	yes	characteristic
44	C₂×#485	C₂²	1	1	yes	characteristic
45	C₂×#485	C₂²	1	1	yes	characteristic
46	C₂×#485	C₂²	1	1	yes	characteristic
47	C₂×#483	C₂²	1	1	yes	characteristic
48	C₂×#483	C₂²	1	1	yes	characteristic
49	C₂×#483	C₂²	1	1	yes	characteristic
50	C₂×#479	C₂²	1	1	yes	characteristic
51	C₂×#479	C₂²	1	1	yes	characteristic
52	C₂×#479	C₂²	1	1	yes	characteristic
53	C₂×#479	C₂²	1	1	yes	characteristic
54	C₂×#477	C₂²	1	1	yes	characteristic
55	C₂×#475	C₂²	1	1	yes	characteristic
56	C₂×#470	C₂²	1	1	yes	characteristic
57	C₂×#467	C₂²	1	1	yes	characteristic
58	C₂×#467	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
61	C₂×#433	C₂²	1	1	yes	characteristic
62	C₂×#428	C₂²	1	1	yes	characteristic
63	C₂×#427	C₂²	1	1	yes	characteristic
64	C₂²×#107	C₂²	1	1	yes	characteristic
65	#2822	—	2	1	no	—
66	#2726	—	2	1	no	—
67	#2722	—	2	1	no	—
68	#2719	—	2	1	no	—
69	#2695	—	2	1	no	—
70	#2689	—	2	1	no	—
71	#2689	—	2	1	no	—
72	#2687	—	2	1	no	—
73	#2687	—	2	1	no	—
74	#2642	—	2	1	no	—
75	#2628	—	2	1	no	—
76	#2625	C₂²	1	1	yes	characteristic
77	#2611	—	2	1	no	—
78	#2553	—	2	1	no	—
79	#2552	C₂²	1	1	yes	characteristic
80	#2550	C₂²	1	1	yes	characteristic
81	#2550	C₂²	1	1	yes	characteristic
82	#2503	C₂²	1	1	yes	characteristic
83	#2499	C₂²	1	1	yes	characteristic
84	#2496	—	2	1	no	—
85	#2492	C₂²	1	1	yes	characteristic
86	#2492	C₂²	1	1	yes	characteristic
87	#2487	C₂²	1	1	yes	characteristic
88	#2475	—	2	1	no	—
89	#2453	C₂²	1	1	yes	characteristic
90	#2453	C₂²	1	1	yes	characteristic
91	#2453	C₂²	1	1	yes	characteristic
92	#2446	C₂²	1	1	yes	characteristic
93	#2442	C₂²	1	1	yes	characteristic
94	#2442	C₂²	1	1	yes	characteristic
95	#2442	C₂²	1	1	yes	characteristic
96	#2441	—	2	1	no	—
97	#2429	C₂²	1	1	yes	characteristic
98	#2423	C₂²	1	1	yes	characteristic
99	#2417	C₂²	1	1	yes	characteristic
100	#2395	C₂²	1	1	yes	characteristic
101	#2360	C₂²	1	1	yes	characteristic
102	#2360	C₂²	1	1	yes	characteristic
103	#2351	C₂²	1	1	yes	characteristic
104	#2346	C₂²	1	1	yes	characteristic
105	#2316	C₂²	1	1	yes	characteristic
106	#2097	C₂²	1	1	yes	characteristic
107	#2097	C₂²	1	1	yes	characteristic
108	#2097	C₂²	1	1	yes	characteristic
109	#2095	C₂²	1	1	yes	characteristic
110	#2088	C₂²	1	1	yes	characteristic
111	#2087	C₂²	1	1	yes	characteristic
112	#2086	C₂²	1	1	yes	characteristic
113	#2085	C₂²	1	1	yes	characteristic
114	#2085	C₂²	1	1	yes	characteristic
115	#2084	C₂²	1	1	yes	characteristic
116	#2076	C₂²	1	1	yes	characteristic
117	#2074	C₂²	1	1	yes	characteristic
118	#2068	C₂²	1	1	yes	characteristic
119	#2068	C₂²	1	1	yes	characteristic
120	#2068	C₂²	1	1	yes	characteristic
121	#2068	C₂²	1	1	yes	characteristic
122	#2066	C₂²	1	1	yes	characteristic
123	#2066	C₂²	1	1	yes	characteristic
124	#2059	C₂²	1	1	yes	characteristic
125	#2059	C₂²	1	1	yes	characteristic
126	#2059	C₂²	1	1	yes	characteristic
127	#2059	C₂²	1	1	yes	characteristic
128	#2059	C₂²	1	1	yes	characteristic
129	#2059	C₂²	1	1	yes	characteristic
130	#2059	C₂²	1	1	yes	characteristic
131	#2059	C₂²	1	1	yes	characteristic
132	#2058	C₂²	1	1	yes	characteristic
133	#2058	C₂²	1	1	yes	characteristic
