Subgroups — #6507436

Order 512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#37339	C₂	1	1	yes	maximal, characteristic
2	#35665	C₂	1	1	yes	maximal, characteristic, complemented
3	#29591	C₂	1	1	yes	maximal, characteristic, complemented
4	#29508	C₂	1	1	yes	maximal, characteristic, complemented
5	#29467	C₂	1	1	yes	maximal, characteristic, complemented
6	#29458	C₂	1	1	yes	maximal, characteristic, complemented
7	#29205	C₂	1	1	yes	maximal, characteristic, complemented
8	#29160	C₂	1	1	yes	maximal, characteristic, complemented
9	#29049	C₂	1	1	yes	maximal, characteristic, complemented
10	#29009	C₂	1	1	yes	maximal, characteristic, complemented
11	#28972	C₂	1	1	yes	maximal, characteristic, complemented
12	#28848	C₂	1	1	yes	maximal, characteristic, complemented
13	#28367	C₂	1	1	yes	maximal, characteristic, complemented
14	#28102	C₂	1	1	yes	maximal, characteristic, complemented
15	#27696	C₂	1	1	yes	maximal, characteristic, complemented
16	#27258	C₂	1	1	yes	maximal, characteristic, complemented
17	#26958	C₂	1	1	yes	maximal, characteristic, complemented
18	#26836	C₂	1	1	yes	maximal, characteristic, complemented
19	#26480	C₂	1	1	yes	maximal, characteristic, complemented
20	#26072	C₂	1	1	yes	maximal, characteristic, complemented
21	#25672	C₂	1	1	yes	maximal, characteristic, complemented
22	#25497	C₂	1	1	yes	maximal, characteristic, complemented
23	#25233	C₂	1	1	yes	maximal, characteristic, complemented
24	#25114	C₂	1	1	yes	maximal, characteristic
25	#25041	C₂	1	1	yes	maximal, characteristic, complemented
26	#24789	C₂	1	1	yes	maximal, characteristic
27	#22201	C₂	1	1	yes	maximal, characteristic, complemented
28	#22092	C₂	1	1	yes	maximal, characteristic, complemented
29	#21462	C₂	1	1	yes	maximal, characteristic, complemented
30	#20877	C₂	1	1	yes	maximal, characteristic, complemented
31	#20557	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#533	C₂²	1	1	yes	characteristic
33	C₂×#519	C₂²	1	1	yes	characteristic
34	C₂×#498	C₂²	1	1	yes	characteristic
35	C₂×#487	C₂²	1	1	yes	characteristic
36	C₂×#485	C₂²	1	1	yes	characteristic
37	C₂×#468	C₂²	1	1	yes	characteristic
38	C₂×#465	C₂²	1	1	yes	characteristic
39	C₂×#465	C₂²	1	1	yes	characteristic
40	C₂×#448	C₂²	1	1	yes	characteristic
41	C₂×#440	C₂²	1	1	yes	characteristic
42	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
43	C₂×#435	C₂²	1	1	yes	characteristic
44	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
45	C₂×#428	C₂²	1	1	yes	characteristic
46	C₂×#419	C₂²	1	1	yes	characteristic
47	C₂²×#103	C₂²	1	1	yes	characteristic
48	#2857	C₂²	1	1	yes	characteristic
49	#2854	C₂²	1	1	yes	characteristic
50	#2790	—	2	1	no	—
51	#2781	—	2	1	no	—
52	#2775	—	2	1	no	—
53	#2757	—	2	1	no	—
54	#2728	—	2	1	no	—
55	#2708	—	2	1	no	—
56	#2681	—	2	1	no	—
57	#2680	—	2	1	no	—
58	#2647	C₂²	1	1	yes	characteristic
59	#2644	C₂²	1	1	yes	characteristic
60	#2609	—	2	1	no	—
61	#2599	—	2	1	no	—
62	#2599	—	2	1	no	—
63	#2581	—	2	1	no	—
64	#2507	C₂²	1	1	yes	characteristic
65	#2500	C₂²	1	1	yes	characteristic
66	#2495	C₂²	1	1	yes	characteristic