134	#2057	C₂²	1	1	yes	characteristic
135	#2057	C₂²	1	1	yes	characteristic
136	#2056	C₂²	1	1	yes	characteristic
137	#2043	C₂²	1	1	yes	characteristic
138	#2036	C₂²	1	1	yes	characteristic
139	#2036	C₂²	1	1	yes	characteristic
140	#2036	C₂²	1	1	yes	characteristic
141	#2036	C₂²	1	1	yes	characteristic
142	#2026	C₂²	1	1	yes	characteristic
143	#2026	C₂²	1	1	yes	characteristic
144	#2016	C₂²	1	1	yes	characteristic
145	#2001	C₂²	1	1	yes	characteristic
146	#1971	C₂²	1	1	yes	characteristic
147	#1969	C₂²	1	1	yes	characteristic
148	#1949	C₂²	1	1	yes	characteristic
149	#1949	C₂²	1	1	yes	characteristic
150	#1947	C₂²	1	1	yes	characteristic
151	#1943	C₂²	1	1	yes	characteristic
152	#1942	C₂²	1	1	yes	characteristic
153	#1942	C₂²	1	1	yes	characteristic
154	#1942	C₂²	1	1	yes	characteristic
155	#1939	C₂²	1	1	yes	characteristic
156	#1935	C₂²	1	1	yes	characteristic
157	#1935	C₂²	1	1	yes	characteristic
158	#1933	C₂²	1	1	yes	characteristic
159	#1933	C₂²	1	1	yes	characteristic
160	#1928	C₂²	1	1	yes	characteristic
161	#1928	C₂²	1	1	yes	characteristic
162	#1927	C₂²	1	1	yes	characteristic
163	#1927	C₂²	1	1	yes	characteristic
164	#1924	C₂²	1	1	yes	characteristic
165	#1924	C₂²	1	1	yes	characteristic
166	#1920	C₂²	1	1	yes	characteristic
167	#1918	C₂²	1	1	yes	characteristic
168	#1916	C₂²	1	1	yes	characteristic
169	#1916	C₂²	1	1	yes	characteristic
170	#1894	C₂²	1	1	yes	characteristic
171	#1892	C₂²	1	1	yes	characteristic
172	#1892	C₂²	1	1	yes	characteristic
173	#1878	C₂²	1	1	yes	characteristic
174	#1878	C₂²	1	1	yes	characteristic
175	#1878	C₂²	1	1	yes	characteristic
176	#1878	C₂²	1	1	yes	characteristic
177	#1872	C₂²	1	1	yes	characteristic
178	#1872	C₂²	1	1	yes	characteristic
179	#1870	C₂²	1	1	yes	characteristic
180	#1865	C₂²	1	1	yes	characteristic
181	#1865	C₂²	1	1	yes	characteristic
182	#1865	C₂²	1	1	yes	characteristic
183	#1865	C₂²	1	1	yes	characteristic
184	#1863	C₂²	1	1	yes	characteristic
185	#1863	C₂²	1	1	yes	characteristic
186	#1853	C₂²	1	1	yes	characteristic
187	#1853	C₂²	1	1	yes	characteristic
188	#1853	C₂²	1	1	yes	characteristic
189	#1852	C₂²	1	1	yes	characteristic
190	#1850	C₂²	1	1	yes	characteristic
191	#1850	C₂²	1	1	yes	characteristic
192	#1847	C₂²	1	1	yes	characteristic
193	#1846	C₂²	1	1	yes	characteristic
194	#1825	C₂²	1	1	yes	characteristic
195	#1808	C₂²	1	1	yes	characteristic
196	#1805	C₂²	1	1	yes	characteristic
197	#1776	C₂²	1	1	yes	characteristic
198	#1771	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	#1753	C₂²	1	1	yes	characteristic
201	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
202	#1736	C₂²	1	1	yes	characteristic
203	C₂×#340	C₂²	1	1	yes	characteristic
204	#1729	C₂²	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂³×C₈	C₂³	1	1	yes	characteristic
210	#552	—	2	4	no	—
211	#552	—	2	4	no	—
212	#552	—	4	2	no	—
213	#552	—	4	2	no	—
214	#544	—	2	4	no	—
215	#544	—	4	2	no	—
216	#541	—	2	4	no	—
217	#541	—	4	2	no	—
218	C₂×C₄⋊Q₈	—	2	1	no	—
219	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×#126	—	2	1	no	—
223	C₂×#126	—	2	1	no	—
224	C₂×#126	—	2	1	no	—
225	C₂×#126	—	2	1	no	—
226	C₂×#125	—	2	1	no	—
227	C₂×#125	—	2	1	no	—
228	C₂×#125	—	2	1	no	—
229	C₂×#125	—	2	1	no	—
230	C₂×#125	—	2	1	no	—
231	C₂×#125	C₂³	1	1	yes	characteristic
232	C₂×#125	C₂³	1	1	yes	characteristic
233	C₂×#125	C₂³	1	1	yes	characteristic
234	C₂×#125	C₂³	1	1	yes	characteristic
235	C₂×#125	C₂³	1	1	yes	characteristic
236	C₂×#123	—	2	1	no	—
237	C₂×#123	—	2	1	no	—
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₂²⋊Q₈	—	2	1	no	—
240	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
252	C₂×#117	—	2	1	no	—
253	C₂×#117	—	2	1	no	—
254	C₂×#117	C₂³	1	1	yes	characteristic
255	C₂×#117	C₂³	1	1	yes	characteristic
256	C₂×#117	C₂³	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	#501	—	2	4	no	—
262	#499	—	2	4	no	—
263	#499	—	2	4	no	—
264	#491	—	2	4	no	—
265	#487	—	2	4	no	—
266	#485	—	2	4	no	—
267	#485	—	2	4	no	—
268	#485	D₄	1	8	yes	—
269	#484	—	2	4	no	—
270	#483	—	2	4	no	—
271	#483	—	2	4	no	—
272	#483	—	2	4	no	—
273	#479	—	2	4	no	—
274	#479	—	2	4	no	—
275	#479	—	2	4	no	—
276	#479	—	2	4	no	—
277	#477	—	2	4	no	—
278	#475	—	2	4	no	—
279	#470	—	4	2	no	—
280	#467	—	2	4	no	—
281	#467	—	2	4	no	—
282	C₄×Q₁₆	—	2	4	no	—
283	C₈×D₄	—	2	4	no	—
284	#433	—	2	4	no	—
285	#428	—	4	2	no	—
286	#427	—	2	4	no	—
287	C₂×#107	—	2	4	no	—
288	C₂×#107	C₂³	1	1	yes	characteristic
289	C₂×#107	C₂³	1	1	yes	characteristic
290	C₂×#107	C₂³	1	1	yes	characteristic
291	C₂×#107	C₂³	1	1	yes	characteristic
292	C₂×#107	C₂³	1	1	yes	characteristic
293	C₂×#107	C₂³	1	1	yes	characteristic
294	C₂×#107	C₂³	1	1	yes	characteristic
295	C₂×#107	C₂³	1	1	yes	characteristic
296	C₂×#107	C₂³	1	1	yes	characteristic
297	C₂×#107	C₂³	1	1	yes	characteristic
298	C₂×#107	C₂³	1	1	yes	characteristic
299	C₂×#107	C₂³	1	1	yes	characteristic
300	C₂×#106	C₂³	1	1	yes	characteristic
301	C₂×#106	C₂³	1	1	yes	characteristic
302	C₂×#106	C₂³	1	1	yes	characteristic
303	C₂×#106	C₂³	1	1	yes	characteristic
304	C₂×#106	C₂³	1	1	yes	characteristic
305	C₂×#106	C₂³	1	1	yes	characteristic
306	C₂×#106	C₂³	1	1	yes	characteristic
307	C₂×#106	C₂³	1	1	yes	characteristic
308	C₂×#106	C₂³	1	1	yes	characteristic
309	C₂×#106	C₂³	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
315	C₂×#103	C₂³	1	1	yes	characteristic
316	C₂×#103	C₂³	1	1	yes	characteristic
317	C₂×#103	C₂³	1	1	yes	characteristic
318	C₂×#103	C₂³	1	1	yes	characteristic
319	C₂×#103	C₂³	1	1	yes	characteristic
320	C₂×#103	C₂³	1	1	yes	characteristic
321	C₂×#103	C₂³	1	1	yes	characteristic
322	C₂×#103	C₂³	1	1	yes	characteristic
323	C₂×#103	C₂³	1	1	yes	characteristic
324	C₂×#103	C₂³	1	1	yes	characteristic
325	C₂×#103	C₂³	1	1	yes	characteristic
326	C₂×#103	C₂³	1	1	yes	characteristic
327	C₂×#103	C₂³	1	1	yes	characteristic
328	C₂×#103	C₂³	1	1	yes	characteristic
329	C₂×#103	C₂³	1	1	yes	characteristic
330	C₂×#103	C₂³	1	1	yes	characteristic
331	C₂×#103	C₂³	1	1	yes	characteristic
332	C₂×#103	C₂³	1	1	yes	characteristic
333	C₂×#103	C₂³	1	1	yes	characteristic
334	C₂×#103	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
340	C₂×#97	C₂³	1	1	yes	characteristic
341	C₂×#97	C₂³	1	1	yes	characteristic