67	#2485	C₂²	1	1	yes	characteristic
68	#2477	—	2	1	no	—
69	#2475	—	2	1	no	—
70	#2465	—	2	1	no	—
71	#2462	—	2	1	no	—
72	#2452	C₂²	1	1	yes	characteristic
73	#2451	C₂²	1	1	yes	characteristic
74	#2446	C₂²	1	1	yes	characteristic
75	#2440	C₂²	1	1	yes	characteristic
76	#2439	C₂²	1	1	yes	characteristic
77	#2434	C₂²	1	1	yes	characteristic
78	#2429	C₂²	1	1	yes	characteristic
79	#2422	C₂²	1	1	yes	characteristic
80	#2421	C₂²	1	1	yes	characteristic
81	#2416	C₂²	1	1	yes	characteristic
82	#2415	C₂²	1	1	yes	characteristic
83	#2409	C₂²	1	1	yes	characteristic
84	#2327	C₂²	1	1	yes	characteristic
85	#2324	C₂²	1	1	yes	characteristic
86	#2323	C₂²	1	1	yes	characteristic
87	#2320	C₂²	1	1	yes	characteristic
88	#2317	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
90	#2290	C₂²	1	1	yes	characteristic
91	#2101	C₂²	1	1	yes	characteristic
92	#2100	C₂²	1	1	yes	characteristic
93	#2097	C₂²	1	1	yes	characteristic
94	#2095	C₂²	1	1	yes	characteristic
95	#2086	C₂²	1	1	yes	characteristic
96	#2085	C₂²	1	1	yes	characteristic
97	#2084	C₂²	1	1	yes	characteristic
98	#2077	C₂²	1	1	yes	characteristic
99	#2073	C₂²	1	1	yes	characteristic
100	#2072	C₂²	1	1	yes	characteristic
101	#2068	C₂²	1	1	yes	characteristic
102	#2068	C₂²	1	1	yes	characteristic
103	#2068	C₂²	1	1	yes	characteristic
104	#2066	C₂²	1	1	yes	characteristic
105	#2066	C₂²	1	1	yes	characteristic
106	#2065	C₂²	1	1	yes	characteristic
107	#2058	C₂²	1	1	yes	characteristic
108	#2057	C₂²	1	1	yes	characteristic
109	#2055	C₂²	1	1	yes	characteristic
110	#2043	C₂²	1	1	yes	characteristic
111	#2043	C₂²	1	1	yes	characteristic
112	#2036	C₂²	1	1	yes	characteristic
113	#2035	C₂²	1	1	yes	characteristic
114	#2035	C₂²	1	1	yes	characteristic
115	#2035	C₂²	1	1	yes	characteristic
116	#2035	C₂²	1	1	yes	characteristic
117	#2033	C₂²	1	1	yes	characteristic
118	#2024	C₂²	1	1	yes	characteristic
119	#2023	C₂²	1	1	yes	characteristic
120	#2013	C₂²	1	1	yes	characteristic
121	#2013	C₂²	1	1	yes	characteristic
122	#2000	C₂²	1	1	yes	characteristic
123	#1990	C₂²	1	1	yes	characteristic
124	#1973	C₂²	1	1	yes	characteristic
125	#1973	C₂²	1	1	yes	characteristic
126	#1968	C₂²	1	1	yes	characteristic
127	#1968	C₂²	1	1	yes	characteristic
128	#1960	C₂²	1	1	yes	characteristic
129	#1956	C₂²	1	1	yes	characteristic
130	#1956	C₂²	1	1	yes	characteristic
131	#1944	C₂²	1	1	yes	characteristic
132	#1944	C₂²	1	1	yes	characteristic
133	#1943	C₂²	1	1	yes	characteristic
134	#1942	C₂²	1	1	yes	characteristic
135	#1941	C₂²	1	1	yes	characteristic
136	#1941	C₂²	1	1	yes	characteristic
137	#1935	C₂²	1	1	yes	characteristic
138	#1935	C₂²	1	1	yes	characteristic
139	#1935	C₂²	1	1	yes	characteristic
140	#1934	C₂²	1	1	yes	characteristic
141	#1934	C₂²	1	1	yes	characteristic
142	#1933	C₂²	1	1	yes	characteristic
143	#1933	C₂²	1	1	yes	characteristic
144	#1933	C₂²	1	1	yes	characteristic
145	#1933	C₂²	1	1	yes	characteristic
146	#1933	C₂²	1	1	yes	characteristic
147	#1928	C₂²	1	1	yes	characteristic
148	#1925	C₂²	1	1	yes	characteristic
149	#1921	C₂²	1	1	yes	characteristic
150	#1921	C₂²	1	1	yes	characteristic
151	#1920	C₂²	1	1	yes	characteristic
152	#1918	C₂²	1	1	yes	characteristic
153	#1893	C₂²	1	1	yes	characteristic
154	#1892	C₂²	1	1	yes	characteristic
155	#1892	C₂²	1	1	yes	characteristic
156	#1892	C₂²	1	1	yes	characteristic
157	#1892	C₂²	1	1	yes	characteristic
158	#1892	C₂²	1	1	yes	characteristic
159	#1880	C₂²	1	1	yes	characteristic
160	#1880	C₂²	1	1	yes	characteristic
161	#1880	C₂²	1	1	yes	characteristic
162	#1877	C₂²	1	1	yes	characteristic
163	#1875	C₂²	1	1	yes	characteristic
164	#1872	C₂²	1	1	yes	characteristic
165	#1865	C₂²	1	1	yes	characteristic
166	#1865	C₂²	1	1	yes	characteristic
167	#1865	C₂²	1	1	yes	characteristic
168	#1865	C₂²	1	1	yes	characteristic
169	#1865	C₂²	1	1	yes	characteristic
170	#1865	C₂²	1	1	yes	characteristic
171	#1865	C₂²	1	1	yes	characteristic
172	#1865	C₂²	1	1	yes	characteristic
173	#1864	C₂²	1	1	yes	characteristic
174	#1863	C₂²	1	1	yes	characteristic
175	#1863	C₂²	1	1	yes	characteristic
176	#1863	C₂²	1	1	yes	characteristic
177	#1863	C₂²	1	1	yes	characteristic
178	#1863	C₂²	1	1	yes	characteristic
179	#1854	C₂²	1	1	yes	characteristic
180	#1853	C₂²	1	1	yes	characteristic
181	#1847	C₂²	1	1	yes	characteristic
182	#1835	C₂²	1	1	yes	characteristic
183	#1825	C₂²	1	1	yes	characteristic
184	#1809	C₂²	1	1	yes	characteristic
185	#1808	C₂²	1	1	yes	characteristic
186	#1808	C₂²	1	1	yes	characteristic
187	#1787	C₂²	1	1	yes	characteristic
188	#1771	C₂²	1	1	yes	characteristic
189	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
190	#1768	C₂²	1	1	yes	characteristic
191	#1763	C₂²	1	1	yes	characteristic
192	C₄×#103	C₂²	1	1	yes	characteristic
193	#1753	C₂²	1	1	yes	characteristic
194	#1752	C₂²	1	1	yes	characteristic
195	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
196	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
197	#1750	C₂²	1	1	yes	characteristic
198	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
199	#1746	C₂²	1	1	yes	characteristic
200	#1735	C₂²	1	1	yes	characteristic
201	#1729	C₂²	1	1	yes	characteristic
202	C₂×#336	C₂²	1	1	yes	characteristic
203	C₂³×Q₈	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	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	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂³×C₈	C₂³	1	1	yes	characteristic
210	C₂³×C₈	C₂³	1	1	yes	characteristic
211	#533	—	4	2	no	—
212	#533	—	4	2	no	—
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×#125	—	2	1	no	—
218	C₂×#123	—	2	1	no	—
219	C₂×#123	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	—	2	1	no	—
224	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂×#121	—	2	1	no	—
229	C₂×#121	C₂³	1	1	yes	characteristic
230	C₂×#121	C₂³	1	1	yes	characteristic
231	#519	—	4	2	no	—
232	#519	—	4	2	no	—
233	C₂×C₄×Q₈	—	2	1	no	—
234	C₂×C₄×Q₈	—	2	1	no	—
235	C₂×C₄×Q₈	—	2	1	no	—
236	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
243	C₂×#117	—	2	1	no	—
244	C₂×#117	—	2	1	no	—
245	C₂×#117	—	2	1	no	—
246	C₂×#117	C₂³	1	1	yes	characteristic
247	C₂×#117	C₂³	1	1	yes	characteristic
248	C₂×#117	C₂³	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂²×C₄²	C₂³	1	1	yes	characteristic