342	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
344	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
345	#400	—	2	1	no	—
346	#400	—	2	1	no	—
347	#400	—	2	1	no	—
348	#400	—	2	1	no	—
349	#400	—	2	1	no	—
350	#400	—	2	1	no	—
351	#400	—	2	1	no	—
352	#400	—	2	1	no	—
353	#400	—	2	1	no	—
354	#400	—	2	1	no	—
355	#400	—	2	1	no	—
356	#400	—	2	1	no	—
357	#400	—	2	1	no	—
358	#400	D₄	1	1	yes	characteristic
359	#399	—	2	1	no	—
360	#399	—	2	1	no	—
361	#399	D₄	1	1	yes	characteristic
362	#398	—	2	1	no	—
363	#398	—	2	1	no	—
364	#398	—	2	1	no	—
365	#398	—	2	1	no	—
366	#398	—	2	1	no	—
367	#398	—	2	1	no	—
368	#398	—	2	1	no	—
369	#398	—	2	1	no	—
370	#398	—	2	1	no	—
371	#398	—	2	1	no	—
372	#398	—	2	1	no	—
373	#398	—	2	1	no	—
374	#398	—	2	1	no	—
375	#398	—	2	1	no	—
376	#398	—	2	1	no	—
377	#398	D₄	1	1	yes	characteristic
378	#397	—	2	1	no	—
379	#397	—	2	1	no	—
380	#397	—	2	1	no	—
381	#397	—	2	1	no	—
382	#397	D₄	1	1	yes	characteristic
383	#397	D₄	1	1	yes	characteristic
384	#397	D₄	1	1	yes	characteristic
385	#396	—	2	1	no	—
386	#396	—	2	1	no	—
387	#395	—	2	1	no	—
388	#395	—	2	1	no	—
389	#394	D₄	1	1	yes	characteristic
390	#394	D₄	1	1	yes	characteristic
391	#393	—	2	1	no	—
392	#393	—	2	1	no	—
393	#391	—	2	1	no	—
394	#391	—	2	1	no	—
395	#391	—	2	1	no	—
396	#391	—	2	1	no	—
397	#391	C₂³	1	1	yes	characteristic
398	#391	C₂³	1	1	yes	characteristic
399	#391	C₂³	1	1	yes	characteristic
400	#391	C₂³	1	1	yes	characteristic
401	#391	C₂³	1	1	yes	characteristic
402	#391	C₂³	1	1	yes	characteristic
403	#391	C₂³	1	1	yes	characteristic
404	#391	C₂³	1	1	yes	characteristic
405	#389	—	2	1	no	—
406	#389	—	2	1	no	—
407	#389	—	2	1	no	—
408	#389	—	2	1	no	—
409	#389	—	2	1	no	—
410	#389	—	2	1	no	—
411	#389	—	2	1	no	—
412	#389	—	2	1	no	—
413	#389	—	2	1	no	—
414	#389	—	2	1	no	—
415	#389	—	2	1	no	—
416	#389	—	2	1	no	—
417	#389	—	2	1	no	—
418	#389	C₂³	1	1	yes	characteristic
419	#389	C₂³	1	1	yes	characteristic
420	#389	C₂³	1	1	yes	characteristic
421	#389	C₂³	1	1	yes	characteristic
422	#389	C₂³	1	1	yes	characteristic
423	#389	C₂³	1	1	yes	characteristic
424	#389	C₂³	1	1	yes	characteristic
425	#389	C₂³	1	1	yes	characteristic
426	#389	C₂³	1	1	yes	characteristic
427	#389	C₂³	1	1	yes	characteristic
428	#389	C₂³	1	1	yes	characteristic
429	#389	C₂³	1	1	yes	characteristic
430	#388	—	2	1	no	—
431	#388	—	2	1	no	—
432	#388	—	2	1	no	—
433	#388	—	2	1	no	—
434	#388	—	2	1	no	—
435	#388	—	2	1	no	—
436	#387	—	2	1	no	—
437	#387	—	2	1	no	—
438	#387	—	2	1	no	—
439	#387	—	2	1	no	—
440	#387	—	2	1	no	—
441	#387	—	2	1	no	—
442	#387	—	2	1	no	—
443	#387	—	2	1	no	—
444	#387	—	2	1	no	—
445	#387	—	2	1	no	—
446	#386	—	2	1	no	—
447	#386	—	2	1	no	—
448	#385	—	2	1	no	—
449	#385	—	2	1	no	—
450	#385	—	2	1	no	—
451	#385	—	2	1	no	—
452	#385	—	2	1	no	—
453	#385	—	2	1	no	—
454	#384	—	2	1	no	—
455	#384	C₂³	1	1	yes	characteristic
456	#382	—	2	1	no	—
457	#382	—	2	1	no	—
458	#382	C₂³	1	1	yes	characteristic
459	#382	C₂³	1	1	yes	characteristic
460	#382	C₂³	1	1	yes	characteristic
461	#381	—	2	1	no	—
462	#381	—	2	1	no	—
463	#380	—	2	1	no	—
464	#380	—	2	1	no	—
465	#380	—	2	1	no	—
466	#380	—	2	1	no	—