251	#498	—	4	2	no	—
252	#487	—	4	2	no	—
253	#485	—	2	4	no	—
254	#468	—	2	4	no	—
255	#465	—	4	2	no	—
256	#465	—	4	2	no	—
257	#448	—	2	4	no	—
258	#440	—	4	2	no	—
259	C₄×SD₁₆	—	4	2	no	—
260	#435	—	2	4	no	—
261	C₈×D₄	—	2	4	no	—
262	#428	—	4	2	no	—
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#107	C₂³	1	1	yes	characteristic
266	C₂×#107	C₂³	1	1	yes	characteristic
267	C₂×#107	C₂³	1	1	yes	characteristic
268	C₂×#107	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×#106	C₂³	1	1	yes	characteristic
274	C₂×#106	C₂³	1	1	yes	characteristic
275	C₂×#106	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	#419	—	2	4	no	—
279	C₂×#103	—	4	2	no	—
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×#102	C₂³	1	1	yes	characteristic
303	C₂×#102	C₂³	1	1	yes	characteristic
304	C₂×#102	C₂³	1	1	yes	characteristic
305	C₂×#102	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂×#97	C₂³	1	1	yes	characteristic
311	C₂×#97	C₂³	1	1	yes	characteristic
312	C₂×#97	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×C₄×C₈	C₂³	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
318	#400	—	2	1	no	—
319	#400	—	2	1	no	—
320	#400	—	2	1	no	—
321	#400	—	2	1	no	—
322	#400	—	2	1	no	—
323	#398	—	2	1	no	—
324	#398	—	2	1	no	—
325	#398	—	2	1	no	—
326	#398	—	2	1	no	—
327	#398	—	2	1	no	—
328	#398	—	2	1	no	—
329	#398	—	2	1	no	—
330	#398	—	2	1	no	—
331	#397	—	2	1	no	—
332	#397	—	2	1	no	—
333	#397	—	2	1	no	—
334	#397	—	2	1	no	—
335	#397	—	2	1	no	—
336	#397	—	2	1	no	—
337	#397	—	2	1	no	—
338	#397	—	2	1	no	—
339	#396	—	2	1	no	—
340	#396	—	2	1	no	—
341	#396	—	2	1	no	—
342	#396	—	2	1	no	—
343	#396	—	2	1	no	—
344	#395	—	2	1	no	—
345	#395	—	2	1	no	—
346	#395	—	2	1	no	—
347	#395	—	2	1	no	—
348	#395	—	2	1	no	—
349	#394	—	2	1	no	—
350	#394	—	2	1	no	—
351	#394	—	2	1	no	—
352	#394	—	2	1	no	—
353	#394	—	2	1	no	—
354	#394	—	2	1	no	—
355	#393	—	2	1	no	—
356	#393	—	2	1	no	—
357	#393	—	2	1	no	—
358	#391	—	2	1	no	—
359	#391	—	2	1	no	—
360	#391	—	2	1	no	—
361	#391	C₂³	1	1	yes	characteristic
362	#391	C₂³	1	1	yes	characteristic
363	#391	C₂³	1	1	yes	characteristic
364	#391	C₂³	1	1	yes	characteristic
365	#391	C₂³	1	1	yes	characteristic
366	#391	C₂³	1	1	yes	characteristic
367	#390	—	2	1	no	—
368	#390	C₂³	1	1	yes	characteristic
369	#390	C₂³	1	1	yes	characteristic
370	#390	C₂³	1	1	yes	characteristic
371	#390	C₂³	1	1	yes	characteristic
372	#389	—	2	1	no	—
373	#389	—	2	1	no	—
374	#389	—	2	1	no	—
375	#389	—	2	1	no	—
376	#389	—	2	1	no	—
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#389	C₂³	1	1	yes	characteristic
381	#389	C₂³	1	1	yes	characteristic
382	#389	C₂³	1	1	yes	characteristic
383	#389	C₂³	1	1	yes	characteristic
384	#389	C₂³	1	1	yes	characteristic
385	#389	C₂³	1	1	yes	characteristic
386	#389	C₂³	1	1	yes	characteristic
387	#389	C₂³	1	1	yes	characteristic
388	#389	C₂³	1	1	yes	characteristic
389	#389	C₂³	1	1	yes	characteristic
390	#389	C₂³	1	1	yes	characteristic
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#388	—	2	1	no	—
398	#388	—	2	1	no	—
399	#388	—	2	1	no	—
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	D₄	1	1	yes	characteristic
404	#388	D₄	1	1	yes	characteristic
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#387	—	2	1	no	—
413	#387	—	2	1	no	—
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	D₄	1	1	yes	characteristic
421	#387	D₄	1	1	yes	characteristic
422	#386	—	2	1	no	—
423	#386	—	2	1	no	—
424	#386	—	2	1	no	—
425	#386	—	2	1	no	—
426	#386	D₄	1	1	yes	characteristic
427	#386	D₄	1	1	yes	characteristic
428	#385	—	2	1	no	—
429	#385	—	2	1	no	—
430	#385	—	2	1	no	—
431	#385	—	2	1	no	—
432	#385	—	2	1	no	—
433	#385	—	2	1	no	—
434	#385	—	2	1	no	—
435	#385	—	2	1	no	—
436	#385	—	2	1	no	—
437	#385	—	2	1	no	—
438	#385	D₄	1	1	yes	characteristic
439	#385	D₄	1	1	yes	characteristic
440	#384	—	2	1	no	—
441	#384	C₂³	1	1	yes	characteristic
442	#384	C₂³	1	1	yes	characteristic
443	#383	—	2	1	no	—
444	#383	—	2	1	no	—
445	#382	—	2	1	no	—
446	#382	—	2	1	no	—
447	#382	C₂³	1	1	yes	characteristic
448	#382	C₂³	1	1	yes	characteristic
449	#380	—	2	1	no	—
450	#380	C₂³	1	1	yes	characteristic
451	#380	C₂³	1	1	yes	characteristic
452	#380	C₂³	1	1	yes	characteristic
453	#380	C₂³	1	1	yes	characteristic
454	#380	C₂³	1	1	yes	characteristic
455	#380	C₂³	1	1	yes	characteristic
456	C₄×C₄⋊C₄	—	2	1	no	—
457	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	—	2	1	no	—
461	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
462	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
463	#376	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	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	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	—	2	1	no	—
498	C₂²×Q₈	—	2	1	no	—
499	C₂²×Q₈	—	2	2	no	—
500	C₂²×Q₈	—	2	2	no	—
501	C₂²×Q₈	—	2	2	no	—
502	C₂²×Q₈	—	2	2	no	—
503	C₂²×Q₈	—	4	1	no	—
504	C₂²×Q₈	—	4	1	no	—
505	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
511	C₂²×D₄	C₂⁴	1	1	yes	characteristic
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
516	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
517	C₂³×C₄	C₂⁴	1	1	yes	characteristic
518	C₂³×C₄	C₂⁴	1	1	yes	characteristic
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	2	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×M₁₆	—	4	1	no	—
529	C₂×M₁₆	—	4	1	no	—
530	C₂×M₁₆	#41	1	4	yes	—
531	C₂²×C₈	—	2	2	no	—
532	C₂²×C₈	—	2	2	no	—
533	C₂²×C₈	—	2	2	no	—
534	C₂²×C₈	—	4	1	no	—
535	C₂²×C₈	—	4	1	no	—
536	C₂²×C₈	—	4	1	no	—
537	C₂²×C₈	—	4	1	no	—
538	C₂²×C₈	—	4	1	no	—
539	C₂²×C₈	—	4	1	no	—
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	—	4	1	no	—
552	C₄⋊Q₈	—	4	1	no	—
553	C₄⋊Q₈	—	4	1	no	—
554	C₄⋊Q₈	—	4	1	no	—
555	C₄⋊Q₈	—	4	1	no	—
556	#125	—	4	4	no	—
557	#123	—	8	2	no	—
558	#123	—	8	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	4	1	no	—
565	C₂²⋊Q₈	—	4	1	no	—
566	C₂²⋊Q₈	—	4	1	no	—
567	C₂²⋊Q₈	—	4	4	no	—
568	C₂²⋊Q₈	—	8	2	no	—
569	C₂²⋊Q₈	—	8	2	no	—
570	C₂²⋊Q₈	—	8	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	4	1	no	—
574	#121	—	4	1	no	—
575	#121	—	8	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	4	1	no	—
581	C₄×Q₈	—	4	1	no	—
582	C₄×Q₈	—	4	1	no	—
583	C₄×Q₈	—	4	1	no	—