467	#380	—	2	1	no	—
468	#380	—	2	1	no	—
469	#380	C₂³	1	1	yes	characteristic
470	#380	C₂³	1	1	yes	characteristic
471	#380	C₂³	1	1	yes	characteristic
472	#380	C₂³	1	1	yes	characteristic
473	C₄×C₄⋊C₄	—	2	1	no	—
474	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	—	2	1	no	—
480	C₄×C₂²⋊C₄	—	2	1	no	—
481	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
482	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
484	#376	—	2	1	no	—
485	#340	C₂³	1	1	yes	characteristic
486	#340	C₂³	1	1	yes	characteristic
487	#340	C₂³	1	1	yes	characteristic
488	#340	C₂³	1	1	yes	characteristic
489	#340	C₂³	1	1	yes	characteristic
490	#340	C₂³	1	1	yes	characteristic
491	#340	C₂³	1	1	yes	characteristic
492	#340	C₂³	1	1	yes	characteristic
493	#340	C₂³	1	1	yes	characteristic
494	#340	C₂³	1	1	yes	characteristic
495	#340	C₂³	1	1	yes	characteristic
496	#340	C₂³	1	1	yes	characteristic
497	#340	C₂³	1	1	yes	characteristic
498	#340	C₂³	1	1	yes	characteristic
499	#340	C₂³	1	1	yes	characteristic
500	#340	C₂³	1	1	yes	characteristic
501	#340	C₂³	1	1	yes	characteristic
502	#340	C₂³	1	1	yes	characteristic
503	#340	C₂³	1	1	yes	characteristic
504	#340	C₂³	1	1	yes	characteristic
505	#336	C₂³	1	1	yes	characteristic
506	#336	C₂³	1	1	yes	characteristic
507	#336	C₂³	1	1	yes	characteristic
508	#336	C₂³	1	1	yes	characteristic
509	#336	C₂³	1	1	yes	characteristic
510	#336	C₂³	1	1	yes	characteristic
511	#336	C₂³	1	1	yes	characteristic
512	#336	C₂³	1	1	yes	characteristic
513	#336	C₂³	1	1	yes	characteristic
514	#336	C₂³	1	1	yes	characteristic
515	C₂²×Q₈	—	2	1	no	—
516	C₂²×Q₈	—	2	1	no	—
517	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
518	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
519	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
520	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	—	2	1	no	—
525	C₂³×C₄	C₂⁴	1	1	yes	characteristic
526	C₂³×C₄	C₂⁴	1	1	yes	characteristic
527	C₂×Q₁₆	—	2	2	no	—
528	C₂×Q₁₆	—	2	2	no	—
529	C₂×Q₁₆	—	2	2	no	—
530	C₂×Q₁₆	—	4	1	no	—
531	C₂×Q₁₆	—	4	1	no	—
532	C₂×Q₁₆	—	4	1	no	—
533	C₂×M₁₆	—	2	2	no	—
534	C₂×M₁₆	—	2	2	no	—
535	C₂×M₁₆	—	4	1	no	—
536	C₂²×C₈	—	2	2	no	—
537	C₂²×C₈	—	2	2	no	—
538	C₂²×C₈	—	2	2	no	—
539	C₂²×C₈	—	2	2	no	—
540	C₂²×C₈	—	4	1	no	—
541	C₂²×C₈	—	4	1	no	—
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	C₂²×C₈	C₂⁴	1	1	yes	characteristic
548	C₂²×C₈	C₂⁴	1	1	yes	characteristic
549	C₂²×C₈	C₂⁴	1	1	yes	characteristic
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	4	1	no	—
554	C₄⋊Q₈	—	4	1	no	—
555	C₄⋊Q₈	—	4	4	no	—
556	C₄⋊Q₈	—	4	1	no	—
557	#126	—	4	4	no	—
558	#126	—	4	4	no	—
559	#126	—	4	4	no	—
560	#126	—	4	4	no	—
561	#125	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	—	4	1	no	—
567	#125	—	4	1	no	—
568	#125	—	4	1	no	—
569	#125	—	4	1	no	—
570	#125	—	4	1	no	—
571	#125	—	4	4	no	—
572	#125	—	4	4	no	—
573	#125	—	4	4	no	—
574	#125	—	4	4	no	—
575	#125	—	4	4	no	—
576	#123	—	4	4	no	—
577	#123	—	4	4	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	4	4	no	—
587	C₂²⋊Q₈	—	4	4	no	—
588	C₂²⋊Q₈	—	4	1	no	—
589	C₂²⋊Q₈	—	4	1	no	—
590	C₂²⋊Q₈	—	4	1	no	—