584	C₄×Q₈	—	4	1	no	—
585	C₄×Q₈	—	4	1	no	—
586	C₄×Q₈	—	4	4	no	—
587	C₄×Q₈	—	4	4	no	—
588	C₄×Q₈	—	4	4	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	4	1	no	—
592	C₄×D₄	—	4	1	no	—
593	#117	—	2	2	no	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	4	1	no	—
597	#117	—	4	1	no	—
598	#117	—	4	4	no	—
599	#117	—	4	4	no	—
600	#117	—	4	1	no	—
601	#117	—	4	4	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	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
637	C₂×C₄⋊C₄	—	4	1	no	—
638	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	4	1	no	—
696	C₂×C₄²	—	4	1	no	—
697	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
698	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
699	C₂×C₄²	C₂⁴	1	1	yes	characteristic
700	C₂×C₄²	C₂⁴	1	1	yes	characteristic
701	C₂×C₄²	C₂⁴	1	1	yes	characteristic
702	C₂×C₄²	C₂⁴	1	1	yes	characteristic
703	C₂×C₄²	C₂⁴	1	1	yes	characteristic
704	#107	—	2	2	no	—
705	#107	—	2	2	no	—
706	#107	—	4	1	no	—
707	#107	—	4	1	no	—
708	#107	—	4	1	no	—
709	#107	—	4	1	no	—
710	#106	—	2	2	no	—
711	#106	—	2	2	no	—
712	#106	—	2	2	no	—
713	#106	—	2	2	no	—
714	#106	—	4	1	no	—
715	#106	—	4	1	no	—
716	#106	—	4	1	no	—
717	C₄⋊C₈	—	2	2	no	—
718	C₄⋊C₈	—	2	2	no	—
719	#103	—	2	2	no	—
720	#103	—	2	2	no	—
721	#103	—	2	2	no	—
722	#103	—	2	2	no	—
723	#103	—	2	2	no	—
724	#103	—	2	2	no	—
725	#103	—	2	2	no	—
726	#103	—	2	2	no	—
727	#103	—	2	2	no	—
728	#103	—	2	2	no	—
729	#103	—	2	2	no	—
730	#103	—	2	2	no	—
731	#103	—	2	2	no	—
732	#103	—	4	1	no	—
733	#103	—	4	1	no	—
734	#103	—	4	1	no	—
735	#103	—	4	1	no	—
736	#103	—	4	1	no	—
737	#103	—	4	1	no	—
738	#103	—	4	1	no	—
739	#103	—	4	1	no	—
740	#102	—	2	2	no	—
741	#102	—	2	2	no	—
742	#102	—	4	1	no	—
743	#102	—	4	1	no	—
744	#102	—	4	1	no	—
745	C₂²⋊C₈	—	2	2	no	—
746	C₂²⋊C₈	—	2	2	no	—
747	C₂²⋊C₈	—	2	2	no	—
748	C₂²⋊C₈	#41	1	4	yes	—
749	#97	—	2	2	no	—
750	#97	—	4	1	no	—
751	#97	—	4	1	no	—
752	C₄×C₈	—	2	2	no	—
753	C₄×C₈	—	4	1	no	—
754	C₄×C₈	—	4	1	no	—
755	C₄×C₈	—	4	1	no	—
756	C₄×C₈	—	4	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	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
796	#95	C₂×D₄	1	1	yes	characteristic
797	#95	C₂×D₄	1	1	yes	characteristic
798	#95	C₂×D₄	1	1	yes	characteristic
799	#95	C₂×D₄	1	1	yes	characteristic
800	#95	C₂×D₄	1	1	yes	characteristic
801	#95	C₂×D₄	1	1	yes	characteristic
802	#95	C₂×D₄	1	1	yes	characteristic
803	#95	C₂×D₄	1	1	yes	characteristic
804	#95	C₂×D₄	1	1	yes	characteristic
805	C₂⁴	—	2	1	no	—
806	C₂⁴	C₂²×D₄	1	1	yes	characteristic
807	C₂⁴	C₂²×D₄	1	1	yes	characteristic
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	8	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×Q₈	—	4	2	no	—
827	C₂×Q₈	—	4	2	no	—
828	C₂×Q₈	—	4	4	no	—
829	C₂×Q₈	—	4	4	no	—
830	C₂×Q₈	—	4	4	no	—
831	C₂×Q₈	—	4	2	no	—
832	C₂×Q₈	—	4	2	no	—
833	C₂×Q₈	—	4	2	no	—
834	C₂×Q₈	—	8	1	no	—
835	C₂×Q₈	—	8	1	no	—
836	C₂×Q₈	—	8	1	no	—
837	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
838	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	4	1	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	8	1	no	—
851	C₂×D₄	—	8	1	no	—
852	C₂×D₄	—	8	1	no	—
853	C₂×D₄	—	8	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	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	2	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	2	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	—	4	1	no	—
883	C₂²×C₄	—	4	1	no	—
884	C₂²×C₄	—	4	1	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
907	C₂²×C₄	C₂×#41	1	2	yes	—
908	C₂²×C₄	C₂⁵	1	1	yes	characteristic
909	SD₁₆	—	4	4	no	—
910	SD₁₆	—	4	4	no	—
911	SD₁₆	—	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	—	8	2	no	—
934	C₂×C₈	—	8	2	no	—
935	C₂×C₈	—	8	2	no	—
936	C₂×C₈	C₂×#41	1	2	yes	—
937	C₂×C₈	C₂×#41	1	2	yes	—
938	C₂×C₈	C₂×#41	1	2	yes	—
939	C₂×C₈	C₂×#41	1	2	yes	—
940	C₄⋊C₄	—	2	4	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	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	—	2	1	no	—
966	C₄⋊C₄	—	2	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	—	8	1	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	—	8	1	no	—
992	C₄⋊C₄	—	8	1	no	—
993	C₄⋊C₄	—	8	1	no	—
994	C₄⋊C₄	—	8	1	no	—
995	C₄⋊C₄	—	8	1	no	—
996	C₄⋊C₄	—	8	1	no	—
997	C₄⋊C₄	—	8	1	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	H(5,𝔽₂)	1	2	yes	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	4	1	no	—
1009	C₂²⋊C₄	—	4	1	no	—
1010	C₂²⋊C₄	—	4	1	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	—	4	2	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	4	2	no	—
1022	C₂²⋊C₄	—	4	2	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	—	8	1	no	—
1027	C₂²⋊C₄	—	8	1	no	—
1028	C₂²⋊C₄	—	8	1	no	—
1029	C₂²⋊C₄	—	8	1	no	—
1030	C₂²⋊C₄	—	8	1	no	—
1031	C₂²⋊C₄	—	8	1	no	—
1032	C₂²⋊C₄	—	8	1	no	—
1033	C₂²⋊C₄	—	8	1	no	—
1034	C₄²	—	2	4	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	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	—	4	1	no	—
1046	C₄²	—	4	1	no	—
1047	C₄²	—	4	2	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	—	8	1	no	—
1054	C₄²	—	8	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	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	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	4	1	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	#532	1	2	yes	—
1075	C₂³	#577	1	2	yes	—
1076	C₂³	C₂³×D₄	1	1	yes	characteristic
1077	Q₈	—	2	2	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	4	8	no	—
1082	Q₈	—	4	1	no	—
1083	Q₈	—	4	1	no	—
1084	Q₈	—	4	1	no	—
1085	Q₈	—	4	1	no	—
1086	Q₈	—	4	1	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	8	4	no	—
1091	Q₈	—	16	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	1	no	—
1094	D₄	—	4	1	no	—
1095	D₄	—	4	1	no	—
1096	D₄	—	4	1	no	—
1097	D₄	—	16	2	no	—
1098	D₄	—	16	2	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	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	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	2	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	2	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	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	4	4	no	—
1140	C₂×C₄	—	4	8	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	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	8	2	no	—