591	C₂²⋊Q₈	C₂×D₄	1	4	yes	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	4	1	no	—
598	C₄×Q₈	—	4	1	no	—
599	C₄×Q₈	—	4	1	no	—
600	C₄×Q₈	—	4	1	no	—
601	C₄×Q₈	—	4	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	#117	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	—	2	2	no	—
607	#117	—	2	2	no	—
608	#117	—	2	2	no	—
609	#117	—	4	4	no	—
610	#117	—	4	4	no	—
611	#117	C₂×D₄	1	4	yes	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	2	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	4	1	no	—
661	C₂×C₄⋊C₄	—	4	1	no	—
662	C₂×C₄⋊C₄	—	4	1	no	—
663	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	1	no	—
688	C₂×C₂²⋊C₄	—	2	1	no	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
703	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
704	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	—	2	1	no	—
711	C₂×C₄²	—	2	1	no	—
712	C₂×C₄²	—	2	1	no	—
713	C₂×C₄²	—	2	1	no	—
714	C₂×C₄²	—	2	1	no	—
715	C₂×C₄²	C₂⁴	1	1	yes	characteristic
716	C₂×C₄²	C₂⁴	1	1	yes	characteristic
717	C₂×C₄²	C₂⁴	1	1	yes	characteristic
718	C₂×C₄²	C₂⁴	1	1	yes	characteristic
719	C₂×C₄²	C₂⁴	1	1	yes	characteristic
720	#107	—	2	2	no	—
721	#107	—	2	2	no	—
722	#107	—	2	2	no	—
723	#107	—	2	2	no	—
724	#107	—	2	2	no	—
725	#107	—	2	2	no	—
726	#107	—	2	2	no	—
727	#107	—	2	2	no	—
728	#107	—	4	1	no	—
729	#107	—	4	1	no	—
730	#107	—	4	1	no	—
731	#107	C₂×D₄	1	4	yes	—
732	#106	—	2	2	no	—
733	#106	—	2	2	no	—
734	#106	—	2	2	no	—
735	#106	—	2	2	no	—
736	#106	—	2	2	no	—
737	#106	—	2	2	no	—
738	#106	—	4	1	no	—
739	#106	—	4	1	no	—
740	#106	—	4	1	no	—
741	#106	C₂×D₄	1	4	yes	—
742	C₄⋊C₈	—	2	2	no	—
743	C₄⋊C₈	—	2	2	no	—
744	C₄⋊C₈	—	2	2	no	—
745	C₄⋊C₈	—	2	2	no	—
746	C₄⋊C₈	—	4	1	no	—
747	#103	—	2	2	no	—
748	#103	—	2	2	no	—
749	#103	—	2	2	no	—
750	#103	—	2	2	no	—
751	#103	—	2	2	no	—
752	#103	—	2	2	no	—
753	#103	—	2	2	no	—
754	#103	—	2	2	no	—
755	#103	—	2	2	no	—
756	#103	—	2	2	no	—
757	#103	—	2	2	no	—
758	#103	—	2	2	no	—
759	#103	—	2	2	no	—
760	#103	—	4	1	no	—
761	#103	—	4	1	no	—
762	#103	—	4	1	no	—
763	#103	—	4	1	no	—
764	#103	—	4	1	no	—
765	#103	C₂×D₄	1	4	yes	—
766	#103	C₂×D₄	1	4	yes	—
767	C₂²⋊C₈	—	2	2	no	—
768	C₂²⋊C₈	—	2	2	no	—
769	C₂²⋊C₈	—	2	2	no	—
770	C₂²⋊C₈	—	4	1	no	—
771	C₂²⋊C₈	C₂×D₄	1	4	yes	—
772	#97	—	2	2	no	—
773	#97	—	2	2	no	—
774	C₄×C₈	—	2	2	no	—
775	C₄×C₈	—	2	2	no	—
776	C₄×C₈	—	4	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	—	2	1	no	—
797	#95	—	2	1	no	—
798	#95	—	2	1	no	—
799	#95	—	2	1	no	—
800	#95	—	2	1	no	—
801	#95	—	2	1	no	—
802	#95	—	2	1	no	—
803	#95	—	2	1	no	—
804	#95	—	2	1	no	—
805	#95	—	2	1	no	—
806	#95	—	2	1	no	—
807	#95	—	2	1	no	—
808	#95	—	2	1	no	—
809	#95	—	2	1	no	—
810	#95	—	2	1	no	—
811	#95	—	2	1	no	—
812	#95	—	2	1	no	—
813	#95	—	2	1	no	—
814	#95	—	2	1	no	—
815	#95	—	2	1	no	—
816	#95	—	2	1	no	—
817	#95	—	2	1	no	—
818	#95	C₂×D₄	1	1	yes	characteristic
819	#95	C₂×D₄	1	1	yes	characteristic
820	#95	C₂×D₄	1	1	yes	characteristic
821	#95	C₂×D₄	1	1	yes	characteristic
822	#95	C₂×D₄	1	1	yes	characteristic
823	#95	C₂×D₄	1	1	yes	characteristic
824	#95	C₂×D₄	1	1	yes	characteristic
825	#95	C₂×D₄	1	1	yes	characteristic