1188	C₂×C₄	—	16	2	no	—
1189	C₂×C₄	—	16	2	no	—
1190	C₂×C₄	#532	1	2	yes	—
1191	C₂×C₄	#577	1	2	yes	—
1192	C₂×C₄	#578	1	2	yes	—
1193	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1194	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1195	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1196	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1197	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1198	C₂×C₄	#585	1	1	yes	characteristic
1199	C₈	—	2	2	no	—
1200	C₈	—	2	2	no	—
1201	C₈	—	2	2	no	—
1202	C₈	—	2	2	no	—
1203	C₈	—	4	1	no	—
1204	C₈	—	4	1	no	—
1205	C₈	—	4	1	no	—
1206	C₈	—	4	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	8	1	no	—
1222	C₂²	—	8	1	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	C₂×#532	1	1	yes	characteristic
1229	C₂²	#3484	1	1	yes	characteristic
1230	C₂²	#3489	1	1	yes	characteristic
1231	C₂²	C₂×#577	1	1	yes	characteristic
1232	C₂²	C₂×#577	1	1	yes	characteristic
1233	C₂²	C₂×#578	1	1	yes	characteristic
1234	C₂²	#3584	1	1	yes	characteristic
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	2	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	4	2	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	8	1	no	—
1251	C₄	—	8	1	no	—
1252	C₄	—	8	1	no	—
1253	C₄	—	8	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	#3492	1	1	yes	characteristic
1263	C₄	#3505	1	1	yes	characteristic
1264	C₄	#3513	1	1	yes	characteristic
1265	C₄	#3520	1	1	yes	characteristic
1266	C₂	—	4	2	no	—
1267	C₂	—	4	2	no	—
1268	C₂	—	16	1	no	—
1269	C₂	#35393	1	1	yes	characteristic
1270	C₂	#60706	1	1	yes	characteristic
1271	C₂	#60723	1	1	yes	characteristic
1272	C₂	#61633	1	1	yes	characteristic
1273	C₂	#61642	1	1	yes	characteristic
1274	C₂	#62204	1	1	yes	characteristic
1275	C₂	#62219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2416	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2290 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #35665	C₂	semidirect
3. #29591	C₂	semidirect
4. #29508	C₂	semidirect
5. #29467	C₂	semidirect
6. #29458	C₂	semidirect
7. #29205	C₂	semidirect
8. #29160	C₂	semidirect
9. #29049	C₂	semidirect
10. #29009	C₂	semidirect
11. #28972	C₂	semidirect
12. #28848	C₂	semidirect
13. #28367	C₂	semidirect
14. #28102	C₂	semidirect
15. #27696	C₂	semidirect
16. #27258	C₂	semidirect
17. #26958	C₂	semidirect
18. #26836	C₂	semidirect
19. #26480	C₂	semidirect
20. #26072	C₂	semidirect
21. #25672	C₂	semidirect
22. #25497	C₂	semidirect
23. #25233	C₂	semidirect
25. #25041	C₂	semidirect
27. #22201	C₂	semidirect
28. #22092	C₂	semidirect
29. #21462	C₂	semidirect
30. #20877	C₂	semidirect
31. #20557	C₂	semidirect

Maximal subgroups

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

subgroup	index
#37339	2
#35665	2
#29591	2
#29508	2
#29467	2
#29458	2
#29205	2
#29160	2
#29049	2
#29009	2
#28972	2
#28848	2
#28367	2
#28102	2
#27696	2
#27258	2
#26958	2
#26836	2
#26480	2
#26072	2
#25672	2
#25497	2
#25233	2
#25114	2
#25041	2
#24789	2
#22201	2
#22092	2
#21462	2
#20877	2
#20557	2