826	#95	C₂×D₄	1	1	yes	characteristic
827	#95	C₂×D₄	1	1	yes	characteristic
828	C₂⁴	C₂²×D₄	1	1	yes	characteristic
829	C₂⁴	C₂²×D₄	1	1	yes	characteristic
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	4	2	no	—
848	C₂×Q₈	—	4	2	no	—
849	C₂×Q₈	—	8	1	no	—
850	C₂×Q₈	—	8	1	no	—
851	C₂×Q₈	—	8	1	no	—
852	C₂×Q₈	—	8	1	no	—
853	C₂×Q₈	C₂²×D₄	1	2	yes	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	4	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	8	1	no	—
890	C₂²×C₄	—	8	1	no	—
891	C₂²×C₄	—	8	1	no	—
892	C₂²×C₄	—	8	1	no	—
893	C₂²×C₄	—	8	1	no	—
894	C₂²×C₄	—	8	1	no	—
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
901	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
902	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
904	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂²×D₄	1	2	yes	—
908	C₂²×C₄	H(5,𝔽₂)	1	2	yes	—
909	C₂²×C₄	C₂⁵	1	1	yes	characteristic
910	Q₁₆	—	4	4	no	—
911	Q₁₆	—	8	2	no	—
912	M₁₆	—	4	4	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	4	4	no	—
934	C₂×C₈	—	4	4	no	—
935	C₂×C₈	C₂²×D₄	1	2	yes	—
936	C₂×C₈	C₂²×D₄	1	2	yes	—
937	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
938	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
939	C₄⋊C₄	—	2	4	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	4	1	no	—
966	C₄⋊C₄	—	4	1	no	—
967	C₄⋊C₄	—	4	1	no	—
968	C₄⋊C₄	—	4	1	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	—	4	2	no	—
982	C₄⋊C₄	—	4	2	no	—
983	C₄⋊C₄	—	4	2	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₄⋊C₄	—	4	2	no	—
989	C₄⋊C₄	—	4	2	no	—
990	C₄⋊C₄	—	4	2	no	—
991	C₄⋊C₄	—	4	2	no	—
992	C₄⋊C₄	—	4	2	no	—
993	C₄⋊C₄	—	4	2	no	—
994	C₄⋊C₄	—	4	2	no	—
995	C₄⋊C₄	—	4	2	no	—
996	C₄⋊C₄	—	4	2	no	—
997	C₄⋊C₄	—	4	2	no	—
998	C₄⋊C₄	—	8	1	no	—
999	C₄⋊C₄	—	8	1	no	—
1000	C₄⋊C₄	—	8	1	no	—
1001	C₄⋊C₄	—	8	1	no	—
1002	C₄⋊C₄	—	8	1	no	—
1003	C₄⋊C₄	—	8	1	no	—
1004	C₄⋊C₄	—	8	1	no	—
1005	C₄⋊C₄	—	8	1	no	—
1006	C₄⋊C₄	—	8	1	no	—
1007	C₄⋊C₄	—	8	1	no	—
1008	C₄⋊C₄	—	8	1	no	—
1009	C₄⋊C₄	—	8	1	no	—
1010	C₄⋊C₄	—	8	1	no	—
1011	C₄⋊C₄	C₂²×D₄	1	2	yes	—
1012	C₄⋊C₄	C₂²×D₄	1	2	yes	—
1013	C₄⋊C₄	C₂²×D₄	1	2	yes	—
1014	C₄⋊C₄	2₋¹⁺⁴	1	2	yes	—
1015	C₂²⋊C₄	—	2	4	no	—
1016	C₂²⋊C₄	—	2	4	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	4	1	no	—
1024	C₂²⋊C₄	—	4	1	no	—
1025	C₂²⋊C₄	—	4	1	no	—
1026	C₂²⋊C₄	—	4	1	no	—
1027	C₂²⋊C₄	—	4	2	no	—
1028	C₂²⋊C₄	—	4	2	no	—
1029	C₂²⋊C₄	—	4	2	no	—
1030	C₂²⋊C₄	—	4	2	no	—
1031	C₂²⋊C₄	—	4	2	no	—
1032	C₂²⋊C₄	—	4	2	no	—
1033	C₂²⋊C₄	—	8	1	no	—
1034	C₂²⋊C₄	—	8	1	no	—
1035	C₂²⋊C₄	—	8	1	no	—
1036	C₂²⋊C₄	—	8	1	no	—
1037	C₄²	—	2	4	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	4	2	no	—
1049	C₄²	—	4	2	no	—
1050	C₄²	—	4	2	no	—
1051	C₄²	—	4	2	no	—
1052	C₄²	—	4	2	no	—
1053	C₄²	—	4	2	no	—
1054	C₄²	—	8	1	no	—
1055	C₄²	—	8	1	no	—
1056	C₄²	—	8	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	D₄²	1	2	yes	—
1070	C₂³	#578	1	2	yes	—
1071	C₂³	C₂³×D₄	1	1	yes	characteristic
1072	Q₈	—	2	2	no	—
1073	Q₈	—	2	2	no	—
1074	Q₈	—	4	1	no	—
1075	Q₈	—	4	1	no	—
1076	Q₈	—	4	1	no	—
1077	Q₈	—	4	1	no	—
1078	Q₈	—	4	1	no	—
1079	Q₈	—	4	1	no	—
1080	Q₈	—	4	1	no	—
1081	Q₈	—	4	1	no	—
1082	Q₈	—	4	1	no	—
1083	Q₈	—	4	1	no	—
1084	Q₈	—	16	2	no	—
1085	Q₈	—	16	2	no	—
1086	D₄	—	4	4	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	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	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	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	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	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	8	4	no	—
1179	C₂×C₄	—	8	4	no	—
1180	C₂×C₄	—	16	2	no	—
1181	C₂×C₄	—	16	2	no	—
1182	C₂×C₄	D₄²	1	2	yes	—
1183	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1184	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1185	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1186	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1187	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1188	C₂×C₄	#585	1	1	yes	characteristic
1189	C₈	—	2	2	no	—
1190	C₈	—	2	2	no	—
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	4	1	no	—
1194	C₈	—	4	1	no	—
1195	C₈	—	4	1	no	—
1196	C₈	—	4	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	C₂×D₄²	1	1	yes	characteristic
1212	C₂²	#3489	1	1	yes	characteristic
1213	C₂²	#3499	1	1	yes	characteristic
1214	C₂²	C₂×#578	1	1	yes	characteristic
1215	C₂²	#3584	1	1	yes	characteristic
1216	C₂²	#3584	1	1	yes	characteristic
1217	C₂²	#3586	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	2	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	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	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	#3489	1	1	yes	characteristic
1247	C₄	#3499	1	1	yes	characteristic
1248	C₄	#3535	1	1	yes	characteristic
1249	C₄	#3544	1	1	yes	characteristic
1250	C₂	—	4	2	no	—
1251	C₂	—	4	2	no	—
1252	C₂	#44758	1	1	yes	characteristic
1253	C₂	#61057	1	1	yes	characteristic
1254	C₂	#61096	1	1	yes	characteristic
1255	C₂	#62168	1	1	yes	characteristic
1256	C₂	#62207	1	1	yes	characteristic
1257	C₂	#62493	1	1	yes	characteristic
1258	C₂	#62523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×D₄	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2395 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#3242	C₂	semidirect
5. #31236	C₂	semidirect
6. #31097	C₂	semidirect
7. #30953	C₂	semidirect
8. #30952	C₂	semidirect
9. #30814	C₂	semidirect
10. #30793	C₂	semidirect
11. #30672	C₂	semidirect
12. #30649	C₂	semidirect
13. #28911	C₂	semidirect
14. #28820	C₂	semidirect
15. #27943	C₂	semidirect
16. #26831	C₂	semidirect
17. #26807	C₂	semidirect
18. #26383	C₂	semidirect
19. #26344	C₂	semidirect
20. #26067	C₂	semidirect
21. #26050	C₂	semidirect
23. #25512	C₂	semidirect
25. #25208	C₂	semidirect
26. #24613	C₂	semidirect
27. #24586	C₂	semidirect
29. #23557	C₂	semidirect
30. #22928	C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3336	2
C₂×#3242	2
#45185	2
#42978	2
#31236	2
#31097	2
#30953	2
#30952	2
#30814	2
#30793	2
#30672	2
#30649	2
#28911	2
#28820	2
#27943	2
#26831	2
#26807	2
#26383	2
#26344	2
#26067	2
#26050	2
#25562	2
#25512	2
#25234	2
#25208	2
#24613	2
#24586	2
#24111	2
#23557	2
#22928	2
#22901	2